UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An experimental investigation of the autorotation of a flat plate Cheng, Shi 1966

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1967_A7 C4.pdf [ 16.63MB ]
Metadata
JSON: 831-1.0093570.json
JSON-LD: 831-1.0093570-ld.json
RDF/XML (Pretty): 831-1.0093570-rdf.xml
RDF/JSON: 831-1.0093570-rdf.json
Turtle: 831-1.0093570-turtle.txt
N-Triples: 831-1.0093570-rdf-ntriples.txt
Original Record: 831-1.0093570-source.json
Full Text
831-1.0093570-fulltext.txt
Citation
831-1.0093570.ris

Full Text

A N E X P E R I M E N T A L I N V E S T I G A T I O N O F T H E A U T O R O T A T I O N O F A F L A T P L A T E b y S H I C H E N G B . S c . E . , N a t i o n a l T a i w a n U n i v e r s i t y , 1963 A T H E S I S S U B M I T T E D I N P A R T I A L - F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M . A . S c . i n t h e D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g W e a c c e p t t h i s t h e s i s a s c o n f o r m i n g to t h e r e q u i r e d s t a n d a r d T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a N o v e m b e r , 1966 In presenting this thesis in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Universi ty of B r i t i s h Columbia, I agree that the Library shal l make i t f ree ly avai lable for reference and study. I further agree that permission for extensive copying of th is thesis for scholar ly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publ ica t ion of th i s thesis for f i n a n c i a l gain shal l not be allowed without my writ ten permission Department o f The Univers i ty o f B r i t i s h Columbia V a n c o u v e r 8, Canada Date '^-^•^C^y^r.^C^z^ i i A B S T R A C T A u t o r o t a t i o n m e a s u r e m e n t s w e r e m a d e f o r a 4 i n c h c h o r d t h i n p l a t e u n d e r a p p r o x i m a t e l y t w o - d i m e n s i o n a l f l o w c o n d i t i o n s i n a l o w s p e e d w i n d t u n n e l . T o d e t e r m i n e t h e i n s t a n t a n e o u s a n g u l a r v e l o c i t y a n d a n g u l a r a c c e l e r a t i o n o f t h e p l a t e , a n e w t e c h n i q u e b a s e d o n t h e p r i n c i p l e o f a n a n g u l a r d i s p l a c e m e n t t r a n s d u c e r w a s d e v e l o p e d . T h e c l o s e l y l i n e a r v a r i a t i o n o f t i p s p e e d s w i t h w i n d s p e e d a n d t h e n o n - l i n e a r c h a r a c t e r i s t i c s o f t h e b u i l d - u p t i m e a n d a n g u l a r a c c e l e r a t i o n w e r e i n v e s t i g a t e d i n t h e w i n d s p e e d r a n g e f r o m 1 0 . 9 f p s to 37 . 3 f p s . T o e x a i r i n e t h e i n s t a n t a n e o u s a e r o d y n a m i c l o a d i n g o n t h e a u t o r o t a t i n g p l a t e as a f u n c t i o n o f a n g u l a r p o s i t i o n o f t h e p l a t e , s u r f a c e f l u c t u a t i n g p r e s s u r e m e a s u r e m e n t s w e r e m a d e , w i t h t h e a i d o f a p r e s s u r e t r a n s d u c e r a n d a d y n a m i c p r e s s u r e s e a l , a n d c o r r e l a t e d w i t h d i s p l a c e m e n t t r a n s d u c e r r e a d i n g s at t h e w i n d s p e e d o f 2 6 . 3 f p s . I n s t a n t a n e o u s a e r o d y n a m i c t o r q u e d u r i n g o n e a u t o r o t a t i o n c y c l e w a s e s t i m a t e d f r o m t h e i n t e g r a t i o n o f t h e f l u i d m o m e n t s r e s u l t i n g f r o m t h e i n s t a n t a n e o u s s u r f a c e p r e s s u r e f l u c t u a t i o n s . S o m e d i s c u s s i o n o f t h e a e r o -d y n a m i c p h e n o m e n a i s g i v e n . I l l C O N T E N T S Page No I. I N T R O D U C T I O N 1 II. I N S T R U M E N T A T I O N 4 2. 1 G e n e r a l Outline 4 2.2 Wind Tunnel 4 2.3 Model ' 5 2.4 Model Supporting S y s t e m 6 2.5 E n d Plates 9 2.6 Angular Displacement T r a n s d u c e r 11 2. 6 . 1 Use of trans d u c e r 11 2.6. 2 Requirements of A n Ideal T r a n s d u c e r 12 2. 6. 3 P r i n c i p l e s of T r a n s d u c e r 14 2.6,4 Co n s t r u c t i o n of T r a n s d u c e r 14 2. 7 C a l i b r a t i o n Equipment of the A n g u l a r Displacement T r a n s d u c e r 17 2. 8 P r e s s u r e T r a n s d u c e r 18 2.9 P r e s s u r e T r a n s d u c e r C a l i b r a t i o n .Apparatus 19 2.10 P r e s s u r e Seal 20 2.11 Photography 22 HI. E X P E R I M E N T A L P R O C E D U R E S 24 3. 1 C a l i b r a t i o n P r o c e d u r e s 24 3. 1. 1 Static and Dynamic P r e s s u r e s Between the E n d P l a t e s 24 3. 1.2 Static and Dynamic C a l i b r a t i o n s of Angul a r Displacement T r a n s d u c e r 24 i v Page No 3.1.3 P r e s s u r e T r a n s d u c e r C a l i b r a t i o n 26 3. 1.4 P r e s s u r e Seal C a l i b r a t i o n 27 ' 3.2 T e s t P r o c e d u r e s 27 3, 2. 1 Kinematic Measurements 27 3. 2. 2 Surface Fluctuating P r e s s u r e Measurements 30 ?viv. ^  E X P E R I M E N T A L R E S U L T S 32 4. 1 Angular V e l o c i t y Measurements 32 4.2 Dependence of T i p Speed on Wind Speed 32 4. 2. 1 Model with end plates 32 4. 2. 2 Model without end plates 33 4. 3 Time, Angular Velocity, and Angular •jA-C3deteiffAt£oa.;.3*i:thj6[' Butid'^prPerib-d: 34 4. 4 Angular V e l o c i t y and Angular A c c e l e r a t i o n During One Autorotation C y c l e 35 4. 5 Surface Fluctuating P r e s s u r e s 36 4. 5. 1 Fluctuating P r e s s u r e During the Build-up p e r i o d 37 4. 5. 2 P r e s s u r e Coefficient vs Angular P o s i t i o n During one Autorotation C y c l e 38 4.6 Torque Coefficient vs Angular P o s i t i o n 39 4.7 Wake Survey 41 V/.V. DISCUSSION 42 5% 1 Autorotation Speed vs Wind Speed 42 5.2 Initial T i p Speed vs Wind Speed 42 5.3 St a b i l i t y of Autorotation 44 V P a g e N o 5 . 4 S o m e A e r o d y n a m i c A r g u m e n t s o n A u t o r o t a t i o n 44 5. 5 F l u c t u a t i n g P r e s s u r e C o e f f i c i e n t 46 V I * S U M M A R Y O F R E S U L T S 47 A P P E N D I C E S A E s t i m a t e s o f thie> R e q u i t e d - W r i t i n g S p e e d o f V i s i c o r d e r f o r 500 c . p . s . C a r r i e r S i g n a l 49 B W a v e P r o p a g a t i o n i n a T u b e 51 B I B L I O G R A P H Y 52 I L L U S T R A T I O N S 54 vi ILLUSTRATIONS Figure No Page No 1 Close-up of Model, Supporting System, and End Plates inside the Tunnel 54 2 Aerodynamic Outline of Wind Tunnel 55 3 Unfinished Model 56 4 Pressure Tap Positions for Model at Defined Zero Angular Displacement 57 5 Finished Model 58 6 Upper Autorotation Stand and Angular Displacement Transducer 59 7 Lower Autorotation Stand and Pressure Seal Unit 60 8 Lower Autorotation Stand 61 9 Switching of Pressure Tube Connection 62 10 Model and its Supporting System - -Looking Down-stream into Wind Tunnel Test Section 63 11 Support and Adjusting Arrangement of End Plate Strut 64 12 End Plate 65 13 Electrical Circuit of Angular Displacement Transducer 66 14 Angular Displacement Transducer 67 15 Calibration- Equipment of the Angular Displacement Transducer 68 16 Speed Control Box 69 17 Circuit of the Speed-Control Box of a DC Motor 70 18 Assembly of the Static Calibration of Angular Dis-placement Transducer 71 v i i F i g u r e No P a g e N o 19 A n g u l a r D i s p l a c e m e n t T r a n s d u c e r C a l i b r a t i o n E q u i p m e n t 72 20 P r e s s u r e T r a n s d u c e r 73 21 D i a g r a m m a t i c L a y o u t of P r e s s u r e T r a n s d u c e r C a l i b r a t i o n A p p a r a t u s 74 22 C i r c u i t of P o w e r A m p l i f i e r 75 23 L o w F r e q u e n c y Power A m p l i f i e r 76 24 Pressure Seal T e s t E q u i p m e n t 77 25 C a l i b r a t i o n A p p a r a t u s of the P r e s s u r e S e a l Uni t 78 26 C a l i b r a t i o n of the A c t u a l W i n d V e l o c i t y B e t w e e n the E n d P l a t e s 79 27 V e l o c i t y P r o f i l e for 2 5 ° C h a m f e r e d E n d P l a t e s along the M o d e l A x i s 80 28 D y n a m i c C a l i b r a t i o n Data of the A n g u l a r D i s p l a c e m e n t T r a n s d u c e r 81-82 29 A n g u l a r D i s p l a c e m e n t T r a n s d u c e r C a l i b r a t i o n D a t a 83 30 P r e s s u r e T r a n s d u c e r C a l i b r a t i o n D a t a 84 31 C a l i b r a t i o n D a t a of P r e s s u r e S e a l Uni ts 85 32 S a m p l e E x p e r i m e n t a l R e c o r d of the K i n e m a t i c M e a s u r e m e n t s 86 33 E x p e r i m e n t a l Setup of the F l u c t u a t i n g P r e s s u r e M e a s u r e m e n t s 87 34 T i p Speed vs W i n d Speed 88 35 Instantaneous Angular Velocity During Acceleration (with end plates) 89 36 Instantaneous Angular Velocity During Acelleration (without end plates) 90 v i i i F i g u r e N o P a g e N o 37 B u i l d - u p T i m e v s W i n d S p e e d 91 38 A n g u l a r A c c e l e r a t i o n v s D i m e n s i o n l e s s A n g u l a r V e l o c i t y ( w i t h e n d p l a t e s ) 92 39 T y p i c a l O s c i l l o s c o p e T r a c e s o f F l u c t u a t i n g P r e s s u r e M e a s u r e m e n t s 9 3 - 9 8 40 P r e s s u r e C o e f f i c i e n t v s A n g u l a r P o s i t i o n 9 9 - 1 0 0 41 P r e s s u r e C o e f f i c i e n t D i s t r i b u t i o n A l o n g the C h o r d at D i f f e r e n t A n g u l a r P o s i t i o n s 101-102 42 T o r q u e C o e f f i c i e n t v s A n g u l a r P o s i t i o n 103 A C K N O W L E D G E M E N T S The author wishes to express his gratitude to P r o f e s s o r G. V. P a r k i n s o n for his advice, encouragement, and s u p e r v i s i o n in this r e s e a r c h programme. The author is also indebted to Dr J.S. Macdonald for his help in setting up the power a m p l i f i e r and to Mr. F. G. B e r r y for his i n s p i r i n g d i s c u s s i o n on the angular displacement transducer. The use of the f a c i l i t i e s of the Department of M e c h a m i c a l E n g i n e e r -ing is g r a t e f u l l y acknowledged. Since r e thanks and deep appr e c i a t i o n are due to the M e c h a n i c a l technical staff in general and to Mr. E. A b e l l and Mr. J. Wiebe in p a r t i c u l a r . Although the author was unable to convince them until the l a s t minute how the fluctuating p r e s s u r e measurements could" be made for an autorotating model, they always c a r r i e d out the work o r d e r s with the greatest patience and s k i l l . Such faithful cooperation and p r e c i s e technology, the author believes, paved the way for the ultimate success of this e x p e r i m e n t a l investigation. F i n a l l y , thanks are e x p r e s s e d to my cla s s m a t e Mr. J. E. Slater whose continued i n t e r e s t and enlightening d i s c u s s i o n s p r o v e d to be most helpful. The ass i s t a n c e r e n d e r e d by Mr. T. Jand a l i in reducing the r e s u l t s is duly appreciated. F i n a n c i a l a s s i s t a n c e was r e c e i v e d f r o m the National R e s e a r c h C o u n c i l of Canada under Grant A586. X SYMBOLS ^ Maximum breadth of the model at a l l angles of attack max <jp Instantaneous magnetic flux i n the p r i m a r y winding * Amplitude of the magnetic flux in the p r i m a r y winding Number of turns of the secondary c o i l Instantaneous magnetic flux linking the secondary c o i l f Frequency of the c a r r i e r signal w C i r c u l a r frequency of the c a r r i e r signal t Time 8 Angular position of model and also angle between the magnetic axis of the p r i m a r y winding and secondary winding e Induced emf in secondary winding S P j Rotor Winding #1 of the Angular displacement transducer S j Stator Winding #1 of the angular displacement transducer S_ Stator winding #2 of the angular displacement transducer P Rotor winding #2 of the angular displacement transducer & Angular acceleration TO Instantaneous angular velocity Autorotation speed U Actual wind velocity V Chart speed of v i s i c o r d e r oscillograph y Amplitude of the c a r r i e r signal o pV Fluctuating P r e s s u r e a u t o Speed of sound C i r c u l a r frequency of piston C a l i b r a t i o n piston amplitude A i r density W r i t i n g speed of v i s i c o r d e r o s c i l l o g r a p h F l u c t u a t i n g p r e s s u r e coe ff i c i e n t ( p 7 1/2 p C h o r d of model To r q u e per unit span T o r q u e coefficient (T / l / 2 p U 2 C 2) Distance along the model chord Amplitude of the e l l i p t i c i n t e g r a l V e l o c i t y P o t e n t i a l 1 1. I N T R O D U C T I O N The phenomenon of autorotation of bodies of c e r t a i n shapes in a t r a n s v e r s e wind presents challenging problems in f l u i d mechanics and engineering p r a c t i c e . F l u i d mechanicians look on the p r o b l e m as an i n t e r -esting separated flow phenomenon on which l i t t l e work has been done as yet, while design engineers have encountered the annoying p r o b l e m that flat antenna elements sometimes exhibit rotation i n d u c e d b y wind. . A p o s s i b l e engineering application is the use of a rotating flap as a h i g h - l i f t or co n t r o l device for the conventional airplane (1) (2). The t e r m autorotation is applied to the steady, a e r o d y n a m i c a l l y -excited rotation of bodies in an a i r stream. A t least two forms of the phenomenon have been observed. The major difference between them is in the d i r e c t i o n of the a i r flow r e l a t i v e to the axis of rotation of the body. In the f i r s t f o r m of autorotation, the axis of rotation is aligned with the wind, and the bodies are bluff c y l i n d r i c a l p r o p e l l e r s . The aerodynamic toy " a e r i a l t o u r b i l l i o n " d e s c r i b e d by L a n c h e s t e r (3), Den H a r t o g (4), and in a recent paper by P a r k i n s o n (5) offers a good example. T h i s f o r m of auto-rotation is not c o n s i d e r e d in the present r e s e a r c h p rogram. It is, in any case, f a i r l y w e ll understood. In the second f o r m of autorotation, a thin flat or c a mbered plate is free to rotate about a spanwise m i d - c h o r d axis in its own plane of s y m m e t r y in the p r e s e n c e of a u n i f o r m wind at right angles to the axis. The s y s t e m is stable at rest, no matter how h a r d the wind is blowing. But if the plate is given an i n i t i a l spin in either direction, 2 i t w i l l a c c e l e r a t e to a h i g h e r s t e a d y r o t a t i o n a l s p e e d - - the s o - c a l l e d a u t o -r o t a t i o n s p e e d . T h e t h e o r y o f f l u i d m o t i o n a s s o c i a t e d w i t h a u t o r o t a t i o n p r e s e n t s t r e m e n d o u s d i f f i c u l t i e s , s i n c e i t d e a l s w i t h u n s t e a d y s e p a r a t e d f l o w . It m a y b e s u r m i s e d t h a t t h e s h a p e o f t h e c y l i n d e r c a u s e s f l o w s e p a r -a t i o n a n d the s h e d d i n g o f v o r t i c e s i n t h e w a k e . T h e r e s u l t i n g a s y m m e t r i c a l f l o w f i e l d d u r i n g e a c h