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Performance of the UBC two-stage light-gas gun Deforge, David James 1993

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PERFORMANCE OF THEUBC TWO-STAGE LIGHT-GAS GUNByDAVID JAMES DEFORGEB.Sc. (Hons.), University of Guelph, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standard.THE UNIVERSITY OF BRITISH COLUMBIAJuly 1993© DAVID JAMES DEFORGE, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of The University of British ColumbiaVancouver, CanadaDate  TU/\( CYCI3 DE-6 (2/88)11AbstractThe performance of UBC two-stage light-gas gun and the associated diagnostics systemswere examined under a variety of shot conditions. In the gas gun, the expansion of gas fromburning gun powder propels a piston which, in turn, compresses and accelerates the lowmolecular weight pump gas. The rising pressure of the pump gas eventually opens a petal valvepermitting the pump gas to propel a projectile towards the target. At the front of the projectile isa metal disk - the flyer plate. In a typical experiment, the behaviour of the target material underthe high pressure conditions that result from the impact between the flyer plate and the target isexamined. In this study, the use of gun powder loads of 46 to 150 g, with helium pump gas,resulted in projectile velocities between 2 and 4 km/s for 5 to 9 g projectiles. The ability tomeasure the projectile velocity with 0.2% uncertainty was demonstrated. Such resolution iscomparable to those obtained with systems used by other researchers. The internal ballistics ofthe gun were modelled with a 1½ dimension Arbitrary Lagrange Eulerian computer code. Thecalculations had limited success in obtaining the measured projectile velocity. The calculationswere also used to estimate the time difference between the arrival of the piston at a preset locationalong the pump tube and the arrival of the projectile at a given distance from the muzzle of thelaunch tube. These calculations showed reasonable agreement with the measured values.Experiments were also performed to examine the orientation and curvature of the flyer plate onimpact with target. The size and orientation of the tilt of the flyer plate were relativelyreproducible for shots with large copper flyer plates in primarily stress-free sabots. The tilt valueswith these projectiles were less than 10 mrad. It was also demonstrated that the flyer platecurvature was consistently concave for copper flyer plate projectiles with radii of curvature ofapproximately 1 m.Performance of the UBC Two-Stage Light-Gas GunTable of ContentsAbstract^  iiTable of Contents ^  iiiList of TablesList of Figures^  viAcknowledgment  ixChapter 1 Introduction1.1 Shock Wave Studies^  11.2 History of the Two-Stage Light-Gas Gun^  21.3 Measurement of the Properties of Shocked Material ^  61.3.1 Measurement Techniques^  81.3.2 Effect of Flyer Plate Tilt and Curvature on Shock Velocity Measurement^ 141.4 Present Investigation^  19Chapter 2 UBC Two-Stage Light-Gas Gun and Diagnostic Equipment2.1 Introduction^  202.2 Components of the UBC Two-Stage Light-Gas Gun^  202.2.1 Breech and Pump Tube^  232.2.2 Coupling Section and Launch Tube^  312.3 Projectile Design and Fabrication^  342.4 Target Chamber and Diagnostics  402.4.1 Laser Velocity Trap^ 402.4.2 Magnetic Velocity Induction System^  422.4.3 Targets for the Measurement of the Flyer Plate Tilt and Curvature^ 47nlivChapter 3 Results and Discussion3.1 Introduction^  633.2 Breech Pressure  633.3 Projectile Velocity^  683.4 Numerical Simulation of the Internal Ballistics of the UBC Two-Stage Light-Gas Gun.. 763.5 Last PV Pin to First Laser Velocity Trap Time Difference Measurements^ 943.6 Flyer Plate Tilt and Curvature^  102Chapter 4 Conclusion4 Conclusions^  119AppendixA. Uncertainty in the Measured Tilt with the Impact of a Curved Flyer Plate duethe Uncertainty in Centring the Target^ 121B. Formulae for Least-Squares Fitting to Flyer Plate Arrival Time Data^ 122Bibliography.^  127VList of Tables2-1 Initial parameters for shots in this study^ 213-1 Maximum breech pressure, powder load and pump tube pressure^ 663-2 Velocity measurements using MAVIS and laser velocity trap 693-3 Projectile velocity, powder load, projectile mass, and pump tube pressure^ 713-4 Powder load, pump tube pressure, PV pin times and fitting parameters  813-5 Measured and calculated projectile velocity for various shots^ 853-6 Coefficients for least squares fits to calculated versus measured projectile velocity data . .893-7 Time difference between last PV pin and first laser trap position, powder load,projectile mass, and projectile velocity^  953-8 Calculated time difference and projectile velocity values for 5.8 and 8.9 g projectiles . . ^ .983-9 Fitting parameters to cap pin arrival time data^  1053-10 Flyer plate tilt, tilt azimuth, radius of curvature and projectile velocity^ 108viList of Figures1-1 Diagram showing two-stage light-gas gun at three times during firing sequence^ 41-2 Diagram of two-stage light-gas gun used by Crozier and Hume^  51-3 Diagram of two-stage light-gas gun used by Curtis^  51-4 Illustration of pressure transition due to shock wave traveling through material^ 71-5 Shock pressure - particle velocity Hugoniot for copper^  91-6 Illustration of pressure transition due to rarefaction wave travelling through previouslyshocked material^  101-7 Cross section of a projectile used with the UBC two-stage light-gas gun^ 121-8 Schematic showing pressure and particle velocity in flyer plate and target^ 131-9 Schematic of use of Hugoniot curve on P - u plane to find shock pressure and particlevelocity^  151-10 Diagram of tilted flyer plate on impact with the target^  171-11 Diagram of curved flyer plate on impact with the target  182-1 Diagram of the UBC two-stage light-gas gun^  222-2 Diagram of breech and pump tube of UBC two-stage light-gas gun^ 242-3 Photograph of signals from breech and pump tube pressure transducers^ 262-4 Circuit of pin conditioner for PV pins^  272-5 Photograph of signals from PV pins  282-6 Cross section of piston^  302-7 Diagram of coupling section with petal valves and projectile^  322-8 Cross sectional and side views of a petal valve^  332-9 Cross section of typical projectile with copper flyer plate^  352-10 Cross section of press used to laminate flyer plate with sabot  36VII2-11 Graph of temperature and pressure cycles used to embed flyer plate in lexan^ 382-12 Photograph of lexan sabots with acceptable and unacceptable stress patterns^ 392-13 Diagram of target chamber with target and projectile velocity diagnostics^ 412-14 Circuit diagram for laser velocity trap^  432-15 Diagrams of jig used to align laser velocity trap^  442-16 Photograph of signals from laser velocity trap  452-17 Cross section of magnetic velocity induction system^  462-18 Schematic for MAVIS alignment^ 482-19 Photograph of signals produced by MAVIS^  492-20 Diagrams of targets used for flyer plate tilt and curvature measurements^ 502-21 Cross section of cap pins used in tilt targets^  502-22 Diagram of jig used to measure position of cap pins in target^  522-23 Diagram of mounted target for tilt and curvature measurements 532-24 Circuit diagram for pin conditioner for cap pins^  552-25 Circuit diagram of system for measuring arrival times of flyer plate at cap pins^ 562-26 Photograph of typical set of cap pin signals for tilt and curvature measurements^ 572-27 Schematic illustrating the origin of an oscilloscope trace from a set of cap pin signals . . . 582-28 Illustration showing the relationship between the uncertainty in the position of the targetand the resulting uncertainty in the tilt ^  613-1 Photograph of typical breech pressure signal^ 643-2 Graph of maximum breech pressure as a function of powder load^ 673-3 Graph of projectile velocity versus projectile mass for shots with similar initialconditions^ 723-4 Graph of projectile velocity versus initial pump tube pressure for shots with similarinitial conditions  733-5 Graph of projectile velocity versus powder load^ 75viii3-6 Graph of PV pin times plotted as a function of piston position^  823-7 Graph of piston velocity as a function of piston position  843-8 Graph of calculated pressure at the base of the projectile as a function of time^ 863-9 Graph of calculated positions of the piston, pump gas shock wave and projectile as afunction of time^  873-10 Graph of the calculated projectile velocity plotted versus the measured projectilevelocity with a petal valve burst pressure of 600 bar^ 883-11 Graph of the calculated projectile velocity plotted versus the measured projectilevelocity to examine the effects of the methods of extrapolation on the calculatedprojectile velocity  913-12 Graph of the calculated projectile velocity plotted versus the measured projectilevelocity with petal valve burst pressures of 300 bar^  923-13 Graph of the calculated projectile velocity plotted versus the measured projectilevelocity with petal valve burst pressures of 300 bar^  933-14 Graph of time difference between firing of the last PV pin and the first laser trap versusprojectile velocity^  973-15 Graph of calculated time difference between firing of the last PV pin and the first laser trapversus the calculated projectile velocity for 5.8 g projectiles ...........^.^. .1003-16 Graph of calculated time difference between firing of the last PV pin and the first laser trapversus projectile velocity for 8.9 g projectiles ^ 1013-17 Graph of flyer plate arrival time as a function of cap pin position^ 1043-18 Graph of flyer plate tilt as a function of projectile velocity for shots with large copperflyer plates in relatively stress free sabots^  1093-19 Graph of tilt azimuth versus projectile velocity for shots with large copper flyer platesin relatively stress free sabots^  1103-20 Graph of flyer plate tilt as a function of projectile velocity for shots with small flyerplates in relatively stress free sabots, shots with large flyer plates in stressed sabotsand shots without flyer plates  1123-21 Graph of tilt azimuth versus projectile velocity for shots with small flyer plates inrelatively stress free sabots, shots with large flyer plates in stressed sabots and shotswithout flyer plates^  1143-22 Graph of flyer plate radius of curvature as a function of projectile velocity^ 115AcknowledgementI would like to thank my supervisor, Dr. Andrew Ng, for his support and guidance and forgiving me the opportunity to work in the two-stage light-gas gun facility. I am especially gratefulto Dr. Peter Celliers and Al Cheuck for their work in performing the experiments and in preparingthe diagnostic and control systems for the lab. I would also like to thank Johnson Wang for hishelp in carrying out the experiments and Andrew Forsman for his technical advice (andequipment).The financial assistance of the National Sciences and Engineering Research Council isgratefully acknowledged.ixChapter 1Introduction1.1 Shock Wave StudiesShock waves provide researchers with a means of studying the behaviour of matter underconditions of very high pressure and temperature. With relaxation times of typically 1 ps[ 1 1, theatoms and molecules in a shocked material are in thermodynamic equilibrium for the duration ofthe shock pulse, which is usually in the nanosecond to microsecond regime. As a result,equilibrium properties of matter at very high pressures and temperatures can be measured usingshock waves.Equation of state properties and other properties determined from shock experiments helpresearchers understand the nature of matter. In particular, shock wave data on materials likegranite, water and hydrogen have provided geophysicists and astronomers with information on theformation and the internal structure of the Earth and other planetsP ,3]. Shock compression hasalso helped researchers understand the chemical decomposition of explosives duringdetonationF4,5 1.In addition to studies of material properties, shock waves are used for materials synthesiswhereby powder targets are compacted with shock waves[6]. As the shock wave passes throughthe powder, individual grains fuse together under the influence of the high pressure andtemperature. The subsequent rarefaction wave then causes decompression of the shockedmaterial. This decompression results in a rapid cooling of the shocked powder. The cooling ratecan be of the order of 108 °C/srl. This shock compaction technique has been used to make alloys(such as AILi 181), ceramics (such as AIN2 [91), and other materials with properties that are difficultor impossible to produce with other techniques. Shock compacted high temperature1Chapter 1. Introduction 2superconductor powders have higher flux pinning-energy than high temperature superconductorsmade with more conventional methods[ 10,11,12 ].In early studies of shock waves, researchers used explosive lenses to generate planarshock waves. This technique was used to produce shock pressures between 100 and 500 kbar[ 131.Today, shock waves are produced in many other ways. The explosive flyer plate method uses anexplosive lens to accelerate a metal flyer plate which generates a shock wave on impact with itstarget. Pressures as high as 10 Mbar are achieved with the explosive flyer plate method[ 14 . 15]. Inmore controlled experiments, single-stage and two-stage light-gas guns are used to accelerate theflyer plates[ 16,17,18]. A single-stage light-gas gun uses a reservoir of compressed hydrogen orhelium to accelerate a flyer plate carrying projectile The maximum pressure attainable usingsingle-stage light-gas guns is of the order of 100 kbar[ 19]. In the first stage of a two-stage light-gas gun, gas from burning gun powder propels a piston which compresses and accelerates thesecond stage which consists of a reservoir of hydrogen or helium pump gas. The pump gas thenpropels the projectile. Shock pressures of 10 Mbar have been attained with a two-stage light-gasgun using a double shock technique[20]. In all of these methods, the shock waves are generatedby the collision of an impactor with a target material.Alternatively, high power lasers and nuclear explosives have also been used to generateshock waves. With high power lasers, shock waves are produced by the rapid expansion of theablated material from the irradiated surface of the target. This has led to shock pressures of theorder of 100 Mbar[21 ]. Shock wave studies using nuclear explosions have been described byRagan[22], Trunin and Vladimirov[ 23,24]. The pressures achieved with these techniques range from70 Mbar, in the study by Ragan, to 4000 Mbar in the study by Vladimirov.1.2 History of the Two-Stage Light-Gas GunBefore the invention of the two-stage light-gas gun, most single-stage guns used gunpowder as a propellant. In such powder guns the projectile is driven by gas from the burning gunpowder. The projectile velocity is limited to roughly 3 km/s[25]. The limiting factors in powderChapter 1. Introduction 3gun and two-stage light-gas gun performance (maximum projectile velocity) are the strengths ofthe guns and the molecular weight of the gases that propel the projectiles[ 26,271. In order toachieve high projectile velocities, it is necessary to maintain a high pump gas pressure at the baseof the projectile. The velocity of the gas, and therefore, the velocity of the projectile, is limited bythe sound speed of the gas. The sound speed of the gas is proportional to the square root of theratio of the gas temperature to the molecular weight of the gas. The gas from smokeless powder,mainly nitrocellulose, has a molecular weight of roughly 28[ 28,29]. The molecular weights ofhydrogen and helium are 2 and 4 respectively. For similar temperatures the sound speeds are 3.7(for hydrogen) and 2.6 (for helium) times that of the gun powder gas. The limitations on the gunstrengths are similar for both powder guns and two-stage light-gas guns so one can attain muchhigher projectile velocities with the two-stage light-gas guns.In a two-stage light-gas gun, gun powder is used to propel a piston which, in turn,compresses and accelerates a reservoir of the helium or hydrogen pump gas (figure 1-1). At somedesired pressure, the valve which separates the pump gas from the projectile, ruptures. Theaccelerated pump gas maintains a high pressure behind the projectile pushing it down the launchtube.Crozier and Hume developed the first two-stage light-gas gun in 19461 301. Figure 1-2shows a diagram of the gun. Using hydrogen as the pump gas, projectile velocities as high as 3.6km/s for 4 g projectiles were achieved with this gun. In the gun used by Crozier and Hume theinitial light-gas pressure was as high as 1250 psi to prevent the piston from damaging the end ofthe pump tube. Another early two-stage light-gas gun was used by Charters to attain velocities ashigh as 4.6 km/s for 0.2 g projectiles [311. Charters used helium as the pump-gas.The main difference between Crozier's and Charters' guns and those currently used is thetapered coupling section introduced by Curtis[321. Figure 1-3 is a diagram of Curtis' gun. Thecoupling section tapers the barrel from the pump tube diameter to the launch tube diameter. Thepiston in this gun is made out of nylon which is much more deformable than the steel used tomake the pump tube and coupling section. When it reaches the coupling section, the piston isl< >I<^>l<GUNPOWDER^ PISTONLIGHT GAS;......^.. ^. VALVE PROJECTILE r2=22Z2Z^";;;;;;.■;;.'""