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Studies on physical properties of egg shells Tung, Marvin Arthur 1967

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STUDIES ON PHYSICAL PROPERTIES OF EGG SHELLS by MARVIN ARTHUR TUNG B . S . A . , U n i v e r s i t y o f B r i t i s h Co lumb ia , i960 A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE I N AGRICULTURE I n t h e Depar tment o f A g r i c u l t u r a l Mechanics We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree a t the 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 , I ag ree t h a t the- L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d v/i t h o u t my w r i t t e n permi s s i o n , D e p a r t m e n t o f A g r i c u l t u r a l Mechanics The 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 V a n c o u v e r 8, Canada D a t e A p r i l , 1967 i i ABSTRACT Physical c h a r a c t e r i s t i c s of egg she l l s and t h e i r relationships to s h e l l strength were studied In 2,733 eggs collected over thirty-two weeks from a f l o c k of. s i x t y Single-Comb White Leghorn p u l l e t s . S h ell strength under q u a s i - s t a t i c loading was measured as maximum force at f a i l u r e and as energy absorbed at f a i l u r e when load was applied at the equator of the egg. Area under the force-deformation curve was taken as energy absorbed by the s h e l l up to f a i l u r e and the slope of the curve as s h e l l s t i f f n e s s . Egg size was measured as egg weight, width and length. Shell weight, thickness at the equator, percent egg as s h e l l , and s h e l l weight per unit surface area were studied as measures of s h e l l quantity. Shape index, roundness, and three concepts of sphericity were used to describe egg shape. Hardness i n r a d i a l sections of ^ 25 s h e l l s was tested with a micro-indentation technique. Variation i n hardness across the thickness of egg she l l s was examined i n r a d i a l and tangential sections of nine s h e l l s . Force at f a i l u r e as a measure of s h e l l strength showed high multiple correlations with combinations of physical properties, whereas energy absorbed at f a i l u r e had r e l a t i v e l y small multiple correlations with physical c h a r a c t e r i s t i c s . Shell s t i f f n e s s was found to be the most Important i l l i n d i r e c t measure of s h e l l strength along with le s s e r effects of egg weight, s h e l l width, shape index, and hardness. Shell quantity c h a r a c t e r i s t i c s , along with egg size and shape, were shown by means of theore t i c a l and s t a t i s t i c a l analyses to be l a r g e l y responsible f o r s h e l l s t i f f n e s s . Shape index proved to be the most sati s f a c t o r y meas-ure of egg shape with respect to reducing residual variance of force at f a i l u r e a f t e r s t i f f n e s s was considered and was Judged to be the most accurate of the shape measurements studied. Shell hardness was found to vary i n a parabolic man-ner across the s h e l l thickness, reaching minimum values near the midpoint of the s h e l l . Comparable hardness gradients were observed i n both r a d i a l and tangential s h e l l sections. No appreciable change i n hardness or I t s gradient resulted from removal of s h e l l membranes with sodium hydroxide solution. The proportions of v a r i a t i o n i n force at f a i l u r e ex-plained by the non-destructive variables s h e l l s t i f f n e s s , egg s i z e , and shape were 60.5, 77.7, and 86.3 percent i n pooled-egg, bi r d average per period, and o v e r a l l b i r d average analyses respectively. i v TABLE OF CONTENTS Page INTRODUCTION 1 REVIEW OF THE LITERATURE 2 EXPERIMENTAL METHODS 6 Sampling Procedures 6 Egg and Shell Physical Properties 6 Egg Size 6 Egg Shape 6 Shell Strength 10 Shell Quantity 13 Shell Hardness 14 Tests of.Radial Sections 14 Tests of Tangential Sections 1? A n a l y t i c a l Procedures 20 RESULTS AND DISCUSSION 21 Egg and Shell Physical Properties 21 Shell Strength 21 Shell S t i f f n e s s 23 Egg Size 27 Egg Shape 27 Shell Quantity 29 Shell Hardness 30 Page Importance to Shell Strength 30 Hardness Gradient 31 Non-Destructive Estimation of Shell Strength 38 SUMMARY 39 LIST OF REFERENCES 41 APPENDIX A 44 APPENDIX B 5^ APPENDIX C 6? v i LIST OF TABLES Table Page 1 Coefficients of Multiple Determination (x 1 0 0 ) f o r Regression of a l l Shell Properties on Shell Strength Expressed as Force and Energy at F a i l u r e . Group 1 , 22 2 Simple Correlations of Shell S t i f f n e s s with Shell Quantity Measurements. Group 1 24 3 Coefficients of Multiple Determination (x 1 0 0 ) f o r Regressions of Shell Quantity, Egg Size, and Shape on S t i f f n e s s . Group 1 . 25 4 Percent Reduction In Residual Variance by Adding Egg Shape Measurements to the Regression of S t i f f n e s s on Force at Fail u r e . Group 1 28 5 Comparison of Non-Destructive Shell Properties with a l l Shell Measurements i n Regression on Force at Failure. Group 1 38 A l Testing Periods and Sample Size k$ A2 Eggs Tested by Bi r d and Period k6 A3 Means and Standard Deviations. Group 1 4-9 Ak Means and Standard Deviations. Group 2 50 A5 Means and Standard Deviations by Period 5 1 v i i T a b l e Page B I S imp le C o r r e l a t i o n C o e f f i c i e n t s . Group 1. Poo led -Egg B a s i s 55 B2 S imp le C o r r e l a t i o n C o e f f i c i e n t s . Group 1. B i r d Average Per P e r i o d B a s i s 56 B3 S imp le C o r r e l a t i o n C o e f f i c i e n t s . Group 1. O v e r a l l B i r d Average B a s i s 57 B4 S imp le C o r r e l a t i o n C o e f f i c i e n t s . Group 2. P o o l e d - E g g B a s i s 58 B5 S imp le C o r r e l a t i o n C o e f f i c i e n t s . Group 2. B i r d Average Per P e r i o d B a s i s 59 B6 S imp le C o r r e l a t i o n s Between Load and S e l e c t e d V a r i a b l e s Por Each T e s t P e r i o d 60 B7 Squares o f S imple and P a r t i a l C o r r e l a t i o n s Between Load and S e l e c t e d V a r i a b l e s . Group 1 6 l B8 Squares o f S imp le and P a r t i a l C o r r e l a t i o n s Between Energy and S e l e c t e d V a r i a b l e s . Group 1 62 B9 Squares o f S imp le and P a r t i a l C o r r e l a t i o n s Between S t i f f n e s s and S e l e c t e d V a r i a b l e s . Group 1 63 viil Table Page BIO Squares of Simple and P a r t i a l Correlations Between Load and Selected Variables. Group 2 64 B l l Squares of Simple and P a r t i a l Correlations Between Energy and Selected Variables. Group 2 65 B12 Squares of Simple and P a r t i a l Correlations Between Stif f n e s s and Selected Variables. Group 2 66 Cl Stepwise Multiple Regression With Load as the Dependent Variable. Group 1. Pooled-Egg Basis 68 C2 Stepwise Multiple Regression With Energy as the Dependent Variable. Group 1. Pooled-Egg Basis 69 C3 Stepwise Multiple Regression With S t i f f n e s s as the Dependent Variable. Group 1. Pooled-Egg Basis 70 C4 Stepwise Multiple Regression With Load as the Dependent Variable. Group 1. Bird Average per Period Basis 71 i x Table Page C5 Stepwise Multiple Regression With Energy as the Dependent Variable. Group 1 . B i r d Average Per Period Basis 7 2 C6 Stepwise Multiple Regression With S t i f f n e s s as the Dependent Variable. Group 1 . B i r d Average Per Period Basis 7 3 C 7 Stepwise Multiple Regression With Load as the Dependent Variable. Group 1 . Overall B i r d Average Basis 7 4 C8 Stepwise Multiple Regression With Energy as the Dependent Variable. Group 1 . Overall B i r d Average Basis 7 5 Q9 Stepwise Multiple Regression With S t i f f n e s s as the Dependent Variable. Group 1 . Overall Bird Average Basis 7 6 CIO Stepwise Multiple Regression With Load as the Dependent Variable. Group 2 . Pooled-Egg Basis 7 7 C l l Stepwise Multiple Regression With Energy as the Dependent Variable. Group 2 . Pooled-Egg Basis 7 8 X Table Page C12 Stepwise Multiple Regression with Stiffness as the Dependent Variable. Group 2. Pooled-Egg Basis 79 C13 Stepwise Multiple Regression With Load as the Dependent Variable. Group 2. Bird Average Per Period Basis 80 Cl4 Stepwise Multiple Regression with Energy as the Dependent Variable. Group 2. B i r d Average Per Period Basis 81 C15 Stepwise Multiple Regression With S t i f f n e s s as the Dependent Variable. Group 2. Bird Average Per Period Basis 82 Cl6 Selected Non-Destructive Characteristics i n Multiple Regression on Load. Group 1. Pooled-Egg Basis 83 C17 Selected Non-Destructive Characteristics i n Multiple Regression on Load. Group 1. B i r d Average Per Period Basis 84 C18 Selected Non-Destructive Characteristics i n Multiple Regression on Load. Group 1. Overall Bird Average Basis 85 Selected Non-Destructive Characteristics i n Multiple Regression on Load f o r Each Test Period LIST OF FIGURES Figure 1. Shadow Photography Method 2. Bellows V a l v a i r Hydrocheck Compression Unit 3. Bellows V a l v a i r Hydrocheck Compression Unit Showing Load C e l l (A) and L.V.D.T. (B) 4. Typical Force-Deformation Curves f o r Egg Shells 5. Tukon Micro-Indentation Hardness Tester 6. Shells Mounted i n Epoxy f o r Hardness Testing A - Radial Tests, B - Tangential Tests, (Mag. x 2) 7 . Photomicrograph of a Radial Section of Egg Shell Showing Indentation at Shell Level .25 (Mag. x 210) 8. Schematic Diagram of an Egg Shell i n the Plane of i t s Equator 9. Hardness Gradient of Shell No. 19a. Tests Made on a Tangential Section 10. Average Hardness Gradient of Shells of Birds No. 5, 9, 19. Tests Made on Tangential Sections Figure 11. Comparison of Radial (upper) (lower) Hardness Gradients b, c. 12. Comparison of Radial (upper) (lower) Hardness Gradients Birds No. 5. 9, 19. z i i i Page and Tangential of Shells 19a, .. 35 and Tangential of Shells of 36 13. Photomicrograph of a Radial Section of Egg Shell Showing Indentations at Shell Levels .25 (A), and .75 (B). (Mag. x 210). 37 x i v LIST OF ABBREVIATIONS AND DEFINITIONS D.P.H., Diamond pyramid hardness. - Load p e r u n i t a r e a o f s u r f a c e c o n t a c t i n kgm./sq.mm. Eggwt, Egg we i g h t . - F r e s h w e i g h t o f t h e egg I n gm. Energy, Energy absorbed a t f a i l u r e . - Amount o f energy absorbed by t h e egg on b e i n g c r u s h e d c a l c u l a t e d as th e a r e a under t h e f o r c e - d e f o r m a t i o n c u r v e i n gm.