r e v o l u t i o n p r o d u c e s i n s t a n t a n e o u s f l u i d f o r c e s a n d m o m e n t s w h i c h a r e c o n d u c i v e to t h e " f r e e - w h e e l i n g " o f the c y l i n d e r . M e a s u r e m e n t o f t h e s e f o r c e s a n d m o m e n t s i s o n e o f t h e o b j e c t s o f t h e p r e s e n t i n v e s t i g a t i o n . S u r p r i s i n g t h o u g h it m a y s e e m , s o m e a e r o d y n a m i c p r o p e r t i e s o f a u t o r o t a t i o n w e r e e x a m i n e d e v e n b e f o r e t h e e r a o f f l i g h t . M a x w e l l (1835) d e m o n s t r a t e d a n d t r i e d to e x p l a i n w h y a n o b l o n g c a r d , w h i l e f a l l i n g f r e e l y i n t h e a i r , t e n d e d to r o t a t e a b o u t i t s l o n g i t u d i n a l a x i s . C r a b t r e e (1) a n d N e u m a r k (2) s u m m e d u p s o m e e a r l i e r r e s e a r c h i n E u r o p e u p to W o r l d W a r II a n d f u r t h e r p r e s e n t e d s o m e a n a l y s i s b a s e d o n p o t e n t i a l f l o w t h e o r y . It w a s p o i n t e d o u t t h a t a n i s o l a t e d r o t a t i n g w i n g c o u l d d e v e l o p c i r c u l a t i o n a n d h i g h l i f t i n t h e m a i n s t r e a m b u t t h a t a m o r e p r a c t i c a l d e v e l o p m e n t w a s a :: f i x e d m a i n p l a n e w i t h a r o t a t i n g f l a p j u s t b e l o w the t r a i l i n g e d g e . A m a t h e -m a t i c a l . . t w o - d i m e n s i o n a l m o d e l o f t h e f l o w w a s d e v e l o p e d b y a s s u m i n g a p o t e n t i a l v o r t e x to b e p o s i t i o n e d b e l o w t h e t r a i l i n g e d g e o f a t h i n a i r f o i l . T h e t h e o r e t i c a l p r e d i c t i o n o f t h e o p t i m u m r e l a t i v e p o s i t i o n o f t h e a i r f o i l -r o t a t i n g f l a p c o m b i n a t i o n w a s c o n f i r m e d b y t h e e x p e r i m e n t a l r e s u l t s . A s to t h e i n v e s t i g a t i o n o f the r o t a t i n g w i n g a l o n e , o n l y a f r e w c r u d e e x p e r i m e n t s w e r e a t t e m p t e d u n t i l r e c e n t y e a r s . J a m e s a n d S t o n e (6) 3 m e a s u r e d t h e a u t o r o t a t i o n s p e e d a n d f o r c e s ( l i f t a n d d r a g ) p r o d u c e d i n a u t o -r o t a t i o n o n a t h r e e c o m p o n e n t b a l a n c e . T h e i r m o d e l s w e r e f l a t a n d c a m -b e r e d t h i n p l a t e s o f v a r i o u s a s p e c t r a t i o s . A s i m p l e c i r c u i t , c o n s i s t i n g o f a c a p a c i t o r , a D . C . p o w e r s u p p l y , a n d a s p r i n g c o n t a c t s w i t c h b u i l t i n o n e e n d o f t h e m o d e l , w a s s e t u p to e s t i m a t e t h e t i m e s b e t w e e n s u c c e s s i v e h a l f r e v o l u t i o n s . A c c e l e r a t i o n a n d t o r q u e d u r i n g the b u i l d - u p p e r i o d w e r e t h e n d e r i v e d f r o m t h e m o v i e f i l m s o f r e c o r d s t a k e n f r o m a ; c a t h o d e - r a y o s c i l l o s c o p e . A f i n a l a t t e m p t w a s t h e v i s u a l i z a t i o n o f a i r f l o w at a l l p a r t s o f the c y c l e d u r i n g a u t o r o t a t i o n , b y m e a n s o f f u m e s o f t i t a n i u m t e t r a -c h l o r i d e . In a s i m i l a r e x p e r i m e n t . B a i r d a n d P i c k (7) s t u d i e d t h e a u t o r o t a t i o n s p e e d as a f u n c t i o n of w i n d s p e e d a n d o f s i z e a n d s h a p e o f a s e r i e s o f r e c t a n g u l a r p l a t e s . A l t h o u g h t h e r e v i e w of p a s t w o r k j u s t d e s c r i b e d i s a d m i t t e d l y f a r f r o m c o m p l e t e , i t i n d i c a t e s t h a t t h e m e c h a n i s m of a u t o r o t a t i o n o f t h i n p l a t e s i s n o t y e t u n d e r s t o o d . A c c o r d i n g l y , t h e f o l l o w i n g r e s e a r c h p r o j e c t is a f a i r l y e l a b o r a t e e x p e r i m e n t to i n v e s t i g a t e , f o r a t h i n f l a t p l a t e u n d e r a p p r o x i m a t e l y t w o -d i m e n s i o n a l c o n d i t i o n s , , t h e c r i t i c a l w i n d s p e e d to c a u s e a u t o r o t a t i o n , the d e p e n d e n c e o f t i p s p e e d on w i n d s p e e d , the t i m e a n d a c c e l e r a t i o n d u r i n g t h e b u i l d - u p p e r i o d , a n d t h e a n g u l a r v e l o c i t y a n d a c c l e e r a t i o n d u r i n g o n e a u t o r o t a t i o n c y c l e . A f i n a l s c h e m e i s to e x a m i n e t h e a m p l i t u d e , m o d u l a t i o n , f r e q u e n t l y , a n d p h a s e o f f l u c t u a t i n g p r e s s u r e o n t h e s u r f a c e o f a n a u t o -r o t a t i n g f l a t p l a t e , a n d t h e r e b y d e t e r m i n e t h e i n s t a n t a n e o u s a e r o d y n a m i c t o r q u e as a f u n c t i o n o f a n g u l a r p o s i t i o n i n t h e a u t o r o t a t i o n c y c l e . II. I N S T R U M E N T A T I O N  2. 1. G e n e r a l Outline Wind tunnel measurements were made for an autorbtating thin plate. The plate was mounted between one set of end plates (section 2.5) so that a p p r o x i m a t e l y two-dimensional flow conditions ex i s t e d over most of the span. A l s o the plate was supported at each end on c o a x i a l spindles. . The upper spindle was r i g i d l y attached to an angular displacement;transducer (section 2.6) so that s y n c h r o n i z a t i o n with the angular,:.motion-.couldbe^achieved. . Into the lower spindle was i n t r o d u c e d a dynamic p r e s s u r e s e a l (section 2.10) to effect the " r e l a y " of the p r e s s u r e signal f r o m the s u r f a c e taps to a p r e s s u r e t r a n s d u c e r (section 2.8). F i g . 1 shows the experiment setup i n the wind tunnel. 2.2 Wind Tunnel The wind tunnel u s e d in this p r o g r a m m e i s a low speed, low turbulence, r e t u r n type. V e l o c i t i e s can be v a r i e d through the range 4. feet p e r second to 150 feet p e r second with turbulence l e v e l of l e s s than 0.1%. . The p r e s s u r e d i f f e r e n t i a l a c r o s s the contraction section of 7:1 a r e a ra t i o is m e a s u r e d on a Betz m i c r o m a n o m e t e r which can be r e a d to 0. 2 m i l l i m e t e r - o f water; the test section v e l o c i t y i s c a l i b r a t e d against the above p r e s s u r e d i f f e r e n t i a l . The test s e c t i o n is rectangular in c r o s s - s e c t i o n . (36 inches by 27 inches) with 45° c o r n e r f i l l e t s . V a r i a t i o n of the c o r n e r f i l l e t s f r o m 6 inches by 6 inches to 4 3/4 inches by 4 3/4 inches compensates for boundary l a y e r growth. The s p a t i a l v a r i a t i o n of v e l o c i t y is l e s s than 0.25%. . Tunnel power is supplied by a 15 horsepower d i r e c t c u r r e n t motor d r i v i n g a c o m m e r c i a l axiflow fan with a m o d i f i e d W a r d - L e o n a r d s y s t e m of speed control. A n 5 aerodynamic outline of the tunnel is shown i n F i g . 2. 2.3 M odel In view of the elaboration involved in machining, only one autorotation model was constructed. The nominal dimensions were 4 inch chord, 12 inch span, and 3/16 inch thickness. To simulate the geometric shape of a thin flat plate, leading and t r a i l i n g edges were ch a m f e r e d off to y i e l d 12 degree s h a r p angles and a s y m m e t r i c a l t r a p e z o i d a l c r o s s section. It was argued that the flat s u r f a c e approximated the flat plate while the other s u r f a c e s p r o v i d e d the n e c e s s a r y r i g i d i t y . Since one of the purposes of the programme was to examine the fluctuating p r e s s u r e on the s u r f a c e of the model, it was intended to convey the p r e s s u r e s i g n a l f r o m s u r f a c e taps v i a s m a l l diameter tubing to an e x t e r n a l l y mounted p r e s s u r e transducer. (Section 2.8) Surface taps with i n t e r n a l tube connections leading to the bottom.end of the model greatly c o m p l i c a t e d the design. Two sheets of a c r y l i c p l a s t i c , which were hollowed out with lightening holes, f u r n i s h e d the upper and lower parts of the f r a m e -work ( r i b s and spars). A p r e s s u r e block was d r i l l e d to effect 90 degree bends for convenient tube connections and was i n c o r p o r a t e d i n the upper-frame-? -• work. On the cambered su r f a c e of the lower framework, a spanwise groove was m i l l e d out to accommodates the bundle of p r e s s u r e tubing. F i g . 3.shows the detailed arrangement together with the aluminum tabs. To p r o v i d e surface f i n i s h and t o r s i o n a l r e s i s t a n c e , the whole f r a m e -work was c o v e r e d withQi-0'20 i n c h thickness aluminum skin. O v e r the flat surface of the skin at mid-span were d i s t r i b u t e d 13 p r e s s u r e taps (no p r e s s u r e tap on the c a mbered surface). F i g . 4 gives the d i s t r i b u t i o n of the p r e s s u r e taps on the model surface. P r e s s u r e tap holes were 0.018 inch i n diameter and were d r i l l e d to match, in d i v i d u a l tube connections, after an epoxy adhesive was applied to bond the a l uminum skin to the f r a m e -work. Polyethylene tubing used to t r a n s m i t the p r e s s u r e from.surface taps was 0. 066 i n c h i n s i d e diameter, 0. 095 inch outside diameter, and 4 feet i n length. F i g . 5 shows the f i n i s h e d model. 2. 4 Model Supporting S y s t e m E a r l i e r i n v e s t i g a t i o n ( 7 ) showed that a two-dimensional model, spanning the tunnel test section (27 inches), experienced c o n s i d e r a b l e bending and v i b r a t i o n and produced inconsistent r e s u l t s . - It was thus decided to c onstruct a model of s h o r t e r span and to eliminate the end effects:by a set of end plates (Section 2. 5). In consequence, the model supporting s y s t e m was mounted insi d e the tunnel and m i n i m u m blockage to the a i r flow was a m a j o r consideration. • In-addition,, the scheme to : m e a s u r e the surface fluctuating p r e s s u r e of an autorotating model brought up at l e a s t three t r i c k y p r o b l e m s i n the design. F i r s t , p r e s s u r e tube connections f r o m s u r f a c e taps to the p r e s s u r e t r a n s d u c e r n a t u r a l l y became an. i n t e g r a l p a r t of the mounting system. Since i t was only p o s s i b l e to take p r e s s u r e readings f r o m i n d i v i d u a l taps one at a time, ease of switching tube connections was e s s e n t i a l . Second, the use of a p r e s s u r e t r a n s d u c e r which i s stationary to m e asure a r e v o l v i n g p r e s s u r e source through rotating p r e s s u r e tubes st r o n g l y suggested that some sor t of dynamic p r e s s u r e seal be adopted to 7 effect the " r e l a y " of the p r e s s u r e signal. - It was then n e c e s s a r y to i n c o r p o r a t e such an arrangement of p r e s s u r e s e a l (Section 2; 10) into the mounting system. T h i r d , i t was intended to set up a synchro type of angular displacement t r a n s d u c e r to indicate the phase of the s u r f a c e fluctuating p r e s s u r e (Section 2. 6). The p r o b l e m of a c c u r a t e l y matching the mechan-i c a l angle of the model to the e l e c t r i c a l angle of the synchro output p r e s e n t e d no l e s s d i f f i c u l t y than the previous two p r o b l e m s (Section 2. 7). E m p h a s is was also p l a c e d on accurate alignment of spindles and constraint of motion to p u r e l y one degree of freedom. Because of these requirements, and that of s m a l l f r i c t i o n damping, it was decided that spindles mounted on b a l l b e a r i n g s with a c y l i n d r i c a l b e a r i n g block be adopted as a c o n s t r u c t i o n technique. F o u r S K F 6202 b a l l b earings were se l e c t e d and u s e d in the design of the upper and lower autorotation stands. • It must be r e a l i z e d that s a t i s f a c t o r y p e r f o r m a n c e of the r e v o l v i n g unit could be obtained only, by c a r e f u l and d i f f i c u l t alignment of four bearings. A two i n c h outside diameter hollow c y l i n d e r p r o v i d e d the body of the b e a r i n g block of the upper autorotation stand. It was counterbored f r o m each end to suitable diameters and depths so that one end p e r m i t t e d seating of the b a l l b earings and the other end p r o v i d e d housing, for the angular d i s -placement tr a n s d u c e r . At the t r a n s d u c e r end of the spindle, a s m a l l hole was d r i l l e d to accommodate the t r a n s d u c e r shaft; thus the spindle and the t r a n s d u c e r shaft could be .tightened up. by a socket head setscrew f r o m outside. A t the model end of the spindle, a deep groove was m i l l e d out d i a m e t r i c a l l y to allow a tongue-and-groove joint of the model tab. The base of the 8 b e a r i n g block was h e l d f i r m l y by a st e e l disk, which i n t u r n was bolted to the flange of the tunnel wall. F i g . 6 shows the drawing of this design. The lower aut6rotation stand was s i m i l a r i n construction. The spindle was mounted i n a tight fit on two b a l l b earings and a counterbored hollow c y l i n d e r s e r v e d as the b e a r i n g block. However, the p r e s s u r e tube connection and the p r e s s u r e seal unit further c o m p l i c a t e d the design. ( F i g s . 7 and 8). The lower model tab was permanently attached by two pins to a hollow c y l i n d r i c a l coupling, the ins i d e diameter of which was determftiediby'.the/ -space n e c e s s a r y for 13 p r e s s u r e tubes. The model end of the spindle was threaded e x t e r n a l l y (9 /16-1ZNC). The coupling and the spindle we re-.then l i n k e d together by a l o c k i n g nut when de s i r e d . The l o c k i n g nut had o r d i n a r y threads (9/16-12NC) at the spindle end and s p e c i a l threads of the same pit c h (1-12NC) at the coupling end so that, when the spindle was held station-ary, it could be screwed up to connect the coupling and screwed down to disconnect the coupling with l i t t l e effort. Switching of tube connections was c a r r i e d out while the lo c k i n g nut was dismantled f r o m the coupling. ( F i g . 9). The lower end of the spindle extended through the tunnel floo r and made up the r e v o l v i n g element of the p r e s s u r e s e a l unit. The stationary element of the p r e s s u r e s e a l unit was bolted onto a semi-annular spacer i n such a way that v a s e l i n e s e a l could be applied constantly. In addition, the spindle was d r i l l e d c o n c e n t r i c a l l y a l l the way through. Into this hole a 9 i piece of polyethylene tubing was introduced. The upper end of this tubing connected the p r e s s u r e tubes f r o m surface taps one at a time in a p l e x i g l a s tube; the lower end connected to the r e v o l v i n g part of the p r e s s u r e seal unit. F i g . 