----Chapter I. Introduction 4COUPLINGBREECH^PUMP TUBE^SECTION^LAUNCH TUBEFigure 1-1: Diagram showing two-stage light-gas gun at different times during the firingsequence.PISTON ENERGYABSORBERS VALVE-PROJECTILELAUN HT BGUN POWDERloom' 11117PISTONN‘b.lt*IPUMP TUBEVALVEA11111111///z/z,weszmurriA111111L.BLOWOUTDISK PROJECTILELAUNCH TUBE 2WGUN POWDERCHAMBERCOUPLINGSECTIONChapter I. Introduction 5THROATFigure 1-2: Diagram of the two-stage light-gas gun used by Crozier and Hume[ 301.Figure 1-3: Diagram of the two-stage light-gas gun used by Curtis[ 32 1.Chapter 1. Introduction 6stopped as it extrudes into the taper. The high initial pump-gas pressure which was used in earlierguns to prevent the piston from damaging the end of the pump tube are not required. With lesspump gas to accelerate and compress, more piston energy is transferred to the projectile. Anadditional gain in gun performance comes from the extrusion of the piston into the couplingsection. As the piston enters the coupling section, the reduction in the cross sectional area causesan increase in the speed of the front face of the piston. The acceleration of the front of the pistonproduces a pressure wave that results in a further increase in the projectile velocity[ 33]. Curtis'gun was used to accelerate 0.1g projectiles to 9 km/s using hydrogen.A number of other small modifications in gun design have come as a result of knowledgegained through experimentation and ballistics calculations. These include changes in the lengthsand diameters of the various sections, increases in the piston mass and the use of slow instead offast burning gun powder[26,34]. These modifications have led to higher projectile velocities. Two-stage light-gas guns now use projectiles ranging from 0.5 cm to 10 cm in diameter and from0.04 g to 1000 g in mass[35].The original two-stage light-gas guns were used for aerodynamics and ballistics studies forthe U.S. military and NASA (NACA)E 30,31 1. Jones et al. were the first to use a two-stage light-gasgun for equation of state studies in 1966[ 36]. Two-stage light-gas guns are also used to studyother properties of shocked material and for materials synthesis. Finally the high impact velocitiesmake these guns suitable for studying the impact of space debris and micrometeoroids (velocitiesof the order of 10 km/s) with materials used in satellites or space vehicles[ 37,38].1.3 Measurement of the Properties of Shocked MaterialA simple pressure versus position diagram of a shock wave is shown in figure 1-4. In thisdiagram the shock wave propagates through a medium which is initially at rest in the lab frame.The shock wave produces jumps in the pressure P and the particle velocity u as it travels throughthe medium at the shock velocity D. For strong shocks P >> Po, uo = 0 and e>> so where e isthe internal energy volume and the subscript o denotes corresponding parameters of theChapter I. Introduction 7PRESSURE SHOCK FRONT EDGE OFMATERIALPOSITIONFigure 1-4: Illustration of the pressure transition due to a shock wave traveling at shock speed Din the laboratory frame of reference. The particle velocity in the unshocked region ahead of theshock front is zero.Chapter I. Introduction 8unshocked state. Under these conditions, the equations describing the conservation of mass,momentum and internal energy across the shock front are respectively:DP =uV = V,,(1—^ [1.2]and^ E P(V —V) 2^ [1.3]The relationship between the shock pressure and particle velocity is known as theHugoniot curve in the pressure - particle velocity plane. As an example the pressure - particlevelocity Hugoniot for copper is shown in figure 1-5. Hugoniot curves are used to relate theshock pressure, particle velocity, shock velocity, shock density and internal energy in the shockedmaterial. The Hugoniot curves can be determined experimentally. With the three conservationequations and one of the Hugoniot curves, the value of any of the five parameters can bedetermined by measuring any one of the other parameters.When the shock wave reaches a free surface, a release or rarefaction wave is formed. Therelease wave then travels back into the shocked material at the local speed of sound cs. Thisproperty is useful in determining the speed of sound in the shocked material[ 39A. Such ararefaction wave is shown in figure 1-6.1.3.1 Measurement TechniquesThe changes in pressure and particle velocity in the shocked material are oftenaccompanied by changes in other properties of the material. These changes include changes incrystal structure and electrical conductivity. Some of the measurement techniques used in shockwave studies are outlined in this section.A wide variety of techniques are used to measure the properties of shocked materials.Electrical probes are used to measure changes in the conductivity of the shocked material.Chapter 1. Introduction 95.0ca 4.0.02EL?. 3.0EL2Y 2.00.cCl)1.00.00.0^1.0^2.0^3.0^4.0^5.0Particle Velocity (km/s)Figure 1-5. Shock pressure - particle velocity Hugoniot for copper with the particle velocity inunshocked copper equal to zero.Chapter 1. Introduction 10PRESSUREPOSITIONFigure 1-6: An illustration of a rarefaction wave traveling through a shocked material at thespeed of sound, c, in the frame moving at the particle velocityChapter 1. Introduction 11Conductivity measurements are used to determine ion concentrations in the shocked material andto detect phase changes in materials, such as silicon, that undergo transitions from an insulator toa conductor at a certain shock pressure[ 41,42]. X-ray diffraction of shocked crystals is used tostudy changes in lattice structure at high pressures[43,441. Raman scattering and emissionspectroscopy are used to detect unstable chemicals that form during the compression[451.Spectroscopy and intensity of light emitted from the shocked material are used to measure theshock temperatures[46,471. Optical methods, such as interferometry, are used to measure thevelocity of the free particles that emerge from the shocked material as the shock reaches the edgeof the target[48,49]. Pressure gauges are used to measure the shock pressure for pressures up to300 kbar[ 151. Finally, shock sensors, such as coaxial shorting pins, are used to measure thevelocity of the shock waves[ 361.The projectile used in equation of state studies with two-stage light-gas guns usuallyconsists of a flat metal flyer plate, a sabot and a tailstock (figure 1-7). The impact between theflyer plate and the target produces shock waves in both the flyer plate and the target. In mostcases, the pressure in the shocked material is determined using the impedance matchingmethod[501. This method uses the fact that the pressure and particle velocity in the shockedregions of the flyer plate and target are equal. Figure 1-8 shows the pressures and particlevelocities as functions of the position within the flyer plate and target in the lab frame at sometime after the initial impact. The particle velocity in the unshocked region of the flyer plate is theinitial projectile velocity w. Similarly, the particle velocity in the unshocked region of the target iszero. The change in particle velocity across the shock front in the target is u. The change inparticle velocity across the shock front in the flyer plate is then w - u. In a typical experiment theprojectile velocity, shock velocity and the initial specific volume of the target are measured. Inthe case where the target and flyer plate are made of the different materials, the Hugoniot curverelating shock pressure to the particle velocity is known for the flyer plate (figure 1-5). ThisChapter 1. Introduction 12FLYERPLATEFigure 1 -7: Cross section of a projectile used in two-stage light-gas gun.Chapter 1. Introduction 13PRESSUREPSHOCKPRESSURE -AFLYERPLATE_1 POSITIONTARGET ►PARTICLEVELOCITYPROJECTILEVELOCITY -POSITIONFigure 1-8: Pressure and particle velocity distributions in the flyer plate and target after impact.The particle velocity graph is in the laboratory reference frame.Chapter I. Introduction 14relationship is expressed asPt, = f (u^ [1.4]where Pip is the shock pressure and ufp is the change in the particle velocity across the shock frontin the flyer plate. As noted above, the change in the particle velocity across the shock front in theflyer plate is ufp = w - u. With this relationship the shock pressure from equation [1.4] for theflyer plate is= f (w — u) .^ [1.5]With the measured shock velocity in the target, D, and the initial specific volume of the target, Vo,equation [1.1] shows that the pressure, 1)1, behind the shock wave is in the target is a linearfunction of u withDuPt =^• [1.6]In figure 9 the pressures from equation [1.6] and equation [1.4] are plotted as functions u. Sincethe pressures and particle velocities in the shocked regions of the flyer plate and the target areequal, the shock pressure is the intersection of the two curves in this figure. That extremelyaccurate projectile and shock velocity measurements, and, therefore, accurate shock pressuremeasurements can readily be obtained in impacts using flyer plates accelerated by a two-stagelight-gas gun makes such a device an excellent means of studying the properties of shockedmaterial.1.3.2 Effect of Flyer Plate Tilt and Curvature on Shock Velocity MeasurementsThe angle between the surface of the target and the flyer plate and the curvature of theflyer plate are important considerations in shock wave experiments. The orientation of the flyerplate when it strikes the target can affect shock speed measurements and experiments where theChapter I. Introduction 15P0^wParticle VelocityFigure 1-9: Schematic of the use of the Hugoniot relating the shock pressure to the particlevelocity in the flyer plate to find the pressure and particle velocity in the target. The solid curveindicates the flyer plate Hugoniot and the large dashed curve indicates the pressure - particlevelocity line for the target.Chapter I. Introduction 16accurate timing of a measurement relative to the shock wave is important. Figures 1-10a and1-11 illustrate respectively, flyer plate tilt and curvature. The tilt is defined as the angle betweenthe normal to the surface of the flyer plate and the axis of the launch tube, the latter being also thenormal to the surface of the target. The tilt azimuth can be defined arbitrarily as the anglebetween the vertical line drawn through the launch tube axis and the projection of the flyer platenormal in the plane perpendicular to the launch tube axis, as shown in figure 1-10b. The tiltazimuth is measured in the clockwise direction when looking along the launch tube axis, from thebreech to the target. The flyer plate may also be slightly deformed at the time of impact. In thisstudy, it is assumed that the deformation of the flyer plate is axi-symmetric and that it can berepresented by a section of a sphere. Accordingly, the deformation can be characterized by aradius of curvature as indicated in figure 1-11.To illustrate the effect of the flyer plate tilt on shock transit time measurements considerthe impact of a 15 mm diameter copper flyer plate on an 1 mm thick planar copper target. Theflyer plate is traveling at 3.0 km/s with a tilt of 10 mrad. With such a tilt the arrival times of thefirst and the last points on the flyer plate at the target will differ by 50 ns. These two points lie atopposite ends across a diameter of the flyer plate. Consequently, in any plane within the targetthat is parallel to the target face, there will be a 50-ns time difference between the first and lastpoints that are traversed by the shock wave resulting from the impact. From the shock wavevelocity versus particle velocity Hugoniot data for copper[ 51], the speed of the shock wave is6.2 km/s so that the transit time for the shock wave through the target is 160 ns. Thus, the arrivaltime of the shock wave at the back of the copper plate will range from 160 to 210 ns as a result ofthe impact tilt.The above example of copper-copper impact is also used to illustrate the effect ofcurvature of the flyer plate on timing measurements. Assume that the flyer plate has no tilt buthas a spherically symmetric distortion with a radius of curvature of +1.0 m (concave). The centreof the front surface of the flyer plate is roughly 30 pm behind the plane through the circumferenceof the flyer plate (15 mm diameter). In any plane parallel to the face of the target, this willTILTAZIMUTHTOP OFTARGETLAUNCH TUBEAXIS (x AXIS)- -11 11LT ANGLENORMAL TOFLYER PLATECIRCLE IN PLANE OFTARGET FACE(PARALLEL TO y-z PLANE)Figure 1.10b: Diagram showing the tilt angle and tilt azimuth which are used to describe the tiltof the flyer plate on impact.Chapter 1. Introduction 17TARGET_TILT^ TUBE ANGLE_), AXIS----).NORMAL TOFLYER PLATEFLYERPLATE/RADIUS• u, DEVIATIONDUE TO TILTFigure 1.10a: Schematic of impact of tilted flyer plate on impact with the target.TARGETFLYERPLATE-> LAUNCH TUBEAXISRADIUS OFCURVATUREChapter 1. Introduction 18DEVIATION DUETO CURVATUREFigure 1-11: Schematic of curved flyer plate on impact with target.Chapter 1. Introduction 19produce a 10 ns delay in the arrival of the shock wave at the centre of the target with respect tothe arrival of the shock wave at any point on the circle with a radius of 7.5 mm from the centre ofthe target. The ability to measure the tilt and curvature of the impact geometry is thus veryimportant in making accurate shock transit time and shock velocity measurements.1.4 Present InvestigationThe main objective of this study is to characterize the performance of the UBC two-stagelight-gas gun and its diagnostic systems. The diagnostics systems for making accurate piston andprojectile velocity measurements are crucial for providing information as input parameters or ascheck values for numerical gun simulations and for the characterization of the shock waves. Theability to predict gun performance is necessary for designing experiments.Chapter 2 describes the gun, the diagnostics, and the measurement techniques used. Thischapter also includes descriptions of the fabrications of the projectiles and of the targets used forflyer plate tilt and curvature measurements. In chapter 3, the experimental results are presentedalong with interpretations of the data. Chapter 3 also contains the results of computer simulationsof the ballistics for some of the shots. A summary of the major findings of the study andsuggestions for further work are given in chapter 4.Chapter 2UBC Two-Stage Light-Gas Gun and Diagnostic Equipment2.1 IntroductionThis chapter contains a description of the UBC two-stage light-gas gun facility along withthe diagnostic equipment and the associated measurement techniques. Also included aredescriptions of the methods used in fabricating targets and projectiles.A schematic of the UBC two-stage light-gas gun is shown in figure 2-1. The gun wasdesigned by Lawrence Livermore National Laboratory and Physics Applications Inc. 1521 to launch14 g projectiles to velocities up to 5 km/s with hydrogen as the pump gas.The initial conditions for the shots in this study are presented in table 2-1. In a typicalshot, the time for the preparation and alignment of the target ranges from a few hours to a fewdays. With the target aligned, the time from the initial shot preparations through the firing andcleaning of the gun is approximately 4 hours.2.2 Components of the UBC Two-Stage Light-Gas GunThis section describes the various components that make up the UBC two-stage light-gasgun. Included are descriptions of the gun itself and the diagnostics used to measure the pistonvelocity and breech pressure.The gun, shown in figure 2-1, consists of the breech, pump tube, coupling section and thelaunch tube. The 3.45 m-long, 5.04 cm-diameter pump tube is initially filled with the pump gas.The coupling section joins the pump tube to the launch tube. The barrel of the coupling sectiontapers the diameter of the gun from 5.08 cm to 2.00 cm over a distance of 17.8 cm. The 3.09 m20Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 21Table 2-1: Initial parameters for shots in this study.ShotPowderLoad(g)Pump TubePressure(Psi)ProjectileMass (g)1 46 60.62 70 60.94 46 60.8 5.1615 55 60.1 5.1576 86 60.4 5.1627 86 90.4 5.1558 120 91.4 5.1459 46 61.1 5.15410 86 96.311 140 90.5 5.82813 60 60.8 5.85714 86 62.6 5.87715 86 60.0 5.89416 86 61.2 5.77017 70 61.2 8.93918 90 62.4 8.83819 75 91.7 5.74020 150 110.8 5.75021 75 92.0 5.75022 90 90.1 8.88323 75 90.9 8.42224 75 89.9 8.55126 60 91.0 8.43627 100 91.6 8.91828 125 91.4 8.95329 150 121.8 8.55030 150 120.7 8.78031 100 92.4 8.86032 100 90.3 8.77233 100 89.9 8.91440 150 124.0 8.5841 150 142.3 8.542 150 156.7 8.59PRESSURETRANSDUCERS PV PINS PETAL VALVESBREECHPISTONagnipPROJECTILE5.08 cm 1 .997± .003 cmLAUNCH TUBEPUMP TUBECOUPLINGSECTION347 cm >l< 22 cm >i<^304 cmBREECH GUNPLUG POWDERFigure 2-1: Diagram showing a cross sectional view of the UBC two-stage light-gas gun.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 23long launch tube guides the projectile and constrains the pump gas as the projectile accelerates.Along its entire length, the launch tube diameter varies between 1.994 and 2.000 cm.2.2.1 Breech and Pump TubeDuring the firing of the gun, the breech contains the burning gun powder which drives thepiston down the pump tube. The piston compresses the reservoir of pump gas in the pump tube.Figure 2-2 shows a cross-section of the breech and pump tube.The ignition of the gun powder is initiated by the firing of the primer at the back of thecartridge. The discharge of a capacitor bank is used to activate a solenoid which drives the firingpin into the primer. The primer produces a flame when struck by the firing pin. This then initiatesthe sequence of ignitions of the primer powder in the cartridge, the gun powder in the flame tubeand finally the gun powder in the breech.The gun powder used in the flame tube and in the breech is HPC 95 (K-SMK-01-3A fromHercules Aerospace) 153]. This powder consists of 78% nitrocellulose, 20% nitroglycerin, 1%potassium nitrate and 1% diphenylamine. The gun powder is in the form of approximately 4 mm-diameter granules, each with 7 perforations. The energy release is 4.73 kJ per gram of the gunpowder. The shots in this study used powder loads between 46 and 150g.The pressure transducers in the breech and pump tube are used to measure the pressure ofthe gas produced by the burning gun powder as the piston accelerates along the pump tube. Thebreech transducer is located at the back of the breech in the breech plug. The pump tubetransducer is located in the pump tube, 10.2 cm in front of the initial position of the front of thepiston (figure 2-2). The transducers are ICP series Quartz Pressure Transducers model number101A03 made by PCB Piezotronics 1541 . The transducer response time is 1 ps and the sensitivity ofthe transducer is 0.50 mV/psi ± 1% for pressures between 0 and 10,000 psi. The pressuretransducer in the breech is covered with electrical tape and surrounded by DC-4 Silicone grease toprotect it from the burning gun powder. This protective measure does not affect the temporalresponse or sensitivity of the transducer.^253.9 cm238.7 cm^147.3 cm--30PRESSURETRANSDUCERS^oc-55.9 cm-3*10.2 cm -N -PRIMERSOLENOIDFIRINGPINBREECHPLUGCARTRIDGEFLAMETUBEChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 24Figure 2-2: Diagram of the breech an pump tube of the UBC two-stage light-gas gun. Thepositions of the PV pins and the pump tube pressure transducer are measured from the initialposition of the front of the piston.