-cm. Len g t h , Egg l e n g t h i n cm. Load, F o r c e a t f a i l u r e . - The f o r c e i n grams a p p l i e d t o the eq u a t o r of t h e egg t h a t r e s u l t s i n s h e l l f a i l u r e , i n gm. Mgmcm2,, S h e l l w e i g h t p e r u n i t s u r f a c e a r e a - i n mgm./sq.cm. P e r s h , P e r c e n t s h e l l . - The r a t i o o f s h e l l w e i g h t t o f r e s h egg w e i g h t i n p e r c e n t . P o l s s o n ' s R a t i o - The r a t i o o f u n i t l a t e r a l c o n t r a c t i o n t o u n i t l o n g i t u d i n a l e x t e n s i o n f o r a s o l i d m a t e r i a l . P r a s p h , P r a c t i c a l s p h e r i c i t y . - The r a t i o formed by d i v i d i n g t h e d i a m e t e r o f a c i r c l e e q u a l i n a r e a t o t h e p r o -j e c t e d a r e a o f a p a r t i c l e by t h e d i a m e t e r of t h e s m a l l e s t c i r c u m s c r i b i n g c i r c l e , i n p e r c e n t . XV P3dsph, P r a c t i c a l three-dimensional sphericity. - The r a t i o formed by d i v i d i n g the diameter of a sphere of volume equal to that of the p a r t i c l e by the diameter of the smallest circumscribing sphere, i n percent. Quasi-Static Loading - The ap p l i c a t i o n of force to a specimen at r e l a t i v e l y low rates. Round, Roundness. - The maximum projected area of the egg divided by the area of the smallest circumscribing c i r c l e , i n percent. Shell Level - P o s i t i o n across the thickness of the egg s h e l l from the outer edge as a f r a c t i o n of s h e l l thickness at that location. Shelw.t, Shell weight. - Weight of the dried s h e l l without membranes, i n gm. Shindx, Shape index. - The r a t i o formed by d i v i d i n g egg width by egg length, i n percent. S t i f f , Shell s t i f f n e s s . - The r a t i o formed by d i v i d i n g force applied to the s h e l l by deformation i n the d i r e c t i o n of applied force, i n gm./micron. Thick, Shell thickness. - Thickness of the s h e l l taken at the egg's equator, i n microns. z v i Totdef, Total deformation. - The ov e r a l l dimensional change In the d i r e c t i o n of applied force, In microns. Trusph, True sphericity. - The r a t i o formed by d i v i d i n g the surface area of a sphere of volume equal to that of the p a r t i c l e by the surface area of the p a r t i c l e , i n percent. Width, Egg width. - The diameter of the egg at i t s equator, i n cm. Young's Modulus - The proportionality constant between stress and s t r a i n i n an e l a s t i c material. x v l i ACKNOWLEDGEMENTS The write r wishes to express his appreciation f o r assistance i n t h i s study bys Professor L.M. Staley who directed t h i s research, provided encouragement, and advice, Dr. J.F. Richards, Department of Poultry Science, f o r counsel on aspects of egg s h e l l strength and the supply of some materials and f a c i l i t i e s , Dr. C.W. Roberts and Professor E.L. Watson f o r serving on the research committee and reviewing t h i s paper, Dr. E. Teghtsoonlan and the Department of Metallurgy f o r advice and f a c i l i t i e s i n the study of hardness, Mr. M. Hudson, foreman, and other s t a f f members of the Poultry Farm who collected and recorded eggs used i n t h i s study, Mr. W. Gleave f o r suggestions which led to construction of shadow photography equipment. INTRODUCTION The proportion of cracked eggs reported by registered grading stations i n Canada has increased by 140 percent since 1953 according to the Poultry Market Review (1964. and 1965). Cray (1953) found that grading stations detected only about 48 percent of a l l eggs cracked up to the time of grading because the remaining 52 percent were removed on the 'farm. Assuming comparable breakage i n fl o c k s whose eggs were not shipped to grading stations and a decrement of 10 cents per dozen, weak shel l s cost the Canadian egg industry approximately 4.2 m i l l i o n d o l l a r s i n 1 9 6 5 . In B.C., where Raffa ( 1 9 6 7) estimates.that 65 percent of a l l eggs pass through registered grading stations, the loss was about 5 9 0 thousand d o l l a r s i n 1 9 6 5 . Cracked eggs have been shown by Brown et a l . ( 1 9 6 6 ) to be more susceptible to b a c t e r i a l spoilage than sound eggs under c e r t a i n adverse conditions, thereby presenting a potential health hazard. Reduction of damage to egg s h e l l s i n mechanical hand-l i n g requires a knowledge of stress l e v e l s which r e s u l t i n s h e l l f a i l u r e . Overall improvement of egg s h e l l strength by either genetic or n u t r i t i o n a l means i s contingent upon selec-t i o n of an appropriate measure of s h e l l strength and i d e n t i f i -cation of s h e l l c h a r a c t e r i s t i c s that contribute to i t s strength. This study was designed to examine a number of physical and mechanical properties of egg s h e l l s and t h e i r influence on two measures of egg s h e l l strength. 2 REVIEW OF THE LITERATURE Early studies on egg s h e l l strength have been reviewed by Tyler (196l). The concept of strength has been described as resistance of the s h e l l to crushing, Impact and puncturing. Rehkugler (1964) studied Impact strength of sh e l l s using various types of cushioning materials. He observed that s h e l l s have a greater capacity to absorb energy under Impact loading than s t a t i c loading. Sluka et a l . (1965) reported the development of an hydrostatic s h e l l strength tester that i s claimed to simulate dynamic situations involving, impact decel-eration of the egg. In a l a t e r paper, Sluka et a l . (1966) presented an analysis of s h e l l stresses under Impact decelera-t i o n which was used to calculate ultimate s h e l l stress. Voisey and Hunt (1967c)described a device used f o r measuring the maxi-mum force imposed on egg s h e l l s by the impact of a f a l l i n g steel rod. In general, resistance of...the s h e l l to crushing i s measured by qu a s i - s t a t i c loading of the s h e l l between two sur-faces. Brooks and Hale (1955) used load at f a i l u r e and also load at f a i l u r e divided by s h e l l thickness as measures of re-sistance to crushing. Presumably the l a t t e r concept was an attempt to evaluate the i n t r i n s i c strength of the s h e l l mate-r i a l by correcting f o r variations i n s h e l l thickness. Rehkug-l e r (1964) introduced the degree of energy absorption by the egg under q u a s i - s t a t i c loading as a measure of s h e l l strength. Energy absorbed by the s h e l l was taken as the area under the 3 l o a d - d e f o r m a t i o n c u r v e up t o t h e p o i n t o f f a i l u r e . S c h o o r l and Boersma (1962) sugges ted t h e use o f s h e l l d e f o r m a t i o n caused by a g i v e n l o a d as a n i n d e x o f s t r e n g t h because s h e l l t h i c k n e s s and p e r c e n t a g e s h e l l a r e more h i g h l y c o r r e l a t e d w i t h d e f o r m a t i o n t h a n b r e a k i n g s t r e n g t h . Hunt and V o i s e y (1966) and R i c h a r d s and S t a l e y (1967) have used maximum f o r c e a t f a i l u r e as a measure o f c r u s h i n g s t r e n g t h . S h e l l s t r e n g t h measurements by p u n c t u r i n g a r e d e -s c r i b e d by Lund e t al.(1938), N o v l k o f f and G u t t e r l d g e (19^9), and T y l e r ( I 9 6 I ) . The ma in advan tage o f p u n c t u r i n g methods i s t h a t s e v e r a l measurements may be made on a s i n g l e egg. Romanoff (19^9), Brooks and Ha le (1955), B rooks (1958). and G a i s f o r d (1965) r e p o r t e d no s i g n i f i c a n t c o r r e l a t i o n be tween egg s i z e and c r u s h i n g s t r e n g t h . I n a s t u d y o f o v e r 300 eggs, S t e w a r t (1936) f o u n d a h i g h l y s i g n i f i c a n t c o r r e l a t i o n ( r = +.260) be tween egg w e i g h t and c r u s h i n g s t r e n g t h . R i c h a r d s and S t a l e y (1967) r e p o r t e d a s m a l l b u t s i g n i f i c a n t s i m p l e c o r r e l a t i o n ( r = +.11, n = 531) be tween s h e l l s t r e n g t h and egg w e i g h t . Egg s i z e as measured by egg w i d t h and egg l e n g t h was shown t o be h i g h l y c o r r e l a t e d w i t h s h e l l s t r e n g t h i n t h e work o f R i c h a r d s and S t a l e y (1967). S h e l l q u a n t i t y measured as s h e l l w e i g h t , p e r c e n t egg as s h e l l , and s h e l l t h i c k n e s s have been shown t o be v e r y h i g h l y c o r r e l a t e d w i t h s h e l l s t r e n g t h by s e v e r a l worke rs , among whom, a r e S h u s t e r (1959), Hunt and V o i s e y (1966) and R i c h a r d s and S t a l e y (1967). An I n d i r e c t method u s i n g s p e c i f i c g r a v i t y o f 4 the whole egg as a measure of s h e l l quantity has been used by Novlkoff and Gutteridge ( 1 9 4 9 ) , Marks and Kinney ( 1 9 6 4 ) and Prank et a l . ( 1 9 6 4 ) . Tyler and Geake ( 1 9 6 1 ) and Hurwitz and Grimlnger ( 1 9 6 2 ) suggest the use of s h e l l weight per u n i t surface area as a more accurate measure of s h e l l quantity. Stewart ( 1 9 3 6 ) studied egg shape and curvature i n r e l a t i o n to s h e l l strength and found small but s i g n i f i c a n t cor-re l a t i o n s between strength and shape measurements. Frank et a l . ( 1 9 6 4 and 1 9 6 5 ) recognized the need to consider s h e l l geometry i n r e l a t i o n to strength. Richards and Swanson ( 1 9 6 5 ) reported egg shape expressed as shape index to be independent of s h e l l thickness and to account f o r 1 5 to 35 percent of the v a r i a b i l -i t y i n crushing strength a f t e r s h e l l thickness was considered. Hunt and Volsey ( 1 9 6 6 ) found egg shape to be the most important s h e l l strength predictor a f t e r s h e l l s t i f f n e s s was considered. Richards and Staley ( 1 9 6 7 ) point out that shape index, when ; included with deformation per unit load increased the c o e f f i -cient of determination of crushing strength by 1 5 and 20 per-cent i n t h e i r pooled-egg and b i r d average analyses respectively. Mechanical properties of egg s h e l l material were f i r s t studied with micro-Indentation hardness te s t i n g by Brooks. and Hale ( 1 9 5 5 ) . They reported the average hardness of ten strong s h e l l s to be s i g n i f i c a n t l y higher than that of ten weak .. s h e l l s . A gradient of hardness was found to exist across the thickness of the s h e l l which increased almost l i n e a r l y toward the outer edge. Rehkugler ( 1 9 6 3 ) developed a technique whereby 5 the modulus of e l a s t i c i t y and ultimate strength of s h e l l material were measured. The behavior of the egg s h e l l under qu a s i - s t a t i c loading has been studied by Brooks and Hale (1955)» Schoorl and Boersma ( 1 9 6 2 ) , Rehkugler ( 1 9 6 4 ) , Gaisford ( 1 9 6 5 ) , Hunt and Voisey ( 1 9 6 6 ) and Richards and Staley ( I 9 6 7 ) with simul-taneous measurement of applied load and resultant deformation of the s h e l l . Each of these investigators has observed that the load-deformation curve i s approximately l i n e a r and that the slope of the curve, or i t s Inverse, i s highly correlated with load at f a i l u r e . Richards and Staley point out the v a l i d i t y of c a l c u l a t i n g the slope of the curve d i r e c t l y as the r a t i o of maximum load and deformation. The l i t e r a t u r e reveals that several physical charac-t e r i s t i c s of the hen's egg s h e l l are important to i t s strength! however,, the roles, of egg si z e , egg shape and s h e l l hardness i n r e l a t i o n to other physical properties and to s h e l l strength are not well understood. This investigation was designed to c l a r i f y r e l a t i o n s between egg size, egg shape, s h e l l quantity, s h e l l hardness measurements and s h e l l strength and to i n v e s t i -gate the f e a s i b i l i t y of non-destructive evaluation of egg s h e l l strength. 6 EXPERIMENTAL METHODS Sampling Procedures A t o t a l of 2 , 7 3 3 eggs were collected during the second and t h i r d weeks of eight four-week periods beginning January the second, 1 9 6 6 , from a f l o c k of s i x t y Single-Comb White Leghorn p u l l e t s i n t h e i r f i r s t year of production. The flo c k , which consisted of equal numbers of birds from the two resultant crosses of a reciprocal mating program, was fed a commercial r a t i o n containing four percent calcium. Individual wire cages allowed i d e n t i f i c a t i o n of eggs produced by each hen. For the purpose of analysis, Group One was made up of the entire sample of 2 , 7 3 3 eggs, whereas a subsample of 4 2 5 eggs from ten a r b i t r a r i l y selected birds of one cross was desig-nated as Group Two f o r the additional t e s t i n g of s h e l l hardness. Egg and Shell Physical Properties Egg Size Physical c h a r a c t e r i s t i c s representing egg size were assumed to be egg weight, width, and length. The fresh weight of each egg was measured to the nearest centigram a f t e r which egg width and length were determined with a pr e c i s i o n of + . 