10 shows the model and the upper and lower autorotation stands i n the test section. 2. 5 E n d P l a t e s Many wind tunnels make use of end plates which fit i n s i d e the n o r m a l test sections to provide approximately two dimensional flow for s h o r t e r span models. The need a r i s e s , for instance, when it is intended to i n c r e a s e the model breadth without causing too much tunnel blockage or s t r u c t u r a l p r o blems. A c o n s i d e r a b l e amount of l i t e r a t u r e i s available on the use of end plates i n conjunction with u n s t a l l e d s t r e a m l i n e d sections. V e r y few r e f e r e n c e s , however, could be found to t h e i r use with models experiencing separated flow. In an investigation of the fluctuating f o r c e s acting on a 1 1 /8 inch stationary c i r c u l a r c y l i n d e r , Keefe (8) studied the effect of a p a i r of 5 1/2 inch c i r c u l a r disks as end plates. It was found that the end plates were rather ineffective at l a r g e spacing between them but that l o c a l two-dimensionality ex i s t e d at a s m a l l spacing equal to three times the c y l i n d e r diameter through-the Reynolds number range f r o m 20, 000 to 100, 000. In a l a t e r report, Cowdrey (9) investigated the m i n i m u m dimensions of rectangular end plates for use with a 4 inch square c y l i n d e r . F l ow v i s u a l i z a t i o n showed that, when the end plates were too s m a l l , entrainment of the flow around the end of the model into the wake caused strong spanwise flow over the r e a r surfaces of the model. The function of the end plates was to: close .the ends of this " c a v i t y " . A c c o r d i n g l y i t was suggested that the m i n i m u m values of the width and of the downstream dimension of the end plates could be taken as 2 ^ and 2 1/2 ^ re s p e c t i v e l y , where ^ was the m a x i m u m max max max breadth of the model at a l l angles of attack. Wind tunnel end plates made of 1/2. i n c h thick b i r c h were designed and use d i n this programme. The c r i t e r i a just d e s c r i b e d s e r v e d as a rough guide i n the design. T o determine the dimensions of the end plates, the 4 i n c h autorotating plate was c o n s i d e r e d (for this purpose only) to be r e -p l a c e d by a 4 in c h rotating c i r c u l a r c y l i n d e r . The spacing between the end plates was chosen as 12 inches (the span of the model was made the same acco r d i n g l y ) . The plates were 16 inches long and 18 inches wide with the model axis 12 inches u p s t r e a m f r o m the t r a i l i n g edge. To allow quick mounting of the model between the end plates, a 4 1/4 inch c i r c u l a r hole with a suitable r e c e s s e d shoulder was d r i l l e d and centered on the model axis, both for the upper and lower end plate. C i r c u l a r disks: with a 4 1 /4 i n c h boss were cut d i a m e t r i c a l l y into two halves and were i n s t a l l e d around the model spindles to make up part of the smooth p a r a l l e l walls of the end plates after mounting. E a c h end plate was bolted to three v e r t i c a l struts positioned as the v e r t i c e s of an ; i s o s c e l e s t r i a n g l e . A c c u r a t e alignment of the end plates was achieved b y independently adjusting the d i f f e r e n t i a l screws,, which were tapped i n t e r n a l l y to accommodate the struts and threaded e x t e r n a l l y to match the flanges bolted onto the tunnel walls and whose p i t c h equaled the d i f f e r e n c e between those of the external and i n t e r n a l threads. S m a l l gaps between the ends, of the model and the end plates were always kept l e s s than 1/32 inch. F i g . 11 gives the drawing of this design and. F i g . 12 shows the end plates with the removable c i r c u l a r disks. Two sets of end plates of s l i g h t l y different design were constructed. Most dimensions were made the same. The difference between them was that the edges of one set were ch a m f e r e d off while those of the other set were rounded. Only one set of end plates was s e l e c t e d for use i n the fluctuating p r e s s u r e measurements. The d e c i s i o n was based.on the spatial u n i f o r m i t y of the a i r flow between the plates. (Section 3. 1. 1) 2. 6' A n g u l a r Displacement T r a n s d u c e r s  2. 6. 1 Use of the T r a n s d u c e r A n angular displacement t r a n s d u c e r was used to indicate the phase of the autorotating.model, y i e l d i n g a continuous h i s t o r y of rotation at constant speed or during a c c e l e r a t i o n . Once such a time h i s t o r y at a.certain wind speed was recorded, many i n t e r e s t i n g features of autorotation would come to light. Among some of the p o s s i b l e investigations are the dependence of tip speed on wind speed, the time and a c c e l e r a t i o n during the build-up period, and the angular displacement, velocity, and a c c e l e r a t i o n during one autorotation c y c l e . Another function is to c o r r e l a t e the phase angle of the fluctuating p r e s s u r e on the s u r f a c e of the model to that of the angular p o s i t i o n of the model. T h i s c o r r e l a t i o n w i l l help explain the m e c h a n i s m of autorotation by the aerodynamic f o r c e s . 12 2. 6. 2' Requirements of an. Ideal T r a n s d u c e r 1) low f r i c t i o n damping and s m a l l moment of i n e r t i a - -n e g l i g i b l e c ompared to that of the autorotation assembly. 2) l i n e a r response or known non-linear response such as a sine or cosine function. 3) output independent of angular v e l o c i t y or angular a c c e l e r a t i o n . 4) high accuracy. 2. 6. 3 P r i n c i p l e s of T r a n s d u c e r s Two types of angular displacement t r a n s d u c e r r:were c o n s i d e r e d in this p r o ject. The f i r s t t r y was a v a r i a b l e - r e s i s t o r transducer; the second attempt, a s u c c e s s f u l one, was a mutual-inductance t r a n s d u c e r . R e s i s t a n c e w i r e wound around an. i n s u l a t i n g r i n g with three t e r m i n a l s , r e p r e s e n t s the s i m p l i f i e d f o r m of a potentiometer. It gives continuous c o n v e r s i o n of r o t a t i o n a l displacements into e l e c t r i c s ignals. As expected, . the response p r o v e d to be f a i r l y . l i n e a r even for l a r g e angles (up to 300°). However, the r e s i s t a n c e i n such potentiometers i n c r e a s e s in< steps rather than continuously when the contact moves f r o m one turn of the r e s i s t a n c e wire to the next. T h i s stepwise v a r i a t i o n - l i m i t s the resolution: of the potentiometer. Another disadvantage was that the l a s t few turns of the r e s i s t a n c e w i r e on either side of the contact t r a v e l were sometimes not a c c e s s i b l e for r e s i s t a n c e v a r i a t i o n . The range of angular movement through which a 13 v a r i a t i o n of the e l e c t r i c a l output takes place ( e l e c t r i c a l angle) was sometimes s m a l l e r than the m e c h a n i c a l angle through which the potentiometer shaft can move. • In view of the high a c c u r a c y desired, this v a r i a b l e - r e s i s t o r t r a n s d u c e r was abandoned. The second attempt was a synchro r e s o l v e r -- a mutual-inductance t r a n s d u c e r u s e d for rotary, displacements. The e l e c t r i c a l c i r c u i t i s shown i n F i g . 13.'-The assembly abd components are shown i n F i g . 14. A synchro is i n p r i n c i p l e a t r a n s f o r m e r . The only difference f r o m a conventional t r a n s f o r m e r is that-the primary, winding can rotate with r e s p e c t to the secondary winding. A s i n a t r a n s f o r m e r , an alternating, c u r r e n t i n the p r i m a r y winding r e s u l t s i n a magnetic flux i n the vi c i n i t y , 66- »/•. cos27rft (!) T p p '•• max It i s seen that the magnetic flux changes s i n u s o i d a l l y i n intensity and d i r e c t i o n with the frequency, of the alternating current. If a secondary winding is p l a c e d i n the same magnetic fi e l d , a voltage i s induced i n the secondary winding and a c u r r e n t w i l l flow through a,load. F r o m Faraday's law, the magnitude of this induced emf i s given by „ d<frs e = -N — r ~ (2) s s dt where N = number of turns of the secondary, c o i l s <fi^  = magnetic flux l i n k i n g the secondary c o i l . If the same flux l i n k s both the p r i m a r y winding and the secondary winding as i n an i d e a l t r a n s f o r m e r ( i . e.. the c o i l axes l i n e up with each other), 14 (<J> ) = <(>_ • = > * cos2irft s max P max (3) and (e o) = E sin 2 T r f t <4> 8 max max where E N (2irf)* max max s Now consi d e r the general case when the magnetic axes of the windings are at an angle 0 to each other. Since only a p o r t i o n of the total magnetic flux e f f e c t i v e l y l i n k s the secondary c o i l , the output depends on the angular displacement and i s p r o p o r t i o n a l to the cosine of that angle. i . e . e = E sin2TTftcos6 (5) s max It follows that, for a given angular position, there i s only one c o r r e s p o n d i n g secondary voltage. If the p o s i t i o n of the p r i m a r y winding is v a r i e d at some constant r o t a r y speed, the amplitude of the secondary voltage w i l l be modulated s i n u s o i d a l l y at the rotation frequency of the p r i m a r y . In other words, the envelope of the amplitude modulated signal during. 180°rotation w i l l take a s i n u s o i d a l form. T h i s is the basi s of dynamic c a l i b r a t i o n of the angular displacement t r a n s d u c e r to be d i s c u s s e d in- Section 2. 7. 2. 6. 4 C o n s t r u c t i o n of the T r a n s d u c e r A s y s t e m u s e d to t r a n s m i t m e c h a n i c a l shaft angles to a remote lo c a t i o n by means of e l e c t r i c a l voltages i s known as a synchro system. Synchros (10) are s m a l l m o t o r l i k e components with m u l t i p l e outputs. The b a s i c s t r u c t u r e c o n s i s t s of a wound r o t o r with connections made through s l i p rings and a wound stator c a r r y i n g two or three p a i r s of windings. In the conventional use, an ac voltage i s applied to the rotor, the p r i m a r y winding; the flux induces voltages i n the stator, the secondary winding. The angular displacement t r a n s d u c e r under, investigation f a l l s under the category of a synchro r e s o l v e r . Most synchro r e s o l v e r s have two-phase stator windings with c o i l axes d i s p l a c e d 90 degrees, and two-phase rotor windings with c o i l axes also at 90 degrees. Thus the induced stator voltages are sine and cosine functions of the displacement angle. i . e. e i = E sin2jiftcos e max .(6) e . = -E sin2irftsin6 s2r max Among the c o m m e r c i a l l y available synchro r e s o l v e r s , the autosyn synchro r e s o l v e r AY-221-3-B was found s a t i s f a c t o r y . . It has a p r i m a r y c o i l impedance of 224 ohms and a secondary c o i l impedance of 52 ohms at 500 c.p. s. excitation, as m e a s u r e d by a Ge n e r a l Radio Impedance Br i d g e . The r o t o r winding 1. P of the angular displacement t r a n s d u c e r was l e f t open c i r c u i t . The rotor winding P was excited by a.Heathkit audio generator model 1G-72. The induced secondary voltage e- ^  was>monitored with a T e k t r o n i x model 564 storage o s c i l l o s c o p e or a l t e r n a t i v e l y was r e c o r d e d continuously by a Minneapolis Honeywell 906c v i s i c o r d e r o s c i l l o g r a p h . The induced secondary voltage e was connected a c r o s s a dummy load of 35 ohms. S w T h i s arrangement was found n e c e s s a r y to eliminate unwanted fluctuation of the applied voltage in. the p r i m a r y . • The r e a s o n is to provi d e a balanced 2 two-phase l o a d such that there i s always a constant r e a c t i o n (constant T R) on the p r i m a r y . T h i s i s s i m i l a r to the case when an. o r d i n a r y static t r a n s -f o r m e r has a fi x e d load. Thus the input impedance on theprimar.y/and.primary -power are independent of shaft angle. F i g . 13 shows the e l e c t r i c a l c i r c u i t of the angular displacement t r a n s d u c e r . As seen f r o m the b a s i c relations d e r i v e d e a r l i e r , the induced secondary voltage depended upon such free p a r a m e t e r s as the amplitude and frequency of the excited source. T h e o r e t i c a l l y the t r a n s d u c e r could be working at any a r b i t r a r y excited voltage, so long as the induction c o i l s were not saturated. However, the v i s i c o r d e r o s c i l l o g r a p h n arrowed the choices of the excited power. The e s s e n t i a l element of a v i s i c o r d e r i s a sub-miniature galvanometer. The t e c h n i c a l number of our galvanometer i s H e i l a n d M1000. It has a c o i l i r e s i s t a n c e of 35 ohms and r e q u i r e s a source r e s i s t a n c e of 3 to 100 ohms as its damping r e s i s t a n c e . Its range of flat frequency response i s f r o m 0 to 600 c.p. s. The amplitude of the excited voltage was so chosen that the m a x i m u m induced secondary voltage a c r o s s the galvanometer c o i l caused exactly 4 inches peak to peak deflection on the photographic paper. The frequency, of the excited voltage was chosen as 500 c.p. s. so that the r e q u i r e d w r i t i n g speed of the v i s i c o r d e r was below the' m a x i m u m w r i t i n g speed of 10, 000 inches per second. (Appendix A). A n additional advantage i s that the modulated signal a u t o m a t i c a l l y provides 2 m i l l i - s e c o n d time m a r k e r s on. the photographic paper. Another point i s perhaps worth mentioning. The signal f r o m the angular displacement t r a n s d u c e r was not demodulated. A n u n s a t i s f a c t o r y attempt 17 was made to demodulate the output with a diode r i n g demodulator followed by an RC ( f i l t e r . . It was found that at its rated excitation frequency the tr a n s d u c e r was s u c c e s s f u l l y demodulated only with a l a r g e capacitor. T h i s l a r g e capacitance in t u r n means a l a r g e time constant or slow dynamic response of the c i r c u i t . The dynamic c a l i b r a t i o n showed cons i d e r a b l e d i s t o r t i o n of the s i n u s o i d a l envelope. Since demodulation s a c r i f i c e d the degree of accuracy, it was abandoned. Z. 7 C a l i b r a t i o n Equipment of Angular Displacement T r a n s d u c e r The purpose of the c a l i b r a t i o n of the angular displacement t r a n s -ducer was to e s t a b l i s h a known r e l a t i o n between the m e c h a n i c a l angle input and the e l e c t r i c a l voltage output. To this end, a c a l i b r a t i o n s y s t e m was set up on the bench. F i g . 