Woodward — TJie Efficiency of Gearing under Friction. 103 

 The energy exerted by the driver during this action is 



U 



_1q 



M. 



and the ratio of energy lost to energy exerted is 



U V Vi r^ ) 2q 



2^-7Mog(l+|)-A'log(l+|; 



(15). 



Let n^ and % represent the numbers of teeth in the driver 

 and follower. Then, but one pair of teeth being in action at 



a time, 



irr, 

 q = — ^ 



When the obliquity is as small as possible, 

 max. r ■= q sin 6 =-r^ cos d 



hence 



tan d = - = - ' and 



q IT 



sin (^ — (p) , . , a\ ^1 — *""/ 



A = r . \ . ^^ = r, (cot ^ — cot (?) = r, \ / 

 ^ sin ^ sin cp ^ ^ ^ nj 



sm sin <p 



8m(d + <p) ' . , , . n^ Hj + TT/ 



/1_ . MA=fi + 1^3! 



\i\ rj 2q^ V?»i nj 27rr^ 



Substituting the above values in (15) and removing r^ from 

 the brackets, we have 



_'iL±^log(l+_^,)" 



^i/ V "i + 'v -^ 



(16). 