0 0 5 cm. using a vernier caliper. Egg Shape Shape index was calculated i n the usual manner as the quotient of egg width and length m u l t i p l i e d by one hundred. Roundness i n a plane p a r a l l e l to the major axis of Fig. 1 . Shadow Photography Method. the egg was measured with the aid of a shadow photograph taken as shown In Fig. 1 and the formulas Roundness = 127 A D 2 (1) where A = area of the shadow cast by the egg, and D = maximum diameter of the shadow. This formula defines roundness as one hundred times the maximum projected area of the egg divided by the area of the smallest circumscribing c i r c l e . A roundness of 1G0 i s approached as the shadow approaches c i r c u l a r i t y . Area of the shadow photograph was measured with a polar compensating planlmeter and shadow length with dividers and a scale to pre c i s i o n l i m i t s of + .01 8 square inch and + .01 inch respectively. The concepts of roundness and sphericity as applied to geology and petrography were c l a r i f i e d by Wadell (1933) from which three measures of sphericity were adapted f o r use i n t h i s study to describe egg shape. Wadell defined true sphericity ass l / j - s • • (2) S where s = surface area of a sphere of volume equal to that of the p a r t i c l e , and S = surface area of the p a r t i c l e . The formula of Tyler and Geake ( 1 9 6 l ) was used to represent the volume of an egg8 that i s , V = . 5 1 2 L B 2 - . 0 6 (3) 3 where V = volume of the egg i n cm.% L = egg length i n cm., and B = egg width i n cm. Por a sphere, surface area and volume are related by s = 4 . 836V 2 / 3 ( 4 ) where s = surface area In cm.2, and V = volume i n cm.30 By substitution of equation (3) In ( 4 ) , the surface area of a sphere with a volume equal to that of an egg was given by s = 4 . 8 3 6 ( . 5 1 2 L B 2 - . 0 6 ) 2 / 3 . ( 5 ) Surface area of the egg was taken from the formula of Mueller and Scott ( 1 9 ^ 0 ) , 9 S = 4 .67W 2 / 3 (6) 2 where S = surface area of the egg In cm. , and W = fresh weight of the egg i n gm., which gave true sphericity based on an index of one hundred as \jj = 100s = 483.6(.512LB2~.06) 2 / 3 . (7) S 4 . 6 7 W 2 / 3 That Is, True sphericity = 103.6^. 512LB 2-.06J 2 / / 3 (8) I t i s noteworthy that t h i s expression of egg shape was derived from three measures of egg slze--egg weight, width, and length. Wadell defined p r a c t i c a l sphericity as: d> = d (9) D where d = diameter of a c i r c l e equal i n area to the area of the p a r t i c l e projection, and D = diameter of the smallest c i r c l e circumscribing the p a r t i c l e . The r e l a t i o n of the diameter of a c i r c l e to i t s area, d = (l.Z7A)1/2, (10) was substituted into equation (9) which resulted i n Cjf> = ^ 1'27A j 1 / 2 (11) as the formula f o r p r a c t i c a l sphericity based on an index of one hundred. I t was noted that p r a c t i c a l sphericity was the square root of the roundness measurement previously discussed; therefore, p r a c t i c a l sphericity of each egg was calculated from 10 (Roundness ) 1 / / 2 (12) P r a c t i c a l three-dimensional sphericity was suggested by Wadell to be; y = d j _ (13) P' where d ? = diameter of the sphere of volume equal to that of the p a r t i c l e , D' = diameter of smallest circumscribing sphere. Using the r e l a t i o n , diameter = 1.24(volumeJ 1^ 3 , (14) f o r a sphere along with the formula of Tyler and Geake f o r the volume of an egg and substituting the length of the egg f o r D', the equation becomes; V = 124(.512LB 2 - . 0 6 ) 1 / 3 (15) L f o r the p r a c t i c a l three-dimensional sphericity of an egg. I t was noted that t h i s measure of egg shape was a function of egg width and length and was therefore s i m i l a r to shape index i n that respect. Shell Strength Two concepts of s h e l l strength under qu a s i - s t a t i c loading were studied--force at f a i l u r e , and energy absorbed up to f a i l u r e . The t e s t i n g machine (Figs. 2 and 3) was a Bellows Valvalr Hydrocheck Compression Unit i n which the piston was moved by compressed a i r at a rate controlled by hydraulic checking valves. This equipment was described i n d e t a i l by Mohsenin (1963). 11 Fig. 3. Bellows Valvair Hydrocheck Compression Unit Showing Load C e l l (A) and L.V..D.T. (B). 12 A force was applied to the egg p a r a l l e l to i t s minor axis by two f l a t brass plates. The lower plate was adjustable v e r t i c a l l y to accommodate eggs of varying size and was ridged near the outer edge to prevent eggs from r o l l i n g off the plate. Load applied to the egg was measured by supporting the lower plate on a s t r a i n gauge load c e l l and feeding the amplified signal to the pen drive (Y-axis) of the XY recorder. Deforma-t i o n of the egg while being crushed was measured by a l i n e a r variable d i f f e r e n t i a l transformer (L.V.D.T.) whose amplified signal was fed to the carriage drive (X-axis) of the XY record-er. S e n s i t i v i t i e s of 600 + 10 grams per inch on the Y-axls and 4 2 + 2 microns per inch on the X-axis were used and the deformation rate was controlled at 44 + 2 microns per second. Typical force-deformation curves f o r two dif f e r e n t eggs appear i n Fig. 4. The curves were l i n e a r , or nearly so, and the point of s h e l l fracture was indicated by the sharp peak on the graph. Four data were obtained from each graph: force at f a i l u r e (max. Y value), energy absorbed up to f a i l u r e (area under the curve up to the point of f a i l u r e ) , t o t a l deformation of the s h e l l (max. X value), and s h e l l s t i f f n e s s (slope of the curve). The graphs were analyzed quickly by means of a modi-f i e d d r a f t i n g set square to which scales were glued that allowed reading force and t o t a l deformation at f a i l u r e d i r e c t l y from the graph. Energy absorbed up to f a i l u r e was taken as one-half the product of maximum force and t o t a l deformation, and s h e l l s t i f f n e s s was calculated as the quotient of maximum force and t o t a l deformation. 13 3.0 2.4 E g 1.8 73 ft 0 1 2 .6 0 - — — •- — — l major division : 42 microns D e f o r m a t i o n Fig. 4. Typical Force-Deformation Curves for Egg Shells. Shell Quantity Shell weight, s h e l l thickness, percent egg as s h e l l , and s h e l l weight per unit surface area were used to express s h e l l quantity. A l i n e was drawn around each egg at i t s equa-tor a f t e r which the egg contents were discarded and the sh e l l s boiled i n . 6 2 5 Molar aqueous sodium hydroxide f o r ten minutes to remove s h e l l membranes and c u t i c l e . The s h e l l s were rinsed thoroughly i n tap water and dried i n an oven at 80°C. f o r 14 twenty-four hours. Dried s h e l l s were weighed to the nearest centigram, and s h e l l thickness to the nearest micron was taken as the average of three measurements at the equator using an anvil-jawed d i a l micrometer. Percent egg as s h e l l was calculated as the quotient of dried s h e l l weight and fresh egg weight expressed i n percent. Egg surface area was estimated using the formula of Mueller and Scott (Equation 6 ) . Shell weight was divided by egg surface area and converted to milligrams per square centimeter. Shell Hardness Tests of Radial Sections Hardness of s h e l l s produced by 10 birds was measured by a micro-indentation technique using the Tukon hardness tester shown i n Pig. 5. and described by Mott (1956). After the s h e l l membranes and c u t i c l e had been removed, a small s t r i p of s h e l l taken from near the equator of each egg was mounted i n epoxy r e s i n as shown In F i g . 6,A. Each test block contained sections of s h e l l from several eggs i n order to minimize the number of blocks made. The epoxy blocks were polished with a series of i n -creasingly f i n e emery papers and two aluminum oxide lapidary wheels to reveal a r a d i a l section of each s h e l l approximately i n the plane of the equator (see F i g . 7 ) . Diamond pyramid hardness was measured along a l i n e at one-quarter the thick-ness of the s h e l l from the outer edge ( s h e l l l e v e l .25) by Pig. 5. Tukon Micro-Indentation Hardness Tester. F i g . 6 . Shells Mounted i n Epoxy f o r Hardness Testing. A - Radial Tests. B - Tangential Tests. (Mag. x2 ) 16 Fig. 7. Photomicrograph of a Radial Section of Egg Shell Showing Indentation at Shell Level , 2 5 . (Mag. x 210) forcing a square-based diamond pyramid into the s h e l l and measuring the diagonals of the recovered indentations with an ocular micrometer on the Tukon tester. The diamond pyramid hardness i s defined as the load per unit area of surface con-tact i n kilograms per square millimeter calculated from the average diagonal length and the formula: D.P.H. = 1 . 8 5 4 4 L (16) d 2 where D.P.H. • diamond pyramid hardness L = load i n kilograms d - average diagonal length i n millimeters. The average of the diagonal lengths of s i x indentations was used to calculate the hardness of each s h e l l at i t s .25 s h e l l 17 l e v e l . A load of 1 0 0 grams on the lndenter was used and the . 2 5 s h e l l l e v e l was chosen because Brooks and Hale ( 1 9 5 5 ) re-ported greater differences i n hardness near the outer edge of the egg s h e l l . B r i t t l e n e s s of the s h e l l material precluded test i n g nearer the outer edge i n r a d i a l sections. Nine s h e l l s , produced by three d i f f e r e n t birds, were selected to measure the hardness across the s h e l l from l e v e l s . 2 5 to . 7 5 . Forty indentations per s h e l l were made at randomly selected s h e l l l e v e l s which were also recorded. The hardness data of each s h e l l were separated into s i x groups f o r which the average hardness and s h e l l l e v e l were calculated. These data were plotted i n order to Identify possible variations i n hardness across the s h e l l . Tests of Tangential Sections A method was developed whereby a tangential section of s h e l l could be exposed to allow t e s t i n g f o r hardness near the edges of the egg s h e l l . The major d i f f i c u l t y presented was that of loca t i n g positions of s h e l l l e v e l s on a tangential section as shown i n Fi g . 8. The p r i n c i p l e used was that of the inte r s e c t i o n of an arc (the s h e l l l e v e l ) and a chord (repre-senting, the exposed surface). Symbols used i n the derivation are; B = egg width at the equator, T = s h e l l thickness at the equator, C - chord length, P = distance along chord from either end, 18 Fig. 8. Schematic Diagram of an Egg Shell i n the Plane of i t s Equator. j = s h e l l l e v e l from outer edge (a decimal number).and x, y = coordinate directions. Intersection of the chord and the arcs w i l l be at points, P = C - x. 2 From the t r i a n g l e , ( V ) 2 B 2 - C 2 and f o r the arcs at various s h e l l l e v e l s x 2 + y 2 = 'B - JT! (17) (18) (19) At the intersections of the arcs with the chord, y = y and equation (18) may be substituted into equation (19) to give 19 x 2 + p£ - c£ = (B - j T l 2 (20) r r 12 j w h i c h may be s o l v e d f o r x. x = ( . 2 5 C 2 - jBT + j 2 T 2 ) 1 / 2 (21) and P = . 5C - ( . 2 5 c 2 - jBT + j 2 T 2 ) 1 / 2 (22) The u n i t s o f B and T were c e n t i m e t e r s and i n c h e s r e s p e c t i v e l y . The l e n g t h o f t h e ch o r d , C, was measured w i t h the M i c r o t o n s t a g e o f t h e Tukon t e s t e r i n u n i t s o f 10 m i c r o n s ; t h e r e f o r e a l l o t h e r u n i t s were c o n v e r t e d t o those o f the M i c r o t o n s t a g e t o g i v e t h e w o r k i n g e q u a t i o n : P - .50 - ( . 2 5 C 2 - 2 . 5 4 x 1 0 6 jBT + 6 . 