15 gives the flow d i a g r a m of this c a l i b r a t i o n system. To check the dynamic response, the angular displacement t r a n s d u c e r was coupled to a d-c shunt motor. The armature of the motor was connected to the d-c t e r m i n a l s of a diode r i n g r e c t i f i e r , the a-c t e r m i n a l s of which were powered by a t r a n s f o r m e r . C o a r s e speed c o n t r o l of the motor was aehleved by adjusting the transformer voltage across the rectifier. To allow fine speed control, the clreult of th© field eeil was modified to eonneet aeross the d=e terminals of a seeend diode ring rectifier similar' to the first one. A potentiometer In series with a field eell provided fine adjust = ment of speed eentroL The transformer, the two rectifiers, and the p©ten= tiometer were angles ed in a gablnet (f ig . l i ) . Fig. 17 gives the eireult dla= gram. In addition, the angular veleelty of the motor transducer assembly was regulated by a s i x - i n c h steel flywheel, and i n t e r p r e t e d by a. G e n e r a l Radio strobotac. F i g s . 18 and 19 show the actual c a l i b r a t i o n equipment. • In the c o u r s e of c a l i b r a t i o n c o n s i d e r a b l e d i f f i c u l t y was encountered i n matching the z e r o s of the m e c h a n i c a l and e l e c t r i c a l angles. The m e c h a n i c a l angle was zero when the h o r i z o n t a l i n d i c a t o r pointed to zero degree on the d i a l . The e l e c t r i c angle was zero when the r o t o r winding was p e r p e n d i c u l a r to the stator winding. Pains were taken to line up. these two angles. One obvious solution was to fix the transducer on the motor shaft to zero e l e c t r i c angle f i r s t and then adjust the d i a l to zero m e c h a n i c a l angle manually. When the e l e c t r i c a l angle, m e c h a n i c a l angle, and the angle i n d i c a t o r were a l l i n p r o p e r position, the setscrew of the flywheel was tightened. Slippage of the t r a n s d u c e r shaft on the s e t s c r e w was o b s e r v e d to cause 2 or 3 degrees of e r r o r . To ensure p o s i t i v e l y no slippage, the p r e v i o u s scheme was r e v i s e d . A hole on the t r a n s d u c e r shaft was d r i l l e d to fit the pointed end of a setscrew. The shaft of the t r a n s d u c e r and that of the motor were l o c k e d permanently together by the setscrew. The matching of the m e c h a n i c a l and e l e c t r i c a l angles: was achieved by adjusting the position of the stator r e l a t i v e to the r o t o r of the t r a n s d u c e r . 2.8 P r e s s u r e T r a n s d u c e r The d e s i r e to m e a s u r e fluctuating acoustic l e v e l p r e s s u r e s , i n the present p r o g r a m m e suggested that use-be made of a t r a n s d u c e r developed by F e r g u s o n (11). Readers are r e f e r r e d to h i s t h e s i s for a detailed 19 d i s c u s s i o n . F o r completeness?-.however, a b r i e f d e s c r i p t i o n is given here. Ferguson's design is a resistance-change type of p r e s s u r e transducer. It u t i l i z e s the dynamic response of a f l e x i b l e rubber diaphragm to the p r e s s u r e fluctuation i n a cavity. A shutter was mounted on a rubber d i a -p h r a g m and p l a c e d half way between an o r d i n a r y flashlight bulb and a light dependent r e s i s t a n c e ( P h i l l i p s type No. B8731 03). . The displacement of the shutter due to diaphragm deflection i n tercepted a p o r t i o n of the light b e a m shining through and thus caused a substantial r e s i s t a n c e change i n the light dependent r e s i s t a n c e . To convert this change i n r e s i s t a n c e to a voltage signal, the light dependent r e s i s t a n c e was included in one a r m of a two-e x t e r n a l - a r m bridge c i r c u i t and connected to a b r i d g e a m p l i f i e r and meter ( E l l i s A s s o c i a t e s BAM-1). However, it was found that, to match the allowable a r m r e s i s t a n c e of the above instrument, i t was; n e c e s s a r y to shunt a c r o s s the L D R a 2, 000 ohm s t r a i n gauge, i n a temperature compensating c i r c u i t . A dummy a r m of s i m i l a r arrangement was set up i n the b r i d g e c i r c u i t to eliminate the t h e r m a l d r i f t problem. . The output f r o m the b r i d g e a m p l i f i e r and meter was displayed on a cathode r a y o s c i l l o s c o p e . The s e n s i t i v i t y of the t r a n s d u c e r was found to be 0. 0005 p s i . F i g . 20 gives the c i r c u i t d i a g r a m and the components of the p r e s s u r e t r a n s d u c e r . 2.9 P r e s s u r e T r a n s d u c e r C a l i b r a t i o n Apparatus The c a l i b r a t i o n technique for the p r e s s u r e t r a n s d u c e r was developed by F e r g u s o n (11) and was m o d i f i e d to include c a l i b r a t i o n data down to 1 c.p. s. A d i a g r a m a t i c layout of the c a l i b r a t i o n apparatus i s shown i n F i g . 21. The cavity of the p r e s s u r e t r a n s d u c e r was connected to one end of a polyethylene tube. Into the opposite end a piston of fine bore was introduced. The piston was r i g i d l y attached to a m i l d steel c a n t i l e v e r beam. The free end of the b e a m was d r i v e n by a Goodmans v i b r a t i o n generator; on the fi x e d end of the b e a m were mounted four s t r a i n gauges i n a br i d g e c i r c u i t to indicate the piston amplitude and phase r e l a t i o n . F luctuating p r e s s u r e s i n the tube were generated by piston o s c i l l a t i o n s . Quantitative p r e s s u r e fluctuations were ca l c u l a t e d f r o m the solution of the boundary value p r o b l e m of i n v i s c i d acoustic wave propagation i n a s e m i - i n f i n i t e 1-dimensional tube (Appendix B). A c c o r d i n g to the the o r y of gasdynamics, the fluctuating p r e s s u r e produced at the piston by its o s c i l l a t i o n s was a function of both piston amplitude and frequency. The c o n t r o l of these two p a r a m e t e r s was p r o v i d e d by the chosen setting of the function generator. Since the function generator was e s s e n t i a l l y a voltage source, i t was n e c e s s a r y to include a power a m p l i f i e r following the function generator and p r e c e d i n g the v i b r a t i o n generator i n the c i r c u i t . The purpose was to effect the impedance matching and to supply the d r i v i n g f o r c e for the v i b r a t i o n generator. A three stage push-pull type of t r a n s i s t o r i z e d power a m p l i f i e r was s p e c i a l l y designed and found s a t i s -f a c t o r y even at v e r y low frequency (e. g. 1 c.p. s.). F i g . 22 gives the c i r c u i t d i a g r a m while F i g . 23 shows the actual a m p l i f i e r . 2. 10 P r e s s u r e Seal As mentioned e a r l i e r , the measurement of the fluctuating p r e s s u r e on the surface of an autorotating model was part of the present investigation. A t l e a s t two different approaches could be c o n s i d e r e d as f e a s i b l e solutions to this scheme. The f i r s t approach suggested that a p r e s s u r e sensor be i n c o r p o r a t e d in the r e v o l v i n g unit and the p r e s s u r e signal be converted to e l e c t r i c voltage and p i c k e d up by s l i p r i n g s . A n alternative was. the use of a dynamic p r e s s u r e seal to r e l a y the p r e s s u r e signal f r o m a r e v o l v i n g p r e s s u r e tap to a stationary p r e s s u r e t r a n s d u c e r . The latt e r method was given p r i o r c o n s i d e r a t i o n because of the p r o b l e m s of i n e r t i a and m i n i a t u r i -zation i n v o l v e d i n the f o r m e r method. In addition to the function of t r a n s m i t t i n g the p r e s s u r e signal to the p r e s s u r e transducer,, the p r e s s u r e s e a l was r e q u i r e d to p r o v i d e a l e a k - p r o o f se a l i n g so that no communication a c r o s s the p r e s s u r e d i f f e r e n t i a l could be p o s s i b l e . The p r e s s u r e d i f f e r e n t i a l i n this case was the s m a l l p r e s s u r e fluctuation with r e s p e c t to the atmosphere and was i n the o r d e r of magnitude f r o m 0. 0005 to 0. 05 p s i , so that only a light seal was needed. However, any leakage in the p r e s s u r e t r a n s m i s s i o n l i n e would.mean the c r i t i c a l r e ading was being contaminated and could i m p a i r the true p r e s s u r e readings to such an extent that it would be almost i m p o s s i b l e to c a l i b r a t e the l o s s . C o n s i d e r a t i o n was also given to the f r i c t i o n damping existent i n the pressure' s e a l unit, as s m a l l f r i c t i o n damping was e s s e n t i a l i n the investigation of autorotation. A c a r e f u l s u r v e y of a l l these factors suggested that the design of a concentric j o u r n a l and sleeve b e a r i n g be adopted as the r e v o l v i n g and stationary elements of the p r e s s u r e seal unit.. The n e c e s s a r y c l e a r a n c e between them was f i l l e d with a thick f i l m of l u b r i c a n t to effect an airtight p r e s s u r e seal. A piece of 2 inch diameter teflon rod, backed up.by a< hollow steel disk, made up the body of the sleeve bearing. A 0.095 inch c e n t r a l hole was d r i l l e d to s e r v e as pa r t of the p r e s s u r e tube leading to the p r e s s u r e transe ducer and was aligned with a s i m i l a r c e n t r a l hole i n the jou r n a l . The j o u r n a l was made f r o m a 3/8 inch teflon tube and part of it was b u r i e d i n the lower model spindle so that it was (i n d i r e c t l y ) supported on r e m o t e l y mounted b a l l b e a r i n g s ins t e a d of on its sleeve bearing. ( F i g . 6) The idea ; was: to p r e s e r v e the c o n c e n t r i c i t y at a l l times and to m i n i m i z e the f r i c t i o n and wear and leakage due to sur f a c e contact and l a t e r a l motion, of the j o u r n a l . To check the effectiveness of the p r e s s u r e seal unit, the c a l i b r a t i o n apparatus of the p r e s s u r e t r a n s d u c e r (Section 2. 9) was adopted for the bench test. T he f i r s t p r a c t i c a l p r o b l e m encountered was the lack of a known p r e s s u r e s o u r c e which was re v o l v i n g . . To cope with this difficulty, two p r e s s u r e s e a l units s h a r i n g the common r e v o l v i n g element were constructed i n the test equipment. A t the input end of a f i r s t p r e s s u r e ' seal unit,, the o s c i l l a t i n g piston was us e d to generate a known fluctuating p r e s s u r e ; . the amplitude and phase shift of the same signal at the output end of a second p r e s s u r e seal unit were examined by the p r e s s u r e t r a n s d u c e r . (Section 2. 8) The r e v o l v i n g element was d r i v e n by an 1 adjustable speed d-c motor .(Fig. 17) through pulleys and rubber-belt. F i g s . 24 and 25 show the setup of this p r e s s u r e s e a l test equipment. 2. 11 Photography The storage c a p a b i l i t i e s of a T e k t r o n i x Type 564 Storage O s c i l l o s c o p e enabled the experimental data to be di s p l a y e d for qualitative-observation and to be r e c o r d e d on f i l m for l a t e r detailed a n a l y s i s . S a t i s f a c t o r y r e s u l t s were obtained by the use of an A s a h i Pentax, single lens reflex, 35 m m c a m e r a with a No. 3, 49 m m c l o s e up lens attachment. The c a m e r a was mounted on the o s c i l l o s c o p e b y means of a s p e c i a l l y designed mounting bracket. F i l m u s e d was Kodak Plus -X P a n c h r o m a t i c an4 best exposure values were found tp t|ef2. 8 at 1/30 sec. Enlargements (4 inches by 5 inches) were printed. O ver two hundred data shots were taken and the m a j o r i t y of the p r o c e s s i n g was p e r f o r m e d i n the dark r o o m of the Department of M e c h a n i c a l E n g i n e e r i n g . 2 4 III. E X P E R I M E N T A L P R O C E D U R E S  3. 1 C a l i b r a t i o n P r o c e d u r e s 3. 1. 1 Static and Dynamic P r e s s u r e s Between the End. Plates Measurements of the three-dimensional static p r e s s u r e di s t r i b u t i o n were made at the wind speed of 26. 3 feet per second. A static p r e s s u r e probe, a L a m b r e c h t micromanometer,, and a t r a v e r s i n g gear were set up for this purpose. It was found that, except for the region about 1/2 i n c h f r o m the walls, the static p r e s s u r e distributions i n the longitudinal d i r e c t i o n became quite u n i f o r m after a distance of 2 inches downstream of the leading edge for both sets of end plates. However, the chamfered i end plates gave m o r e u n i f o r m static p r e s s u r e di s t r i b u t i o n both i n the l a t e r a l and t r a n s v e r s e d i r e c t i o n s . It was thus decided to pick the chamfered plates for better flow conditions i n the fluctuating p r e s s u r e measurements. In addition, the effect of the end plates on the dynamic p r e s s u r e ; was investigated. A pi t o t - s t a t i c tube mounted midway between the end plates r e g i s t e r e d 5% i n c r e a s e of wind v e l o c i t y i n the range f r o m 6 to 50 feet per second. The v e l o c i t y p r o f i l e along the model m i d - c h o r d axis was found v e r y uniform; the spanwise v a r i a t i o n i n v e l o c i t y was i n the o r d e r of 1% at the wind speed of 26. 3 feet per second. Results of this investigation are shown i n F i g s . 26 and 27. 3. 1. 2-Static and Dynamic C a l i b r a t i o n s of Angular Displacement T r a n s d u c e r Extensive bench tests showed that the dynamic response of the t r a n s -ducer was instantaneous below 2, 000 rpm. T h i s is well above the estimated upper l i m i t of the autorotation speed. A l s o the outputs of the induced secondary voltage r e m a i n e d unchanged either at constant speed or during a c c e l e r a t i o n . A s expected, the envelope of the amplitude modulated signal c o i n c i d e d with a known si n u s o i d a l sig n a l of the same frequency and of the same amplitude f r o m the function generator. Data of the dynamic c a l i -b r a t i o n are inc l u d e d i n F i g . 