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 25The pressure signals are displayed on an oscilloscope and photographed. The signals for atypical shot are shown in figure 2-3. The 1-i.ts response of the transducer is much faster than the5 ms/div writing speed of the oscilloscope so that the signal shown in figure 2-3 yields the actualpressure pulse shape. The widths of the oscilloscope traces limit the resolution of the pressuremeasurements to approximately 150 psi. The maximum breech pressure is obtained from thebreech transducer signal.The pump tube pressure transducer starts to measure the pressure of the gun powder gasonly after it has been passed by the piston. The breech pressure transducer signal reaches itsmaximum before the onset of the pump tube pressure transducer signal. Thus, the pump tubetransducer cannot be used for maximum gun powder pressure measurements. Also, the ringing inthe pump tube transducer signal renders it next to impossible to make reasonable pressuremeasurements. In the future, the signal from the pump tube pressure transducer may be used as acheck for a ballistics calculation that models the burning of the gun powder.Piston velocity pins (PV pins) are placed along the pump tube 55.9 cm, 147.3 cm, 238.7cm and 253.9 cm from the initial position of the front of the piston. Each pin is inserted into thepump tube though a 4 mm diameter hole. The PV pins are charged, insulated wires. Figure 2-4shows the circuit diagram for each of the PV pins. The pins, initially charged to -150V, becomeshorted to the pump tube wall when struck by the moving piston. The PV pins provide timeversus piston position data for piston velocity measurements. The last pin may also be used as atiming signal when a timing pulse is desired 2 to 3 ms before the projectile strikes the target.Knowledge of the piston velocity at various positions along the pump tube provides insight intothe ballistics involved in launching the projectile.The photograph in figure 2-5 shows the PV pin signals for a typical shot. The fast-risetime of the signal makes it impossible to display the details of the signal rise on an oscilloscopetrace that shows all of the signals. The 0.015 pF capacitor discharges across a resistance of100 f2 so the signal has a half-amplitude decay time, t in, of the order of 1 Rs. This is much lessChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 26 PUMP TUBEPRESSURESIGNALMAXIMUMBREECHPRESSURE BREECHPRESSURESIGNALFigure 2-3: Photograph of the signals from the breech and pump tube pressure transducers. Inthis shot the horizontal axis has a scale of 5 ms/div and the vertical axis has a scale of 0.5 V/div or1,000 psi/div.-150 V1 MCIOSCILLOSCOPE50 SIChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 27PINCONDITIONERPV PIN 50nFigure 2-4: Circuit diagram for PV pins.PV PIN SIGNALS* •*^••^I.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 28Figure 2-5: Photograph of a typical set of PV pin signals. The scale for the horzontal axis is 2ms/div andthe scale for the vertical axis is 5V/div.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 29than the 2 ms per division scale on the oscilloscope so that the falling edge of the signal isindistinguishable from the rising edge.The timing of the individual pin signal is measured from the photograph using a travelingmicroscope. These are then converted to time differences between the firing of the first PV pinand the firing of the other pins. In this manner the time reference for the first PV pin signal is setto zero. The line width of the oscilloscope trace corresponds to roughly 0.2 ms which is of theorder of 25 to 30 % of the temporal separation between the two closest PV pin signals.However, under the microscope the edges of each PV pin signal become quite sharp. The timedifferences are measured between the rising or falling edge of the first pin signal and thecorresponding rising (or falling) edges of the other pin signals. This yields two sets ofmeasurements from each photo. The two sets of times are then averaged to produce the PV pintimes. The uncertainty in each time measurement is roughly 0.04 ms for shots 1 to 7, 14 to 17, 40and 42 and, due to poor photo quality, 0.1 ms for shot 13. A digital oscilloscope was used inshots 8 through 11. The uncertainty in the time measurements for these shots is 0.02 ms. Theuncertainty in the piston position when the PV pin shorts out to the pump tube is estimated at 2mm. This is half the diameter of the hole through which the PV pin is inserted into the pumptube. The two closest PV pins are 152.4 mm apart so the 2 mm uncertainty is roughly 1% of thedistance between the PV pins. The piston velocity between the last two PV pins is usually greaterthan 200 m/s so the 2 mm uncertainty results in a temporal uncertainty of at most 0.01 ms.A LeCroy TDC 4208 time-to-digital converter[ 55] was used to measure the arrival times ofthe piston at the third and fourth PV pins for shots 18 through 33, 40 and 42. The time-to-digitalconverter has a resolution of 1 ns so, in these shots, the uncertainty in the time measurements ismuch smaller than that obtained with the oscilloscopes. For these shots, it is evident that theuncertainty in the time measurements is negligible when compared to the uncertainty in the pistonposition.Figure 2-6 shows a piston cross section. The piston is a nylon cylinder with lead disks (foradded mass) and a phenolic disk at the end facing the breech. Nylon is fairly incompressible yet/PHENOLIC DISK44.5 cm ^JPISTON CAPLEAD WEIGHTS^0-RING \jalNYLON PISTON^IP^Figure 2-6: Cross section of piston.Chapter 2. UBC No-Stage Light-Gas Gun and Diagnostic Equipment 30Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 31deforms easily. The deformability makes it possible to stop the piston with little or no damage tothe coupling section[ 321 . The phenolic disk at the breech end of the piston prevents movement ofthe piston when the pump tube is evacuated and then pressurized before the shot. The o-ring onthe piston restricts the flow of pump gas or gun powder gas around the piston. The added massfrom the lead disks helps the piston maintain the high pump gas pressure as the projectileaccelerates[271 . The piston mass is 1.0 kg for all of the shots in this study.2.2.2 Coupling Section and Launch TubeThe coupling region between the pump tube and launch tube is shown in fig. 2-7. Thefigure shows the tapered coupling section, petal valves and projectile. As mentioned in section1.2, the coupling section provides a means of stopping the piston and aids in maintaining a highpressure at the base of the projectile. In addition to stopping the piston, the coupling section mustwithstand higher gas pressures than any other gun section. As a result, the strength of thecoupling section is one of the main limiting factors of gun performance[561 .The pair of petal valves prevents the acceleration of the projectile until the pump gaspressure reaches a specified pressure. A diagram of a petal valve is shown in figure 2-8. Thevalve is a 1.57 mm-thick, 57 mm-diameter 304 stainless steel disk which is scored with a cross of0.82 mm-deep grooves. These grooves provide a controlled burst geometry and burst pressurefor the valves. The two petal valves are butted against each other with the grooves aligned in thesame orientation for both valves. The static burst pressure for a single petal valve isapproximately 4500 psi (300 bar) [57]. The pressure build-up that causes the valves to rupture isnot static but dynamic. As a result the 300 bar static burst pressure provides only a roughestimate of the actual burst pressure for the petal valves.The launch tube contains the projectile as it accelerates from rest to its muzzle velocity.The projectile is placed roughly 4 cm inside the beginning of the launch tube. The 3.05 m barrelof the launch tube has a smooth bore with maximum and minimum values in bore diameter of20.00 and 19.94 mm respectively.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 32COUPLING SECTIONPETAL VALVES/ ^PROJECTILEPUMP TUBELAUNCH TUBE4 cm te---)1It— 17.8 cmI—314 cm le 7 cm 41Figure 2-7: Diagram showing the coupling section, and the placement of the petal valves and theprojectile.CROSS SECTIONFRONTMACHINEDGROOVES0.157 cm0.076 cmChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 33Figure 2-8: Diagram of a petal valve used with the UBC two-stage light-gas gun.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 342.3 Projectile Design and FabricationProjectiles for two-stage light-gas guns must withstand accelerations of up to 10 7 m/s2[33]. As a result, the projectiles must be free of cavities or high stress regions. Projectiles withcavities or high stress regions will have a high probability of breaking apart during the launchcycle[581 .A schematic diagram of a projectile is shown in figure 2-9. The projectile consists of acopper flyer plate, a lexan (polycarbonate) sabot and a polyethylene tailstock. The diameter ofthe flyer plate increases towards the back of the projectile. This helps secure the flyer plate in thesabot during the acceleration. The lexan in the sabot is capable of withstanding pressures as highas 125,000 psi[591 . This is the equivalent of an acceleration of 3x10 7 tn/s2 for projectiles used inthis study. The tailstock is designed such that the pressure against the base of the projectile helpsseal the tailstock against the barrel of the launch tube[ 601 . This seal prevents the blow-by of thepump gas during the projectile acceleration.Figure 2-10 shows the press developed for embedding the flyer plate into the lexansabot[611 . The flyer plate is centred on the alignment die. A lexan cylinder is then placed on topof the flyer plate. Pressure from a hydraulic press is applied to the lexan cylinder and flyer platethrough the piston. The lexan is constrained around its circumference by the steel girdle. Acopper-constantan thermocouple, placed in a hole in the steel girdle, is used to monitor thetemperature during the projectile fabrication process. The temperature controller measures thetemperature through the thermocouple and adjusts the heat output of the heater. The copperspacer between the base of the girdle and the pedestal is used to position the sabot in the centralregion of the girdle for uniform heating. The ceramic discs above the piston and below thepedestal reduce the heat flow through the top and bottom of the sabot. The press is alsosurrounded with ceramic insulation and aluminum foil to reduce heat loss to the surroundings.Such insulation is necessary to make the temperature of the flyer plate and sabot as uniform aspossible.FLYERPLATE19.96±.01 mmChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 35POLYETHYLENETAILSTOCKFigure 2-9: Cross sectional diagram of a copper flyer plate projectile.ERAMICtDISK THERMOCOUPLEPISTONLEXANSABOT,PEDESTALTEMPERATURECONTROLLERHEATERSTEELGIRDLECOPPERSPACER• CERAMIC::DISK-JFLYERPLATEALIGNMENT _-41DIEChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 36TOHYDRAULICCYLINDERFigure 2-10: Cross sectional diagram of press used to embed flyer plate into lexan sabot.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 37Figure 2-11 shows the sabot pressure and temperature cycles used to embed the flyer plateinto the sabot. The pressure on the sabot is initially set at 4,000 psi. The temperature is increasedfrom room temperature at approximately 2°C/minute. When the thermocouple temperaturereaches 140°C, the lexan begins to flow around the flyer plate and the pressure begins to drop. Atthis point the pressure is increased to 6,000 psi. The temperature of the press continues toincrease until it reaches 170°C where it is held for 30 minutes and then lowered at 15°C/hour for10 hours. This heating and cooling cycle is necessary to minimize stress-producing temperaturegradients within the sabot.The residual stress within the cooled sabot is examined with a pair of crossed polarizers.Figure 2-12 shows the stress pattern in two sabots. Sabot A, produced with the procedureoutlined in the previous paragraph, shows an acceptable stress pattern. A modified version of thepress shown in figure 2-10 was used to produce sabot B. In fabricating sabot B, the insulatingceramic disk at the base of the pedestal was replaced with a large steel disk and the cooling ratewas 40°C/hour. Sabot A has little or no stress within 12 mm behind the flyer plate whereas sabotB has a relatively large amount of stress indicated by the thicker and more varying light orangeregion immediately behind the flyer plate. Both sabots have stress beyond the 12 mm regionbehind the flyer plate. The stressed region in sabot A is removed when the sabot is machined forits insertion into the polyethylene tailstock. The stress in sabot B can be removed by repressingand reheating the sabot in the manner outlined in the previous paragraph.The acceptable sabot is machined and pressed into the polyethylene tailstock to form theprojectile in figure 2-9. Care must be taken while machining the sabot and tailstock to ensure thatthe normal to flyer plate is parallel to the axis of the projectile. It is estimated that the normal tothe flyer plate is parallel to the projectile axis to within 0.5 mrad (o-Ah,)[58].There are four different types of projectiles used in this study. These projectiles havemasses of roughly 5.2 g, 5.8 g, 8.5 g, and 8.9g. The 5.2 and 5.8 g projectiles do not have copperflyer plates. These lexan projectiles consist of the polyethylene tailstock and a flat faced lexansection similar in length to the sabots used in projectiles with copper flyer plates. In the 5.8 gChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 38^ 1500ED_1001$a)a)506000cD4000 CD20000^2^4^6^8Time (hours)Figure 2-11: Graph showing the temperature and pressure cycles used to embed a copper flyerplate in a lexan sabot resulting in an acceptable stress profile within the sabot. The temperature ofthe constantan thermocouple is indicated by the solid line and the pressure on the sabot isindicated by the dashed line.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 39A:FLYER PLATESABOTk 2.5 cmFLYER PLATE2 cm1 B: SABOT 2 cmk 2.5 cmFigure 2-12: Photographs of sabots with acceptable and unacceptable stress patterns. The sabotswere viewed through an orange filter and a pair of crossed polarizers. Sabot A has an acceptablestress pattern and sabot B has a poor stress pattern.Chapter 2. UBC Twp-Stage Light-Gas Gun and Diagnostic Equipment 40projectiles the lexan section is approximately 2 mm longer than that in the 5.2 g projectiles. Theother two types of projectiles differ in the size of the copper flyer plate. The 8.5 and 8.9 gprojectiles have 1.5 mm thick flyer plates with diameters of 17 mm and 18 mm respectively.At room temperature and atmospheric pressure, the diameter of the tailstock is 0.2%larger than the inner diameter of the launch tube so the projectile must be cooled before it isinserted into the launch tube. As the projectile warms up the tailstock expands to form a seal withthe barrel of the launch tube.2.4 Target Chamber and DiagnosticsThe target chamber is shown in figure 2-13 together with the target and projectile velocitymeasurement equipment. The laser velocity trap and magnetic velocity induction system(MAVIS), located between the launch tube muzzle and the target, are used to measure theprojectile velocity. Target locations range from 50 to 60 cm from the muzzle If present, residualgas in the target chamber will lead to frictional heating of the projectile thus reducing its speed.To mitigate the effect of gas friction, the pressure in the target chamber is reduced to roughly20 mTorr before the shot. Care is also taken to shield the diagnostics equipment and the ports ofthe target chamber from debris produced by the projectile impact with the target.2.4.1 Laser Velocity TrapThe laser velocity trap consists of a set of three helium-neon laser and photo-diode pairs.The trap yields a set of arrival time versus position data as the projectile crosses the series of laserbeams. Each of the laser beams intersects the axis of the launch tube at a desired distance alongthe path of the projectile. The distance between the first and second laser beams is 108.8 ± 0.2mm and the distance between the second and third laser beams is 286.6 ± 0.2 mm. HewlettPackard 5082-4220 PIN photo-diodes [621 are used to detect the decrease in laser intensity as theprojectile crosses the laser beams. The circuit diagram for the laser velocity trap is illustrated inLAUNCHTUBEHeNe LASERSSHRAPNEL GUARDSPHOTO-DIODES108.8 mmI.<^>--< 286.6 mm --›-60 cmTARGETChapter 2. UBC Two -Stage Light-Gas Gun and Diagnostic Equipment 41Figure 2-13: Schematic of target chamber showing launch tube muzzle, laser velocity trap,MAVIS, target and shrapnel guards.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 42figure 2-14. The time difference between the photo-diode signals is measured with the time-to-digital converter and a digital oscilloscope.The jig shown in figure 2-15 is used to align the laser beams in the laser velocity trap. Thejig consists of a set of pin holes which can be adjusted along a pair of steel rods. The rods extendfrom a plug which is inserted into the muzzle of the launch tube such that the pin holes lie alongthe axis of the launch tube. The lasers and the pinholes are aligned such that the light passingthrough the pinholes produces a photo-diode reading of roughly three quarters of the valuewithout the pinholes. The distances between the laser beams are determined by the spacing of thepinholes in the jig. The uncertainty in the spacing measurements is less than 0.2 mm.Figure 2-16 shows the laser velocity trap signals recorded by an oscilloscope for a typicalshot. A time-to-digital converter is also used for these measurements. It is set to record the timeat which the photo-diode voltage reaches 0.5 V to avoid any mis-measurement due a gasprecursor in front of the projectile. The temporal resolutions of the digital oscilloscope and thetime-to-digital converter are 50 ns and 1 ns respectively. The photo-diodes have a response timeof less than 1 ns. The time interval between the closest laser beams is of the order of 30 ps for aprojectile traveling at 4 km/s so that the uncertainty due to the finite resolution in the timemeasuring devices is at most 0.2%.2.4.2 Magnetic Velocity Induction SystemThe magnetic velocity induction system[631 (MAVIS) is shown in figure 2-17. TheMAVIS uses two ring-magnet and pick-up coil pairs to obtain arrival time versus position data forprojectiles with metal flyer plates. The magnets are Ceramic 5 Ring Magnets made by Permac[ 641 .The projectile travels through the 25 mm diameter hole through the centre of the MAVIS. Eddycurrents are induced in the flyer plate as it passes through the magnetic field of each of thepermanent ring-magnets. A pick-up coil, located at the centre of each of the magnets, is used tomeasure the change in the magnetic field due to the flyer plate eddy currents. The time-to-digitalChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 43PHOTODIODES^AMPLIFIERSSIGNALDIVIDERSOSCILLOSCOPETIME-TO-DIGITALCONVERTERFigure 2-14: Circuit diagram for the laser velocity trap.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 44 25 mm500 mmO I TOPVIEW20 mmSIDEVIEWMUZZLEINSERTAPERTURESFigure 2-15: Diagrams showing the top and side views of the jig used to align the laser velocitytrap.SIGNAL.FROM SECOND." PHOTO-DIODEI SIGNAL.... .FROM THIRD.