4 5 2 x 1 0 6 j 2 T 2 ) 1 / 2 ( 2 3 ) A computer program was w r i t t e n t o c a l c u l a t e the t e s t l o c a t i o n P f o r v a r i o u s v a l u e s of j when C, B, and T were p r o v i d e d . The p r e c i s i o n e r r o r l i m i t s u s i n g t h i s method t o l o c a t e s h e l l l e v e l s on a t a n g e n t i a l s u r f a c e were e s t i m a t e d t o be + 1 . 2 p e r c e n t . Nine s h e l l s whose hardness g r a d i e n t s were measured I n r a d i a l s e c t i o n s were a l s o t e s t e d t a n g e n t l a l l y a t s h e l l l e v e l s . 0 2 , . 1 0 , . 2 0 , . . . . . 9 0 . A p i e c e o f s h e l l b e a r i n g a l i n e c o r r e s p o n d i n g t o t h e e q u a t o r o f t h e s h e l l was mounted i n an epoxy b l o c k such t h a t a t a n g e n t i a l s e c t i o n a t t h e e q u a t o r c o u l d be exposed from t h e o u t s i d e (see F i g . 6,B). Three i n d e n t a t i o n s were made a t each d e s i g n a t e d s h e l l l e v e l s t a r t i n g from one edge o f t h e exposed s e c t i o n a l o n g a narrow s t r i p on e i t h e r s i d e o f the e q u a t o r . A d u p l i c a t e s e t of i n d e n t a t i o n s was t h e n made s t a r t i n g a t the o p p o s i t e edge o f t h e exposed a r e a so t h a t t h e 20 average, of s i x indentations was used to calculate hardness at each s h e l l l e v e l . A f t e r tests were made from l e v e l . 0 2 to . 5 0 , the test block was cast i n epoxy so that the o r i g i n a l block could be ground away to expose a s i m i l a r s h e l l section from the inside on which l e v e l s . 5 0 to . 9 0 were tested. The duplicate t e s t i n g of l e v e l . 5 0 provided a t o t a l of twelve Indentations from which the hardness at that l e v e l was calculated, A test was conducted to determine whether the hard-ness gradient was affected by removing s h e l l membranes and c u t i c l e with b o i l i n g sodium hydroxide solution. Membranes were stripped mechanically from pieces of three s h e l l s that were then tested f o r hardness tangentially and compared with other samples of the same s h e l l s that had been treated with sodium hydroxide. A n a l y t i c a l Methods F a c i l i t i e s of the University of B r i t i s h Columbia Computing Center, which include an I.B.M. 7 0 4 0 d i g i t a l computer were used to calculate data derived from o r i g i n a l measurements and to analyze the r e s u l t s of t h i s study. Means, standard de-vi a t i o n s , simple and p a r t i a l correlations, simple and multiple l i n e a r regressions, and stepwise multiple regressions were calculated with a method s i m i l a r to that of Ralston and Wllf ( I 9 6 0 ) . Snedecor ( 1 9 5 6 ) and Ezeklel and Fox ( 1 9 5 9 ) were used as references In the Interpretation of s t a t i s t i c a l analyses. A p l o t t i n g program was also employed to f i t polynomial curves 21 by the method of least squares to the hardness gradient data. A l l eggs tested i n t h i s study formed Group One which was studied on a pooled basis with each egg contributing a set of variables to the analysis. Data of i n d i v i d u a l birds f o r each test period were then averaged and analyzed on a bird average per period basis. Overall averages were calculated f o r those birds having complete records over a l l eight test periods to form the basis of the third, analysis. Eggs tested for hard-ness constituted Group Two which was examined on both pooled-egg and b i r d average per period bases. RESULTS AND DISCUSSION Appendix A contains general sample data, means and standard deviations f o r a l l analyses. Results of simple and p a r t i a l c o r r e l a t i o n analyses appear i n Appendix B. Stepwise multiple regressions which successively eliminated n o n - s i g n i f i -cant independent variables were tabulated i n Appendix C along with selected multiple l i n e a r regressions using only non-de-structive s h e l l measurements i n r e l a t i o n to force at f a i l u r e . EKK and Shell Physical Properties Shell Strength The mean strength of eggs i n th i s study was 3557 + 578 grams when measured as force at f a i l u r e , and 27.5 + 6.1 gm.-cm. when taken as energy absorbed while being crushed by a quas i - s t a t i c force applied at the s h e l l equator. 22 V a r i a t i o n i n force at f a i l u r e was more completely accounted for by physical c h a r a c t e r i s t i c s of the s h e l l than was v a r i a t i o n i n energy absorbed at f a i l u r e . (Table 1 and Appendix C). TABLE 1 COEFFICIENTS OF MULTIPLE DETERMINATION (x.100) FOR REGRESSION OF ALL SHELL PROPERTIES ON SHELL STRENGTH EXPRESSED AS FORCE AND ENERGY AT FAILURE. GROUP 1. Pooled-Egg Bird Av. Per Overall B i r d Basis Period Av. Force 62.2 79.6 89.0 Energy 20.2 41.1 61.8 If physical properties were assumed to be capable of explaining v a r i a b i l i t y i n s h e l l strength measured as energy absorption, the r e l a t i v e l y large residual variance i n the re-gressions on energy indicated that, important factors had been overlooked or that the present method of analysis was unsuitable. Relationships among variables may d i f f e r from b i r d to b i r d such that strong relationships within birds were masked by analyzing samples composed of eggs from several birds. This contention was supported by the fact that Richards and Staley (1967)found inconsistent relationships between s h e l l c h a r a c t e r i s t i c s f o r d i f f e r e n t birds. Coefficients of multiple determination were found to be consistently higher f o r regressions using averages rather than i n d i v i d u a l egg data (Table 1). To a certain extent t h i s r e s u l t was to be expected because the averaging process tends 2 3 to reduce the effects of random errors due to precision l i m i t s of measurement. Another major source of random v a r i a t i o n could have been that of the measured strength of the s h e l l which was composed primarily of the ceramic material, c a l c l t e . Ceramics c h a r a c t e r i s t i c a l l y show considerable v a r i a t i o n i n strength (Hayden et a l . 1965s Rehkugler, 1 9 6 3 ) which could r e s u l t i n an appreciable range of strengths measured f o r ostensibly i d e n t i -cal egg s h e l l s . For t h i s reason, strength of i n d i v i d u a l egg s h e l l s may well defy complete explanation i n terms of physical properties. Average values f o r s h e l l strength and physical properties of a small sample of eggs are therefore recommended when evaluating the strength of s h e l l s produced by i n d i v i d u a l birds. Shell S t i f f n e s s Egg s h e l l s t i f f n e s s was found to be the most impor-tant single predictor of s h e l l strength measured as force at f a i l u r e . Coefficients of determination were 5 7 . . 1 . 7 2 . 9 , and 7 8 . 5 percent for Group One pooled-egg, b i r d average per period and o v e r a l l b i r d average analyses respectively. These re s u l t s are s l i g h t l y higher than those of Richards and Staley ( 1 9 6 7 ) who reported corresponding values of 4 9 . 0 and 62 . 4 percent f o r pooled=egg and b i r d average samples. St i f f n e s s alone explained only 8 . 4 , 2 0 . 4 , and 2 5 . 1 percent of the v a r i a t i o n i n energy absorbed at f a i l u r e i n pooled-egg,, b i r d average per period and o v e r a l l b i r d average data respectively. 24 Egg s h e l l s t i f f n e s s was highly correlated with measures of s h e l l quantity (Table 2). The fact that each of the s h e l l quantity c h a r a c t e r i s t i c s was highly correlated with s t i f f n e s s was not surprising i n view of t h e i r strong i n t e r — c o rrelation. TABLE 2 SIMPLE CORRELATIONS OF SHELL STIFFNESS WITH SHELL QUANTITY MEASUREMENTS. GROUP 1. Pooled-Egg Basis Bird Av. Per Period Overall Bird Av. Shell weight .701 .755 .853 Thlckness .836 .914 .956 Percent s h e l l .849 .921 .944 Shell wt./area .846 .918 .958 Relationships between s h e l l s t i f f n e s s and other physical properties were examined further by stepwise multiple regression of egg siz e , shape, and s h e l l quantity measurements on s t i f f n e s s (Tables C3, C6 , and C9). In the pooled-egg sample, egg width and roundness were important i n addition to s h e l l quantity with a c o e f f i c i e n t of multiple determination of 76.1 percent. Bird average per period analyses revealed the importance of egg shape as roundness and true sphericity i n addition to s h e l l quantity with an R of 90.2 percent. Width was included with s h e l l quantity i n the ov e r a l l b i r d average analysis to give R 2 = 95.2 percent. Addition of a l l egg size and shape variables to the regression of s h e l l quantity measures on s t i f f n e s s reduced the residual v a r i a t i o n i n s t i f f n e s s by 25 5.9, 20.5, and 34.9 percent i n pooled-egg, b i r d average per period, and o v e r a l l b i r d average analyses respectively.. (Table 3). These analyses show the existence of a strong relationship between s h e l l s t i f f n e s s and s h e l l quantity along with minor contributions by egg size and shape. TABLE 3 COEFFICIENTS OF MULTIPLE DETERMINATION (x 100) FOR REGRESSIONS OF SHELL QUANTITY, EGG SIZE, AND SHAPE ON STIFFNESS. GROUP 1. Pooled-Egg Basis , Bird Av. Per Period Overall Bird Av. Shell quantity* 74.6 87.8 , 93.7 S h e l l quantity, 76.1 egg s i z e * * 90.3 95.9 and shape*** * Shell weight, thickness, percent s h e l l , and s h e l l weight/area ** Egg weight, width, and length *** Shape index, roundness, true sphericity, p r a c t i c a l sphericity, and p r a c t i c a l three-dimensional sphericity. Voisey and Hunt (1967,b) developed a th e o r e t i c a l analysis of stresses i n the egg s h e l l under external loads. They showed that when force i s applied to the poles of the egg, deformation of the s h e l l Is given by: ^ U V S q - V ^ P R (24) 2ET 2 where § = deformation i n the d i r e c t i o n of applied load, V = Poisson's r a t i o f o r s h e l l material, P = load applied, 26 R = one-half of egg width, E = Young's modulus f o r s h e l l material, and T = thickness of s h e l l . S t i f f n e s s of the s h e l l i s defined as the r a t i o of force to deformation which i s P = 2ET 2 (.25) 8 /3(1-V*)R If Polsson'.s r a t i o and Young's modulus f o r s h e l l material are assumed to be constant and the substitution, .5B = R where B - egg width i s made, a l l constants may be combined to give: S t i f f n e s s = k_T_ (26) B where k = 4E In the present study, force was applied at the equator of the egg; therefore, a s i m i l a r analysis of factors involved i n s h e l l s t i f f n e s s would be complicated by the lack of symmetry i n a plane normal to the d i r e c t i o n of applied force. Egg shape would undoubtedly be an Important factor i n the analysis of s t i f f n e s s when force i s applied to the equator. From the previous discussions i t may be concluded that t h e o r e t i c a l and s t a t i s t i c a l analyses indicate that egg sh e l l s t i f f n e s s i s l a r g e l y a r e f l e c t i o n of s h e l l quantity along with probable effects of egg size and shape. 27 Egg Size Egg size measured either as egg weight or width re-mained as a s i g n i f i c a n t Independent variable i n the stepwise multiple regressions on force and energy absorbed at f a i l u r e f o r Group One (Appendix C). In s i m i l a r analyses of Group Two: both egg weight and length remained i n the regressions. Aft e r s h e l l s t i f f n e s s had been considered, the three measures of egg: size In combination explained 7.7. 