Jan. 38, 191S 



Study of Plow Bottoms 



171 



From equations (70), (71), (72), and (47) the following are obtained; 

 Table VIII. — Values (in inches) for — 



dz 



■^=o.oooo2244[{vH^-4S.5vt+s42){2vH-4S-5'v)]+'o 





d^z 



^=o.oooos244[{vH^-4S.5vt+s42){2V')+(2vH-45.svy] 



^^ (.2382+1. i26x-io.o3)^ 

 dt 2x — 1.1262+20.78 



(,.,38,+..,.6,-,o.03)g-.(g)'+o..38(g)-+.../(g)(g) 

 2a:— 1.1262+20.78 



dy (-^^+4^-41)^ 

 dt 



(73) 

 (74) 



(75) 

 (76) 



(77) 



(78) 



(79) 



3-6>'-i.5 



^^ (-2X+42.4x)g-2(g)^-3.6(g)' 

 dt^ S.6y-i.s 



The plow moved forward with a velocity of 36 inches per second, giving 



.^=36^ (80) 



From equations (74), (75), (76), {77), (78), (79), and (80) the values 

 listed in Table IX are computed. 



Table IX. — Values for — 



By making the proper substitutions from (80), (74), (76), and (78) in 

 equations (54), (57), (58), and (59) the values of the direction cosines 

 for the normals A^ the tangents to the path T, and the perpendiculars 

 to the planes formed by the normals and tangents R for three points 

 are computed and listed in Table X. 