^PHOTO-DIODEChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 45RISE INDICATING^RISE INDICATINGTHE ARRIVAL OF THE THE ARRIVAL OF THEPROJECTILE AT THE PROJECTILE AT THESECOND LASER BEAM THIRD LASER BEAMFigure 2-16: Photograph of a pair of laser velocity trap signals. The scale of the horizontal axis is5 gs/div and the scale for the scale for the vertical axis is 0.2 V/div. The two signals were storedon a digital oscilloscope. The photograph is a double exposure. The width of a recordedoscilloscope trace is four times that displayed on the oscilloscope at any time and two exposuresare needed to display both signals in one photograph.j• ? ? ry.MAt T ALUMINUM HOUSINGGAS -STRIPPERChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 46PROJECTILE...._>. IF--152.4 mm--.1 25 mmFigure 2-17: Cross sectional diagram of Magnetic Velocity Induction System.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 47converter and a digital oscilloscope are used to measure the time difference between the two pick-up coil signals.The conical gas stripper at the front of the MAVIS directs gas away from the projectile.The MAVIS is positioned such that its axis lies along the axis of the launch tube (figure 2-18). Ahelium-neon laser is inserted into the breech end of the launch tube such that its beam lies alongthe launch tube axis. A brass plug with a concentric 1 mm aperture is inserted into the launchtube muzzle to reduce the beam spot size. The MAVIS is then aligned such that the laser beampasses through 0.2 mm-diameter holes at the centres of a pair of Plexiglas plugs that are insertedinto its ends. The distance between the pick-up coils is 152.39 ± .03 mm. This distance wasmeasured with a traveling microscope before the MAVIS was assembled.Figure 2-19 shows a typical pair of pick-up coil signals. The contribution of the flyer platemagnetic field to the magnetic field at the pick-up coil reaches a maximum when the flyer platearrives at the pick-up coil. As a result, the current induced in the pick-up coil changes direction.The time difference between the arrival of the flyer plate at the two pick-up coils is measuredfrom the zero voltage intercepts of the pick-up coil signals.2.4.3 Targets for the Measurement of the Flyer Plate Tilt and CurvatureFlyer plate tilt and curvature measurements require accurate determination of the arrivaltimes of the flyer plate at several points on the target. The target for the tilt and radius ofcurvature measurements is shown in figure 2-20. The target consists of an array of cap pins gluedinto an aluminum target body. Dynasen cap pins 1651 , shown in figure 2-21, are used to measurethe arrival times of the flyer plate at various points. The target has one centre cap pin and 4 or 6pins equally spaced around the centre pin at a radius of either 7.0 mm or 7.5 mm. The cap pins,initially biased to -350 V, short out when the impact of the flyer plate produces a pressure of 75kbar or more. The short circuit is produced when the material in the pin cap, accelerated by theshock wave produced by the flyer plate impact, closes the gap that separates the cap from the pinterminal. The inner region of the target face is recessed with respect to the outer edge thusTARGETBRASSAPERTUREChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 48PLEXIGLASSAPERTURESFigure 2-18: Schematic of the alignment of the MAVIS and target along the axis of the launchtube. The Plexiglas apertures in the MAVIS are removed when the target is aligned.8.16U TRIG ara.alChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 49-SrZERO VOLTAGEINTERCEPT OFFIRST PICK-UPCOIL SIGNAL:-ZERO VOLTAGEINTERCEPT OFSECOND PICK-UPCOIL SIGNALFigure 2-19: Photograph of the pick-up coil signals produced by the MAVIS. The scale on thehorizontal axis is 5 gs/div and the scale on the vertical axis is 1 V/div. The time between thesignals is measured from the zero voltage intercepts as indicated on the photograph.BRASSCAP INSULATOR411195,..1■11..91 mmChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 50CABLESA 44 mm3 mmmmFRONT^CROSS SECTIONFigure 2-20: Target used to measure the tilt and curvature of the flyer plate on impact..065 ± .013 mm^CONDUCTORSFigure 2-21: Cross section of the cap pins used in the targets for tilt and curvature measurements.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 51allowing the cap pins to protrude from the target without affecting the placement of a microscopeslide used in aligning the target (the use of the microscope slide is described below). Theprotrusion of the pins ensures that the pins are fired by the shock wave produced by the impact ofthe flyer plate on the cap. Also, it is easier to check that the pins lie in the same plane when theyprotrude from the face of the target.Care is taken to ensure that the ends of the cap pins lie approximately in the same plane asthe raised outer edge of the target. In preparing the target, the raised outer edge of the target isbutted against an optical flat. The cap pins are inserted through the holes in the target, pushedagainst the optical flat and epoxied in place. To ensure that the pins remain butted against theoptical flat, the pins are pressed against the optical flat while the epoxy hardens.The positions of the ends of the cap pins relative to the plane defined by the raised outeredge were measured for shots 26 through 33. These pin height measurements are performed onthe x-y translation mount shown in figure 2-22. The target is mounted such that two of the outerpins lie in the horizontal plane (x-y plane in figure 2-22) that contains the centre pin. Pin heightsmeasurements are made for the three cap pins and for each side of the raised edge of the target.The pin height is the difference between the drive micrometer (x-direction) readings where theprobe rod comes in contact with the pin and the line defined by the points on the raised edge ofthe target. Resistance is measured between the probe rod and the target so contact is indicated bya drop in resistance to less than 100After the pin heights are measured, the target is epoxied into an aluminum mounting plate.The aluminum plate is then attached to a steel mount in the target chamber using three screwswhich can be adjusted to render the plane of the target face perpendicular to the launch tube axis.The mounted target is shown in figure 2-23.The HeNe laser used to align the MAVIS is also used to align the targets (figure 2-18).The target is positioned with the laser beam on the centre cap pin. To ensure that the face of thetarget is perpendicular to the launch tube axis, the axial laser beam is reflected off of a microscopeMICROMETERSl'X TRANSLATION MOUNTY TRANSLATION MOUNTPROBE ROD^) \CAPPINSChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 52OHMMETERFigure 2-22: Jig used to measure the positions of the ends of the cap pins with respect to theraised outer edge of the target face.STEELTARGETMOUNTALUMINUM MOUNTING PLATEChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 53ADJUSTMENT SCREWSTARGETFigure 2-23: Diagram showing a mounted flyer plate tilt and curvature target.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 54slide placed in a plane along the raised outer edge of the target. The target is then adjusted suchthat the reflected laser beam returns to the centre of the aperture in the muzzle of the launch tube.The arrival times of the flyer plate at the cap pins are measured with a pair of high speedoscilloscopes. The pin conditioner shown in figure 2-24 provides the -350 V bias across the twoterminals of the pin. The diagram in figure 2-25 shows the connections between the cap pins andthe oscilloscopes. The pin signals are split with signal dividers. Half of each signal travelsdirectly to the master trigger-fiducial generator. The signal from the first pin that fires will triggerthe oscilloscopes and produce a time fiducial. The other half of each of the pin signals is delayedwith delay cables. There are three lengths of delay cables which delay the signal by 100, 200 and300 ns. The delayed signals are combined in groups of two or three, along with the fiducial, anddisplayed on the oscilloscopes. Figure 2-26 shows a photograph of two different groups of thecap pin signals.Before each shot, a timing measurement between the fiducial and a simulated cap pinsignal is made for each of the pins. In these measurements a mercury switch replaces one of thecap pins in figure 2-25. The closure of the mercury switch simulates the shorting of a cap pin. Inthese simulations only one pin is fired at a time so that the trigger and fiducial pulsesaccompanying the simulated cap pin signal are produced by that signal. The timing measurementobtained from each of these pin simulations thus corresponds to the case where the cap pinrecorded is the first pin to fire.The time between the fiducial and the cap pin signal for each cap pin is measured from thephotograph (figure 2-26). This measurement is then compared to the timing measurements foundusing the mercury switch. Figure 2-27 shows a schematic of a trace that displays the signals forpin "i" and pin "j". In this example, pin "i" is the first pin to fire (t i=0) and pin "j" fires at sometime tj.0 after pin "i". The time measurements from the mercury switch simulations are At; forpin "i" and dti for pin "j". Because pin "i" fires first, the time delay between the fiducial and thepin "i" signal is dti. If pin "j" fires at the same time as pin "i" (t3=0) then the time between thefiducial, produced by the signals from both pin "i" and pin "j", and the signal for pin "j" is just-350 V1 MCIOSCILLOSCOPECAP PIN1 50 525052Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 55PINCONDITIONERFigure 2-24: Circuit diagram of the pin conditioner which provides a 350 V bias across the cappin.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 56CAP^PIN^SIGNALPINS CONDITIONERS DIVIDERS DELAY CABLES100 nsSIGNALCOMBINER200 ns ^b^OTHERCAP PINS^1 MASTERTRIGGER FIDUCIALGENERATOROSCILLOSCOPE1^1-Figure 2-25: Circuit diagram for measuring the arrival time of the flyer plate at the cap pins.C IA zChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 57FIDUCIAL^CAP PIN SIGNALSFigure 2-26: Photograph of a typical set of cap pin signals for flyer plate tilt measurement. Thescale for the horizontal axis is 50 ns/div and the scale for the vertical axis is 1 V/div,Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 58DELAY CABLE "i"DELAY CABLE "j"MASTER TRIGGERPIN "i"PIN "j" t >0OTHER PINSFIRE AT t> 0FIDUCIALGENERATORSIGNALCOMBINERPIN "i"^PIN "j"FIDUCIAL SIGNAL SIGNAL'I.■m•m=•••••••=r\.....m•Mm.•.Pf'‘*t■I■PMIAtiAt. jEXTERNAL TRIGGERSIGNAL INPUTFigure 2-27: Schematic illustrating the origin of an oscilloscope trace from the set of cap pinsignals.Chapter 2. VBC Two-Stage Light-Gas Gun and Diagnostic Equipment 59If the firing of pin "j" occurs at the time tj>0 after pin "i", the time between the fiducial, producedby the signal from pin "i", and the pin "j" signal is titi plus the time between the firings of pin "i"and pin "j" (tj). Thus, the arrival time of the flyer plate at any cap pin with respect to the arrivaltime of the flyer plate at the first pin that fires, the tj values, can be measured by comparing thetime measurement between the fiducial and the cap pin signal with the timing measurement thatwould occur had that cap pin been the first pin to fire.The uncertainty in the flyer plate arrival times comes from a variety of sources. Theuncertainty in the distance between the end of the cap pin and the plane defined by the raised edgeof the target, cY Scph, is approximately 10 pm. This spatial uncertainty results in a temporaluncertainty ofarcs astph [2.1]wwhere w is the projectile velocity. In the cap pins, there is an uncertainty in the distance betweenthe cap and the pin terminals, crscpcap, of 13 pm[641 . The speed at which the cap closes the gapbetween itself and the rest of the pin is the free surface velocity of the inside surface of the brasscap. The free surface velocity is roughly twice the particle velocity behind the shock [511  In animpact between a copper flyer plate and the brass cap, the particle velocity is roughly half theprojectile velocity so the free surface velocity is close to the projectile velocity. In an impact witha lexan projectile, the particle velocity in the brass is roughly 20% of the projectile velocity so thesurface velocity of the cap is only 40% of the projectile velocity. The temporal uncertaintyresulting from ascpcap isaTcpcap scpcap kw[2.2]where k is the ratio of the free particle velocity of the cap to the projectile velocity. k equals 1 forcopper flyer plate shots and 0.4 for lexan projectile shots. The uncertainties arcph and crTcpcap areChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 60independent and it is assumed that the uncertainties represent Gaussian distributions so theircontribution to the uncertainty in the arrival time measurements isamp ilar2eph 4cPcv^ [2.3]Or CT Tcp [2.4]wThe time measurements from the oscilloscopes have an uncertainty of 1 ns for both the mercuryswitch and cap pin signals. The total uncertainty in the individual time delay measurements liesbetween 4 ns for a projectile velocity of 4 km/s and 8 ns for a projectile velocity of 2 km/s forcopper flyer plate shots. In the lexan projectile shots the total uncertainty is between 10 ns and 20ns for projectile velocities of 4 km/s and 2 km/s respectively. In all cases, most of the uncertaintyis due to the cap pins and the pin heights.The uncertainty in the centring of the target on the axis of the launch tube, a is-stc, --estimated to be 0.5 mm. This uncertainty causes an uncertainty in the tilt measurements for shotswith curved flyer plates. Figure 2-28 shows the measured tilt that results from uncertainty in thecentring of the target. For a radius of curvature given byr2R2 [2.5]41, 'where rcp is the distance from the centre of the target to the outer ring of cap pins and dci, is thedistance by which the centre of the target lags behind the ring a radius rcp from the centre, thecontribution to the angular uncertainty in the tilt, in radians, is[2.6]SURFACE OFFLYER PLATE CAP PIN "1"CAP PIN "2"LINE JOINING POINTS ONFLYER PLATE THAT STRIKECAP PINS "1" AND "2"TARGETa:CAP PIN "1"SURFACE OFFLYER PLATELAUNCH- TUBE AXISLINE JOINING POINTS ONFLYER PLATE THAT STRIKECAP PINS "1" AND "2"CAP PIN "2"TARGETb:LOCATION OF CAP PIN "1"WITHOUT UNCERTAINTYAteLAUNCHTUBE AXISLOCATION OF CAP PIN "2"WITHOUT UNCERTAINTYcpStcChapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 61Figure 2 -28: Illustrations showing the relationship between the spatial uncertainty in the positionof the target (0sm.) and the related angular uncertainty in the tilt(aA . In both figures a and b,the flyer plate with radius of curvature, R, strikes the target with no tiltto the launch tubeaxis. In figure a, the target is centred on the launch tube axis and the flyer plate curvature doesnot effect the tilt measured between cap pins "1" and "2". In figure b, the target is offset thedistance crsk with respect to the launch tube axis. The resulting tilt measured between cap pins" 1 " and "2 " is aAtc.Chapter 2. UBC Two-Stage Light-Gas Gun and Diagnostic Equipment 62The effect of the uncertainty in centring the target on the radius of curvature measurement isnegligible. The uncertainty in overlapping the position of the reflected axial laser beam in thealignment of the target is also approximately 0.5 mm. Since the distance between the launch tubemuzzle and the target is roughly 0.5 m, this results in an angular uncertainty in the tilt alignmentof the target of 0.5 mrad, crAt,,,. The radius of curvature is not effected by the uncertainty in theinitial tilt in the target.Chapter 3Results and Discussion3.1 IntroductionThis chapter presents and discusses the performances of the gun and of the diagnosticsystems.3.2 Breech PressureFigure 3-1 shows the pressure signal from the breech and pump tube pressure transducersfor Shot 29. Initially, the pressure increases as the burning powder more than compensates forthe increase in breech volume as the piston moves forward slowly. The pressure peaks anddecreases as the effect of the piston motion becomes greater than that of the burning gun powder.The pressure drops to roughly 1,000 psi by the time the piston reaches the coupling section.The piston comes to a rather abrupt stop when it reaches the coupling section. Thisproduces a pressure pulse that travels back towards the breech. The pressure signal in figure 3-1shows a few reflections of the pressure pulse as it travels back and forth in the pump tube. Thepulse has a period of about 9 ms. The ratio of the specific heats of the gun powder gas is roughly1.3 and the powder load for the pressure signal in figure 3-1 was 100 g. Assuming that all of thepowder burns and the total volume of the breech is roughly six liters, the adiabatic speed of soundin the gas is approximately 800 m/s. The round trip distance that the pulse travels is then 7 m.This is roughly twice the combined length of the breech and pump tube sections.Figure 3-1 also shows the pump tube transducer signal. The sharp rise in the signal isproduced by the sudden increase in the pump tube pressure from roughly 100 or 200 psi to thebreech pressure of a few thousand psi as the breech end of the piston passes the pressure63Chapter 3. Results and Discussion 64 PUMP TUBEPRESSURESIGNALBREECHPRESSURESIGNALMAXIMUMBREECHPRESSUREREFLECTIONS OF PRESSURE PULSEFROM ABRUPT STOPPAGE OF PISTONFigure 3-1: Photograph of the signals from the breech and pump tube pressure transducers. Inthis shot the horizontal axis has a scale of 5 ms/div and the vertical axis has a scale of 0.5 V/div or1,000 psi/div.Chapter 3. Results and Discussion 65transducer. In all of the shots, the maximum breech pressure is reached before the onset of thepump tube pressure transducer signal. The pressure pulse produced by the abrupt stopping of thepiston, seen in the breech pressure transducer signal, is also present in the pump tube pressuretransducer signal.The maximum breech pressure, powder load and initial pump tube pressure data arepresented in table 3-1. The maximum breech pressure is measured from the oscilloscope trace forthe breech pressure transducer. Figure 3-2 shows the maximum breech pressure plotted againstthe powder load for various pump tube pressures. The data in figure 3-2 shows that therelationship between the gun powder load and the maximum pump tube pressure is fairly linear.A linear least-squares fit to the data is included for visualization purposes. The graph alsoindicates that the initial pump tube pressure seems to have little effect on the maximum breechpressure.The burn rate Brat, of the gun powder, in mm3/s, isBraf, = AspcPgpk [3.1]where ilep is the surface area of the gun powder in mm2, Pgp is the gun powder gas pressure inpsi, c, the burn-rate coefficient, is roughly 0.64 mm/s, and k, the burn-rate power-law constant, is0.76 for M2, a