28. It must be noted, however, that, as the motor speed was not 100% regulated, a phase r e l a t i o n existed between the tr a n s d u c e r output and the s i n u s o i d a l s i g n a l . T h e r e were times, however, when the phase differ e n c e did v a n i s h as in d i c a t e d by arrows on the r e c o r d i n g paper. The dynamic c a l i b r a t i o n d e s c r i b e d above showed great p r o m i s e . Since the angular motion has not effect whatsoever on the output c h a r a c t e r i s t i c s of the induced secondary voltage, the data of the static c a l i b r a t i o n apply equally w e l l to any angular speed. T h i s p e r f o r m a n c e g r e a t l y s i m p l i f i e d the p r o c e s s of c a l i b r a t i o n and expedited the ana l y s i s of the data l a t e r on. The object of the static c a l i b r a t i o n was then to make the most of the available instrumentation. Since the optimum frequency and amplitude of the excitation s i g n a l were established (paragraph 2. 6. 4), the static c a l i -b r a t i o n was well on the way. B y turning a 360° p r o t r a c t o r fastened to the flywheel past a fixed h o r i z o n t a l indicator, the angular displacements of the tr a n s d u c e r were c a l i b r a t e d . The co r r e s p o n d i n g voltage outputs were r e c o r d e d by the v i s i c o r d e r photographic paper. Data of this c a l i b r a t i o n are plotted on F i g . 29- The s o l i d c u r v e i s a cosine function. 26 3. 1. 3 P r e s s u r e T r a n s d u c e r C a l i b r a t i o n F o r a constant value of fluctuating ^ pressure;"amplitude- at a given frequency and a tube of given length and diameter, the amplitude and phase of the t r a n s -ducer signal was governed by two f a c t o r s : b r i d g e a m p l i f i e r gain setting and light dependent r e s i s t a n c e value. C a l i b r a t i o n of the a m p l i f i e r gain was achieved by two s t r a i n gauges mounted i n a temperature compensating two a r m b r i d g e c i r c u i t . A f t e r connections had been made to the b r i d g e a m p l i f i e r and meter,, the b r i d g e balance obtained, an i n t e r n a l r e s i s t a n c e (0. 5 M ohm) i n the above instrument was shunted a c r o s s one a r m of the s t r a i n gauge c i r c u i t . The unbalance caused a c u r r e n t to flow i n the b r i d g e and a meter reading was r e g i s t e r e d . Adjustment of the gain c o n t r o l v a r i e d this reading and, for convenience, it was set at 70 on the upper s c a l e of the meter face. On the other hand, the light dependent r e s i s t a n c e value v a r i e d with the light i n t e n s i t y or the power input to the light bulbs., The extreme s e n s i t i v i t y of the t r a n s d u c e r output to light intensity suggested that a consistent way of setting light intensity be adopted. A known p r e s s u r e , generated by the o s c i l l a t i n g p i ston at 10 c.p. s. , was introduced to the t r a n s -ducer cavity by means of a 4 foot, 0. 066 i n s i d e diameter, polyethylene tube. Adjustment of the light c i r c u i t potentiometer c o n t r o l l e d the t r a n s d u c e r output and allowed a standard signal to be established. The above p r o c e d u r e s were repeated at the beginning of each s e r i e s of tests and p r o v e d to be s a t i s f a c t o r y i n p r o d u c i n g consistent r e s u l t s . C a l i b r a t i o n curves for a range of frequencies 1 - 12 c y c l e s / s e c o n d are shown i n F i g . 30. 2 7 3 . 1.4 P r e s s u r e : Seal C a l i b r a t i o n Init i a l bench testing showed that a s m a l l amount of v a s e l i n e was, sufficient to s e a l the gap between the teflon j o u r n a l and b e a r i n g but that e x c e s s i v e vaseline would block the p r e s s u r e t r a n s m i s s i o n l i n e . . If the latte r unfortunately were the case., the p r e s s u r e signal would be lo s t completely i n the p r e s s u r e s e a l unit. A l s o i t was found that the p r e s s u r e s e a l was most efficient i n the static, condition. The amplitude and phase shift at the output end of the p r e s s u r e s e a l of a known p r e s s u r e signal were compared with the c a l i b r a t i o n data of the p r e s s u r e transducer. No d i s c r e p a n c y was noticeable. However, the p r e s s u r e seal when operating i n dynamic conditions introduced a new pro b l e m . The fluctuating p r e s s u r e a r i s i n g f r o m the rotation of the p r e s s u r e tubing p r o v e d to cause amplitude modulation of the p r e s s u r e signal at the frequency of rotation ( F i g . 3 1 ) . The theory (Appendix B) did not take into account this factor and it was di f f i c u l t to eliminate completely in experiment. A f i n a l r e s o r t was to me a s u r e the effect of rotating tubing on ; i n d i v i d u a l p r e s s u r e taps i n the fluctuating p r e s s u r e measurement and to subtract this amount f r o m the r e s u l t i n g p r e s s u r e signal, (paragraph 3 . 2 . 2 ) The effect of a leaking p r e s s u r e tube was also investigated. A hole p u r p o s e l y p i e r c e d through the tubing caused much attenuation of the p r e s s u r e signal. It was thus decided, i n case of doubt, to c l a i m the maximum p r e s s u r e fluctuation for i n d i v i d u a l taps as the fi n a l experiment r e s u l t s . 3 . 2 T e s t P r o c e d u r e s 3 . 2 . 1 K i n e m a t i c Measurements K i n e m a t i c measurements of the autorotating plate i n the wind tunnel i n c l u d e d the autorotation speed, the time and a c c e l e r a t i o n during the b u i l d -up period, and the angular displacement, velocity, and a c c e l e r a t i o n during the autorotation c y c l e . With the exceptions of the d-c motor and its speed c o n t r o l box, the c a l i b r a t i o n equipment for the angular d i s p l a c e m e n t t r a n s d u c e r ( F i g . 19) was u s e d i n this measurement. As before, the r o t o r winding of the t r a n s d u c e r was excited at 500 c. p. s. by the audio generator. • But the r o t o r in this case was d r i v e n by the model spindle i n s t e a d of by the motor shaft. The c o r r e s p o n d i n g t r a n s -ducer output was fed into the v i s i c o r d e r o s c i l l o g r a p h . • F o u r out of the seven I r e c o r d i n g channels i n the above instrument were set up. Channel 1 was used to r e c o r d the output of the stator winding, S^ or the angular displacement of the model. The galvanometer c o i l of channel 6 was u s e d as a dummy load for the stator winding (paragraph 2. 6.4). Since the r e c o r d f r o m channel 1 was su f f i c i e n t to-indicate the angular motion of the model, the output of channel 6 was not needed. H o r i z o n t a l adjustment of the galvanometer m i r r o r r e m o v e d the r e f l e c t e d light b e a m away f r o m the r e c o r d i n g plane so that the signal of channel 6 did not show up on the r e c o r d i n g paper. To pro v i d e two m i l l i - s e c o n d time m a r k e r s positioned near the edges of the r e c o r d i n g paper,, channels 4 and 5 were connected i n p a r a l l e l to the function generator. The signal f r o m the function generator was a 500 c.p. s. t r i a n g u l a r wave. T y p i c a l o s c i l l o g r a p h r e c o r d s are shown in ; F i g . 32 (the time m a r k e r s did not show up because of the l i m i t e d space in the photograph; ). In a l l autorotation measurements, the angular displacement of the model was i n t e r p r e t e d by the t r a n s d u c e r amplitude. In o r d e r to produce consistent r e s u l t s in subsequent tests, c a l i b r a t i o n of the t r a n s d u c e r ampli tude was c a r r i e d out before taking any quantitative measurements. The tr a n s d u c e r outputs of the two most important angular positions, i.e. zero and 90° angular position, were checked c a r e f u l l y f r o m time to time. The c a l i b r a t i o n data were then applied to a l l other angular positions. The angular position of the model was adjusted manually to zero angular p o s i t i o n with the flat s u rface of the model facing the front side panel of the tunnel. Since the shaft of the rotor was r i g i d l y attached to the model spindle, the magnetic axis of the rotor winding a c c o r d i n g l y took up a definite orientation. B y turning the b e a r i n g block of the upper autoro-tation stand on the tunnel flange, the angular p o s i t i o n of the stator could be adjusted to c o r r e s p o n d to 90° e l e c t r i c a l angle or m i n i m u m output position. T h i s c a l i b r a t i o n p r o c e d u r e was p r e f e r a b l y c a r r i e d out when the wind was off. The c a l i b r a t i o n for 90° angular p o s i t i o n or m a x i m u m output p o s i t i o n was l e s s t r i c k y and could even be p e r f o r m e d during autorotation. It has been shown that, for a given angular position, there is only one tr a n s d u c e r output (paragraph 2.6.3) and that the t r a n s d u c e r outputs are independent of angular motion (paragraph 3 .1.2). It follows that the m a x i mum t r a n s d u c e r amplitude at any autorotation speed always re p r e s e n t s the o c c u r r e n c e of 90° angular position. B y c o n t r o l l i n g the amplitude setting of the audio generator in such a way that the m a x i m u m tr a n s d u c e r output caused 4 inches peak to peak m a x i m u m deflection on the r e c o r d i n g 30 paper, the tr a n s d u c e r amplitude at 90 angular position was ca l i b r a t e d . K i n e m a t i c measurements of the autorotating plate were made under two different-flow conditions : model mounted between chamfered end plates and without end plates. Wind v e l o c i t y was i n c r e a s e d by s m a l l increments until the c r i t i c a l wind speed to initiate autorotati.cn was reached- F r o m then on wind v e l o c i t y was i n c r e a s e d Ln steps by 5 feet p e r seond . O v e r the tested wind speed range f r o m 0 to 35 feet p e r second, the model was excited f r o m rest, with no exceptions, by a stick- S h o r t l y before the model was excited manually, the r e c o r d d r i v e switch of the v i s i c o r d e r was t r i g g e r e d by a remote con t r o l switch to allow a complete h i s t o r y of angular motion to be r e c o r d e d f r o m the beginning of the build-up p e r i o d to steady autorotation. The r e c o r d i n g speed was 25 inches of r e c o r d i n g paper per second. O v e r eight hundred feet of such r e c o r d s were obtained f r o m the v i s i c o r d e r in these measurements. 3. 2. 2 Surface F l u c t u a t i n g P r e s s u r e Measurements Quantitative surface fluctuating p r e s s u r e measurements were made under approximately two-dimensional conditions, i.e. model mounted between the c h a m f e r e d end plates, at the wind speed of 26. 3 feet per second. The p r e s s u r e t r a n s d u c e r output was allowed to b u i l d up on the storage s c r e e n of the T e k t r o n i x Type 564 O s c i l l o s c o p e . To c o r r e l a t e the phase of the fluctuating p r e s s u r e to the angular position of the model, a signal f r o m the angular displacement t r a n s d u c e r was dis p l a y e d s i m u l t a n -eously on the same screen. The storage c a p a b i l i t i e s of the O s c i l l o s c o p e 31 e n a b l e d s u c h d a t a to b e r e c o r d e d o n f i l m f o r l a t e r d e t a i l e d a n a l y s i s . F a s t s w e e p s p e e d s p r o v i d e d d a t a o n f r e q u e n c y a n d p h a s e r e l a t i o n o f t h e p r e s s u r e s i g n a l , w h i l e s l o w s w e e p s p e e d s e n a b l e d t h e a m p l i t u d e m o d u -l a t i o n to b e o b s e r v e d . C o r r e l a t i o n o f s u r f a c e p r e s s u r e a n d m o d e l a n g u l a r d i s p l a c e m e n t w a s o b t a i n e d f o r b o t h t h e t r a n s i e n t b u i l d - u p p e r i o d a n d at s t e a d y s t a t e r o t a t i o n . . T h e b u i l d - u p r e g i o n w a s i n v e s t i g a t e d b y t r i g g e r i n g t h e C R O s w e e p w h i l e the m o d e l w a s s t a t i o n a r y , i . e . b e f o r e t h e m o d e l w a s e x c i t e d m a n u a l l y . F i n a l l y , t h e e f f e c t o f t h e r o t a t i n g t u b e o n t h e p r e s s u r e s i g n a l w a s e x a m i n e d b y b l o c k i n g o f f i n d i v i d u a l p r e s s u r e t a p s w i t h S c o t c h t a p e . T h e p r e s s u r e t r a n s d u c e r o u t p u t w a s r e c o r d e d o n t h e s t o r a g e s c r e e n d u r i n g t h e b u i l d - u p p e r i o d a n d d u r i n g a u t o r o t a t i o n as b e f o r e . T h e a b o v e p r o c e d u r e s w e r e r e p e a t e d f o r 13 p r e s s u r e t a p s , the p r e s s u r e r e a d i n g s b e i n g t a k e n f r o m i n d i v i d u a l t a p s o n e at a t i m e . T h e s w i t c h i n g o f p r e s s u r e t u b e c o n n e c t i o n s w a s c a r r i e d o u t w h e n t h e w i n d w a s o f f a n d w h e n the m o d e l w a s d i s m a n t l e d f r o m t h e l o w e r a u t o r o t a t i o n s t a n d a n d the u p p e r a u t o r o t a t i o n s t a n d w a s l i f t e d up b y t w o m e t a l w e d g e s o u t s i d e t h e t u n n e l c e i l i n g . . ( F i g . 9) T h e e x p e r i m e n t a l s e t u p f o r t h e f l u c t u a t i n g p r e s s u r e m e a s u r e m e n t s i s s h o w n i n F i g . 33 . I V . E X P E R I M E N T A L R E S U L T S 4 . 1 A n g u l a r V e l o c i t y M e a s u r e m e n t s T h e a n g u l a r d i s p l a c e m e n t t r a n s d u c e r d e s c r i b e d i n s e c t i o n 2. 6 p r o v i d e d a . u s e f u l m e a n s to d e t e r m i n e t h e i n s t a n t a n e o u s a n g u l a r v e l o c i t y o f the a u t o r o t a t i n g m o d e l . A s s e e n f r o m F i g . 32, the k i n e m a t i c m e a s u r e -m e n t s p r o d u c e d c o n t i n u o u s ( a m p l i t u d e - m o d u l a t e d ) s i g n a l s o f a n g u l a r d i s -p l a c e m e n t o n t h e v i s i c o r d e r o s c i l l o g r a p h p a p e r . T h e i n s t a n t a n e o u s a n g u l a r p o s i t i o n s o f t h e m o d e l w e r e t h e n i n t e r p r e t e d f r o m the c o r r e s p o n d i n g t r a n s -d u c e r a m p l i t u d e s . B y m e a s u r i n g t h e d i s t a n c e s b e t w e e n t w o c o n s e c u t i v e n o d e s a n d d i v i d i n g t h i s v a l u e b y t h e t i m e s c a l e o f 25 i n c h e s p e r s e c o n d , t h e p e r i o d a n d t h u s t h e a v e r a g e r o t a t i o n a l s p e e d d u r i n g 180 d e g r e e s o f r o t a t i o n w e r e d e t e r m i n e d . T h i s n e w t e c h n i q u e o f m e a s u r i n g a n g u l a r v e l o c i t y h a s a d v a n t a g e s o v e r t h e c o n v e n t i o n a l s t r o b o s c o p e i n t h a t it c o u l d o p e r a t e at e x t r e m e l y l o w r o t a t i o n a l s p e e d s a n d c o u l d e v e n d e t e c t t h e i n s t a n -t a n e o u s a n g u l a r v e l o c i t y d u r i n g a c c e l e r a t i o n . 4 .2 D e p e n d e n c e o f T i p S p e e d o n W i n d S p e e d  4 . 2 . 