17.0, and 3^ .9 percent of the residual v a r i a t i o n i n force at f a i l u r e f o r Group One pooled-egg, b i r d average per period, and o v e r a l l b i r d average analyses respectively. Egg width was found to be the most important measure of egg size i n multiple regression with s t i f f n e s s on force at f a i l u r e . Decreases of 4.4, 5.5. and 24.2 percent i n the re-sidual variance of force at f a i l u r e resulted from including egg width with s t i f f n e s s i n the three Group One analyses. Egg Shape Egg shape measured as shape index, roundness, prac-t i c a l s phericity, and p r a c t i c a l three-dimensional sphericity had highly s i g n i f i c a n t p o s i t i v e simple correlations with force and energy absorbed at f a i l u r e i n Group One pooled-egg and b i r d average per period analyses. True sphericity showed highly s i g n i f i c a n t negative simple correlations with both measures of s h e l l strength i n these analyses. 28 Table 4 was used to compare the f i v e egg shape measurements on the basis of t h e i r reduction of the residual variance i n force at f a i l u r e a f t e r s h e l l s t i f f n e s s had been considered. Shape index and p r a c t i c a l three-dimensional sphericity showed consistently greater contributions to the regressions i n each analysis than did the other measures of egg shape. TABLE V PERCENT REDUCTION IN RESIDUAL VARIANCE BY. ADDING EGG SHAPE MEASUREMENTS TO THE REGRESSION OF STIFFNESS ON FORCE AT FAILURE. GROUP 1. Pooled-Egg Basis Bi r d Av. Per Period Overall Bird Av. Shape index 5 . 3 1 3 . 3 1 9 . 5 Roundness 3 . 5 1 1 . 1 14.4 True sphericity 3 . 0 6 . 6 1 5 . 8 P r a c t i c a l sphericity 3 . 5 1 0 . 7 14 .0 P r a c t i c a l three dimensional sphericity 5 . 3 1 3 . 3 1 9 . 5 P r a c t i c a l three-dimensional sphericity was highly correlated with shape index (r = . 9 9 9 ) > therefore, comparable res u l t s f o r these shape measurements were expected. This simi-l a r i t y can be examined In the formula by which p r a c t i c a l three-dimensional sphericity was calculated: P3dsph = 124C512LB 2 - . 0 6 ) 1 / 3 . ( 1 5 ) 29 When cubed, ( P 3 d s p h ) 3 = 976,190 B_ - 114.400 L2 L3 (27) Substituting shape Index, Shindx = 100B and noting that the L second term may be omitted because i t Is very small compared with the f i r s t (about .1$), gives; P3dsph = 4.6(Shindx) 2^ 3 (approximately). (28) Roundness proved to be the most important measure of egg shape i n the stepwise multiple regressions on force and energy absorbed at f a i l u r e i n b i r d average per period and over-a l l b i r d average analyses of Group One; however, i n regressions of egg shape with s t i f f n e s s on force at f a i l u r e , shape index was s l i g h t l y superior to roundness i n explaining residual v a r i a t i o n . I t i s noteworthy that'measurement of roundness and p r a c t i c a l sphericity was of r e l a t i v e l y low accuracy because a planimeter was used to f i n d the projected area of the egg. Application of average geometrical relationships of eggs i n the derivation of true sphericity and p r a c t i c a l three-dimen-sional sphericity detracted from t h e i r accuracy as measures of egg shape. In general, shape index was found to be the most suitable measurement of egg shape. Shell Quantity Egg weight, s h e l l thickness, percent egg as s h e l l , and s h e l l weight per unit area were highly intercorrelated and a l l had high p o s i t i v e correlations with both measures of s h e l l 30 strength. Shell thickness alone accounted f o r 45.6, 62.4, and ?4.2 percent of the v a r i a t i o n In force at f a i l u r e , and 9.8, 19.0, and 26.2 percent of energy absorbed i n pooled-egg, b i r d average per period, and.overall b i r d average analyses respectively. P a r t i a l c o r r e l a t i o n analyses (Table B7) showed ,that s h e l l thickness was second only to s t i f f n e s s i n explaining re-sidual v a r i a t i o n of force at f a i l u r e i n pooled-egg and b i r d average per period samples a f t e r a l l other variables were con-sidered. In corresponding analyses (Table B8), thickness was the most important c h a r a c t e r i s t i c with respect to explaining residual v a r i a t i o n i n energy absorbed. Shell Hardness Importance to Shell Strength Egg s h e l l hardness measured at the .25 s h e l l l e v e l had s i g n i f i c a n t correlations of .207 and .277 with force at f a i l u r e i n pooled-egg and b i r d average per period analyses. In i t s c o r r e l a t i o n with energy absorbed at f a i l u r e , hardness was of significance only on a bi r d average per period basis. Stepwise multiple regression of a l l variables as b i r d averages per period indicated that hardness was important i n both force and energy absorbed at f a i l u r e . A f t e r a l l other ch a r a c t e r i s t i c s were considered, hardness explained .24 and 7.77 percent of the residual v a r i a t i o n of load with corres-ponding percentages of .33 and 8.38 f o r maximum energy absorbed 31 i n the two analyses. The simple c o r r e l a t i o n c o e f f i c i e n t of .740 between s h e l l hardness and crushing strength reported by Brooks and Hale (1955) and Brooks (1958) was not confirmed by t h i s study. Several differences between methods of selecting eggs, testing of hardness, and treatment of data were evident. The present study made use of a large sample of eggs produced by ten birds of a single cross fed a common ra t i o n and housed i n one room, whereas the e a r l i e r work was done on the ten weakest and strong-est eggs of a heterogeneous sample. Brooks and Hale considered hardness at the surface of the s h e l l extrapolated from measure-ments at s h e l l l e v e l s . 2 5 , . 5 0 , and .75 i n contrast to tests made only at l e v e l . 2 5 In t h i s study. In view of the large discrepancies reported f o r the Importance of hardness to egg sh e l l strength, further Investigations are warranted to c l a r i f y genetic and environmental effects on s h e l l hardness. Hardness Gradient Radial section tests of egg she l l s indicated that hardness was not uniform between s h e l l l e v e l s . 2 5 and .75. Hardness tests of tangential sections from l e v e l .02 to . 9 0 revealed a c u r v i l i n e a r gradient of hardness across the s h e l l . The hardness gradient found by f i t t i n g polynomial curves to the data of a representative s h e l l appears i n Fig. 9 t and the average gradient f o r nine sh e l l s i s i n Fig . 10. In a l l cases a second degree polynomial expression was observed t a f i t the 32 .1 .2 .3 .4 .5 .6 .7 .8 .9 Shell Level From Out9ide F i g . 9. Hardness Gradient of S h e l l No. 19a. Tests Made on a T a n g e n t i a l S e c t i o n . Equation of the Curve: D.P.H. = 178.2 - 340.6x + 552.6X2 Standard E r r o r of Estimate = 3.84, - 244. 7X3 R2 = .968 S h e l l L e v e l F r o m O u t s i d e Fig. 1 0 . Average Hardness Gradient of Shells of Birds No. 5 , 9 , 1 9 . Tests made on Tangential Sections. Equation of the Curves D.P.H. = 1 7 4 . 3 - 2 1 0 .IX + 216.6X 2 Standard Error of Estimate = 9 . 3 8 , R 2 = .7^2 34 data s a t i s f a c t o r i l y with only a small decrease i n the standard error of estimate on using the cubic equation. Comparison of r a d i a l and tangential hardness tests of the same s h e l l between s h e l l l e v e l s . 2 0 and . 7 0 resulted i n s i m i l a r curves. The data f o r three s h e l l s of one b i r d were plotted i n Fig. 1 1 with separate curves f i t t e d to r a d i a l and tangential points. The average hardness gradient curves f o r nine shells produced by three birds were included i n F i g . 1 2 . Examination of r a d i a l and tangential test r e s u l t s revealed that the gradient of hardness across the egg s h e l l from l e v e l s . 2 0 to .7 0 was la r g e l y independent of s h e l l orientation. Mechanical and chemical s h e l l membrane removal were compared by duplicate tangential hardness tes t i n g between l e v e l s . 0 2 and . 9 0 of three s h e l l s that gave the following hardness gradient equations: - Mechanical membrane removal D.P.H. = 1 8 0 . 3 - 248.2X + 253-OX 2 Standard Error of Estimate = 1 3 . 0 1 , R 2 = . 6 8 9 - Chemical membrane removal D.P.H. = 1 7 2 . 6 - 2 2 1 .5X + 224.IX 2 2 Standard Error of Estimate = 9 . 2 1 , R = . 7 7 9 Graphs of the two gradients were examined v i s u a l l y and judged to be es s e n t i a l l y s i m i l a r . On the basis of t h i s comparison, chemical removal of s h e l l membranes was assumed to have no appreciable effect on s h e l l hardness. Fig. 1 1 . Comparison of Radial (upper) and Tangential (lower) Hardness Gradients of Shells 1 9 a , b, a Radial Data, x Tangential Data. Equations of the Curves: D.P.H. (Radial) = 182.6 - 283.2X + 318. 7X2 Standard Error of Estimate = 7.42, R 2 = .558 D.P.H. (Tangential) = 177.5 - 260.4X + 289.4X2 Standard Error of Estimate = 6.27, R 2 = .6l4 36 Fig. 12. Comparison of Radial (upper) and Tangential (lower) Hardness Gradients of Shells of Birds No. 5, 9, 19. o Radial Data, x Tangential Data. Equations of the Curvess D.P.H. (Radial) = 168.6 - 199.9X + 233.4X2 Standard Error of Estimate = 8.83, R 2 = .317 D.P.H. (Tangential) = 174.2 - 233.OX + 262.9X 2 Standard Error of Estimate = 8.37, R 2 = .396 37 Pig. 1 3 . Photomicrograph of a Radial Section of Egg Shell Showing Indentations at Shell Levels . 2 5 ( A ) , and . 7 5 (B). (Mag. x 2 1 0 ) The discovery of a c u r v i l i n e a r gradient of hardness across the thickness of the egg s h e l l with a maximum at the outer edge, a minimum midway and a r e l a t i v e high again near the inner edge was not compatible with the report by Brooks and Hale ( 1 9 5 5 ) of a l i n e a r gradient Increasing toward the out-er s h e l l edge. The main point of disagreement was that of the hardness at s h e l l l e v e l . 7 5 because both studies contended that hardness was greater at l e v e l . 2 5 than , 5 0 D i f f i c u l t y was experienced when testi n g hardness near the inner edge of the s h e l l i n r a d i a l sections because inden-tations often caused cracking of the s h e l l (see Fig. 1 3 ,B) 38 which produced unusually large, i n v a l i d indentations. Hardness calculated from indentations enlarged by s h e l l cracking would re s u l t i n spuriously low values; therefore, such indentations were discarded i n t h i s study. Tangential t e s t s of sh e l l s be-tween l e v e l s .02 and .90 were found to minimize the incidence of cracking near edges of the s h e l l and to confirm the presence of a parabolic hardness gradient across the egg s h e l l . Hard-ness and i t s gradient across the thickness of the s h e l l i s worthy of further investigation. Non-Destructive Estimation of Shell Strength Multiple regressions of non-destructive measurements on egg s h e l l strength measured as force at f a i l u r e were .examined i n r e l a t i o n to corresponding regressions containing a l l s h e l l c h a r a c t e r i s t i c s (Table 5). TABLE 5 COMPARISON OF NON-DESTRUCTIVE SHELL PROPERTIES WITH ALL SHELL MEASUREMENTS IN REGRESSION ON FORCE AT FAILURE. GROUP 1 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ Pooled-Egg Bird Av„ Per Overall Bird Basis Period Av c A l l Shell Properties 62.2 79.6 89.0 Non-Destructive Properties* 60.5 77.7 86.3 * S t i f f n e s s , egg weight, width, length, and shape index. Deletion of destructive measurements of s h e l l quan-t i t y caused small reductions i n the c o e f f i c i e n t s of multiple 39 determination. The a b i l i t y of non-destructive measurements to explain a large proportion of the v a r i a t i o n i n force at f a i l u r e Indicated t h e i r Importance i n estimating t h i s measure of s h e l l strength. Egg weight, egg width, egg length, and shape index may be measured quickly and precisely by methods outlined i n t h i s study. Shell s t i f f n e s s may be estimated with the use of a device s i m i l a r to that of Schoorl and Boersma (1962) which allows measurement of deformation under a non-destructive load, or a compression tes t i n g machine that has been modified to automatically terminate loading at a predetermined force. SUMMARY Egg s h e l l strength measured as maximum force and energy absorbed under q u a s i - s t a t i c loading was studied i n r e l a t i o n to s h e l l s t i f f n e s s , egg s i z e , egg shape, s h e l l quan-t i t y and hardness. 