nitrocellulose based gun powder very similar to our powder[ 66 .29]. With moresurface area, a shot with a large powder load produces a higher initial breech pressure andtherefore a higher burn rate than a small powder load shot. As a result the rate at which thebreech pressure increases and the maximum breech pressure are larger for shots with largerpowder loads. The actual relationship between the maximum gun-powder gas pressure and thepowder load is difficult to predict because the higher breech pressures are accompanied by higherpiston velocities. With higher piston velocities, the effect of the expanding breech volume on thebreech pressure is also larger.Chapter 3. Results and Discussion 66Table 3-1: Maximum breech pressure and related dataShot Powder Load(g)Initial PumpTube Pressure(psi)Maximum BreechPressure(±150 psi)7 86 90.4 27508 120 91.4 43759 46 61.1 135010 86 96.3 295011 140 90.5 545012 60 63.7 205013 60  60.8 195014 86 62.6 295015 86 60.0 235016 86 61.2 275017 70 61.2 250018 90 62.4 270021 75 92.0 250022 90 90.1 310023 75 90.9 275024 75 89.9 250026 60 91.0 195027 100 91.6 340028 125 91.4 470029 150 121.8 650031 100 92.4 350032 100 90.3 360033 100 89.9 37507.06.01.00.040^60^80^100^120Powder Load (g)140 160•^Chapter 3. Results and Discussion 67Figure 3-2: Graph of maximum breech pressure measurements plotted as a function of the gunpowder load. Initial pump tube pressures of 60, 90 and 120 psi are indicated by closed circles,open circles and open squares respectively. The solid line indicates a linear least-squares fit to allof the data.Chapter 3. Results and Discussion 683.3 Projectile VelocityAs shown in section 1.3, accurate measurement of the projectile velocity is an importantproperty in determining the shock pressure. In these measurements, we use the laser velocity trapand MAVIS systems described in sections 2.4.1 and 2.4.2.Table 3-2 shows the projectile velocities obtained with the MAVIS and with the laservelocity trap for shots where both systems were used. The table also includes the percentagedifference between the measurements. The data shows that the velocity measurements obtainedfrom the two systems are in agreement to within 0.2% for projectile velocities between 2 and 4km/s for all but one of the shots. This is not surprising as the estimated uncertainty in the velocitymeasurements for each of the systems is roughly 0.2%. In shot 32 the projectile velocity foundusing the MAVIS is 1% greater than that indicated by the laser velocity trap. In this shot thetime-to-digital converter did not work properly so the measurements were made from the digitaloscilloscope traces.The noise in the laser velocity trap signals increases with the projectile velocity. This ispossibly due to the pump gas traveling past the projectile (blow-by gas) and blocking the laserbeams. As a result, the accuracy of the laser velocity trap declines with higher velocities. Theblow-by gas has little effect on the MAVIS signals. In addition, the magnitude and the slope ofthe MAVIS signal increase with the projectile velocity. This makes it easier to measure theprojectile velocity with the MAVIS as the velocity increases.The accuracy of the methods used for measuring projectile velocities in this studycompares favorably with that of techniques described by other researchers. X-ray radiographyoutlined by Jones et al. and Van Thiel et iii.[36,671 is superior to optical diagnostics in that the x-rays are not absorbed or scattered by blow-by gas. In such measurements, x-ray pulses are usedto produce snap shots of the projectile as it travels between the muzzle and the target. Theuncertainty in the projectile velocity measurements using x-rays is 0.1%. Kondo et al. describe asystem similar to the MAVIS in which pick-up coils are used to detect the magnetic flux of amagnet which is embedded in the projectile[681. The uncertainty in the projectile velocityChapter 3. Results and Discussion 69Table 3-2: Projectile velocity data from MAVIS and the laser velocity trap for shots whereboth systems were used.Shot MAVIS(km/s)Laser Trap(km/s)Difference(%)13 2.548 2.547 0.0414 3.186 3.181 0.1615 3.834 3.834 017 2.466 2.465 0.0418 2.835 2.835 023 2.491 2.489 0.0824 2.505 2.504 0.0430 3.807 3.816 0.2431 3.008 3.010 0.0732 3.039 3.069 1.033 2.960 2.968 0.27Chapter 3. Results and Discussion 70measurements made with this system is 0.7%. The authors note that the uncertainty can begreatly reduced by increasing the distance between the pick-up coils. In the system used byKondo et al. the distance between the pick-up coils is 60.6 mm. The MAVIS pick-up coils are152.4 mm apart. Finally, cap pins have also been used to measure projectile velocity[ 691. The tiltand curvature in the flyer plate on impact affect the accuracy of this type of projectile velocitymeasurement. The uncertainty in such measurements is roughly 1%.Table 3-3 shows the projectile velocity, powder load, projectile mass and pump tubepressure for nearly all of the shots in this study. Figure 3-3 shows the projectile velocity plottedagainst projectile mass. All of the shots plotted in figure 3-3 have the same gun powder load andinitial pump tube pressure. The only variation in the initial conditions between these shots is inthe projectile mass. For the shots in the graph, the increase in the projectile mass of roughly 50%from 5.8 g to 8.5 g results in a decrease in the projectile velocity of approximately 13%.The effect of the initial pump tube pressure on projectile velocity is demonstrated in figure3-4. In this figure the projectile velocity is plotted against the initial pump tube pressure for shotswith the same powder load and projectile mass. The graph contains three groups of shots. Forshots 6 and 7, the powder load was 86 g and the projectile mass was 5.2 g. The increase in pumptube pressure from 60 psi to 90 psi is accompanied by a decrease in the projectile velocity ofroughly 4%. For shots 18 and 22, the powder load was 90 g and the projectile mass was 8.9 g.In this case the increase in the pump tube pressure from 60 psi to 90 psi is accompanied by anincrease in the projectile velocity of 1%. In shots 40, 41 and 42, the powder load was 150 g andthe projectile mass was 8.5 g. The projectile velocities for these shots vary little over the range ofpump tube pressures. With the limited data, the opposite and small effects of initial pump tubepressure on projectile velocity would suggest that the latter has a very weak dependence on theformer. In comparison, the effect of projectile mass on projectile velocity is much stronger.Although shots 18 and 22 have slightly higher powder loads than shots 6 and 7, the projectilevelocities for shots 18 and 22 are still lower due to the larger projectile masses.Chapter 3. Results and Discussion 71Table 3-3: Projectile velocities and related data.ShotPowderLoad(g)Pump TubePressure(Psi)ProjectileMass(g)ProjectileVelocity(mss)2.1701 46 60.62 70 60.9 2.3704 46 60.8 5.161 2.1305 55 60.1 5.157 2.3416 86 60.4 5.162 3.1697 86 90.4 5.155 3.0398 120 91.4 5.145 3.7179 46 61.1 5.154 2.10110 86 96.3 3.08311 140 90.5 5.828 4.07913 60 60.8 5.857 2.54814 86 62.6 5.877 3.18415 86 60.0 5.894 2.83416 86 61.2 5.770 3.24817 70 61.2 8.939 2.46618 90 62.4 8.838 2.83519 75 91.7 5.740 2.88020 150 110.8 5.750 4.24021 75 92.0 5.750 2.87422 90 90.1 8.883 2.87323 75 90.9 8.422 2.49224 75 89.9 8.551 2.50626 60 91.0 8.436 2.20027 100 91.6 8.918 2.98228 125 91.4 8.953 3.38029 150 121.8 8.550 3.79130 150 120.7 8.780 3.80931 100 92.4 8.860 3.00932 100 90.3 8.772 3.05433 100 89.9 8.914 2.96440 150 124.0 8.58 3.80841 150 142.3 8.5 3.75842 150 156.7 8.59 3.8191^t^1^1^I^1^1^1^7^I^-1"^1^IF - 1^1^I^1^I^1^1^1^111921OWN=MO230024- 1^I^1^1^I^1^1^1^1^I^1^1^1^1^I^1^1^1^1^I^1^1^1^f _3.02.92.80-5° 2.7ta)2.602.52.4Chapter 3. Results and Discussion 725.0^6.0^7.0^8.0 9.0 10.0Projectile Mass (g)Figure 3-3 Projectile velocity plotted versus projectile mass for shots with the same initial pumptube pressure and the same powder load. The pump tube pressure for the data shown was 90 psiand the powder load was 75 g.Chapter 3. Results and Discussion 734.0E3.50a)"t3 3.0*ETo_2.51^1^1 I^1^1 I^1^1 1^1^1• 40 4^1• 42-• =MN• 6• 7A18 A22lay1^1^1^I^i^1^1^I^i^1^1^I^1^1^i^I^1^1^1^I^1^1^140^60^80^100^120^140 160Initial Pump Tube Pressure (psi)Figure 3-4: Projectile velocity plotted versus initial pump tube pressure for shots with the sameprojectile mass and the same powder load. The solid circles indicate shots where the powder loadwas 86 g and the projectile mass was 5.2 g. The open triangles indicate shots where the powderload was 90 g and the projectile mass was 8.9 g. The solid diamonds indicate shots where thepowder load was 150 g and the projectile mass was 8.5 g.Chapter 3. Results and Discussion 74The small effect of the initial pump tube pressure on the projectile velocity has also beenfound in a numerical simulation of the internal ballistics of a two-stage light-gas gun performed byGlenn[70,711. Glenn shows that, for a given piston velocity, there is a range of initial pump tubepressures which produces the highest projectile velocities. Shots with initial pump tube pressuresabove or below this range have lower projectile velocities. In a shot where the initial pump tubepressure is too low, the high pressure behind the projectile is only maintained for a relatively shortduration. When the initial pump tube pressure becomes too high, the petal valve bursts too soonwhen the piston is still a long way from the end of the pump tube. By the time the gas in thecoupling section reaches its maximum pressure, the projectile is traveling too fast and has gonetoo far down the launch tube to be affected by the maximum in the pressure. It appears that, fromthe small effect of the pump tube pressure on the projectile velocity observed in this experiment(figure 3-4), the initial pump tube pressures used in this study lie within the range where variationsin the initial pump tube pressure have little effect on the projectile velocity.With little or no reduction in projectile velocity accompanying an increase in the pumptube pressure, it is desirable to use a higher initial pump tube pressure. In such cases, more of thepiston energy goes into compressing the pump gas. As a result, the piston has a lower velocitywhen it reaches the coupling section. The force exerted on the coupling section, by the piston, isthen lower. This reduces the amount of damage to the coupling section, increasing its lifetime.The projectile velocity is plotted against powder load for various projectile masses infigure 3-5. In this graph the projectiles are grouped into those with projectile masses between 5.1and 5.9 g and those with masses between 8.4 and 9.0 g. The results show a strong correlationbetween projectile velocity and powder load for projectiles in each group regardless of thevariation in the initial pump tube pressures. Also, there is a clear separation between the data forthe two different projectile mass groups. The projectile velocities for the projectiles in the lightermass group are roughly 10% greater than those in the heavy mass group for shots with the samegun powder load. In figure 3-5, the general trend in the relationship between the projectileChapter 3. Results and Discussion 754.5 ^1■3'E..:' 3.5(-50a)>a) 3.0t.)-ja)rf0- 2.52.040^60^80^100^120Powder Load (g)4.0140^16028Figure 3-5: Graph of projectile velocity plotted as a function of gun powder load. The projectilesare grouped into those with masses between 5.1 and 5.9 g and those with masses between 8.4 and9.0 g. Data for projectiles with masses between 5.1 and 5.9 g are indicated by solid diamonds anda solid line. Data for the projectiles with masses between 8.4 and 9.0 g are indicated by opencircles and a dashed line. The curves which indicate quadratic fits to each of the data sets areprovided for visualization purposes.Chapter 3. Results and Discussion 76velocity and the gun powder load for each projectile mass group is represented by a quadraticcurve.As mentioned earlier, it is difficult to explain the relationship between maximum breechpressure and the powder load. With the powder gas accelerating the piston, the pistonaccelerating and compressing the pump gas and finally the pump gas accelerating the projectile,the relationship between the gun powder load and the projectile velocity is even more difficult toexplain. The important information drawn from figure 3-5 is that, for the shots in this study, thereis a well defined relationship between the powder load and the projectile velocities for projectilesof the same mass.3.4 Numerical Simulation of the Internal Ballistics of the UBC Two -Stage Light-Gas GunA 1 Y2 dimension Arbitrary Lagrange Eulerian computer code was used to simulate theperformance of the UBC two-stage light-gas gun. The computer code, written byL.A.Glenn[7°,71 ], has been used to simulate the performance of guns at the Lawrence LivermoreNational Laboratories and at the NASA/Ames Laboratory. The basic fluid dynamics treatmentused in the calculation is described in a Glenn's paper describing a code for modelling the fluidflow in a water cannonlni.The conservation equations for the pump gas ared(pA) pA aidtdu 1+(p) --c-fc = 0and[3.2][3.3]de P dp _ 0dt p2 dx[3.4]Chapter 3. Results and Discussion 77where c is the specific internal energy, P is the pressure, p is the mass density, u is the particlevelocity, x is the spatial coordinate and t is time. The time derivative operator isd,^0— 0— + ykx,t )—dt a^ac [3.5]withv(x, t) = u—s(x,t)^ [3.6]where v(x,t) is the particle velocity with respect to the local coordinate frame traveling with thevelocity s(x,t) relative to the lab. Equations [3.2] to [3.4] represent an Eulerian model whens = 0, and a Lagrangian model when s = u. In the calculation developed by Glenn, s(x,t) is variedfrom cell to cell such that there is little variation in the cell widths.In the present calculation, the pump gas is divided into 100 cells between the piston andthe projectile. All of the cells have approximately the same width. The cell boundary at the frontof the piston travels at the piston velocity and the cell boundary at the base of the projectiletravels at the projectile velocity.In this study, a perfect-gas equation of state was used for helium. The forces due tofriction between the piston, pump gas and projectile and the barrel of the gun are neglected. Also,the calculation does not model the extrusion of the piston into the coupling section. Instead, thepiston is treated as a volumeless object that is not affected by the reduction in cross sectional areaas it enters the coupling section. The input parameters for the calculation include the diameters ofthe pump tube and launch tube, the positions of the ends of the pump tube, coupling section andlaunch tube with respect to the initial position of the front of the piston, the initial pump gasinternal energy and density, the piston velocities for a set of piston positions, the maximum pistonposition, the petal valve burst pressure, the piston mass and the projectile mass. The projectileand the petal valves are positioned at the end of the coupling section. The piston velocity is set tozero when the piston reaches the maximum piston position. The maximum piston position isChapter 3. Results and Discussion 78usually set to the end of the launch tube. One notable parameter not included in the input is thegun powder load. Instead of modeling the bum of the gun powder, the calculation usesexperimental piston velocity data to determine the compression and acceleration of the pump gas.It was mentioned in section 2.2.2 that the burst pressure of the petal valves used with theUBC two-stage light-gas gun is not accurately known. The static burst pressure of a single petalvalve is approximately 300 bar. Two valves are used in tandem in all of the shots in this study andthe rupture of the valves is not a static process. A burst pressure of 600 bar was assumed in thelargest number of simulations. Calculations were also performed for burst pressures of 300 barand 900 bar to examine the effect of the burst pressure on the calculated projectile velocity.In a typical calculation, the piston. velocity history is inputted into the code as a set of sixor ten position-velocity points. The first of the position-velocity points is at the initial pistonposition and the last of the points is 2.5 m from the initial piston position. The piston velocityhistory is constrained to lie on the line joining adjacent points. After the piston travels past thelast position-velocity point, the piston is treated as a free moving body. The only force acting onthe coasting piston is that due to the pump gas.The piston velocity history was obtained from the PV pin data. As noted in section 2.2.1,the PV pin times are measured between the rising or falling edge of the first pin signal and thecorresponding rising (or falling) edges of the other pin signals. The two sets of times are thenaveraged to produce the PV pin times. A cubic polynomial was fit to the four PV pin position-average time data for each shot. The piston velocity is the inverse of the slope of the cubic curvein the position-time (x,t) plane. For the cubic relationship between the time and position,t =aP.