1 M o d e l W i t h E n d P l a t e s R e p e t i t i v e t r i a l s i n d i c a t e d the e x i s t e n c e o f a c r i t i c a l w i n d s p e e d ". b e l o w w h i c h t h e p h e n o m e n o n o f a u t o r o t a t i o n w a s n o t o b s e r v e d . A t e a c h w i n d s p e e d a b o v e t h i s v a l u e , t h e r e w e r e t w o e q u i l i b r i u m r o t a t i o n a l s p e e d s . T h e l o w e r r o t a t i o n a l s p e e d o f t h e t w o w a s a n u n s t a b l e o n e , g i v i n g t h e r e q u i r e d r p m f o r a u t o r o t a t i o n , w h i l e t h e h i g h e r r o t a t i o n a l s p e e d w a s t h e s t a b l e a u t o -r o t a t i o n s p e e d . T h e r e s u l t s of t h i s m e a s u r e m e n t a r e d i s p l a y e d i n t h e f o r m o f t i p s p e e d v s w i n d s p e e d i n F i g . 34. In t h e a b s e n c e o f r e l i a b l e d a t a f o r 33 the time-dependent separated flow problems, none of the re s u l t s presented here are c o r r e c t e d for tunnel blockage. The autorotation tip speed is seen to i n c r e a s e n e a r l y l i n e a r l y with wind speed, with values of the o r d e r of 5 0 % of the wind speed. The scatter in the data is s m a l l . The i n i t i a l tip speed, however, dec r e a s e s with wind speed, indicating that a s m a l l e r i n i t i a l spin was r e q u i r e d for autorotation at higher wind speeds and c o n v e r s e l y a l a r g e r i n i t i a l spin was r e q u i r e d at lower wind speeds. The wind speed for which the two tip speeds coincide was the c r i t i c a l wind speed to initiate autorotation. Thus the plot of tip speed vs wind speed enables the upper and lower l i m i t c y cles of the autorotation of the flat plate to be established. In the wind speed range below the c r i t i c a l wind speed, there is no p o s s i b i l i t y of autorotation. In the region confined by the ab s c i s s a , the c r i t i c a l wind speed, and the i n i t i a l tip speed curve, the i n i t i a l r p m is not suf f i c i e n t for the wind to take over and the angular motion w i l l be damped out completely after a few c y c l e s . O n l y in the region above the c r i t i c a l wind speed and above the i n i t i a l tip speed curve is autorotation p o s s i b l e . T h i s i m p l i e s that, if the plate was given any i n i t i a l speed gr e a t e r than or equal to the m i n i m u m i n i t i a l speed, it would undoubtedly a c c e l e r a t e to its f i n a l autorotation speed, reached when an energy balance was obtained over one complete cycle. 4. 2. 2 Model Without End Plates The i n i t i a l and autorotation tip -speed curves in this case show exactly the same trend and agree f a i r l y well in the low wind speed range with those obtained with end plates. The effects of the end plates are to lower the c r i t i c a l wind speed and to r a i s e both the autorotation and i n i t i a l speeds under s i m i l a r damping conditions and at the same wind velocity. Results of this measurement are plotted on F i g . 34 for comparison. 4.3. Time, A n g u l a r Velocity, and A n g u l a r A c c e l e r a t i o n in the Build-up -!•  P e r i o d In the p r o c e s s of reducing the autorotation speed f r o m the v i s i c o r d e r o s c i l l o g r a p h paper, it was found that the t r a n s i t i o n f r o m the transient b u i l d -up p e r i o d to the steady state rotation was not c l e a r l y defined. It was thus decided to plot the instantaneous angular v e l o c i t y vs time for each wind speed and identify the region below 9 8 % of the fi n a l r o tational speed as the build-up p e r i o d . Results of this measurement are presented in F i g s . 35 and 36. A l l such curves star t with a dotted section c o v e r i n g ther p e r i o d of the manually applied i n i t i a l spin and a l l but the curve for the c r i t i c a l wind speed show the feature that the angular v e l o c i t y i n c r e a s e s almost l i n e a r l y at the be-ginning of the build-up p e r i o d and approaches the autorotation speed g r a d -u a l l y and smoothly. A l s o it is noted that the effect of a high wind speed is a r a p i d i n c r e a s e of angular v e l o c i t y over a short p e r i o d of time. F o r example, at the wind speed of 37.3 fps where the i n i t i a l speed d i f f e r s most widely f r o m the autorotation speed (the i n i t i a l speed lowest and autorotation speed highest), the build-up time is only 3. 0 seconds, while at the wind speed of 15. 8 fps where the i n i t i a l speed is much c l o s e r to the autorotation speed, it takes 5. 3 seconds or n e a r l y twice as much time for the same model to go through the build-up period. Results of the build-up time at 35 different wind speeds are presented in F i g . 3 7 . A l l these r e s u l t s indicate the fact that the excitation torque is appre-ciable at high wind speed and is b a r e l y enough to overcome the f r i c t i o n damping at low wind speed. Qualitatively, this i m p l i e s that the mean aero-dynamic torque and angular a c c e l e r a t i o n would be much greater at high wind speed. Since the data giving the instantaneous angular v e l o c i t y vs time were already tabulated, quantitative r e s u l t s of angular a c c e l e r a t i o n could be d e r i v e d f r o m simple g r a p h i c a l or n u m e r i c a l differentiation. D i r e c t g r a p h i c a l measurement of the slopes of the angular v e l o c i t y - time curves "was;: used, and the res u l t s are plotted in the f o r m of angular a c c e l e r a t i o n 6* vs the dimensionless angular v e l o c i t y w/ou where ° auto to is the autorotation speed, on F i g . 3 8 . auto r > & A l l the a c c e l e r a t i o n curves c o n f i r m the previous two observations. F i r s t , the rate of change of angular v e l o c i t y declines f r o m an approximate-l y constant value at the beginning of the build-up p e r i o d un t i l the steady state is reached, where the mean angular a c c e l e r a t i o n is zero. Second, the mean angular a c c e l e r a t i o n and thus the resultant torque are greater at higher wind speeds. Since a high mean angular a c c e l e r a t i o n leads to a low build-up period, this agrees with the conclusion of F i g . 37 that the build-up p e r i o d is longer at lower wind speeds. 4.4 Angular V e l o c i t y and Angular A c c e l e r a t i o n During One Autorotation . C y c l e The instantaneous angular v e l o c i t y was examined by studying the output of the angular displacement t r a n s d u c e r during one autorotation cycle; the angular a c c e l e r a t i o n was d e r i v e d f r o m the instantaneous angular velo-. c i t y vs time curve. A s shown in F i g . 32 the tr a n s d u c e r output is an a m p l i -tude-modulated signal at the frequency of rotation. A smooth envelope was drawn v e r y c a r e f u l l y and the height of the envelope was m e a s u r e d to 0.01 inch at time in t e r v a l s of 2 m i l l i s e c o n d s . It was found that the wave f o r m of such an envelope was v e r y c l o s e l y s i n u s o i d a l and that the d i s c r e p a n c y was o the same o r d e r of magnitude as that of the static c a l i b r a t i o n data of the transducer. ( F i g . 29). A c c o r d i n g to the theory of the tr a n s d u c e r ( p a r a -graph 2. 6. 3), the amplitude modulated s i g n a l takes a s i n u s o i d a l wave f o r m only when the angular displacement is i n c r e a s i n g at a constant rate, i . e . constant angular v e l o c i t y during one complete cycle. It follows that, within the a c c u r a c y of the present investigation, the angular v e l o c i t y remains constant and the angular a c c e l e r a t i o n remains zero during one autorotation cy c l e . 4. 5, Surface F l u c t u a t i n g P r e s s u r e s Surface fluctuating p r e s s u r e measurements were made both for the tra n s i e n t build-up p e r i o d and for steady state rotation at the wind speed of 26. 3 fps. T y p i c a l o s c i l l o s c o p e t r a c e s of fluctuating p r e s s u r e signals are shown in F i g . 39- In each photograph the upper signal r epresents the out-put f r o m the p r e s s u r e transducer; the lower s i g n a l r epresents the output f r o m the angular displacement transducer. The frequency of a fluctuating p r e s s u r e s i g n a l was obtained by counting the number of complete cycles within a definite p e r i o d of time. The phase angle of a fluctuating p r e s s u r e s i g n a l was c o r r e l a t e d to that of the instantaneous angular position of the model. A constant time lag of 10 m i l l i s e c o n d s was taken into account in the 37 analysis of the fluctuating p r e s s u r e during steady state rotation. ( F i g . 30b). The'magnitude of the p r e s s u r e signal was determined by the (verti c a l ) deviation f r o m the r e f e r e n c e line of zero output ( t h i r d h o r i z o n t a l l i n e f r o m top) with suction giving upward displacements, and this r eading was c o n -v e r t e d to p r e s s u r e units a c c o r d i n g to F i g . 30a. C o r r e c t i o n in the o r d e r of 1 0% ( F i g . 39e) due to (rotating) tube effect was made to individual p r e s s u r e signals (paragraph 3. 1.4 and 3.2.2). 4. 5. I. F l u c t u a t i n g P r e s s u r e D u r i n g the B u i l d - u p - P e r i o d It is i n t e r e s t i n g to note that during the build-up p e r i o d the frequency of the fluctuating p r e s s u r e always equals the frequency of rotation. F i g . 39a shows that the frequently builds up f r o m 2 cps to 10 cps in about 28 cyc l e s . Although one might anticipate at le a s t two relevant frequencies, r e p r e s e n t i n g the wake vortex formation and the model angular motion, the lat t e r appears to be the predominant factor. The amplitude of the fluctuating p r e s s u r e grows gradually as the model accelerates.. I r r e g u l a r , unorganized wave forms of the p r e s s u r e signal were o b s e r v e d at the in i t i a t i o n of autorotation ( F i g . 39b). However, this phenomenon i s t e m p o r a r y and l a s t e d only for the f i r s t few c y c l e s or before the amplitude i n c r e a s e d to the steady state value, about 5 times the i n i t i a l value. It must be pointed out that, although the p r e s s u r e t r a n s d u c e r s i g n a l appears to be l a r g e r in some cases at the ini t i a t i o n of autorotation, the true magnitude of the fluctuating p r e s s u r e is actually s m a l l e r than that obtained during steady-state rotation. The apparent decrease in fluctuating p r e s s u r e amplitude with i n c r e a s i n g frequencly is a result: of the i n c r e a s -38 i n g a t t e n u a t i o n o f t h e t r a n s d u c e r s i g n a l . T h e r e f o r e c a r e m u s t b e t a k e n to c h o o s e t h e r i g h t c a l i b r a t i o n c u r v e ( F i g . 30) i n the r e d u c t i o n o f d a t a d u r i n g t h e b u i l d - u p p e r i o d . In s h o r t , t h e t r a n s i e n t b u i l d - u p p e r i o d i s c h a r a c t e r i z e d b y the s i m u l -t a n e o u s i n c r e a s e o f b o t h t h e f r e q u e n c y a n d a m p l i t u d e o f t h e p r e s s u r e f l u c t u a t i o n s . 4 . 5. 2 P r e s s u r e C o e f f i c i e n t v s A n g u l a r P o s i t i o n D u r i n g O n e A u t o r o t a t i o n  C y c l e J u s t as i n t h e t r a n s i e n t b u i l d - u p p e r i o d , t h e f r e q u e n c y o f t h e s u r f a c e f l u c t u a t i n g p r e s s u r e c o i n c i d e s w i t h t h e f r e q u e n c y o f r o t a t i o n . S i n c e t h e r o t a t i o n a l f r e q u e n c y i s s t a b l e d u r i n g a u t o r o t a t i o n , t h e f r e q u e n c y o f the f l u c t u a t i n g , p r e s s u r e r e m a i n s s t a b l e . T h e s m o o t h w a v e f o r m : o f t h e p r e s s u r e s i g n a l r e p e a t s i t s e l f v e r y f a i t h f u l l y f o r e v e r y 3 6 0 ° r o t a t i o n ( F i g . 39c a n d 39d) . L i t t l e o r n o a m p l i t u d e m o d u l a t i o n w a s o b s e r v e d . H o w e v e r , t h e w a v e f o r m i s d e f i n i t e l y n o t s y m m e t r i c a l w i t h r e s p e c t to t h e r e f e r e n c e l i n e . T h e p r e s s u r e c o e f f i c i e n t s f o r a l l 13 t a p s v s a n g u l a r p o s i t i o n a r e g i v e n i n F i g . 4 0 . It i s n o t e d t h a t f o r t a p s N o . 2, N o . 5 a n d N o . 6 t h e n e g a t i v e p r e s s u r e p e a k s a r e v e r y s l i g h t l y l o w e r t h a n t h e p o s i t i v e p r e s s u r e p e a k s a n d t h a t f o r the r e m a i n i n g t a p s t h e n e g a t i v e p e a k s a r e h i g h e r . T h e d i f f e r e n c e i s b i g g e s t f o r t h e t a p s c l o s e to t h e l e a d i n g e d g e , i . e. , t a p s N o . 13, N o . 12, N o . 11 a n d N o . 10, a n d i s s m a l l e s t f o r t h e t a p s c l o s e to t h e t r a i l i n g e d g e ; i . e . t a p s N o . 1 a n d N o . 2. T h e t a p s p o s i t i o n e d i n t h e c e n t r a l p a r t o f t h e c h o r d g i v e d i f f e r e n c e s o f p e a k r e a d i n g s f a l l i n g i n b e t w e e n t h e s e e x t r e m e s . T h i s s u g g e s t s t h a t the l e a d i n g e d g e p r e s s u r e s 39 make more contribution to the (clockwise) aerodynamic torque than the t r a i l i n g edge p r e s s u r e s . T h i s observation was l a t e r c o n f i r m e d by the torque calc u l a t i o n . (Section 4. 6). With r e g a r d to the phase of the s u r f a c e fluctuating p r e s s u r e , it is almost i m p o s s i b l e to draw any simple conclusions. N e a r l y a l l the taps -r e a c h t h e i r zero, maximum, and m i n i m u m at different angular positions. F o r example, taps No. 13, No. 12, No. 11, No. 10 and No. 9 r e a c h their m i n i m u m p r e s s u r e around 7 5° and taps No. 8, No. 7, No. 6, No. 5, No. 4 No. 3, No. 2 and No. 1 around 86°. The angular p o s i t i o n where the taps r e a c h their m a x i m u m is l e s s w ell defined and spreads over the f a i r l y wide range f r o m 220° to 296°. A f i n a l r e m a r k is that with the exception of taps No. 13, No. 12, No. 11, and No. 10, the p r e s s u r e reading is negative over the greater part of the cycle. 4.6 Torque C o e f f i c i e n t vs Angular P o s i t i o n A e r o d y n a m i c torque during one autorotation cycle was obtained by the indirect, tedious method of integration of the instantaneous moments of the surface p r e s s u r e s . The d i s t r i b u t i o n of instantaneous fluctuating p r e s s u r e over the plate for 10 degree increments of angular p o s i t i o n was d e r i v e d f r o m F i g . 