1. Losses caused by egg s h e l l f a i l u r e were estimated to be about 590 thousand d o l l a r s i n B r i t i s h Columbia and 4.2 m i l l i o n d o l l a r s i n Canada f o r the year 1965. 2. Physical properties of s h e l l s accounted f o r 62.2, 79.6, 89.O percent of the v a r i a t i o n i n strength measured as force at f a i l u r e i n pooled-egg, b i r d average per period, and o v e r a l l b i r d averages respectively. Corresponding figures f o r s h e l l strength measured as energy absorbed 40 at f a i l u r e were 20.2, 41.1, and 6l.8 percent i n the three analyses. 3. Mean values f o r s h e l l c h a r a c t e r i s t i c s were recommended when evaluating s h e l l strength of i n d i v i d u a l birds due to i n t r i n s i c strength v a r i a t i o n of the b r i t t l e s h e l l material. 4. Shell s t i f f n e s s was found to be the most important single predictor of crushing strength. Egg s i z e , egg shape, s h e l l quantity, and hardness were also related to s h e l l strength. 5. The t h e o r e t i c a l l y derived conclusion that s t i f f n e s s was related to s h e l l quantity, egg size and shape was v e r i f i e d by s t a t i s t i c a l analysis of the data. 6. Shape Index proved to be the most satisfactory measure of egg shape when compared with roundness and sphericity concepts. 7 . Egg shells were hardest at the outer surface, r e l a t i v e l y hard near the inner surface, and softest midway across the s h e l l . 8. Similar gradients of hardness were observed i n r a d i a l and tangential test sections of s h e l l material. 9. The non-destructive physical properties of s t i f f n e s s , egg size , and shape may be used to estimate crushing strength of an egg s h e l l . 41 LIST OF REFERENCES Brooks, J . , and H.P. Hale. 1955. Strength of the s h e l l of the hen's egg. Nature 175: 848-849. Brooks, J. 1958. Strength i n the egg. Soc. Chem. Ind. Mono. No. 7. Texture i n Foods, London. 149-178. Brown, W.E., R.C. Baker and H.B. Naylor. 1966. The micro-biology of cracked eggs. Poultry S c i . 45: 284-287. Cray, R.E., 1953. Cracked eggs costing industry too much money. Poultry Process. Market. 59s 10. Ezekiel, M., and K.A. Fox. 1959. Methods of c o r r e l a t i o n and regression analysis. 3rd Ed. John Wiley and Sons, Inc. London. Frank, F.R., R.E. Burger and M.H. Swanson. 1964. The relationships between selected physical c h a r a c t e r i s t i c s and the resistance to s h e l l f a i l u r e of Gallus domestlcus eggs. Poultry S c i . 43: 1228-1235. . 1965. The relationships among s h e l l membrane, selected chemical properties, and the resistance to s h e l l f a i l u r e of Gallus domestlcus eggs. Poultry S c i . 44: 63-69. Gaisford, M.J. 1965. The a p p l i c a t i o n of s h e l l strength measurements i n egg s h e l l q u a l i t y determination. B r i t . Poultry S c i . 6: 193-196. Hayden, W., W.G. Moffatt and J. Wulff. 1965. Structure and properties of materials. Volume I I I , Mechanical behaviour. John Wiley and Sons, Inc. London. Hunt, J.R., and P.W. Volsey. 1966. Physical properties of egg s h e l l s . 1. Relationship of resistance to com-pression and force at f a i l u r e of egg s h e l l s . Poultry Sc i . 45: 1398-1404. Lund, W.A., V. Helman and L.A. Wllhelm. 1938. The re-l a t i o n s h i p between egg s h e l l thickness and strength. Poultry Sci. 17: 372-376. Marks, H.L., and T.B. Kinney, J r . 1964. Measures of egg s h e l l quality. Poultry S c i . 43: 269-271. Mohsenin, N. 1963. A testing machine f o r determining the mechanical and rheological properties of a g r i c u l t u r a l products. Penn. State Univ. Agr. Expt. Sta. B u l l . 701. 42 Mott, B.W. 1956. Micro-Indentation hardness testing. Butterworth's S c i e n t i f i c Publications. London. Mueller, CD., and H.M. Scott. 1940. The porosity of the egg-shell i n r e l a t i o n to ha t c h a b i l i t y . Poultry S c i . 19: I63-I66. Novikoff, M. and H.S. Gutteridge. 1949. A comparison of cert a i n methods of estimating s h e l l strength. Poultry Sci. 28: 339-343. Poultry Market Review. 1964. Poultry D i v i s i o n and Markets Information Section, Production and Marketing Branch, Department of Agriculture, Ottawa, Canada. . 1965. Poultry D i v i s i o n and Markets Information Section, Production and Marketing Branch, Department of Agriculture, Ottawa, Canada. Raffa, J. 1967. D i s t r i c t Superintendent (Poultry), Production and Marketing Branch, Canada Department of Agriculture, Vancouver. Personal communication. Ralston, A., and H.S. Wllf. i960. Mathematical methods f o r d i g i t a l computers. John Wiley and Sons, Inc. Rehkugler, G.E. 1963. Modulus of e l a s t i c i t y and ultimate strength of the hen's egg s h e l l . J. Agric. Eng. Res. 8: 352-35^ . . 1964. Egg handling equipment design. Trans. Amer. Soc. Agric. Eng. 7: 174-177. Romanoff, A.L., and A.J. Romanoff. 1949. The avian egg. London: Chapman and Hall Ltd. Richards, J.F., and M.H. Swanson. 1965. The relationship of egg shape to s h e l l strength. Poultry S c i . 44: 1555-1558. Richards, J.F., and L.M. Staley. 1967. The relationships between crushing strength, deformation and other physical measurements of the hen's egg. Poultry Sci. 46 ( i n press). Schoorl, P., and H.Y. Boersma. 1962. Research on the quality of the egg s h e l l . Proc. 12th World's Poultry Cong. 432-435. Shuster, D. 1959. Relationship of s h e l l strength to certain c h a r a c t e r i s t i c s of chicken eggs. Unpublished M.S. Thesis. Pennsylvania State University. 3^ Sluka, S.J., E.L. Besch and A.H. Smith. 1965. A hydro-s t a t i c tester f o r egg s h e l l strength. Poultry Sci. 44: 1494-1500. . 1966. Calculation and analysis of stresses i n egg s h e l l s . Winter Meeting. Amer. Soc. Agric. Eng. Paper No. 66-808. Snedecor, G.W. 1956. S t a t i s t i c a l methods. 5th Ed. The Iowa State University Press, Ames, Iowa. Stewart, G.P. 1936. Shell c h a r a c t e r i s t i c s and t h e i r relationship to the breaking strength. Poultry S c i . 15s 119-124. Terepka, A.R. 1963. Structure and c a l c i f i c a t i o n i n avian egg s h e l l . Exptl. C e l l Bes. 30: 171-182. Tyler, C. 1961. Shell strength: I t s measurement and relationship to other factors. B r i t . Poultry S c i . 2: 3-19. Tyler, C., and F.H. Geake. 1961. Studies on egg s h e l l s XV - C r i t i c a l appraisal of various methods of assessing s h e l l thickness. J. S c i . Pood Agric. 12: 281-289. Voisey, P.W., and J.R. Hunt. 1967a. Relationship between applied force, deformation of egg s h e l l s and fracture force. J. Agric. Eng. Res. ( i n press). . 1967b. Physical properties of egg s h e l l s . 4. Stress d i s t r i b u t i o n i n the s h e l l . ( i n press). . 1967c. The behavior of egg s h e l l s under impact. J. Agric. Eng. Res. ( i n press). Wadell, H. 1933. Sphericity and roundness of rock p a r t i c l e s . Jour, of Geology. 41: 310-331. 44 APPENDIX A 5^ TABLE A l TESTING PERIODS AND SAMPLE SIZES Period Dates of Period , No. of Eggs Tested 1 Jan. 2 - Jan. 29 342 2 Jan. 30 - Feb. 26 366 3 Feb. 27 - Mar. 26 351 4 Mar. 27 - Apr. 23 342 5 Apr. 24 - May 21 343 6 May 22 - Jun. 18 325 7 Jun. 19 - J u l . 16 322 8 J u l . 17 - Aug. 13 3^2 Total Sample Size 2,733 TABLE A2 EGGS TESTED BY BIRD AND PERIOD 46 Period Bird 1 2 3 4 5 6 7 8 Totals 1* 6 6 6 6 6 6 6 6 48 2 6 5 6 6 6 6 6 6 ! 47 3* 5 1 0 2 0 0 0 0 8 ^ 6 7 6 6 6 6 6 6 49 5* 6 7 6 6 6 6 6 6 49 6 5 6 6 6 6 6 6 6 47 7* 5 6 6 6 6 6 6 6 47 8 5 6 6 6 6 6 6 6 47 9* 5 6 6 6 6 6 6 6 47 10 5 6 5 5 6 6 6 6 45 11* 7 7 6 6 6 6 6 6 50 12 6 7 6 6 6 6 6 6 49 13* 6 7 4 0 6 6 6 3 38 14 6 5 6 6 6 5 6 6 46 15* 5 5 6 6 6 6 6 6 46 16 7 7 5 6 6 6 6 6 49 17* 5 6 6 6 6 6 6 5 46 18 7 6 6 6 6 6 6 6 49 19* 5 6 6 6 6 6 5 6 46 20 4 5 5 6 6 6 6 6 44 * Shells from these birds tested f o r hardness. cont'd. TABLE A2 — Continued 47 Period Bird. 1 2 3 4 5 6 7 8 Totals 21 5 6 6 6 6 6 6 6 47 2 2 . 5 7 6 6 6 6 6 6 48 23 6 6 4 6 6 6 6 6 46 24 5 6 6 6 6 6 6 6 47 25 6 8 6 6 6 6 6 6 50 26 6 5 6 6 5 5 6 6 45 27 5 7 6 6 6 6 6 6 48 28 6 7 6 6 6 6 6 6 49 29 6 7 6 6 6 6 6 6 49 30 6 0 0 6 6 6 6 6 36 31 5 5 4 6 6 6 6 6 44 32 5 6 7 6 6 6 6 6 48 33 6 6 6 6 6 0 0 6 36 34 6 7 6 6 6 6 6 6 49 35 7 7 6 6 6 6 6 6 50 36 5 6 6 6 6 5 3 6 43 37 5 4 4 6 2 5 5 6 37 38 6 6 7 6 6 6 6 6 49 39 7 6 7 6 6 6 6 6 50 40 6 7 7 6 6 6 6 6 50 41 6 6 6 6 6 6 4 6 46 42 7 6 6 6 6 6 6 6 49 cont'd... TABLE A2 — Continued 48 Period Bird 1 2 3 , 4 5 6 7 8 Totals 43 6 6 6 6 6 6 6 6 48 44 6 7 7 6 6 6 6 6 50 45 5 7 6 6 6 6 6 6 48 46 5 6 6 6 6 5 6 6 46 47 6 6 7 6 6 6 5 6 48 48 6 7 7 6 6 0 0 6 38 49 5 7 7 0 0 0 0 0 19 50 6 7 6 6 6 6 6 6 49 51 7 7 7 6 6 6 6 6 51 52 6 7 7 6 6 6 6 6 50 53 5 6 7 6 6 6 6 6 48 54 5 7 5 6 6 6 6 6 47 55 6 7 6 5 6 0 0 6 36 56 5 6 7 6 6 6 6 6 48 57 5 6 6 6 6 6 6 4 45 58 6 7 7 6 6 6 6 6 50 59 6 6 7 6 6 6 6 6 49 60 7 6 7 6 6 6 6 6 50 49 TABLE A3 MEANS AND STANDARD DEVIATIONS. GROUP 1 . B i r d Av. Per Pooled-Egg Basis Period Overall B i r d Av. n=2733 n=46l n=53 Mean S.D. Mean S.D. Mean S.D. Load 3557.0 578.3 3554.0 447.2 3559.0 375.2 Totdef 154.2 18.51 154.4 11.71 154.6 9.202 S t i f f 23.30 4.264 23.26 3.498 23.26 3.062 Energy 27.54 6.096 27.55 4.027 27.60 3.142 Eggwt 58.94 4.354 58.92 4.017 59.02 3.308 Width 4.267 .118 4.265 .109 4.270 .095 Length 5.802 .215 5.802 .187 5.797 .136 Shelwt 5.299 .574 5.292 .521 5.295 .483 Thick 331.1 28.79 331.0 25.55 331.0 24.30 Persh 8.992 .745 8.977 .644 8.968 .575 Mgmcm2 74.89 6.393 74.81 5.613 74.79 5.211 Shlndx 73.62 2.732 73.58 2.368 73.72 1.902 Round 72.87 2.955 72.82 2.494 72.94 1.894 Trusph 97.81 .845 97.80 .569 97.79 .464 Prasph 85.3^  1.746 85.31 1.472 85.39 1.112 P3dsph 80.88 2.013 80.85 1.743 80.94 1.397 50 TABLE A4 MEANS AND STANDARD DEVIATIONS. GROUP 2. Pooled-Egg Basis B i r d Av. Per Period Basis n-425 n=74 Mean S.D. Mean S.D,  Load 3766.0 538.5 3755.0 411.8 Totdef 151.8 17.96 152.4 10.91 S t i f f 25.15 4.666 25.02 3.867 Energy 28.60 5.385 28.59 2.988 Eggwt 59.16 4.749 58.95 4.242 Width 4.271 .129 4.264 .119 Length, 5.793 .185 5.789 .135 Shelwt 5.544 .668 5.506 .625 Thick 3^ 3.7 28.73 3^ 2.6 25.30 Persh 9.359 .729 9.318 .628 Mgmcm.2 78.08 6.780 77.72 6.100 Shindx 73.77 2.295 73.69 1.856 Round 73.03 2.576 72.94 2.120 Trusph 97.63 1.108 97.63 .567 Prasph 85.44 1.515 85.38 1.246 P3dsph 81.00 1.686 80.94 1.358 D.P.H. 137.7 11.60 137.8 6.663 51 TABLE A5 MEANS AND STANDARD DEVIATIONS; BY PERIOD Period 1 Mean S.D. 2 Mean S.D. 3 Mean S.D. Load 37^ 3.0 569.0 3720.0 590.9 3620.0 511.6 Totdef 161.3 17.69 151.2 18.05 150.6 17.06 S t i f f 23.41 3.918 24.91 4.73& 24.31 4.243 Energy 30.28 6.174 28.17 5.815 27.31 5.153 Eggwt 55.21 3.371 56.63 3.381 58.31 3.906 Width 4.191 .099 4.217 .099 4.244 .109 Length 5.638 .185 5.702 .180 5.794 .199 Shelwt 5.034 .532 5.256 .562 5.318 .576 Thick 331.2 28.46 338.7 29.75 335.5 28.17 Persh 9.111 .695 9.277 .785 9.117 .731 Mgmcm2 74.29 6.116 76.27 6.725 75.68 6.401 Shindx 74.39 2.661 74.02 2.559 73.32 2.706 Round 73.33 2.840 73.22 2.848 72.72 2.889 Trusph 97.81 .708 97.69 .706 97.70 .745 Prasph 85.62 I.665 85.55 1.658 85.25 1.703 P3dsph 81.45 1.944 81.17 1.880 80.67 1.994 TABLE A5 — Continued 52 Period 4 Mean S.D. 5 Mean S.D. 6 Mean S.D. Load 3529.0 525.1 3718.0 570.8 3398.0 557.6 Totdef 154.2 17.22 154.6 18.55 155.3 19.04 S t i f f 23.10 3.886 24.29 4.180 22.09 3.958 Energy 27.30 5.498 28.88 6.360 26.53 6.105 Eggwt 59.15 3.523 59.60 4.022 60.73 4.004 Width 4.272 .099 4.278 .106 4.313 .115 Length 5.809 .194 5.836 .205 5.863 .185 Shelwt 5.309 .551 5.410 .563 5.357 .578 Thick 328.0 27.40 333.8 28.87 328.5 28.86 Persh 8.971 .691 9.078 .723 8.820 .728 Mgmcm2 74.82 6.169 75.89 6.273 74.20 6.401 Shindx 73.62 2.692 73.36 2.698 73.62 2.623 Round 74.04 2.816 73.46 3.O63 72.12 2.670 Trusph 97.77 .803 97.76 .733 97.89 .799 Prasph 86.03 1.645 85.69 1.794 84.91 1.578 P3dsph 80.88 1.975 80.69 1.983 80.88 1.926 TABLE A5 — Continued Period 7 8 Mean S.D. Mean S.D. Load 3418.0 568.1 3277.0 545.2 Totdef 154.7 19.55 151.9 18.96 S t i f f 22.30 3.994 21.77 3.961 Energy 26.62 6.307 25.04 5.878 Eggwt 61.00 4.344 61.31 4.183 Width 4.311 .121 4.322 .120 Length 5.886 .190 5.906 .230 Shelwt 5.394 .582 5.325 .562 Thick 328.2 28.33 323.9 27.75 Persh 8.839 .708 8.685 .711 Mgmcm2 74.48 6.278 73.30 6.207 Shindx 73.30 2.489 73.28 3.150 Round 72.03 2.518 71.90 3.181 Trusph 97.83 1.098 98.03 .862 Prasph 84.86 1.489 84.77 1.899 P3dsph 80.65 I.831 80.63 2.326 54 APPENDIX B 55 TABLE BI SIMPLE CORRELATION COEFFICIENTS GROUP 1. POOLED-EGG BASIS. 