+bP.x+c x2 +d ,x 3 [3.7]the piston velocity isv = (bp, +2c p,x +3d x 2 ) -1^[3.8].Chapter 3. Results and Discussion 79In equations [3.7] and [3.8], t is the arrival time of the piston at position x, vpi is the pistonvelocity at x, and api, bpi, cpi and dp; are the fitting parameters.In order to examine the effect of the uncertainty in the average PV pin trigger times,projectile velocities were calculated for piston velocity histories where the uncertainties wereincluded in the trigger times. Two piston velocity histories were calculated to examine the effectof the uncertainties for each shot. In one of the piston velocity histories, the trigger times (withthe associated uncertainties) that were used in the cubic fit were chosen to produce the maximumpiston velocity at the last point in the piston position-velocity input data. In the other history, thetrigger times were chosen to produce the minimum piston velocity at the last point in the pistonposition-velocity input data.The choice to use the piston velocity histories with the maximum and minimum pistonvelocity at the last point in the piston position-velocity input data is based on the assumption thata change in the piston velocity at the last point has a larger effect on the calculated projectilevelocity than at any of the other points. For a small change in the pump gas volume AV, thechange in pump gas energy AE is given byAE = PAY^ [3.9]where P is the pump gas pressure. The rate at which energy is transferred from the piston to thepump gas isdE = P—dV= PAptv pidt^dt[3.10]where isis the cross sectional area of the pump tube. With the pressure increasing as the pistontravels down the pump tube, the effect of a change in piston velocity on the rate at which theenergy is transferred to the pump gas is greatest at the last of the piston position-velocity points.Also, after the piston travels past the last of the position-velocity points, the piston deceleration isChapter 3. Results and Discussion 80calculated solely from the pump gas pressure. The uncertainty in the piston velocity at the lastinput directly affects the energy transferred from the piston to the pump gas after the pistonpasses the last point.The data from the PV pins provide information on the piston motion between the first andlast pins. The calculation requires the piston velocity at the initial piston position. In this study,two methods are used to extrapolate the initial piston velocity from the curve defined by equation3.8. In one of the methods, the initial piston velocity is found using equation 3.8. With thismethod, the initial piston velocity is generally greater than 100 m/s. In the other method, it isassumed that the initial piston velocity is zero. A quadratic equation is fit between the initialpiston position and that of the first PV pin. The quadratic is chosen such that its magnitude andslope match those of equation 3.8 at the position of the first PV pin.The PV pin trigger times and the parameters for the cubic fits to the piston position-timedata are shown in table 3-4. Figure 3-6 shows the PV pin trigger times plotted against the PV pinposition for shot 8. Also shown in figure 3-6 is the cubic fit joining the average PV pin triggertimes. The piston velocity for shot 8 is plotted versus piston position in figure 3-7. The shape ofthe velocity curve suggests initial rapid acceleration of the piston when the gun powder gaspressure is highest and pump tube pressure is low. As the pump tube pressure becomes largerthan that of the gun powder gas, the piston starts to decelerate. The piston velocity histories withthe maximum and minimum final piston velocities are included in figure 3-7. The three pistonvelocity histories shown in figure 3-7 are extended to the initial piston position with values foundusing equation 3.8. The quadratic extrapolation from the piston velocity history for average PVpin trigger times to the initial piston position is also shown.Calculations were performed for shots 1, 4 to 11, 13 to 17, 40 and 42. For each shot,projectile velocities were calculated for burst pressures of 300, 600 and 900 bar with the initialpiston velocity extrapolated by extending the curve defined by equation 3.8. These calculationswere performed for piston velocity histories calculated for the average PV pin trigger times andfor the piston velocity histories with the maximum and minimum piston velocity at the last inputTable 3-4: PV times and related data including coefficients of cubic fits to the PV times. The arrival time of the piston at the PV pin,the PV pin time, is equal to api + bper + c per2 + dpix3 where x is the position of the PV pin with respect to the initial position of the frontof the piston.ShotPowderLoad(g)PumpTubePressure(psi)PV Pin 1Time(ms)PV Pin 2Time(ms)PV Pin 3Time(ms)PV Pin 4Time(ms)Cubic Fit Coefficientsa •P1(ms)b •PI(ms/m)c •PI(ms/m2)d •.P1(ms/m3)1 46 60.6 0 4.80 ± .04 8.76 ± .06 9.48 ± .07 -3.90 7.61 -1.53 0.2314 46 60.8 0 5.27 ± .04 9.63 ± .07 10.35 ± .07 -4.30 8.26 -1.61 0.2385 55 60.1 0 4.94 ± .04 8.99 ± .04 9.65 ± .05 -4.06 7.96 -1.66 0.2516 86 60.4 0 3.72 ± .05 6.69 ± .04 7.14 ± .05 -2.91 5.55 -0.88 0.0997 86 90.4 0 3.68 ± .02 6.61 ± .05 7.06 ± .06 -2.90 5.55 -0.90 0.0998 120 91.4 0 3.10 ± .02 5.50 ± .02 5.88 ± .02 -2.58 5.06 -1.04 0.1409 46 61.1 0 5.34 ± .02 9.74 ± .02 10.48 ± .02 -4.41 8.67 -1.85 0.28810 86 96.3 0 3.78 ± .02 6.76 ± .02 7.26 ± .02 -3.26 6.51 -1.55 0.24011 140 90.5 0 2.74 ± .02 4.86 ± .02 5.20 ± .02 -2.31 4.55 -0.98 0.13713 60 60.8 0 4.31 ± .10 7.87 ± .10 8.47 ± .10 -3.55 6.99 -1.49 0.23414 86 62.6 0 3.56 ± .01 6.38 ± .01 6.83 ±.02 -2.91 5.68 -1.11 0.15015 86 60.0 0 4.21 ± .02 7.49 ± .02 8.03 ± .02 -3.61 7.16 -1.63 0.24116 86 61.2 0 3.62 ± .01 6.40 ± .01 6.82 ± .01 -2.91 5.60 -0.96 0.10317 70 61.2 0 4.10 ± .03 7.28 ± .02 7.81 ± .01 -3.63 7.33 -1.96 0.29540 150 124.0 0 2.46 ± .01 4.35 ± .01 4.70 ± .01 -2.87 5.69 -1.06 0.12542 150 151.0 0 2.18 ± .01 4.45 ± .01 4.75 ± .01 -3.52^_ 7.22 -1.81 0.285Chapter 3. Results and Discussion 821.0^1.5^2.0^2.5^3.0Piston Position (m)Figure 3-6: Graph of the PV pin times plotted as a function of the piston position for shot 8. Thecubic curve joining the average PV pin times is represented by the solid curve. The two curvescalculated from the PV pin trigger times with the uncertainties in the times taken into account areindicated by the dashed curve and the dot-dashed curve.6.05.04.03.02.01.00.00.5Chapter 3. Results and Discussion 83500 1^1^1^1^1^1^I^1 -1 1 T 1 1 1 1 T 7 1 1 1 1 1 1 1 1^400 —1.Z^ /^-_1 I^_PV pin 2^PV pin 4 —O -^75^/>200^ ,i/ I^cO^ _ /PV pin 17)^.^.E._• _- :. —100 — :-:.^ -PV pin 3^:-I 0^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^1^/^1^1^1^1^1^1^1^1^/^1^1^1 ■0.0 0.5^1.0 1.5^2.0Piston Position (m)2.5 3.05 300 —Figure 3-7: Graph of the piston velocity plotted as a function of the piston position for shot 8.The piston velocity history from the average PV pin times is represented by the solid curve. Thetwo piston velocity histories calculated from the PV pin trigger times with the uncertainties in thetimes taken into account are indicated by the dashed curve and the dot-dashed curve. The dottedcurve indicates the quadratic extrapolation from the curve for the average PV pin data to an initialpiston velocity equal to zero.Chapter 3. Results and Discussion 84point. Projectile velocities were also calculated from the piston velocity histories from theaverage PV pin trigger times with the quadratic extrapolation to the initial piston position. Aburst pressure of 600 bar was used in these calculations. The calculated projectile velocities areshown in table 3-5.The calculated pressure at the base of the projectile for shot 8 is plotted versus time infigure 3-8. Figure 3-9 shows the calculated positions of the piston, projectile and the front of ashock wave reverberating in the pump gas. For this calculation, the burst pressure was 600 barand the piston velocity was calculated from the average PV pin times with the extrapolation to theinitial piston position using equation 3.8. In the calculation, the projectile is placed at the sameposition as the petal valves so that, before the petal valves rupture, the pressure at the base of theprojectile is also the pressure at the petal valves. Initially, the motion of the piston produces ashock wave that is reflected between the piston and the petal valves. This shock wave results in aseries of spikes in the pressure at the petal valves. The pressure increases as the pistoncompresses the pump gas. Eventually, the shock pressure at the petal valves is high enough toburst the petal valves. At this time the projectile starts moving. The piston continues to compressthe pump gas and for a limited time the shock wave is still able to reach the projectile after it isreflected from the piston. Eventually, the projectile velocity becomes so high that the shock wavenear the piston cannot reach the projectile before it leaves the gun.Figure 3-10 shows the calculated projectile velocity plotted versus the measured projectilevelocity for calculations assuming a burst pressure of 600 bar for the petal valves. The initialpiston velocity for these calculations was found using equation 3.8. A linear least-squares fit tothe data and a line indicating the ideal case where the calculated velocity is equal to the measuredvelocity are included in the graph. All but two of the calculated velocities lie above the ideal lineand most of the calculated values lie within 0.5 km/s of the ideal line. The data showprogressively larger deviations from the ideal line for lower velocities. The coefficients from theleast squares fit to the data are shown in table 3-6.Table 3-5: Calculated projectile velocity values.Shot Measured Velocity(mss)Calculated Velocity(km/s)a b c d e f g h i j1 2.170 2.654 2.312 3.124 2.752 2.482 2.183 2.870 2.795 - 3.2604 2.130 2.809 2.133 3.020 2.833 2.530 2.105 2.656 2.881 - 3.1305 2.341 2.631 2.436 3.079 2.728 2.460 2.611 2.781 2.758 2.769 3.0796 3.169 3.430 3.139 3.973 3.441 3.043 2.772 3.475 3.542 3.544 4.0047 3.039 3.389 3.091 3.491 3.424 2.871 2.865 3.193 3.603 3.381 3.7588 3.717 3.809 3.452 3.926 3.829 3.524 3.179 3.596 3.815 3.686 4.2269 2.101 2.474 2.348 2.564 2.468 2.336 2.224 2.422 2.474 2.291 2.66710 3.083 3.042 2.980 3.318 3.187 2.811 2.611 2.781 3.306 3.157 3.52711 4.079 3.844 3.460 4.293 3.863 3.551 3.183 3.969 4.119 3.708 4.29813 2.548 2.751 2.194 3.536 2.742 2.565 2.097 3.306 2.841 - 3.75514 3.184 3.211 3.181 3.412 3.317 3.016 2.853 3.209 3.449 3.257 3.60315 2.834 3.023 2.813 3.122 3.038 2.681 2.623 2.882 3.118 2.904 3.25416 3.248 3.406 3.281 3.549 3.454 3.201 3.082 3.334 3.597 3.540 3.74317 2.466 2.666 2.525 2.746 2.677 2.416 2.302 2.548 2.672 2.581 2.83540 3.808 3.566 3.376 3.769 3.561 3.368 3.768 3.803 3.597 4.03742 3.819 3.910 3.685 3.634 3.558 3.362 3.910 4.066 4.093a: 600 bar burst pressure, piston velocity history from average PV pin times, initial piston velocity from equation 3.10b: 600 bar burst pressure, piston velocity history with lowest final piston velocity, initial piston velocity from equation 3.10c: 600 bar burst pressure, piston velocity history with highest final piston velocity, initial piston velocity from equation 3.10d: 600 bar burst pressure, piston velocity history from average PV pin times, initial piston velocity equal to zero (quadratic fit)e: 300 bar burst pressure, piston velocity history from average PV pin times, initial piston velocity from equation 3.10f: 300 bar burst pressure, piston velocity history with lowest final piston velocity, initial piston velocity from equation 3.10g: 300 bar burst pressure, piston velocity history with highest final piston velocity, initial piston velocity from equation 3.10h: 900 bar burst pressure, piston velocity history from average PV pin times, initial piston velocity from equation 3.10i: 900 bar burst pressure, piston velocity history with lowest final piston velocity, initial piston velocity from equation 3.10j: 900 bar burst pressure, piston velocity history with highest final piston velocity, initial piston velocity from equation 3.10"-" indicates a calculation where the pump gas pressure failed to reach the petal valve burst pressureChapter 3. Results and Discussion 86120 1^I^I^I^I^I^1^Till I I^I I^I10002 8022ci) 600a) 40CC5200 1-77--"(17711 1 ,^I II6^8^9^10^11Time (ms)Figure 3-8: Graph of the calculated gas pressure at the petal valves - the base of the projectileplotted as a function of time after the piston starts moving. The petal valves have the same initialposition as the projectile.petal valve/breaks II^I^I^1^I^I^I^I^I^I^I^I^I^I^I^I^I^I^I Chapter 3. Results and Discussion 876.0 —5.04.00 3.00_2.0 L1.0 ----0.00.0 2.0^4.0^6.0^8.0^10.0^12.0Time (ms)Figure 3-9: Graph of the calculated positions of the piston, the projectile and a shock wave in thepump gas as a function of time after the piston starts moving. The position of the shock wave isindicated by the solid line. The position of the projecitle is indicated by the dashed line. Theposition of the piston is indicated by the dot-dashed line.4.51MM4 .0E3.500a)"ta3) 3.0c.)as 2 . 5Va.▪ 15o11o 40I^I^I^I^I^I^I^I^I^I^I^I^I^t^I^I^I^I^I^I^1^I2.5^3.0^3.5^4.0 4.5Measured Velocity (km/s)Chapter 3. Results and Discussion 88Figure 3-10. Graph of the calculated projectile velocity plotted as a function of the measuredprojectile velocity with a petal valve burst pressure of 600 bar. The solid line indicates the idealcase where the calculated projectile velocity equals the measured projectile velocity. The dashedline indicates the linear least squares fit to the data. The error bars indicate the spread ofprojectile velocity values that result from the uncertainty in the PV pin times.Chapter 3. Results and Discussion 89Table 3-6: Coefficients from linear least squares fit to calculated versus measured projectilevelocity data. The linear equation for the fit is calculatedvelocity = q +r x measured velocitywhere both velocities are expressed in km/s.Burst Pressure(bar) qr300 0.9+.1 0.66±.05600 1.1±.2 0.70±.06900 1.1±.2 0.75±.06Chapter 3. Results and Discussion 90The positions of the ends of the error bars in figure 3-10 are the projectile velocitiescalculated from the piston velocity histories with the maximum and minimum piston velocities atthe last piston position-velocity point. Generally, the piston velocity history with the maximumfinal piston velocity results in the highest calculated projectile velocity. Similarly, the pistonvelocity histories with the lowest final piston velocity produce the lowest calculated projectilevelocities. The error bars for the calculated projectile velocities range from 0.1 km/s to 0.6 km/s.Figure 3-11 shows the projectile velocities calculated using the two different methods forextrapolating the initial piston velocity history from the curve defined by equation 3.8. Theprojectile velocities in figure 3-11 were calculated with the piston velocity histories for theaverage PV pin times. The petal valve burst pressure was 600 bar. There is little differencebetween the results of the two calculations for each shot. This may be due to the fact thatinitially, before the piston reaches the first PV pin, the pump tube pressure is relatively low. Mostof the energy transferred from the piston to the pump gas occurs at later times when the pumptube pressure is higher and the piston has accelerated to a higher velocity. The acceleration of theprojectile depends more on the piston velocity history during these times.Figures 3-12 and 3-13 along with figure 3-10 show the effect of the petal valve burstpressure on the calculated projectile velocity. The calculated projectile velocity is plotted againstthe measured projectile velocity for burst pressures of 300 bar and 900 bar for figures 3-12 and 3-13 respectively. In these graphs, the piston velocity history between the initial piston position andthe first PV pin was found using equation 3.8. The coefficients from linear least-squares fits tothe data are shown in table 3-6. Although the slope of the least-squares fit lines increases withburst pressure, the slopes for the three burst pressures are less than unity. There is also anincrease in the calculated projectile velocity which accompanies the increase in the burst pressure.There are a number of possible problems with the computer code and the input data thatcan affect the calculated projectile velocity. It is evident, from the projectile velocities calculatedfrom the piston velocity histories with the maximum and minimum final piston velocity, that thepiston velocity history has a fairly strong effect on the calculated projectile velocity. There areChapter 3. Results and Discussion 914.54.0E0 3.50a)la 3.0cr5crs 2.52.02.0^2.5^3.0^3.5^4.0^4.5Measured Velocity (km/s)Figure 3-11. Graph of the calculated projectile velocity plotted as a function of the measuredprojectile velocity with two different methods of extrapolating the piston velocity from the PV pincurve to the initial piston position. The petal valve burst pressure was 600 bar for all of thecalculations. The solid line indicates the ideal case where the calculated projectile velocity equalsthe measured projectile velocity. The open circles indicate calculations where the PV pin curvewas extended to the initial piston position. The closed squares indicate calculations where aquadratic equation was used to extrapolated the piston velocity between the initial piston positionand the first PV pin.0 4.0E3.50a)3.00a)2.51^  4.02.5^3.0^3.5 4.5Chapter 3. Results and Discussion 92Measured Velocity (km/s)Figure 3-12. Graph of the calculated projectile velocity plotted as a function of the measuredprojectile velocity with a petal valve burst pressure of 300 bar. The solid line indicates the idealcase where the calculated projectile velocity equals the measured projectile velocity. The dottedline indicates the linear least squares fit to the data.2.5^3.0^3.5^4.0Measured Velocity (km/s)Chapter 3. Results and Discussion 93Figure 3-13. Graph of the calculated projectile velocity plotted as a function of the measuredprojectile velocity with a petal valve burst pressure of 900 bar. The solid line indicates the idealcase where the calculated projectile velocity equals the measured projectile velocity. The dash -dot line indicates the linear least squares fit to the data.Chapter 3. Results and Discussion 94additional details to the piston velocity histories that were not measured with the four PV pins.This is especially relevant in the latter part of the piston velocity history where the pistondeceleration is calculated solely from the pressure of the pump gas. Another possible problemwith the calculation lies in the fact that the extrusion of the piston into the coupling section is nottaken into account. Neither the initial extrusion nor the effect that the coupling section has instopping of the piston are modeled in the calculation.In the calculation, the petal valves and the projectile are placed at the end of the taper inthe coupling section. The petal valves are actually placed 7 cm from the end of the taper and theprojectile is placed a further 4 cm inside the launch tube. Another possible source of error in thecalculation comes from the fact that friction is not taken into account. The computer codeactually has the ability to include gas friction in the calculation. The gas friction was included inthe calculations for some of the early test calculations and it was found that the effect of the gasfriction is negligible so gas friction was not included in the later calculations. The computer codedoes not have the ability to model the sliding friction of the projectile or piston. Finally, it wasassumed that an ideal gas equation of state can be used for helium. The available data seems toindicate that the gun operates in a temperature and pressure range where the equation of state ofthe gas is close to idearqThe numerical ballistics simulation used in this study provides reasonable estimate of theprojectile velocity for the UBC two-stage light-gas gun. The results of the calculations offersome insight into the internal ballistics involved in launching a projectile.3.5 Last PV Pin to First Laser Velocity Trap Time Difference MeasurementsThe time difference, dt, between the signals from the triggering of the last (fourth) PV pinand the first laser velocity trap is an important parameter in experiments where a triggering pulsea few milliseconds in advance of the arrival of the