40 for a l l 13 taps. It is r e c a l l e d that due to c o n s t r u c t i o n d i f f i c u l t i e s only the flat s u r f a c e has p r e s s u r e taps. It was t h e r e f o r e assumed that the flow pattern repeated e v e r y half c y c l e and that the image taps, after d i s p l a c i n g 180°, could r e g i s t e r the p r e s s u r e readings on the cambered, surface at the same angular position. T h i s assumption was j u s t i f i e d e x p e r i m e n t a l l y by rotating the model in the r e v e r s e d i r e c t i o n . A s expected, a tap r e g i s t e r e d the p r e s s u r e reading of its image tap when the model was rotating in the u s u a l d i r e c t i o n . T y p i c a l r e s u l t s for 0°, 30 , 60°, 120°, and 150° are pres e n t e d in F i g . 41. As seen f r o m F i g . 41, there is unfortunately some scatter of data of the C ' values. A l s o the p r e s s u r e d i s t r i b u t i o n is unknown close to the P leading and t r a i l i n g edges, where it is i m p o s s i b l e to arrange a p r e s s u r e tap. To cope with this p r o b l e m and to s i m p l i f y the computations, the f o l -lowing assumption was made. It was assumed that the p r e s s u r e coefficient could be c o n s i d e r e d as constant over short in t e r v a l s along the chord. In other words, the a r e a under the C 1 curve was approximated by the sum of P a s e r i e s of rectangles. The d i f f e r e n t i a l moment was thus the product of the recta n g u l a r a r e a and its c o r r e s p o n d i n g moment a r m f r o m the center tap; the resultant moment at a c e r t a i n angular position was the summation of these d i f f e r e n t i a l moments. The r e s u l t i n g torque coefficient vs angular position is presented in F i g . 42. It turns out to be a f a i r l y s y m m e t r i c a l curve with zero torque at o o o 14 and 104 , m a x i m u m d r i v i n g torque at 60 , and m a x i m u m r e s i s t i n g torque at 150°. A plan i m e t e r was used to es t a b l i s h the mean torque co--2 efficient, which was found to be 2. 1 x 10 or equivalent to a se c t i o n a l t o r --3 que of 1.91 x 10 l b - f t / f t . C l e a r l y the excitation torque must balance the mean damping torque of the bearings and rotating seal, and the or d e r of magnitude seems reasonable, since the present system, with its greater constaints, would be expected to have higher damping torque than the tour-b i l l i o n apparatus, d e s c r i b e d in Section 1, and this was re p o r t e d to have -4 damping torque of the or d e r of 10 l b - f t . (5). It is i n t e r e s t i n g to note that the torque coefficient curve is v e r y c l o s e l y s i n u s o i d a l . 4.7 Wake Survey A short qualitative wake survey was c a r r i e d out with a DISA 55A01 constant temperature hot wire anemometer. A few observations were made during the steady state rotation at the wind speed of 26. 3 fps. It was found that the sense of rotation of the model had a definite influence on the wake geometry. If the position of the hot wire probe was fixed downstream and to one side of the model, the anemometer output gave clean and well~:organized h a r m o n i c signals while the model was rotating in one di r e c t i o n , but m e s s y and e r r a t i c signals while the model was rotating in the opposite d i r e c t i o n . T h i s is pos i t i v e indication that in the f o r m e r case the wake was deflected away f r o m the probe and the position of the probe was outside the wake while in the latter case the wake was deflected towards the probe and the position of the probe was inside the wake. T h i s o bservation was supported by the previous argument that rotation of the plate could develop c i r c u l a t i o n . A s a r e s u l t of the additional v e l o c i t y f i e l d due to this c i r c u l a t i o n , the wake exhibited angular de-fl e c t i o n s i m i l a r to the deflection of s t r e a m l i n e s in the p r o b l e m of u n i f o r m flow past a c i r c u l a r c y l i n d e r with c i r c u l a t i o n in potential flow theory. V. DISCUSSION 5. 1 Autorotation Speed vs Wind Speed F i g . 34 shows that the autorotation speed i n c r e a s e s almost l i n e a r l y with the wind speed. However, the autorotation curves, if extended, would not pass through the o r i g i n but would i n t e r s e c t the a b s c i s s a at about 6 feet p e r second. T h i s displacement is almost c e r t a i n l y a function of the amount of m e c h a n i c a l damping torque, in the r e v o l v i n g elements. Thus, the auto-rotation speed during the p r e s s u r e measurements of section 4.5 at a wind speed of 26. 3 fps was 9. 5 cps, c o r r e s p o n d i n g to a tip speed of 10. 0 fps. T h i s gives a point l y i n g to the right of the autorotation curves of F i g . 34, although the aerodynamic conditions were the same as for the curve with end plates. P r e s u m a b l y the explanation is the i n c r e a s e d m e c h a n i c a l damp-ing caused by the rotating p r e s s u r e s e a l of the tube connections. A l s o the ratio of tip speed to wind speed is about 0.5 for the case of the model with end plates and is about 0. 45 for the case of the model without end plates. These r e s u l t s agree g e n e r a l l y with the data quoted by C r a b t r e e (1) and compare favourably with the measurements by James and Stone (6) and by B a i r d and P i c k (7), both using the stroboscope technique. The i n c r e a s e of autorotation speed for the same model when .. mounted between end plates was also o b s e r v e d in (1). 5. 2 Ini t i a l T i p Speed vs Wind Speed No r e f e r e n c e to the measurement of the i n i t i a l speed r e q u i r e d for autorotation could be found in the t e c h n i c a l l i t e r a t u r e . T h i s is probably because the measurement of instantaneous angular v e l o c i t y during a c c e l e r -ation is beyond the capability of a stroboscope. 43 It i s i n t e r e s t i n g to note that the general shape of the i n i t i a l speed curve is i n c l i n e d downward and indicates that the higher the wind speed, the lower the i n i t i a l tip speed. It is argued that at higher wind speeds m o re energy could be extracted f r o m the stream. The excitation torque in this case would be greater and thus the tendency to autorotate about the axis of s y m m e t r y i n c r e a s e s with wind speed. P e r h a p s equally i n t e r e s t i n g is the c o m p a r i s o n of the present tip speed vs wind speed curves with those of the 'a e r i a l t o u r b i l l i o n ' worked out by P a r k i n s o n (5). It is noted that these two forms of autorotation y i e l d the same tr e n d i n the autorotation curves and show an i n c r e a s e of autorotation speed with wind speed. However, the i n i t i a l tip speed curves show completely r e v e r s e d trends -- the i n i t i a l tip speed curves of the ' a e r i a l t o u r b i l l i o n ' i n c r e a s e with wind speed. T h i s seems to be a c o n t r a d i c t o r y r e s u l t at f i r s t glance. It must be r e c a l l e d , however, that the m e c h a n i s m of autorotation of the ' a e r i a l t o u r b i l l i o n ' i s completely different and is attributed to the se c t i o n a l flow separation and reattachment c h a r a c t e r i s t i c s of a D-section c y l i n d e r . A 'very considerable i n i t i a l spin' is r e q u i r e d to produce a r e l a t i v e wind v e l o c i t y at a s u f f i c i e n t l y high angle of attack to overcome the adverse p r e s s u r e gradient and cause flow reattachment on the afterbody i n the wake. Static f o r c e measurements by Santosham (13) showed that the D-section c y l i n d e r changes its reattachment c h a r a c t e r i s t i c s on the afterbody in the angle of attack range f r o m 36° to 60°. It follows that the i n i t i a l tip speed had to be gr e a t e r than half of the wind speed to allow a l a r g e apparent angle of attack of the same o r d e r of magnitude. Hence the i n i t i a l tip speed must i n c r e a s e with wind speed. 5. 3 S t a b i l i t y of Autorotation The r e s u l t s of the kinematic measurements show c l o s e l y l i n e a r c h a r a c t e r i s t i c s of i n i t i a l and autorotation speeds and nonlinear c h a r a c t e r -i s t i c s of the build-up time and angular a c c e l e r a t i o n during the transient b u i l d -up period. At high wind speeds, the i n i t i a l speed is low, the autorotation speed is high, the build-up.time is short, and the angular a c c e l e r a t i o n is l a r g e . Conversely, at low wind speeds, the i n i t i a l speed is high, the auto-rotation speed is low, the build-up time is long, and the angular a c c e l e r a t i o n is s m a l l . It follows that autorotation is m o re stable at high wind speeds and is l e s s stable at low wind speeds. If the damping l e v e l is constant, the wind v e l o c i t y is the dominant factor i n the s t a b i l i t y of autorotation. 5.4 Some A e r o d y n a m i c Arguments on Autorotation The flow pattern during one autorotation c y c l e is f a i r l y c o m plicated and is not f u l l y understood as yet. However, the fluctuating p r e s s u r e measurements, the aerodynamic torque distribution, and the wake s u r v e y indicate the following: V o r t i c e s were undoubtedly f o r m e d f r o m the shear l a y e r s separating f r o m the plate leading and t r a i l i n g edges during the autorotation cycle. The leading edge v o r t i c e s exerted a l a r g e influence on the fluctuating p r e s s u r e s ; the effect of the t r a i l i n g v o r t i c e s was l e s s noticeable in the fluctuating p r e s s u r e measurements, as the t r a i l i n g v o r t i c e s were swept downstream i n a r e a r w a r d , downward d i r e c t i o n . N e ar 8 0 the f l u i d p a r t i c l e s adjacent to the plate experienced a v e l o c i t y component n o r m a l to the plate as a r e s u l t of the angular motion of the plate. The r e l a t i v e v e l o c i t y was t h e r e -fore at a negative angle of attack to the surface of the plate near the leading edge. The flow t h e r e f o r e r e m a i n e d attached to the upper s u r f a c e as 8 i n c r e a s e d to appreciable p o s i t i v e values; flow s e p a r a t i o n was delayed. A s 8 i n c r e a s e d further, the flow was unable to r e m a i n attached to the s u r f a c e while p a s s i n g around the sharp leading edge to the upper s u r f a c e and tended to f o r m a s e p a r a t e d shear l a y e r . T h i s khear l a y e r then r o l l e d up, due to the r e v e r s e d flow effect i n separation, and f o r m e d a separation bubble or l o c a l i z e d r e g i o n of l a m i n a r separated flow near the leading edge. The c h a r a c t e r i s t i c of this r e g i o n was high v e l o c i t y and low p r e s s u r e as : indicated by the high suctions for taps No. 13, No. 12, and No. 11 f r o m 8 = 33° to 75° ( F i g . 40a. ). The s i z e of the separation bubble s e e m e d to grow r e a r -ward, as 6 i n c r e a s e d further. The p r e s s u r e f i n a l l y r e a c h e d i t s highest suction peak as indicated by the p r e s s u r e readings of taps No. 13, No. 12, No- 11, No. 10, and No. 9 for 8 = 75°. At this instant, the separation produced v e r y strong i n t e r a c t i o n with the plate as shown by the l a r g e p r e s s u r e co e f f i c i e n t of the o r d e r of minus 5. F o r s t i l l l a r g e r values of 8 the suction peak d e c r e a s e d f a i r l y r a p i d l y as shown by taps No. 13, No, 12 andNo. 11. T h i s seemed to be an i n d i c a t i o n that the separation bubble had grown u n t i l the upper surface flow was completely separated- The c i r c u -lation of the flow then c a r r i e d the trapped vortex r e a r w a r d and downward. 5.5 F l u c t u a t i n g P r e s s u r e Co e f f i c i e n t As seen f r o m F i g . 40. the fluctuating p r e s s u r e coefficient has its l a r g e s t peak to peak v a r i a t i o n for leading edge taps (No. 13 and No. 12) and s m a l l e s t for t r a i l i n g edge taps (No. 1 and No. 2). The v e r y high suction peak o c c u r r i n g at about 75° was explained by the flow separation and f o r -mation of v o r t i c e s (Section 5. 4). The v e r y high positive p r e s s u r e co-efficient was p r o b a b l y due to the contribution of the time-dependent l o c a l a c c e l e r a t i o n t e r m i n the equation of motion of the f l u i d for unsteady flow. Thus, the c o r r e s p o n d i n g equations for i r r o t a t i o n a l steady flow B e r n o u l l i ' s .equation » » p + l /2pU = p + 1/2 PU 00 CO IT2 2 oo oo evaluating the p r e s s u r e coefficient in t e r m s of the v e l o c i t i e s , no longer hold 94 for an unsteady flow problem. A n additional t e r m P g t which i s an unknown function of time should be added to the right hand side of jB.erno.ulli's equation and C '. is m o d i f i e d accordingly. A l s o it must be pointed out that the instantaneous v e l o c i t y of the p a r t i c l e s near the plate was the vector sum of the free s t r e a m v e l o c i t y and the v e l o c i t y induced by the angular motion of the plate. The o c c u r r e n c e of the highest p o s i t i v e p r e s s u r e coefficient was for tap'No. 13 at 9 = 300°. As the rotational speed was 9- 5 cps, the v e l o c i t y r e l a t i v e to the plate was about 140% of the free s t r e a m v e l o c i t y . Thus a p r e s s u r e coefficient based on this r e l a t i v e wind v e l o c i t y would be reduced to the o r d e r of 1.8. 47 V I . S U M M A R Y O F R E S U L T S Results of this investigation are s u m m a r i z e d as follows: 1. The autorotation speed and i n i t i a l speed show n e a r l y l i n e a r v a r i a t i o n with wind speed. The autorotation speed i n c r e a s e s with wind speed; the i n i t i a l speed d e c r e a s e s with wind speed. 2. The build-up time is shorter and the mean angular a c c e l e r a t i o n is l a r g e r for higher wind speeds; the build-up t i m e is longer and the mean angular a c c e l e r a t i o n is s m a l l e r for-low wind speeds. 3. During the steady state autorotation cycle, the angular v e l o c i t y r e m a i n s constant to the a c c u r a c y of measurement p o s s i b l e i n this investigation; i . e . about 5%. 4. During the build-up period, the frequency and amplitude of the s u r f a c e fluctuating p r e s s u r e i n c r e a s e s i m u l t a n e o u s l y as the rotat-i o n a l speed builds up imm e d i a t e l y after the manual excitation. 5. During the steady state rotation, the frequency of the su r f a c e fluctuating p r e s s u r e is equal to the frequency •of, au^o potation::; The amplitude is the l a r g e s t for leading edge taps and is the s m a l l e s t for the t r a i l i n g edge taps. T h e r e i s no simple phase re l a t i o n . L i t t l e or no amplitude modulation is observed. 