11=2733. Load Totdef S t i f f Energy E««wt Width Length Shelwt P3dsph .184 .179 .047 .233 -.081 .403 -.715 -.105 Prasph .161 .135 .055 .191 -.109 .314 -.685 -.108 Trusph -.084 .278 -.253 .097 .116 .311 .123 -.200 Round .163 .136 .056 .192 -.111 .310 -.689 -.109 Shindx .185 .179 .047 .234 -.082 .400 -.718 -.106 Mgmcm2 .665 -.351 .846 .289 .241 .128 . 188 .899 Persh .650 -.377 .849 .263 -.045 -.123 -.022 .735 Thick .675 -.321 .836 .314 .241 .131 .194 .860 Shelwt .576 -.252 .701 .279 .640 .490 .479 Length -.055 -.050 -.010 -.066 .737 .347 Width .177 .178 .048 .227 .867 .905 Persh Eggwt .117 . 061 .071 .119 .957 .950 Mgmcm2 Energy .843 .705 .290 -.087 -.066 -.091 Shindx S t i f f .755 -.457 .904 -.075 -.046 -.092 Round Totdef .222 -.027 .115 -.311 -.348 -.276 Trusph -.017 .997 .904 -.074 -.045 -.093 Prasph .904 .122 .903 .999 -.086 -.066 -.092 P3dsph Prasph Trusph Round Shindx Mgmcm2 Persh Thick r . 0 5 - - 0 3 7 56 TABLE B2 SIMPLE CORRELATION COEFFICIENTS GROUP 1. BIRD AVERAGE PER PERIOD BASIS. n=46l. Load Totdef S t i f f Energy Eggwt Width Length Shelwt P3dsph .245 .264 .065 .350 -.016 .421 -.682 -.069 Prasph .230 .230 .070 .319 -.055 .349 -.682 -.081 Trusph -.139 .398 -.311 .090 .135 .276 .119 -.232 Round .231 . .231 .070 .320 -.055 .3^ 8 -.683 -.082 Shindx .244 .264 .064 .3^9 -.016 .421 -.683 -.069 Mgmcm2 .773 -.486 .918 .401 .292 .183 .230 .899 Persh .769 -.505 .921 .388 -.012 -.093 .010 .722 Thi ck .790 -.451 .914 .436 .281 .182 .223 .868 Shelwt .649 -.370 .755 .356 .680 .547 .510 Length .^.081 -.136 .014 -.142 .733 .372 Width .206 .164 .099 .262 .893 .920 Persh Eggwt .134 .011 .118 .118 .951 .967 Mgmcm2 Energy- .849 .523 .452 -.081 -.083 -.074 Shindx S t i f f .854 = .513 .942 -.075 -.064 -.086 Round Totdef -.002 -.025 .106 -.376 -.429 -.312 Trusph -.019 .999 .942 -.074 -.064 -.086 Prasph .941 .111 .941 .999 -.080 -.081 -.073 P3dsph Prasph Trusph Round Shindx Mgmcm2 Persh Thick r = .05 .092 r = .120 01 57 TABLE B3 SIMPLE CORRELATION COEFFICIENTS GROUP 1. OVERALL BIRD AVERAGE BASIS. n=53 Load Totdef S t i f f Energy Eggwt Width Length Shelwt P3dsph .226 ! .324 .024 .389 .166 .542 -.593 .019 Prasph .170 .283 -.005 .317 .140 .500 -.617 .001 Trusph -.113 .523 -.323 .172 .095 .241 .073 -.278 Round .166 .287 -.009 .316 .143 .504 -.614 -.002 Shindx .233 .320 .032 .393 .165 .540 -.595 .025 Mgmcm2 .842 -.556 .958 .473 .388 .258 .313 .928 Persh .792 -.630 .944 .390 .129 ^12 .142 .793 Thick .861 -.520 .956 .512 .395 .276 .318 .915 Shelwt .809 -.376 .853 .535 .703 .569 .514 Length .137 -.070 .169 .074 .68? .354 Width .415 .291 .218 .531 .912 .940 Persh Eggwt .401 .134 .285 .430 .962 .981 Mgmcm2 Energy- .844 .413 .501 -.062 -.120 -.049 Shindx S t i f f .886 -.574 .985 -.086 -.140 -.085 Round Totdef -.136 .022 .145 -.404 -.459 -.331 Trusph .019 .999 .984 -.080 -.133 -.080 Prasph .984 .151 .985 1.000 -.070 -.129 -.057 P3dsph Prasph Trusph Round Shindx Mgmcm2 Persh Thick r = . 2 6 8 r . o i " - 3 M TABLE B4 i SIMPLE CORRELATION COEFFICIENTS GROUP 2. POOLED-EGG BASIS. n=425 58 Load Totdef S t i f f Energy Eggwt Width Length Shelwt Thick p. P.R; .207 -.136 .265 .067 -.073 -.159 .009 .184 .275 P3dsph .119 .059 .039 .139 .095 .472 -.539 .014 -.045 Prasph .145 .049 .068 .149 .068 .370 -.500 .029 -.014 Trusph -.172 .203 -.268 .004 .000 .265 .053 -.223 -.279 Round .144 .047 . 068. .147 .067 . 368 -.501 .028 -.013 Shindx .118 .059 . 038 .139 .095 .473 -.539 .013 -.045 Mgmcm2 .683 =.503 .866 .-201 .482 .361 .377 .923 .947 Persh .655 - . 514 .854 .171 .210 .106 .172 .773 .898 Thick .703 -.477 . 864- .233 .474 .354 .382 .882 Shelwt .628 -.423 .765 .210 .781 . 647 .604 Length .170 -.125 .216 .. 047 .767 .486 .957 Mgmcm2 Width .304 -.066 .266 .198 .900 ~. 035 -.074 Shindx Eggwt .328 -.139 .336 .166 .862 .005 -.017 Round Energy .777 .644 .171 .035 .198 -.304 -.339 Trusph Stiff .750 -.625 .037 .999 .863 .006 017 Prasph Totdef .027 .863 .198 .861 .999 -.034 -. 074 . P3dsph -.159 -.090 -.214 -. 091 -.161 .301 .358 D.P.H. P3dsph Piasph Trusph Round Shindx Mgmcm2 Persh r 0 5 = -095 59 TABLE B5 SIMPLE CORRELATION COEFFICIENTS GROUP 2. BIRD AVERAGE PER PERIOD BASIS. n=74 Load Totdef Stiff Energy Eggwt Width Length Shelwt Thick D.P.H. .27? .039 .213 .283 -.133 -.225. .042 . 071 .195 P3dsph .188 .021 .090 .244 .3^ 6 .621 - 3^ 0 .168 .051 Prasph .241 .059 .116 . 320 .287 .532 -.346 .161 .075 Trusph •-. 308 .290 -. 349 -.121 -.072 .127 -.127 -. 31^  -.378 Round .234 .058 .111 .311 .283 .529 -. 3^ 9 .155 .069 Shindx .184 .023 .087 .242 .341 .618 -.344 .163 .048 Mgmcm2 .831 -723 .923 .390 .623 .503 .557 .943, .969 Persh .812 -. 706 .902 .378 .380 .258 .391 .812 .924 Thick .869 -.704 .942 .442 .616 .503 .553 .919 Shelwt . 76? -.656 .846 .369 .847 .738 .706 Length .324 -.390 .428 .065 .756 .525 .959 Mgmcm2 Width .436 -.305 .435 .273 .942 .042 -.076 Shindx Eggwt .483 -.392 .518 .254 .907 .066 -.024 Round Energy- .775 .233 .415 \ .158 .249 -.411 -.458 Trusph Stiff .895 -. 733 .150 .999 .907 .073 -.018 Prasph Totdef -.427 .906 .248 .906 1.000 . 046 -.073 P3dsph -.284 -.182 -.244 -.191 -.288 .177 .247 D.P.H. P3dsph Prasph Trusph Round Shindx Mgmcm2 Persh TQ5 = .227 r > 0 1 = .296 60 TABLE B6 SIMPLE CORRELATIONS BETWEEN LOAD AND SELECTED VARIABLES FOR EACH TEST PERIOD r-01 S t i f f . Eggwt Width Length Shindx Round P3dsph Pd. 1 n=342 .106 .138 .772 .263 .273 .080 .111 .029 .108 Pd. 2 n=366 .103 .134 .773 .239 .241 . 060 .109 .081 .109 Pd. 3 n=351 .105 .137 .752 .301 .295 .114 .100 .059 .101 Pd. 4 n=342 .106 .138 .753 .284 .307 .071 .130 .082 .129 Pd. 5 n=343 .106 .138 .706 .255 .358 -.032 .271 .171 .271 Pd. 6 n=325 .109 .142 .739 .255 .312 .041 .199 .142 .199 Pd. ? n=322 .109 .143 .726 .325 .3^ 7 .064 .226 .210 .224 Pd. 8 n=342 .106 .138 .744 . 250 .322 -.025 .226 .205 .225 A l l pds. n=2733 .037 .049 .755 .117 .177 -.055 .185 .163 .184 61 TABLE B7 SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN LOAD AND SELECTED VARIABLES. GROUP 1. Pooled-n: -Egg Basis =2733 Bird Av. Per Period n=46l Overall B i r d Av. n=53 100(sc ) 2 * ? 100(sc)* ! 100(pc) ** '* 0 100(sc) 2 10O(pc) ** * 2 i o o ( x > c r * * S t i f f . 57.05 17 .64 72.91 13.62 78.52 7.60 Eggwt 1 .37 .00 1 .78 .65 1.6.08 .24 Width 3.12 . 22 4.26 .17 17.25 2 .44 Length .30 .05 .65 .02 1 .87 1.45 Shelwt 33.21 .37 42.12 .76 65.42 3.49 Thick 45.58 1 .43 62.38 2 .86 74.17 2.21 Persh 42.19 .08 59.09 • 96 62.6,5 1 .44 Mgmcm2 44.16 .03 59.68 .00 70.91 .83 Shindx 3.43 .07 5.93 .17 5.45 8.93 Round 2.67 .49 5.35 .70 2 .77 5.56 Trusph .71 .00 1.92 1.23 1.28 4.45 Prasph 2.60 .46 5.29 •43 2.88 2.27 P3dsph 3.39 .37 5.98 .03 5.09 4 .64 p_o 05*** p = ! o i * * * .16 .24 .16 .24 .84 1 .43 .86 1 .47 7.20 12.12 9.24 15.44 * 100(simple correlation) ? ** 100(partial c o r r e l a t i o n ) ^ *** 100(minimum co r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t at indicated l e v e l ) 62 TABLE B8 SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN ENERGY AND SELECTED VARIABLES. GROUP 1 • Pooled-Egg Basis n=2?33 Bird Av. n= Per Period 461 Overall n=53 Bird Av. 100(sc) 2 * 2 100(pc) 100(sc) •* 2 * 9 100(sc) 2 100 ( p c r * « * 2 100(pc) ** S t i f f 8.43 .01 20.43 .07 25.12 1.41 Eggwt 1.41 .02 1.39 .59 18.49 .20 Width 5.16 .06 6.86 .16 28.21 1.82 Length .43 .01 2.02 .03 .55 1.69 Shelwt 7.79 •33 12.69 .70 28.62 3.55 Thick 9.83 1.64 18.99 3.26 26.23 2.47 Persh 6.92 .04 15.03 1.03 15.23 .74 Mgmcm2 8.32 .05 16.05 .00 22.37 1.20 Shindx 5.45 .08 12.21 .13 15.47 8.84 Round 3.69 .26 10.25 .63 9.96 4.58 Trusph .94 .05 .81 1.32 2.95 3.39 Prasph 3.65 .23 10.16 .37 10.02 1.82 P3dsph 5.41 .19 12.27 .01 15.09 4.48 P=.05*** P=.01*** .16 .24 .16 .24 .84 1.43 .86 1.47 7.20 12.12 9.24 15.44 * 100(simple correlation) 2 ** 100(partial correlation) *** 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t at ^ indicated l e v e l ) 63 TABLE BO-SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN STIFFNESS AND SELECTED VARIABLES. GROUP 1 Pooled-Egg Basis Bird Av. PerPeriod Overall Bird Av. n=2733 n=46l n=53 100(sc) 2* 100(pc) 2 100(sc) 2 * 100(pc) 2** 100(sc ) 2 * 100(pc) 2** Eggwt .51 .03 1.40 . 02 8.12 .02 Width .23 .04 .97 .04 4.74 3.00 Length .01 .00 .02 .01 2.85 1.02 Shelwt 49.11 .04 57.02 .62 72.71 5.32 Thick 69.82 4.70 83.50 8.17 91.30 6.16 Persh 72.08 .04 84.90 .06 89.19 3.78 Mgmcm2 71.62 .10 84.18 .84 91.74 10.28 Shindx .22 .00 .41 .00 .10 .29 Round .31 .15 .49 .54 . 01 .12 Trusph 6.40 .00 9.66 .31 10.44 .63 Prasph .31 .09 .49 .25 .00 .30 P3dsph .22 .02 .43 .02 .06 .59 P=.05*** p=.01*** .16 .24 .16 .24 .84 1.43 .86 1.47 7.20 12.12 9.24 15.44 * 100(simple correlation) 2 ** 100(partial correlation) 100(minimum cor r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t at 2 indicated l e v e l ) 64 TABLE BIO SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN LOAD AND SELECTED VARIABLES. GROUP 2. Pooled-Egg Basis Bird Av. Per Period Basis n=425 n=74 lOO(so) 2* 100(pc)2»» lOO(sc) 2* 100(pc)2»» S t i f f 56.19 15.39 80.17 22.63 Eggwt 10.76 1.06 23.32 5.82 Width 9.22 .20 19.04 .97 Length 2.89 •98... 10.47 2.21 Shelwt 39.38 1.60 58.80 .44 Thick 49.41 2.32 75.43 9.49 Persh 42.88 .01 65.90 5.56 Mgmcm2 46.69 .47 69.12 .66 Shindx 1.40 .09 3.40 .03 Round 2.06 .33 5.45 2.91 Trusph 2.97 .18 9.48 4.22 Prasph 2.10 .38 5.79 3.37 P3dsph 1.41 .07 3.53 . .04 D.P.H. 4.27 .24 7.69 7.77 p=.05*** .91 .94 5.18 6.25 P..01*** 1.55 1.60 8.78 10.56 * 100(simple correlation) 2 ** 100(partial correlation) *** 100(minimum co r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t at indicated l e v e l ) 65 TABLE B l l SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN ENERGY AND SELECTED VARIABLES. GROUP 2. Pooled-Egg Basis B i r d Av. Per Period Basis n=425 n=74 lOO(sc) 2* lOO(pc) 2** lOO(so) 2* lOO(po) 2** S t i f f 2.93 .15 17.24 .16 Eggwt 2.75 .89 6.44 4.71 Width 3.92 .19 7.45 1.21 Length .22 .87 A3 1.87 Shelwt 4.43 1.35 13.58 .04 Thick 5.42 2.56 19.50 10.02 Persh 2.92 .00 14.29 6.32 Mgmcm2 4.03 .37 15.18 1.50 Shindx 1.94 .15 5.84 .00 Round 2.16 .33 9.68 3.31 Trusph .00 .16 1.47 4.64 Prasph 2.22 .38 10.21 3.85 P3dsph 1.94 .02 5.95 .06 D.P.H. .45 .33 8.03 8.38 p=.05*** .91 .94 5.18 6.25 P=.01*** 1.55 1.60 8.78 10.56 * 100(simple correlation) 2 ** 100(partial correlation) *** 100(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t at indicated l e v e l ) 66 TABLE B12 SQUARES OF SIMPLE AND PARTIAL CORRELATIONS BETWEEN STIFFNESS AND SELECTED VARIABLES, GROUP 2, Pooled-Egg Basis n=425 Bird Av. Per Period Basis n=74 Eggx?t 11 . 3 2 1 . 5 2 26.81 .41 Width 7 . 0 6 .02 18 . 96 .00 Length 4 . 6 7 . 6 8 18 . 3 4 . 0 3 Shelwt 5 8 . 5 4 2 . 0 6 7 1 . 5 4 . 4 9 Thick 7 4 . 6 8 9 . 5 0 8 8 . 7 6 27.20 Persh 72.88 .82 81.40 > .82 Mgmcm2 7 4 . 9 1 1.18 8 5 . 1 7 .01 Shindx .14 . 1 0 . 7 6 .40 Round . 4 7 . 