projectile at the target is required. The valuesof this time difference for various values of powder load, projectile mass and projectile velocityare shown in table 3-7.Chapter 3. Results and Discussion 95Table 3-7: Time difference between firings last PV pin and first laser trap, powder load, projectilemass and projectile velocity.Shot Powder Load(g)ProjectileMass(g)ProjectileVelocity(km/s)TimeDifference(ms)15 86 5.894 2.834 3.11216 86 5.770 3.248 2.66017 70 8.939 2.466 3.28118 90 8.838 2.835 2.82519 75 5.740 2.880 2.93720 150 5.750 4.240 1.93121 75 5.750 2.874 3.00422 90 8.883 2.873 2.78523 75 8.422 2.492 3.12824 75 8.551 2.506 3.21927 100 8.918 2.982 2.65830 150 8.780 3.809 2.01531 100 8.860 3.009 2.66033 100 8.914 2.964 2.62940 150 8.58 3.808 2.00242 150 8.59 3.819 2.071Chapter 3. Results and Discussion 96Figure 3-14 shows At as a function of the projectile velocity for projectile masses between5.7 and 5.9 g and for those between 8.4 and 9.0 g. This graph demonstrates a fairly strongrelationship between At and the projectile velocity for the two projectile mass groups. Quadraticcurves are used to help visualize the trends in the data.The projectile velocity calculations outlined in the previous section provide insight into therelative positions of the data for the two projectile mass groups in figure 3-14. In each of theprojectile velocity calculations the petal valves rupture after the piston passes the last of the PVpins. The time difference, At, may be considered as a combination of the time difference, At bbetween when the piston passes the last of the PV pins and when the petal valves burst and thetime difference, dt2, between when the petal valves burst and when the projectile passes the firstlaser beam in the laser velocity trap. Assuming that the time it takes to accelerate the projectilefrom rest to a given velocity is independent of the projectile mass, the only difference in zit for thetwo mass groups in figure 3-14 is in At] . A heavier projectile requires a higher pump gas pressureand, therefore, a larger piston velocity than those needed by a lighter projectile to reach the samevelocity. With the larger piston velocity between the last PV pin and the piston position at whichthe petal valves break, the value of At] for a given projectile velocity is smaller for the heavierprojectile. Consequently, for a given projectile velocity, the total time difference, tit, is smallerfor the heavier projectile.The computer code used in section 3.4 to calculate the projectile velocity was also used tocalculate At. As noted above, in all of the calculations the petal valves burst after the pistonpassed the last of the PV pins. The PV pin trigger times and the piston velocity histories are,therefore, independent of the projectile mass. It is assumed, then, that the piston velocity historyfor any shot can be used to calculate the projectile velocity and time difference for a projectilewith a different mass launched under the same initial conditions. The projectile velocities and timedifferences for 5.8 g and 8.9 g projectiles, calculated from the piston velocity histories for theshots in section 3.4, are shown in table 3-8. In these calculations the piston velocity histories2.5^3.0^3.5^4.0Projectile Velocity (km/s)2.02.51.52.03.03.54.511^1^1^1 1^1^1^1 1^1^1^11^I^I^I30,40I^I^1^1^i^I^I^1^1^1^I^1^1^1^I^1^1^1^1Chapter 3. Results and Discussion 97Figure 3-14. Graph of the time difference between the firings of the last PV pin and the first laservelocity trap plotted against the projectile velocity. Data for projectiles with masses between 5.7and 5.9 g are indicated by the solid diamonds - dashed line. Data for projectiles with massesbetween 8.4 and 9.0 g are indicated by the open circles - solid lines. The curves which indicatequadratic fits to the data are provided for visualization purposes.Chapter 3. Results and Discussion 98Table 3-8: Calculated time difference and projectile velocity for 5.8 g and 8.9 g projectile masses.ProjectileMass(g)Piston VelocityHistory(Shot)Calculated .Projectile Velocity(km/s)Calculated TimeDifference(ms)5.81 2.401 3.8264 2.401 3.7635 2.549 3.4996 3.323 2.5787 3.286 2.4538 3.696 2.1599 2.382 3.95810 2.948 2.63711 1 3.844 2.05013 1 2.751 3.75214 1 3.211 2.6091513 3.023 3.0451613 3.406 2.46917 3.069 2.94240 3.893 1.86542 4.093 1.6698.91 2.044 4.0694 2.051 4.0925 2.199 3.7796 2.894 2.7707 2.950 2.6458 3.303 2.3199 2.014 4.29910 2.659 2.86411 3.448 2.13813 2.094 3.99114 2.819 2.73515 2.619 3.20716 2.980 2.585172,3 2.677 3.240403 3.524 1.997423 3.874 1.7831 projectile mass in original shot was 5.8 g2 projectile mass in original shot was 8.9 g3 time difference measuredChapter 3. Results and Discussion 99were determined from the average PV pin times with the initial piston velocity found usingequation 3.8. The burst pressure of the petal valves was 600 bar.Figures 3-15 and 3-16 show the calculated time differences plotted against the calculatedprojectile velocities for projectile masses of 5.8 and 8.9 g respectively. The measured At is alsoplotted versus the calculated projectile velocity for those shots where both At and the PV pintimes were measured. The projectile velocities for the measured At values were calculated withpiston velocity histories from the average PV pin times, initial piston velocities from equation 3.8and a petal valve burst pressure of 600 bar. In both graphs, the measured At values are equal toor slightly larger than the calculated values for the few data points available. This may be due tothe fact that the calculated projectile velocities are generally greater than the measured values forthe noted calculation parameters. With the negative slope in the graphs of At versus projectilevelocity and the assumption that the calculation produces a reasonable estimate of At, one expectsthat the calculated At values are lower than the measured values for a given calculated projectilevelocity.In figure 3-15 the calculated At values for the shots with the initial pump tube pressures of90 psi are lower than those of the shots with the 60 psi pump tube pressures. With the largerinitial pump tube pressure in the 90 psi shots, the piston position at the time at which the petalvalves break is closer to the last PV pin. As a result, the contribution by the time between thefiring of the last PV pin and the bursting of the petal valves to At is smaller. Also, the two Atvalues for the calculations with projectile velocities near 3.0 km/s seem to lie significantly abovethose for calculations with projectile velocities near 3.3 km/s. The difference in the At values forthese two groups of data is due to the number of times that the shock wave in the pump gas isreflected between the piston and the petal valves in the time between the arrival of the piston atthe last of the PV pins and the time at which the petal valves burst. As shown in figure 3-9, thepetal valves rupture when the shock pressure is greater than 600 bar when shock wave reachespetal valves. In each of the 3.3 km/s calculations the shock wave is reflected between the pistonand the petal valves three times before the petal valves rupture. In the 3.0 km/s calculations, the2.5^3.0^3.5^4.0Calculated Velocity (km/s)4.54.03.53.02.52.01.52.0 4.5■•• •0••■t iff I^1^1^1 1^1^1^I I^I^I^I•1^1„^ 1^1 ^ I^1^1^I^1^I••• •Chapter 3. Results and Discussion 100Figure 3-15: Graph of the calculated time difference between the firings of the last PV pin andthe first laser velocity trap plotted against the calculated projectile velocity for 5.8 g projectiles.The calculated data are indicated by the solid circles, solid squares, solid diamonds and solidtriangles for initial pump tube pressures of 60, 90, 120 and 150 psi respectively. The open circlesindicate the measured 41 values for shots in which tit and the PV pin times are measured. Theinitial pump tube pressure for these shots was 60 psi.2.5^3.0^3.5Calculated Velocity (km/s)2.02.51.52.04.54.03.53.0■I^I^I^I^I^,^,^I^I^1^1^i^I^I^,^1^1^1I••^im11111_._■ ..III 0^A .._• _I 1^1^I^I I4.0Chapter 3. Results and Discussion 101Figure 3-16: Graph of the calculated time difference between the firings of the last PV pin andthe first laser velocity trap plotted against the calculated projectile velocity for 8.9 g projectiles.The calculated data are indicated by the solid circles, solid squares, solid diamonds and solidtriangles for initial pump tube pressures of 60, 90, 120 and 150 psi respectively. The opensymbols indicate the measured zit values for shots in which zit and the PV pin times are measured.The open squares, open diamonds and open triangles indicate the measured data with initial pumptube pressures of 90 psi, 120 psi and 150 psi respectively.Chapter 3. Results and Discussion 102shock pressure of the third reflection is below 600 bar and the petal valves do not burst. In thesecalculations the petal valves burst on the fourth reflection. The added time for the fourthreflection significantly increases the value of At for the 3.0 km/s calculations.3.6 Flyer Plate Tilt and CurvatureIt was noted in the introduction that accurate measurements of the flyer plate tilt andradius of curvature and their shot-to-shot reproducibility are necessary for accurate shock wavestudies. Here, measurements have been made on projectiles with and without copper flyer plates.The flyer plate tilt and radius of curvature measurements were performed on shots 16 to 22 and26 to 33. Of these fifteen shots, shots 16, 19, 20 and 21 used projectiles without copper flyerplates, shots 17 and 18 used projectiles with 18 mm diameter copper flyer plates but the sabotsshowed significant levels of stress, shots 26 and 29 used projectiles with 17 mm flyer plates insabots with minimal stress and shots 22, 27, 28, 30, 31, 32 and 33 used projectiles with 18 mmdiameter copper flyer plates in sabots with minimal stress. In shots 26 to 33, the heights of thecap pins were characterized as outlined in section 2.4.3.The intersection of the plane parallel to the face of the projectile with the ring of cap pinsyields a sinusoidal relationship between the arrival time of the flyer plate at each pin and theangular position. Accordingly,Acr + ;,cos(60„ — [3.111where Tn is the arrival time of the flyer plate at pin n, en is the angular position of pin n measuredin the clockwise direction from the top of the target, A cp, Be,, and 0 are constants obtained from aleast-squares fit to the data. Appendix B shows the formulae used to determine the least-squaresfit and uncertainties in the fitting parameters. These formulae are also outlined by Guest[ 731. Thetilt in the flyer plate, 13, isChapter 3. Results and Discussion 103wBfl= reP [3.12]where w is the projectile velocity and r c.p is the radius of the ring of cap pins. In the case wherethe cap pins are equally spaced, the fitting parameter A cp is the average arrival time of the flyerplate at the ring of cap pins. Figure 3-17 shows the cap pin times and fitted curve for shot 30. Asindicated, the tilt azimuth is located by the angular position on the target with the latest (largest)arrival time. With the definitions of Tn and On noted above, the tilt azimuth is the fittingparameter 0. The data for the tilt, and tilt azimuth measurements are presented in table 3-9.In addition to measurements of the tilt and tilt azimuth, the data from the tilt experimentscan be used to estimate the curvature of the flyer plate. The curvature of the flyer plate orprojectile face can be measured by comparing the arrival time of the flyer plate at the centre pinwith the average flyer plate arrival time at the outer pins. Assuming that the curvature of the flyerplate has spherical and axial symmetry one can estimate the radius of curvature, R, asr 22d, [3.13]where rcp is the distance from the centre pin to the outer pins and cici, is the distance by which thecentre of the flyer plate lags behind the flyer plate at the distance rcp from the centre. Thedistance dcp is= w(Acp — Tc) [3.14]where Tc is the arrival time of the flyer plate at the centre of the target.The tilt values found in this study are similar to those found in other studies[ 36,74,751. Allbut one of the shots with large copper flyer plates embedded in relatively stress free sabots had tiltvalues less than 10 mrad. The studies by Jones et al[ 36], and by Mitchell and Nellis[74,751 claim toChapter 3. Results and Discussion 1041 111 ^1^1 1 1, 11^T1■•1 30252015cuE-111T^1111 1 1111 7 55111050 —tilt azimuth -->_5 - .11.1.11,Iii!iii0.0^1.0^2.0^3.0 4.0^5.0^6.0^7.01111111111111111111 ."Angular Position (rad)Figure 3-17: Graph of the flyer plated arrival time measurements plotted as a function of theposition around the target for shot 30. The sinusoidal curve through the data points is the leastsquares fit of equation 3.14 to the data. The tilt azimuth is the angle between the top of the targetand the last place on the target to be struck by the flyer plate.Chapter 3. Results and Discussion 105Tables 3-9: Fitting parameters to cap pin arrival times and tilt values.shotprojectiletypeFitting Parameterstilt13(mrad)32±8A cp(ns)Bcp(ns)tilt azimuth0(rad)16 1 66±12 69±17 3.9±.217 2 82±4 91±6 2.89±.06 32±218 2 55.0±1.5 51.6±1.3 2.43±.04 19.5±.519 1 16±13 18±18 2.6±1.0 7±720 1 25±8 16±11 3.9±.6 9±621 1 471a 501a 3.61a 19±na22 3 7.9±1.3 6±2 3.4±.3 2.6±.726 4 20.4±1.5 27±5 0.66±.08 8.5±1.627 3 -0.2±1.8 8±4 1.3±.3 3.3±1.528 3 3±3 6±4 0.9±.7 3±229 4 156±3 49±4 0.57±.08 25±230 3 13.6±1.6 12±2 2.53±.18 6.3±1.231 3 23±3 20±4 2.5±.2 8.5±1.732 3 9.7±1.0 19±2 2.71±.07 8.2±.833 3 35.1±.7 42±2 2.18±.02 17.6±.9projectile type 1 - lexan without a copper flyer plateprojectile type 2 - 18 mm copper flyer plate with stressed sabotprojectile type 3 - 18 mm copper flyer plateprojectile type 4 - 17 mm copper flyer plateChapter 3. Results and Discussion 106have tilt values of the order of 1° (17 mrad) for projectile diameters between 20 and 28 mm. Theprojectile velocities used by Jones et al ranged from 2.2 to 8.0 km/s. In the study by Mitchell andNellis, the projectile velocities ranged from 5.3 to 6.8 km/s. The resolution of these tiltmeasurements is 0.5 mrad for Jones and 0.2 mrad for Mitchell and Nellis. These values are muchbetter than the 2 mrad uncertainties for the shots in this study in which the projectiles had largeflyer plates embedded in sabots with minimal stress. The difference in the accuracy of the tiltmeasurements comes from better pin position measurements and better pins. In the study byJones et al., the individual pin heights were known to within 2 gm and the gaps between the pincaps and the pins were measured to within 2 gm using x-rays. Mitchell and Nellis used metaltargets in their study. The pins were butted against the back of the target and the target playedthe role that the cap does with the cap pins in shorting the pins. Mitchell and Nellis used twodifferent pin designs. In one of the designs, a 1 to 2 gm coating of anodized aluminum is used toseparate the conductors. The other design uses 6 gm thick sheet of Mylar to insulate the pin fromthe target. The positions of the pins were measured to within 1 p.m with an optical gauge.In addition to the uncertainty in the tilt values from the cap pin times, one must alsoconsider the contribution of the initial shot conditions to the uncertainty in the tilt and tilt azimuth.As noted in chapter 2, the uncertainty in the tilt due to the alignment of the target is aAta = 0.5mrad. The uncertainty due to centring the target is0.5a" = —R mrad [3.15]where R is the radius of curvature of the flyer plate in metres. The uncertainty in the degree towhich the normal to the flyer plate is parallel to the edge of the tailstock (the wall of the launchtube) is crAfp = 0.5 mrad. These uncertainties are independent of each other and the uncertainty inthe measurement of the tilt with the cap pins. The total uncertainty in the tilt is then°r,„ = . 1o213^A+ G2 + o2 tc + cr2 .^[3.16]ta^AChapter 3. Results and Discussion 107The total uncertainty in the tilt azimuth is°TILTC r AZ = a • [3.17]The tilt, tilt azimuth and radius of curvature data along with the projectile velocity are presentedin table 3-10.Figure 3-18 shows the tilt measurements plotted as a function of projectile velocity for theprojectiles with large flyer plates in sabots with minimal stress. Shot 33 which had a significantlysmaller tailstock diameter than other shots in this group was not included in this figure. Fromfigure 3-18, it appears that there is little dependence of the tilt on the projectile velocity. It isnotable the tilt values for shots 30, 31 and 32 in which the MAVIS was used are somewhatgreater than those for shots 22, 27 and 28 where the MAVIS was not used. The MAVIS mayaffect the flow of the pump gas within the target chamber. This may in turn affect the motion ofthe projectile within the target chamber. The interaction of the magnets within the MAVIS withthe flyer plate may also affect the tilt of the projectile.Figure 3-19 shows the tilt azimuth values plotted against the projectile velocities for theprojectiles with large flyer plates embedded in sabots with minimal stress. In the three shots (22,27 and 28) in which the MAVIS was not used, the tilt azimuth values vary between 0.8 and 3.4rad while in shots (30, 31 and 32) in which the MAVIS was used the tilt azimuth values vary onlya small amount. In the latter, the MAVIS may play a significant role in causing the tilt. If theeffect of the MAVIS on the projectile are similar for the three shots then this could result in thesimilar tilt azimuth values.Shots 31 and 32 were performed to test the shot-to-shot reproducibility in the tilt and thetilt azimuth. The tilt values are nearly identical for the two shots and the tilt azimuth values arevery close. The shot parameters for shots 27 and 33 differ slightly from those in shots 31 and 32.In shot 27, the MAVIS which was used to measure the projectile velocity for shots 31 and 32 wasnot used. The tilt for shot 33 is more double those for other shots with large flyer platesChapter 3. Results and Discussion 108Table 3-10: Flyer plate tilt, tilt azimuth, radius of curvature and related data.shotprojectiletypeprojectilevelocity(km/s)tiltii(mrad)tiltazimuth0(rad)centrepin time2",,(ns)centrelagdcp(m)radius ofcurvatureR(m)16 1 3.248 32+8 ' 3.9±.2 37±12 -90±60 -0.317 2 2.466 32±2 2.89±.07 85±6 7±17 4.518 2 2.835 19.5±1.0 2.43±.05 63±5 23±14 1.319 1 2.880 7±7 2.6±1.0 4±14 -40±60 -0.820 1 4.240 9±6 3.9±.6 29±9 20±50 221 1 2.874 19±na 3 .6±na 52±14 10±na 222 3 2.873 2.6±1.1 3.4±.4 12±5 11±14 2.526 4 2.200 9±2 0.7±.2 52±7 70±15 0.4027 3 2.982 3.3±1.7 1.3±.5 9±5 27±15 0.928 3 3.380 3±2 0.9±.7 14±4 37±17 0.729 4 3.791 25±2 0.57±.08 na na na30 3 3.809 6.3±1.5 2.53±.2 22±4 30±15 0.831 3 3.009 8.5±1.9 2.5±.2 28±5 15±18 1.832 3 3.054 8.2±1.2 2.71±.14 19±5 27±15 0.933 3 2.964 17.6±1.4 2.18±.08 48±5 39±15 0.6projectile type 1 - lexan without