6 . The instantaneous d i s t r i b u t i o n of aerodynamic torque is f a i r l y s y m m e t r i c a l and re s u l t s in a s m a l l positive mean torque of 1.91 3 o x 10" l b - f t / f t during 180° of rotation. i i 7. The wake exhibited angular deflection as a r e s u l t of the c i r c u l a t i o n developed during autorotation. 48 8. F l o w sepa r a t i o n is delayed during autorotation. L e a d i n g edge v o r t i c e s are developed i n a separation bubble f r o m about 33° to 7 5° and p e e l off above 90°. A P P E N D I X A E S T I M A T E O F T H E R E Q U I R E D W R I T I N G S P E E D O F V I S I C O R D E R F O R 500 C Y C L E S P E R S E C O N D C A R R I E R S I G N A L L i g h t B e a m D i s p l a c e m e n t y = y Q s i n wt ( 1 ) C h a r t D i s p l a c e m e n t z - Vt ( 2 ) H e n c e ' y = y Q s i n 2 5 . (3) • .... , . . dy w wz iA\ ~~- = y — cos — dz Jo V V T h e d i s t a n c e t r a v e l e d b y t h e l i g h t b e a m d u r i n g o n e c o m p l e t e c y c l e c a n b e e x p r e s s e d b y /• jr. J 0 h d z ( 5 ) S u b s t i t u t i n g (4) i n t o (5) 2TTV 4." v l c ( W / i u. 2 w 2 -2 wz . J o v = 4 T T V I 2 w 2 2 w z , y 0 v 2 C 0 S ~ d z 0 wz C h a n g i n g v a r i a b l e s f r o m ~ t o cf> 7 2 s = f \ / 1 + y ' ^ c o s 2 * 4 V f ^ 2 / + 2 w 2 2 w 2 2 s i n <t> d<t> m r C ' 2 / — h ¥ J y + — \ y 1 - U s i n • d<f> w h e r e k = / 0 9 ° w 2 \ / v V o T h i s i s e l l i p t i c i n t e g r a l o f the s e c o n d k i n d . To evaluate this i n t e g r a l n u m e r i c a l l y we r e c a l l w • 2irf - 2ir(500) - 1000 ir rad/sec v = 2 inch (4 inches peak ffa peak deflection) }o V = 25 inch/sec T h e r e f o r e the amplitude of the e l l i p t i c i n t e g r a l is 1T/2, and the modulus is k , . / M i o V 2 a - 1 25 2+4(10*)ir 2 . E(k, ir/2) - 1 f r o m (5) J 2 2 + _ 2 | ^ = 8 i n c h / c y c l e S - 4 |/ * -r- , 1 0 % T h i s r e s u l t is c l o s e l y checked for high frequency signals since the t r a v e l distance during each quarter c y c l e can be approximated by the amplitude (2 inches) of the sine curve without too much difference. F o r 500 cps signal the light b eam tr a v e l s c y c l e . . inch „r>nn inch 500 /rocon:; x 8 / , = 4 0 0 0 / second cy c l e second T h i s is well within the range of allowable writing speed of 10 , 0 0 0 inches per second for standard c o l l e c t o r lens. 51 A P P E N D I X ; B W A V E P R O P A G A T I O N IN A T U B E The p r e s s u r e developed by the piston o s c i l l a t i o n s (section 2.9) at the input end of the tube was cal c u l a t e d f r o m one dim e n s i o n a l acoustic theory (12). A t the piston, p' (t) = a p fl 6 cos n t where piston displacement = 6 sin ^ t t . The effect of phase l a g and attenuation due to vi s c o u s d i s s i p a t i o n at the output end of the tube were avoided by conducting the c a l i b r a t i o n of the tr a n s d u c e r with the same length of tubing as was used in the actual experiment. 52 B I B L I O G R A P H Y 1. C r a b t r e e , L. F. 2. Neumark, S. 3. Lanchester, F. W. 4. D e n H a r t o g , J. P. "The Rotating F l a p as a H i g h - L i f t Device", A e r o n a u t i c a l R e s e a r c h C o u n c i l T e c h n i c a l Report C u r r e n t P a p e r No. 480, I960. "Rotating A i r f o i l s and-Flaps", J o u r n a l of The R o y a l A e r o n a u t i c a l Society, January, 1963 pp. 47-,61. "Aerodynamics", Constable, London, 1907, pp. 43-45. " M e c h a n i c a l V i b r a t i o n s " , M c G r a w - H i l l , New York, 1956, pp. 299-305. 5. P a r k i n s o n , G. V. "On the P e r f o r m a n c e of Lanchester's ' A e r i a l T o u r b i l l i o n ' " , National P h y s i c a l L a b o r a t o r y A e r o Report 1069, August, 1963. . 6. James, D. B. Stone, J. W. 7. B a i r d , H. Pick, R. "The C h a r a c t e r i s t i c s of T h i n Wings Autorotating about a Spanwise A x i s " , Department of A e r o n a u t i c a l Engineering, U n i v e r s i t y of B r i s t o l , Undergraduate Report No. 63, June, 1961. "Autorotation of F l a t P l a t e s " , Senior Y e a r P r o j e c t Report, Department of M e c h a n i c a l Engineering, U n i v e r s i t y of B r i t i s h Columbia, A p r i l , 1964. 8.. Keefe, R. T. "An.Investigation of the F l u c t u a t i n g F o r c e s A c t i n g on a Stationary C i r c u l a r C y l i n d e r i n a Subsonic Stream, and of the A s s o c i a t e d Sound F i e l d " , . U n i v e r s i t y of Toronto, Institute of A e r o p h y s i c s Report No. 76, September, 1961. 9- Cowdrey, C. F. "A Note on the Use o f E n d Plates to P r e v e n t T h r e e - D i m e n s i o n a l Flow at the Ends of B l u f f C y l i n d e r s " , National P h y s i c a l L a b o r a t o r y Report 1025, June, 1962. 10. P h i l c o T e c h n o l o g i c a l Center " S e r v o m e c h a n i s m Fundamentals and- E x p e r i -ments", P r e n t i c e - H a l l , New J e r s e y , 1964. 53 11. Ferguson, N. "The Measurement of Wake and Surface E f f e c t s in the S u b c r i t i c a l F l o w P a s t a C i r c u l a r C y l i n d e r at r e s t and in V o r t e x - e x c i t e d O s c i l l a t i o n 1 M.A.Sc Thes i s , U n i v e r s i t y of B r i t i s h Columbia, September, 1965. 12. Liepmann, H. W. "Elements of Gas Dynamics", Wiley, 1957 Chap. 3. 13. Santosham, T. V. " F o r c e Measurements on B l u f f C y l i n d e r s and A e r o e l a s t i c Galloping of a Rectangular C y l i n d e r " M.A.Sc. Th e s i s , U n i v e r s i t y of B r i t i s h Columbia, F e b r u a r y , 1966. 54 C L O S E - U P O F M O D E L , S U P P O R T I N G S Y S T E M , A N D E N D P L A T E S I N S I D E T H E T U N N E L F i g . 1 T u r n i n g Vanes T h i r d D i f f u s e r F o u r t h D i f f u s e r in A E R O D Y N A M I C O U T L I N E O F W I N D T U N N E L F i g . 2 U N F I N I S H E D M O D E L F i g . 3 4" T a p N o . 1 2 3 4 5 6 7 8 9 10 11 12 13 D i s t a n c e f r o m C e n t e r T a p ( in) 1 . 1 1 / 1 6 1 7 / 1 6 1 1 / 8 •3/4 1 /2 1 / 4 0 1 / 4 1 /2 3 / 4 . 1 1 / 8 1 7 / 1 6 1 1 1 / 1 6 P R E S S U R E T A P P O S I T I O N S F O R M O D E L A T D E F I N E D Z E R O A N G U L A R D I S P L A C E M E N T F i g . 4 58 F I N I S H E D M O D E L F i g . 5 F i g . 6 U P P E R A U T O R O T A T I O N S T A N D A N D A N G U L A R D I S P L A C E M E N T T R A N S D U C E R 6 0 F ig . 7 L O W E R A U T O R O T A T I O N S T A N D A N D P R E S S U R E S E A L U N I T 61 1. T u n n e l F l a n g e 2. B e a r i n g B l o c k 3. M o d e l S p i n d l e 4. P l e x i g l a s T u b e C o n n e c t i o n 5. L o c k i n g N u t 6. C y l i n d r i c a l C o u p l i n g 7. S e m i - a n n u l a r S p a c e r 8. S t a t i o n a r y E l e m e n t o f t h e P r e s s u r e S e a l U n i t L O W E R A U T O R O T A T I O N S T A N D F i g . 8 62 1. M o d e l 2. C y l i n d r i c a l C o u p l i n g 3. L o c k i n g N u t 4 . B e a r i n g B l o c k V . S W I T C H I N G O F P R E S S U R E T U B E C O N N E C T I O N F i g . 9 M O D E L A N D I T S S U P P O R T I N G S Y S T E M L O O K I N G D O W N S T R E A M I N T O W I N D T U N N E L T E S T S E C T I O N F i g . 10 64 S U P P O R T A N D A D J U S T I N G A R R A N G E M E N T O F E N D P L A T E S T R U T F i g . 11 F i g . 12 E N D P L A T E W i n d i n g s ( R o t o r ) i E L E C T R I C A L C I R C U I T O F A N G U L A R D I S P L A C E M E N T T R A N S D U C E R F i g . 13 67 . S t a t o r 2. R o t o r a n d S l i p R i n g s 3. B r u s h e s a . C o m p o n e n t s § 5* »o -a > 4 1 i * y b . A s s e m b l y A N G U L A R D I S P L A C E M E N T T R A N S D U C E R F i g . 14 H E A T H K I T A U D I O G E N E R A T O R 1 G - 7 2 H E W L E T T P A C K A R D L O W F R E Q U E N C Y F U N C T I O N G E N E R A T O R . A N G U L A R D I S P L A C E M E N T J ^ R A N S D U C E ^ O S P E E D C O N T R O L B O X v./ H O N E Y W E L L V I S I C O R D E R ° 9 0 6 C — o D I R E C T C U R R E N T M O T O R C A L I B R A T I O N E Q U I P M E N T O F A N G U L A R D I S P L A C E M E N T T R A N S D U C E R F i g . 15 S P E E D C O N T R O L B O X F i g . 16 70 C I R C U I T O F T H E S P E E D C O N T R O L B O X O F A D C M O T O R A R R O W A IS C O A R S E C O N T R O L . A R R O W B IS F I N E C O N T R O L F i g . 17 71 1. M o t o r 2. F l y w h e e l 3. 3 6 0 ° P r o t r a c t o r 4 . H o r i z o n t a l A n g l e I n d i c a t o r 5. A n g u l a r D i s p l a c e m e n t T r a n s d u c e r A S S E M B L Y O F T H E S T A T I C C A L I B R A T I O N O F A N G U L A R D I S P L A C E M E N T T R A N S D U C E R F i g . 18 1 . F u n c t i o n G e n e r a t o r 2 . V i s i c o r d e r O s c i l l o g r a p h 3 . R e m o t e C o n t r o l S w i t c h 4 . S t r o b o s c o p e 5. T r a n s d u c e r 6 . A u d i o G e n e r a t o r 7 . M o t o r 8 . S p e e d C o n t r o l B o x 9 . S t o r a g e O s c i l l o s c o p e A N G U L A R D I S P L A C E M E N T T R A N S D U C E R C A L I B R A T I O N E Q U I P M E N T F i g . 19 [NJ a n d M e t e r L D R - L i g h t D e p e n d e n t R e s i s t a n c e a . B R I D G E C I R C U I T F i g . 20 L o w F r e q u e n c y F u n c t i o n G e n e r a t o r H e w l e t t P a c k a r d M o d e l 2 0 2 A V i b r a t i o n G e n e r a t o r G o o d m a n s M o d e l V 4 7 P o l y e t h y l e n e T u b e P r e s s u r e T r a n s d u c e B r i d g e A m p l i f i e r a n d M e t e r E l l i s A s s o c i a t e s B A M - 1 C . R . O . T e k t r o n i x N o . 5 0 2 A D I A G R A M M A T I C L A Y O U T O F P R E S S U R E T R A N S D U C E R C A L I B R A T I O N A P P A R A T U S F i g . 21 75 + 12v $ 390-& | 25-f t 2WS30 IMT^I. fs\^ F u n c t i o n G e n e r a t o r 12v 1 2 0 - ^ 5 i l 2 N 3 0 5 4 F u s e F u s e V i b r a t i o n j G e n e r a t o r ' 2 N 3 6 1 5 > C I R C U I T O F P O W E R A M P L I F I E R F i g . 22 \ 76 L O W F R E Q U E N C Y P O W E R A M P L I F I E R F i g . 23 1. P r e s s u r e S e a l U n i t ( i n p u t ) 2 . R e v o l v i n g E l e m e n t o f P r e s s u r e S e a l 3 . B a l l B e a r i n g B l o c k s 4 . P u l l e y a n d R u b b e r B e l t 5 . P r e s s u r e S e a l U n i t ( o u t p u t ) P R E S S U R E S E A L T E S T E Q U I P M E N T F i g . 2 4 1. F u n c t i o n G e n e r a t o r 2. A m p l i f i e r 3. V i b r a t i o n G e n e r a t o r a n d P i s t o n 4 . P r e s s u r e S e a l U n i t s 5. P r e s s u r e T r a n s d u c e r 6. B A M - 1 7 . S t o r a g e O s c i l l o s c o p e 8 . M o t o r 9- S p e e d C o n t r o l B o x C A L I B R A T I O N A P P A R A T U S O F T H E P R E S S U R E S E A L U N I T F i g . 2 5 00 C A L I B R A T I O N O F T H E A C T U A L W I N D V E L O C I T Y B E T W E E N T H E E N D P L A T E S F i g . 26 80 c .2 V) c Q 5 4 3 2 / O -2--3--4 -5 --6 H o w Direction -12 -lo - 8 - 6 - 4 Longi-rudinal -2 o 2 Dimension (In) V E L O C I T Y P R O F I L E F O R 25 C H A M F E R E D E N D P L A T E S A L O N G T H E M O D E L A X I S F i g . 27 O 2D AO 60 g o IOO J20 140 160 /SO M E C H A N I C A L I N P U T A N G L E ( D E G R E E S ) A N G U L A R D I S P L A C E M E N T T R A N S D U C E R C A L I B R A T I O N D A T A Fig . 29 oo 84 350f 300 2SC a. cs c cn ^ 150 V O ^ 100 Q II IO 9 -it / ' /2 8 7 / y / / \ /// / M ibevs or\ c [oenci es urves ore iirv C p s i / i 50 • 00/ .002 .003 .004 .005 .006 .007 F i g . 30 6 8 / O Frequency (cps) T R A N S D U C E R C A L I B R A T I O N D A T A F O R U S E W I T H A T U B E 4 . 0 F T L O N G , 0. 066 - I N C H D I A M E T E R 14 85 i l l i J i l l lU f I l l i l l l J I l l l i liUiiiii iij mi MilJiMlllllllllililllll P r e s s u r e S i g n a l at the Output E n d of a Static P r e s s u r e S e a l P i s t o n D i s p l a c e m e n t iiiiiiueiuiiiiHiiiiiiiiiiiiiiiiiilil u u i l i l l i l i i t l i i l Liiliulii P r e s s u r e S i g n a l at the Output E n d of a D y n a m i c P r e s s u r e S e a l at 10 c. p . s. P i s t o n D i s p l a c e m e n t f • i'fliRNWMillllllllill t l i i i it- ft 11J i I IK urn mm ;|j||||||li||||!l||||||ff||||||| nil iiti !iiiiiiijjiiiiiiiiii,iiitiiiii P r e s s u r e S i g n a l at the Output E n d of the S a m e D y n a m i c P r e s s u r e Seal at 20 c. p . s. P i s t o n D i s p l a c e m e n t C A L I B R A T I O N D A T A O F P R E S S U R E S E A L U N I T S F i g . 31 S A M P L E E X P E R I M E N T A L R E C O R D O F T H E K I N E M A T I C M E A S U R E M E N T S F i g . 32 oo T I P S P E E D v s W I N D S P E E D F i g . 34 F i g . 3f. I N S T A N T A N E O U S A N G U L A R V E L O C I T Y D U R I N G A C C E L E R A T I O N ( m e a s u r e m e n t w i t h o u t e n d p l a t e s ) B U I L D - U P TIME vs WIND S P E E D F ig . 37 / -Locus of. initial Q.n§ ulocr ye/oc frfes < U= 37-5 f PS \ \ \ \ 2t>3 f PS K \ \ _ fS.Q fps o-25 a.So oTfS Dimensionkss Anju/ar Velocity ^/^auto l.oo A N G U L A R A C C E L E R A T I O N v s D I M E N S I O N L E S S A N G U L A R V E L O C I T Y ( w i t h e n d p l a t e s ) F i g . 38 93 T i m e B a s e . 5s / d i v A m p l i t u d e . 5 v / d i v T i m e B a s e . 2 s / d i v A m p l i t u d e . 5 v / d i v a . T r a n s i e n t b u i l d - u p ( T a p N o . 8) T Y P I C A L O S C I L L O S C O P E T R A C E S O F F L U C T U A T I N G P R E S S U R E M E A S U R E M E N T S F i g . 39 94 T i m e B a s e . 1 s /div A m p l i t u d e . 5 v / d i v RIIHnlHitilll mm mwmm IBIII1 T i m e B a s e . 1 s /div A m p l i t u d e . 5v / d i v b . T r a n s i e n t b u i l d - u p ( T a p N o . 8) T Y P I C A L , O S C I L L O S C O P E T R A C E S O F F L U C T U A T I N G P R E S S U R E M E A S U R E M E N T S F i g . 39 T i m e B a s e 50 m s / d i v A m p l i t u d e . 5 v / d i v • • • • • H i b . T a p N o 13 ( d u r i n g s t e a d y s t a t e r o t a t i o n ) T Y P I C A L O S C I L L O S C O P E T R A C E S O F F L U C T U A T I N G P R E S S U R E M E A S U R E M E N T S F i g . 39 • 9 6 T Y P I C A L O S C I L L O S C O P E T R A C E S O F F L U C T U A T I N G P R E S S U R E M E A S U R E M E N T S F i g . 39 97 T a p # 13 T i m e B a s e 20 m s / d i v A m p l i t u d e .. l v / d i v T a p # 3 T i m e B a s e 20 m s / d i v A m p l i t u d e , l v / d i v e. P r e s s u r e S i g n a l d u e to t u b e e f f e c t T Y P I C A L O S C I L L O S C O P E T R A C E S O F F L U C T U A T I N G P R E S S U R E M E A S U R E M E N T S F i g . 39 98 T i m e B a s e . 2 s / d i v A m p l i t u d e . 5 y / d i v f. U n s u c c e s s f u l b u i l d - u p ( T a p N o . 8) T Y P I C A L O S C I L L O S C O P E T R A C E S O F F L U C T U A T I N G P R E S S U R E M E A S U R E M E N T S F i g . 39 F ig . 14.0 a. PRESSURE COEFFICIENT vs ANGULAR POSITION FOR INDIVIDUAL TAPS F i g . 40 b . P R E S S U R E C O E F F I C I E N T v s A N G U L A R P O S I T I O N F O R I N D I V I D U A L T A P S o o 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0093570/manifest

Comment

Related Items