1 5 1.24 1 . 6 6 Trusph 7.17 . 5 1 12.19 . 1 3 Prasph .46 . 1 3 1 . 3 5 1 . 6 1 P3dsph . 1 5 . 6 5 .81 .38 D. P „ H, 7.00 . 0 3 4 . 5 5 .22 Par„ 0 5 * * * P=° 01*** .91 1 . 5 5 . 9 4 1 . 6 0 5.18 8 . 7 8 6 . 2 5 10 . 5 6 * 100(simple correlation) 2 ** 100(partial correlation) *** 10Q(minimum c o r r e l a t i o n c o e f f i c i e n t s i g n i f i c a n t at indicated level) 67 APPENDIX C 68 TABLE Cl STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 1, POOLED-EGG BASIS. n=2733 Independent Variable Analysis 1 F 2 1 - Ratio 3 \ 4 S t i f f 581. 40 581. 49 582. 04 582. 47 586. 72 Eggwt • 10 — - - >-Width 4. 35 13. 74 29. 33 89. 06 88. 06 Length 1. 09 1. 01 1. 03 - — Shelwt 9. 57 10. 80 28. 02 28. 04 77. 48 Thick 39. 53 39. 45 39. 84 39. 77 41. 18 Persh 1. 91 2. 24 2. 77 2. 47 57. 81 Mgmcm2 1. 01 • 92 1. 16 1. 30 — Shindx 2. 24 2. 14 2. 10 7. 37 6. 80 Round 13. 21 14. 90 16. 95 19. 04 19. 24 Trusph 0 20 0 11 — — Prasph 12. 23 13. 93 16. 23 18. 33 18. 55 P 3 d s p h 9. 56 9. 79 10. 75 11. 18 10. 37 10 OR2 62. 2 62. 2 62. 2 62. 2 62. 2 F . 0 5 = 3 ' 8 / + F . o i = 6 - 6 ^ 69 TABLE C2 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 1. i POOLED-EGG BASIS. n=2733 F - Ratio Independent Variable Analysis 1 2 3 4 5 S t i f f .22 .22 _ Eggwt .84 .75 .74 1.18 12.42 Width 1.14 1.01 1.03 .60 — Length .14 — — — --Shelwt 9.52 9.38 9.46 11.98 11.50 Thick 45.27 45.21 48.93 48.99 49.30 Persh .67 .63 .65 — — Mgmcm2 1.86 1.84 1.89 11.70 11.23 Shindx 2.58 4.85 4.87 5.63 7.69 Round 6.71 7.39 7.51 6.87 6.29 Trusph 1.89 1.79 1.79 3.04 76.21 Prasph 5.93 6.57 6.65 6.03 5.44 P3dsph 5.23 5.36 5.40 5.25 4.73 10 OR2 20.2 20.2 20.2 20.1 20.1 F.o 5 - 3'8i+ F .01 = 6.64 70 TABLE C3 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 1. POOLED-EGG BASIS. n=2733 Independent Variable Analysis 1 F - Ratio 2 3 4 Eggwt .57 1.22 1.64 .87 Width 1.22 6.43 10.69 17.43 14.48 Length .06 .30 — — — Shelwt 1.41 1.34 1.1.2 2.17 65.02 Thick 134.53 135.17 135.41 136.09 145.53 Persh .88 .92 .86 — — Mgmcm2 3.33 3.59 3.39 19.64 233.89 Shindx .04 — — — — Round 4.09 4.41 5.00 3.57 . 18.15 Trusph .03 ; — — Prasph 2.40 2.55 2.96 2.16 — P3dsph .68 1.01 1.75 — 1.0 OR2 76.1 76.1 76.1 76.1 76.1 p . o 5 - y-^ p.oi " 6-61t 71 TABLE C4 STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 1. :• BIRD AVERAGE PER PERIOD BASIS. n=46l F - Ratio Independent Variable Analysis 1 2 3 4 5 S t i f f 70.32 71.85 71.59 71.49 72.98 Eggwt 3.51 6.06 11.28 11.28 11.18 Width 1.08 1.02 — — — Length .06 — — — Shelwt 4.37 12.71 12.06 12.12 12.09 Thick 13.05 13.35 1.3.61 14.71 15.36 Persh 3.64 13.24 12 .53 12.40 1.1.96 Mgmcm2 .15 — — — Shindx .97 .88 .82 — — Round 3.46 3.34 3.87 4.49 91.04 Trusph 6.05 10.13 26.15 33.41 31. 36 Prasph 2.20 2.09 2.52 2.48 — P3dsph .21 .26 - - — 10 OR2 79.6 79.6 79.6 79.5 79.4 F . 0 5 3.86 F . 0 l 6.69 72 TABLE C5 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 1. BIRD AVERAGE PER PERIOD BASIS. n=46l F - Ratio Independent Variable Analysis 1 2 ? 4 5 S t i f f .35 .33 .32 — — Eggwt 3.00 3.41 6.03 11.25 11.19 Width .94 .89 1.03 — — Length .13 .16 — — — Shelwt 3.72 12.39 12.53 12.03 12.07 Thick 14.93 15.02 15.24 15.52 17.62 Persh 4.24 13.23 13.32 12.42 11.99 Mgmcm2 .05 —, — — — Shindx .82 .82 1.54 .76 — Round 3.04 3.00 3.73 3.19 108.41 Trusph 6.22 6.36 11.22 30.58 37.03 Prasph 1.84 1.80 2.34 1.96 — P3dsph .12 .12 — — 100R2 41.1 41.1 41.0 40.8 40.5 p.05 " 3- 8 6 p . o i - 6 - 6 9 73 TABLE C6 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 1. BIRD AVERAGE PER PERIOD BASIS. n=46l Independent Variable. Analysis 1 F -2 Ratio i 4 5 Eggwt .13 .12 > Width .14 .18 1. 88 2.02 — Length . 04 • 06 •- — Shelwt 2.89 2.89 3. 93 6.78 127.00 • Thick 39.98 40.15 40. 26 42.09 41.20 Persh .28 .28 • 33 — Mgmcm2 3.87 3.88 4. 33 25.57 179.09 Shindx .02 — — — — Round 2.42 2.68 2. 73 10.11 93.93 Trusph 1.46 1.45 2. 88 2.67 19.83 Prasph 1.13 1.27 1. 28 — P3dsph .16 .29 1. 1.78 10 OR2 90.3 90.3 90.3 90.2 90.2 F , 0 5 = 3.86 F.01 - 6' 69 74 TABLE C 7 STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 1. OVERALL BIRD AVERAGE BASIS. n=53 F - Ratio Independent Variable Analysis 1 2 3 4 5 S t i f f 3.06 2.85 2.50 3.84 5.3^  Eggwt .07 — — — Width .79 .92 4.20 3.05 14.42 Length .46 .48 — — --Shelwt 1.17 4.58 3.68 2.60 10.53 Thick .84 1.12 1.17 — — Persh .45 — — — — Mgmcm2 .30 4.10 3.39 3.09 8.68 Shindx 3.09 3.39 2.48 2.04 — Round 1.87 2.30 3.62 3.70 5.28 Trusph 1.49 2.74 1.84 1.23 .— Prasph .65 .84 P3dsph 1.37 1.39 1.43 100R2 89.0 88.8 88.5 87.8 87.2 F .05 4.09 4.07 4.07 4.06 4.05 r . o i 7.33 7.27 7.26 7.23 7.20 75 TABLE C8 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 1. OVERALL BIRD AVERAGE BASIS. n=53 F - R a t i o Independent V a r i a b l e A n a l y s i s 1 2 3 4 5 S t i f f . 5 9 1 . 0 3 Eggwt . 0 9 Width . 6 7 4.40 3.14 2.41 1 8 . 6 7 L e n g t h . 5 8 __ -Shelwt 1.12 3 . 8 7 2.61 1 . 8 3 14.40 T h i c k . 9 5 1 . 5 3 . 8 7 P e r s h . 2 5 — Mgmcm2 . 3 8 3 . 5 6 2 . 2 7 2 . 3 7 1 7 . 5 2 S h i n d x 3.24 2 . 9 3 2 . 1 6 1. 70 Round 1 . 6 0 1.84 2 . 3 9 2.12 5.82 Trusph 1.24 1.78 . 9 4 P r a s p h . 5 5 . 6 3 —-P3dsph 1.44 I . 8 3 1 . 3 7 1 . 1 3 10 OR 2 61.8 61.0 5 9 . 3 57.8 55.8 p.o 5 4 . 0 9 4 . 0 7 4 . 0 6 4 . 0 5 4.04 p.oi 7 . 3 3 7.27 7.24 7 . 2 1 7 . 1 9 76 TABLE C9 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 1. OVERALL BIRD AVERAGE BASIS. n=53 F - R a t i o Independent V a r i a b l e A n a l y s i s 1 2 3 4 5 Eggwt .01 — Width 1.23 2.62 5.96 10.61 17.32 Length M .67 2.35 — — Shelwt 2.04 4.17 4.03 15.37 26.25 T h i c k 2. ?4 3.04 3.21 3.05 5.24 Persh 1.56 1.80 1.92 1.69 — Mgmcm2 4.27 7.42 7.51 11.54 36.30 Shindx .17 .27 — — Round .16 2.97 3.97 2.66 — Trusph .27 1.08 1.14 — Prasph .03 — P3dsph .27 .35 — 10 OR2 95.9 95.9 95.9 95.6 95.2 P 05 F . 0 l 4.08 7.31 4.07 7.27 4.06 7.24 4.05 7.21 4.04 7.19 TABLE CIO STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 2. POOLED-•EGG BASIS. n=425 Independent Variable Analysis 1 F -2 Ratio 3 4 5 S t i f f 74.74 75.28 74.75 75.01 74.44 Eggwt 4.79 5.18 7.25 8.61 12.81 Width .83 1.09 2.97 2.56 --Length 4.41 4.33 3.08 2.98 8.80 Shelwt 7.07 8.95 8.57 9.51 10.11 Thick 9.63 10.06 9.54 9.23 9.06 Persh .04 — -- — Mgmcm2 2.26 7.59 7.25 8.27 8.73 Shindx .52 3.74 2.77 2.33 — Round .99 .83 — — — Trusph .80 .80 — — Prasph 1.16 .99 .74 P3dsph .18 _= D.P.H. .99 .99 1.07 --10 OR2 60.2 60.2 60.0 59.9 59.6 P.0 5 = 3.86 P_ 0 1 =6.70 78 TABLE C l l STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 2. POOLED--EGG BASIS. , n=425 F - Ratio Independent Variable Analysis 1 2 3 4 S t i f f .60 _ _ Eggwt 4.09 4.84 6.59 7.82 12.55 Width .78 1.05 2.87 2.42 — Length - 3.81 4.00 2.71. 2.58 7.89 Shelwt 6.18 8.54 8.19 9.04 9.97 Thick 10.66 10.43 9.79 9.42 9.21 Persh .03 — — Mgmcm2 1.92 6.89 6.58 7.52 8.23 Shindx .64 3.51 2.52 2.08 — Round 1. 01 .97 — Trusph .73 .80 — Prasph 1.18 1.13 .71 --P3dsph .06 — D.P.H. 1.36 1.42 1.51 — 10 OR2 11.8 11.7 11.3 10.8 10.2 F Q 5 = 3.86 F = .01 = 6.70 79 TABLE C12 STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 2. P00LED-•EGG BASIS. n=425 F - Ratio Independent Variable Analysis 1 2 3 4 5 Eggwt 6.46 , 8.01 10.50 10.26 10.03 Width .06 — — Length 2.71 3.26 5.01 4.74 4.70 Shelwt 8.93 9.21 9.99 9.98 9.74 Thick 43.63 43.90 43.72 44. 38 44. 30 Persh 3.65 3.91 4.24 4.07 4.16 Mgmcm2 5.32 5.77 6.37 6.24 6.14 Shindx .44 . 36 -- — — Round .41 .49 .35 .30 --Trusph 2.06 2.67 4.14 3.88 4.06 Prasph .35 .42 .29 »=. P3dsph 2.69 2.71 6.17 5.89 6.35 D.P.H. .14 — 10 OR2 79.3 79.3 79.3 79.2 79.2 P05 " 3'86 F = .01 = 6.70 80 TABLE C13 STEPWISE MULTIPLE REGRESSION WITH LOAD AS THE DEPENDENT VARIABLE GROUP 2. BIRD AVERAGE PER PERIOD BASIS. n=74 F - Ratio Independent Variable Analysis 1 2 3 4 •5 S t i f f 16.97 17.58 16.89 16.88 16.91 Eggwt 3.38 8.43 7.72 6.47 7.98 Width .67 1.02 3.42 .19 — Length 1.21 1.74 3.42 3.62 8.22 Shelwt .44 6.29 6.10 6.95 6.84 Thick 6.13 6.19 6.35 5.07 5.02 Persh 2.72 4.73 4.77 5.51 5.44 Mgmcm2 .17 — -- — Shindz .09 .35 — — Round 1.44 1.36 -- --Trusph 2.47 3.47 2.95 Prasph 1.70 1.63 1.44 — P3dsph .00 — — — D.P.H. 4.92 5.52 7.58 8.97 9.50 10 OR2 87.1 87.0 86.7 85.7 85.7 F.o5  p.oi 4.00 7.08 4.00 7.07 3.99 7.05 3.99 7.04 . 3.99 7.03 81 TABLE Cl4 STEPWISE MULTIPLE REGRESSION WITH ENERGY AS THE DEPENDENT VARIABLE GROUP 2. BIRD AVERAGE PER PERIOD BASIS. n=74 F - Ratio Independent Variable Analysis 1 2 3 4 5 S t i f f .11 Eggwt 2.77 3.21 4.77 4.50 9.43 Width .68 .94 2.57 1.96 --Length 1.10 1.16 2.57 3.90 11.34 Shelwt .15 .19 Thick 6.43 7.97 8.12 7.94 7.09 Persh 2.93 3.50 5.53 5.01 6.20 Mgmcm2 .42 .47 6.72 6.14 7.50 Shindx .05 .20 — Round 1.59 1.81 2.16 — Trusph 2.57 2.84 2.61 2.15 Prasph 1.89 2.14 2.53 P3dsph .00 — D.P.H. 5.38 5.57 5.89 8.80 9.54 100R2 46.2 46.1 45.8 42.2 40 .3 3.99 3.99 3.99 7.05 7.04 7.03 .05 '.01 4.00 7.08 4.00 7.07 82 TABLE C15 . STEPWISE MULTIPLE REGRESSION WITH STIFFNESS AS THE DEPENDENT VARIABLE GROUP 2. BIRD. AVERAGE PER PERIOD BASIS. n=74 ' p - Ratio Independent Variable Analysis 1 2 Eggwt .17 .52 2.90 2.41 7.78 Width .00 — — Length .04 .04 — . — Shelwt .26 1.90 2.36 ; 1.90 — • Thick 22.57 23.45 27.11 28.26 438.08 Persh .44 .97 1.23 .93 Mgmcm2 .00 — • _ _ • — Shindx .19 .20 i— Round .96 1.03 .88 — — Trusph .08 .15 v -31 :'i • — . Prasph .94 1.01 .86 — P3dsph .15 . 20 .84 6.34 4.59 D.P.H. .16 .16 — '. — 100R2 90.8 90.8 90.8 ; 90.6 90.0 P , 0 5 4. 00 4. 00 3.99 3.99 3.99 F.01 7.08 7.07 7.05 7.04 7,03 83 TABLE C16 SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD. GROUP 1 POOLED-EGG BASIS. 11=2733 A n a l y s i s 1 2 3 4 5 S t i f f 1 0 3 . 5 * 3 7 3 1 . 3 * * I O 3 . 2 3748.7 102.5 3911 .9 101.5 3 7 4 5 . 6 101.5 3 7 2 4 . 3 Eggwt - 5 1 . 1 28.4 -46.6 25.8 - 3 1 . 3 9 5 . 1 —-; —•-• ,• Width 3 2 3 9 . 3 17.8 2069.0 7 2 . 7 I 6 9 1 . 6 204.0 • 691.3 1 3 2 . 0 L e n g t h -542.8 1 . 4 175.8 3 . 2 S h i n d x - 6 1 . 7 2 . 6 — — 3 1 . 8 1 5 0 . 6 — Sy 3 6 3 . 9 364.0 3 6 4 . 1 3 6 9 . 2 3 7 0 . 4 Constant -1973.5 - 5 9 5 0 . 4 - 4 2 0 5 . 2 -1146.6 - 1 7 5 9 . 2 10 OR 2 6 0 . 5 6 0 . 4 6 0 . 4 5 9 . 3 5 9 . 0 F.o 5 - 3: 84 P = . 0 1 6.64 * P a r t i a l R e g r e s s i o n C o e f f i c i e n t ** F - R a t i o 84 TABLE Cl? SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD. GROUP 1 BIRD AVERAGE PER PERIOD BASIS. n=46l A n a l y s i s 1 2 3 4 5 S t i f f 111.0* 1365.1** 111.2 I369.6 109.1 1444.1 107.6 1375.0 107.6 1256.6 Eggwt -82.5 16.7 -85.9 1.8.3 -41.9 57.6 — — Width 1377.1 1.2 3012.5 31.5 1.8 76.1 85.8 — 505.3 27.0 L e n g t h 1564.3 4.1 477.1 5.2 — . — — S h i n d x 90.9 2.1 — — 35.8 69.7 --Sy 212.6 212.8 213.8 217.3 226.6 Constant -15807.5 -9586.2 -4517.2 -1582.3 -1104.0 10 OR 2 77.7 77.5 77.3 76.5 74.4 F.05 " 3-86 F .01 = 6.69 * P a r t i a l R e g r e s s i o n C o e f f i c i e n t ** F - R a t i o 85 TABLE C18 SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD. GROUP 1 OVERALL BIRD AVERAGE BASIS. n=53 Analysis 1 2 3 4 5 S t i f f 110.3* 221.8** 109.8 221.1 105.8 225.1 107.8 223.6 102.3 204.0 Eggwt -114.3 4.9 -114.6 4.9 -35.2 5.1 — — Width 188.3 .0 4073.1 8.7 2018.5 14.4 — 922.8 15.9 Length 3690.0 1.6 867.7 2.6 — — — Shindx 225.3 .9 — — 40.4 12.1 — Sy 146.2 146.1 148.4 159.0 154.4 Constant -31061.2 -•14655.3 -5442.5 -1928.1 -2762.3 10 OR2 86.3 86.0 85.3 82.7 83.7 F.05 4.05 4.04 4.04 4.03 4.03 F.01 7.20 7.19 7.18 7.17 7.17 * P a r t i a l Regression Coefficient ** F - Ratio 8 6 TABLE C19 SELECTED NON-DESTRUCTIVE CHARACTERISTICS IN MULTIPLE REGRESSION ON LOAD FOR EACH TEST PERIOD F - Ratio of Independent Variable Period 1 4 7 2 . 2 6 3.08 .59 . 2 3 . 0 3 6 2 . 4 2 504.14 2.51 1.77 .17 .34 6 2 . 0 3 424.04 5.74 1 . 1 3 . 2 3 .01 60.4 4 420.69 . 7 2 1.06 .09 . 1 3 6O.5 5 3 3 6 . 9 6 4.40 5.18 . 5 2 1 . 0 3 57.7 6- 462.08 2 3 . 7 1 2 . 0 9 .91 .08 6 3 . 4 7 3^5.51 . 1 5 .08 . 5 1 .64 60.4 8 462.92 5.38 .10 5.62 4 . 2 6 6 3 . 3 F . 0 5 = 3.87 F.oi " 6« 7 2 

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