a copper flyer plateprojectile type 2 - 18 mm copper flyer plate with stressed sabotprojectile type 3 - 18 mm copper flyer plateprojectile type 4 - 17 mm copper flyer plateChapter 3. Results and Discussion 10910.08.0-Z'EL5 6.0E..,I'— 4.02.01^1^1^I^1^I^1^-I^I^1^I^1^I^1^I^1^-I^1^1^I^1^1310/30MI=2722,■I32OE280.0 I^I^I^I^I^I^I^I^I^I^1^I^1^1^I^1^I^1^I^I^1^I^1^I2.0 2.5^3.0 3.5^4.0^4.5Projectile Velocity (km/s)Figure 3-18: Graph of the tilt measurements plotted as function of the projectile velocity forprojectiles with large flyer plates embedded in relatively stress free sabots. The open circlesindicate shots where the MAVIS was used and the open triangles indicate shots where theMAVIS was not used.3227(31 30a 281^1^I^1^1^1^I^I^1^1^1 1^I^1^1^1^1^I,^1^1^12.5^3.0^3.5^4.0^4.5Projectile Velocity (km/s)0.5 '2.0Chapter 3. Results and Discussion 1104.0 I^I^I^1^1^1^1^1^i^1^1^1^T^1^1^1^1^1^1^1^13.52255' 3.045 2.5Ri< 2.01.51.0Figure 3-19: Graph of the tilt azimuth measurements plotted as function of the projectile velocityfor projectiles with large flyer plates embedded in relatively stress free sabots. The open circlesindicate shots where the MAVIS was used and the open triangles indicate shots where theMAVIS was not used.Chapter 3. Results and Discussion 111embedded in sabots with minimal stress. The diameter of the tailstock for the projectile in shot 33differed from that of the other projectiles. As noted in section 2.3, the diameter of the tailstockshould be 0.2% greater than the maximum diameter of the launch tube such that the projectile issealed into the launch tube before the shot. The maximum diameter of the launch tube is 20.00mm. The tailstock diameter for shot 33 was only 20.01 mm. The smaller tailstock diameter mayhave affected the seal between the tailstock and the launch tube. With a weak seal, the projectilemay not have been as constrained to follow the launch tube as the projectiles in other shots. Theloose fit may have also allowed the flow of pump gas around the projectile. This pump gas mayhave in turn affected the acceleration of the projectile within the launch tube or the trajectory ofthe projectile after it left the launch tube. Any of these possible effects of the smaller tailstockmay result in a tilt that differs from similar shots.A graph of the tilt plotted against projectile velocity for the projectiles without flyer plates,projectiles with small flyer plates in sabots with minimal stress and projectiles with large flyerplates in stressed sabots is presented in figure 3-20. The tilt values in this figure are generallygreater than those in figure 3-18. The variation in the tilt values within each projectile group isalso greater. These observations may be a consequence of the lack of data for these types ofprojectiles with only two shots for the projectiles with small flyer plates in relatively stress freesabots, two shots for projectiles with large flyer plates in stressed sabots and three shots for theprojectiles without copper flyer plates.The group of shots without flyer plates has largest variation in the tilt values. Theseprojectiles have lower masses than the flyer plate projectiles. The distribution of the mass is alsodifferent. These two properties may affect the way the projectile behaves in pump gas in thetarget chamber. The large variation in the tilt values may also be due to distortion in the face ofthe projectile. As noted in section 2.4.3, the uncertainty in the projectile arrival timemeasurements for these shots is somewhat greater than that for the shots with copper flyer plates.This increased uncertainty is reflected by the relative sizes of the uncertainties in the tilt values.MM.20 7...,I^I4.5Chapter 3. Results and Discussion 112-I^I1^1-^1353025cC:3;- 20Er4=4 15 1^1^I^1 I^'Im:..171026-I -1^1^I^1^I^I^1^1^1^1162918i■191mI^I^1^I^I^I^I^I^I^I^I^1^1^I^II^,^1111^2.5^3.0^3.5 4.0Projectile Velocity (km/s)Figure 3-20: Graph of the tilt measurements plotted as function of the projectile velocity. Thesolid squares indicate the projectiles without flyer plates. The solid circles indicate the projectileswith large flyer plates in stressed sabots. The open squares indicate the projectiles with small flyerplates in sabots with minimal stress.02.0Chapter 3. Results and Discussion 113The size and the variation in the size of the tilt for the shots where small flyer plates wereembedded in sabots with minimal stress may be due to error in centring the target. In these shots,the radius of the flyer plates was only 1 mm larger than the radius of the ring of cap pins. Themeasured tilt values may be exaggerated by distortion near the edge of the flyer plate or by theflow of lexan around the edge of the flyer plate. These effects may not be seen in shots where thedifference between the radius of the flyer plate and that of the ring of cap pins is greater.Large tilt values are also seen in the two shots with large flyer plates in stressed sabots. Inthese shots the sharp acceleration of the projectile may result in the delamination of the flyer platefrom the sabot. In such a case, the flyer plate is less constrained than in other shots.Consequently, the flyer plate may rotate more than one embedded in a sabot.A graph of tilt azimuth versus projectile velocity for projectiles without flyer plates,projectiles with small flyer plates in sabots with minimal stress and projectiles with large flyerplates in stressed sabots is shown in figure 3-21. Although there is a wide variation between thetilt azimuth values for the three projectile types, there is little variance within each group.Assuming that the forces that cause the tilt are present in all shots, this result may be possible ifthe different projectile types respond to the forces in different ways. In such a case the tiltazimuth values may vary by only a small amount for each projectile type.Figure 3-22 shows the radius of curvature plotted as a function of the projectile velocity.In all of the shots where the projectiles had flyer plates, the flyer plate was concave on impact.The curvature of the flyer plate seems to be fairly constant over the range of projectile velocities.The type of flyer plate projectile seems to have little effect on the curvature. Both concave andconvex curvature were measured in the projectiles that do not have the flyer plates.The curvature of the flyer plates may be due the variation in the load supported by thelexan sabot. The lexan near the edge of the projectile has less to support than that near the centre.Consequently, the lexan may flow towards the edge of the projectile. Under such flow, the lexansupporting the flyer plate may take on a concave curvature. The lexan may also flow around theedge of the flyer plate. The flow may force the edges of the flyer plate forward creating theI II II20 -■ IFIIIIIIIIIIIJIIIII -I16■11■141.1amam■■■0111M19k1718i■1129.^.^.^.^I^.^...1..6.^I^.^i^,^. -IMIMI.I26 .4.03.5"c-3 3.0.._,5 2.5E*Ri< 2.0F-1.51.00.5Chapter 3. Results and Discussion 1142.0^2.5^3.0^3.5^4.0 4.5Projectile Velocity (km/s)Figure 3-21: Graph of the tilt azimuth measurements plotted as function of the projectile velocity.The solid squares indicate the projectiles without flyer plates. The solid circles indicate theprojectiles with large flyer plates in stressed sabots. The open squares indicate the projectiles withsmall flyer plates in sabots with minimal stress.•17MM.=MD220 03121■ —2718 _32Chapter 3. Results and Discussion 1155.0 1-^1^1^1^1^1^i^1^1^1^1 ■2830Who4.03.00 2.00cf)La 1.0crscc0.020 7.26 33116-1.02.01 1 1^1^1^1^I^1^1^1^1^1^12.5^3.0^3.5^4.0 4.5Projectile Velocity (km/s)Figure 3-22. Graph of the radius of curvature measurements plotted as function of the projectilevelocity. The closed squares indicate shots without flyer plates. The closed circles indicateprojectiles with large flyer plate shots with stressed sabots. The open squares indicate shots withsmall flyer plates in relatively stress free - sabots. The open circles indicate large flyer plate shotsin relatively stress - free sabots.Chapter 3. Results and Discussion 116concave curvature. In the projectiles without copper flyer plates the lexan does not have tosupport a flyer plate. In this case, the edge of the projectile may lag behind the centre due tosliding friction between the projectile and the wall of the launch tube. The effect of the slidingfriction should also be present in the flyer plate projectiles but it may be smaller than that of theflowing lexan.The distortion of the flyer plate has been seen in other studies[ 67,75,76]. In the study byMitchell and Nellis[75], the time difference between the arrival of the flyer plate at the centre of thetarget and at a radius of 9 mm were measured for tantalum, aluminum and copper flyer plates.The flyer plates in the Mitchell and Nellis study had diameters of 25 mm and ranged in thicknessfrom 1 mm to 3 mm. The tantalum flyer plate shots had consistently concave curvature radii ofcurvature of roughly 1.3 m. The copper flyer plate shots were convex on impact with radii ofcurvature of approximately -1.3 m. The aluminum flyer plate shots showed no preferredcurvature. In the other studies, the diameters of the flyer plates were 77 mm (Bernier)[ 76l and 54mm (Van Thiel et al.)[67]. Both Bernier and Van Thiel et al. observed concave distortions in theirflyer plates. Bernier used 10 mm thick copper and aluminum plates with projectile velocitiesbetween 1.7 and 2.8 km/s. Bernier measured radii of curvature that were greater than 100 m and2.5 m for the copper and aluminum flyer plates respectively. In Van Thiel's study, radii ofcurvature between 2 and 4 m were measured for tantalum flyer plates with projectile velocities of7 km/s.Bernier outlines a way of estimating the curvature of the flyer plates. In his calculation,Bernier assumes that the radius curvature in the sabot is smaller than that in the flyer plate. In thisway the flyer plate is treated as a disk supported around its perimeter. For such an arrangement,the centre of the flyer plate lags behind a point at a radius r from the centre by the distanced- (3p„Fr 2 (1— tic.,,))^2^2^4h 0216.En,h,2^(2r° r + (1— vc,, )) [3.18].Chapter 3. Results and Discussion 117In equation [3.18], po is the mass density of copper (8.9x10 3 kg,/m3), T is the average projectileacceleration, vo, is the Poisson's ratio for copper (0.34), r is the distance from the centre of theprojectile to the cap pins (7.0 mm), Ec. is the modulus of elasticity for copper (11.5x10 10 kg/m.s2), ho is the flyer plate thickness (1.5 mm) and ro is the radius of the flyer plate (9 mm). Theaverage acceleration is estimated asW2r +.w2L[3.19]where w is the projectile velocity and L is the distance that the projectile travels before striking thetarget. L is approximately 3.5 m. With r equal to rcp (7 mm), [3.18] yields a centre lag, d, of40 gm for a 3 km/s projectile velocity shot. This corresponds to a radius of curvature of 0.6 m.The approach used by Bernier is based on the assumption that the radius of curvature inthe lexan sabot is smaller than that in the flyer plate. The lag of the centre of the sabot withrespect to its perimeter, d3, can be calculated with the assumption that the force on the sabot dueto the pump gas is distributed evenly over its rear face. In such a case the lag, d3, isd pirvsr522E,[3.20]where p„. is 1.2x103 kg/m3, us is 0.4, r3 is the distance from the centre to the edge of the projectile10 mm, and E, is 1.3x109 kg/m•s2 . With these values, the radius of curvature in the sabot for a 3km/s shot is 2 m. This is greater than the radius of curvature calculated for the flyer plate so theassumption that the flyer plate is supported around its perimeter may not be valid for theprojectiles in this study. The radius of curvature values, for 3 km/s shots in this study, lie betweenthe calculated radius of curvature values for the sabot and for the perimeter supported flyer plateso the calculations used by Bernier seem to produce reasonable rough estimates.The calculations by Bernier also use the assumption that the acceleration of the projectileChapter 3. Results and Discussion 118is proportional to the square of the projectile velocity. With this assumption, the radius ofcurvature for a 4 km/s shot should be almost half that for a 3 km/s shot. The radius of curvaturedata in this study do not follow this trend. The projectile acceleration is highest at the beginningof the flight and is negligible over the 50 cm between the muzzle of the launch tube and the target.The flyer plate may relax due to the reduction in acceleration in the latter part of the flight. As aresult, the flyer plate may lose some of its curvature.Chapter 4ConclusionIn this study we have used a number of diagnostic techniques to characterize theperformance of the UBC two-stage light-gas gun. The diagnostic systems for projectile velocitymeasurements, flyer plate tilt measurements and flyer plate curvature measurements were alsoexamined and compared with other techniques. The major demonstrations in this study include:projectile velocity measurements with an uncertainty of roughly 0.2% with both the laser velocitytrap and MAVIS velocity measurement systems; fairly strong dependence of the projectilevelocity on the powder load and the projectile mass with relatively weak dependence on the initialpump gas pressure; marginal reproducibility in the flyer plate tilt and curvature for a given set ofshot conditions for projectiles with copper flyer plates in relativelyalues are comparable to thosefound with similar systems. Some insight into the internal ballistics of the two-stag stress freesabots; and consistently concave curvature in copper flyer plates. The tilt of copper flyer plateson impact can be measured to within 2 mrad. The tilt ve light-gas gun was obtained using acomputer simulation.In future work it is recommended that better cap pins be used in order to obtain accurateequation of state data. Equation of state measurements require both accurate projectile velocityand shock wave velocity measurements. As mentioned above, the projectile velocity can bemeasured to a relatively high degree of accuracy. However, the poor temporal resolution of thecap pins used in this study may limit the accuracy of the shock wave velocity measurements. Thecap pins may also be used to generate trigger signals for other shock measuring devices. Such a119Chapter 5. Conclusion 120trigger signal may also require a more accurate measurement of the flyer plate tilt which ispossible with better cap pins.AppendixA. Uncertainty in the Measured Tilt with Curved Flyer Plate due to Uncertainty inCentring TargetIn chapter 2, the radius of curvature R is defined asr2R = 2d[A l ]where d is the distance from centre of the flyer plate to the plane defined by the circle .with aradius r from the centre. Assuming that the flyer plate has no tilt on impact, each point a radius rfrom the centre leads or lags the centre of the target by the amountr2d = 2R. [A.2]In the tilt and curvature measurements, one cap pin is placed at the centre of the target and sixcap pins are placed a distance rcp from the centre. With the uncertainty in the position of thecentre of the target with respect to the launch tube axis, ask., the outer ring of six cap pins may beshifted by ask with respect to the centre of the flyer plate. The largest and smallest distancesfrom the centre from the flyer plate to an outer ring cap pin arerL = rq +ask^[A.3]andr = r — crS^cp^Stc [A.4]121Appendix 122respectively. These points lie at opposite ends of the same diameter of the target. The distancesby which the centre of the flyer plate lags behind the points at rs and ilarefor the pin at rs andr2 –2r o- +a-2d= cP^Stc^Stc2Rr2 +2r a- + a-2d = q' s"2R[A.5][A.6]for the pin at rL. The uncertainty in the tilt associated with the difference between these twopoints isOrdL – dS CT Ate — rs_ 2&[A.7][A.8]B. Formulae for Least-Squares Fitting to Flyer Plate Arrival Time DataThe impact of a planar flyer plate on the ring of cap pins is essentially a slice of the cylinderdefined by the cap pins with the plane defined by the surface of the flyer plate. The arrival timesof the flyer plate at the cap pins can be fitted to the equation= Aq, + Bq, cos(-2rur +^ [B.1]Appendix 123In equation [B.1] Acp is the average arrival time of the flyer plate at the cap pins, Bcp is thetemporal size of the tilt, n indicates the pin number, N is the total number of pins and 0 is the tiltazimuth. The pins are placed rci, from the centre and are equally spaced around the target. Theset of arrival times Tn is initially fitted to the equationT = AcP + CcP^Ncos(-2nir )+ DcP sin(-2mrN )^[B.2]The amplitudes C cp and Bog, are related to Bcp and 0 with the equations13q, = Ve2p+D,27,^ [13.3]and^tan _i(Dcq,^[B.2]In the least-squares fit, the equationX2 = E[T, – A – Cq'^N^Ncos(—)2ng  Dq, sin( 2N ^[B.4]is minimized with respect to Acp, CI, and Dcp. By setting the derivatives of equation [B.4] withrespect to Acp, Cep and Dcp equal to zero we haveIT„ = NAq, + CE[cos(-2nif A+D E[sin(-2nr )],^[B.5]N^Nnn-^nn ^nn.E[T cos(-2nn- )] = Aq, E[cos(2—N )1 + Cq, E[cos2 (27-jLr + D„, E[cos( 2—N)sin(2--7)] [B.6]NAppendix 124and) sin ( 2Nnir 3 +^Esin2 ( 2 Nnx )3 [B.7]E[T sin(2nir )]= E[sin(1)]+ Cq, [cos( 2Nn7rThe following relationships hold with an even number of equally spaced pins:[cos( 2Nnir )3. rsin( 2 Nn7c )3. ccos( 2 lynx.  )sin(2Nng  )l. 0,andl[cos2 (2nn- )]_ zEsin2 ( 2nn- _ N .n^N^N^2With these simplifications equations [B.5] to [B.7] becomeET.= NA,I„E[Tcos(-3--nx )]= —N CcpN^2[B.103[B.113[B.8][B.9]andE[T. sin(-27ur = —N Dq,N^2 [B.12]The coefficients of the least-squares fit are thenE[T„ – Aq, – Cg, cos( 2nr  ) Dq, sin( 2nr  )]22 n^ N^NCr rn =N – 3[B.18]Appendix 125ET„Aq, = n N ,2 EEK cos(2nr  )3C ^n NN[B.13][B.14]andDcp =2 Z[T sin( 2ng )]n ^N [B.15] NWith these relationships the equations [B.3] and [B.4] becomeBq, = —2 11{E[T,, sin(-2 7r )D2 +(EU:, cos( 2n7r )D2N ^N ^N[B.16]andE[Tn sin( 2nir )]Ca = tall-1 { n^2N }[Tn cos(-f7)][B.17]The uncertainty in the total arrival time Tn isWith this, the uncertainty in A cp is[B.19]r22^es 20. 2^."'cpa Cep LI DT 24nBcpp^N ••[B.23]Appendix 126Using equation [B.13] this becomes2a 2^a TnAcp^N • [B.20]Similarly, using equations [B.14] and [B.151, the uncertainties in CI, and Dcp area  = 0' 2T E[C0S2 (-2 nn )] = 24'Ccp^n n [B.21]and2^2 v rsin 2 1 2 701 „Dcp =^4-0 L^=T  N[B.22]Using equation [B.3], the uncertainty in Bcp isFinally using equation [B.4], we haveIAatan# = sec's la‘r [B.24]The uncertainty in # is then2a 2a; =sec-4 (0)cri.2 =^m •X rn 2""CP[B.25]Bibliography[1] N.W.Ashcroft and N.D.Merman, Solid State Physics (Saunders College, Philadelphia,1976) chapter I[2] T.J.Ahrens in Shock Waves in Condensed Matter 1985, edited by Y.M.Gupta (Plenum, NewYork, 1985) p 571[3] A.C.Mtchell and W.J.Nellis, J. 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