Brakes : frequently asked questions

Question 1
Doug,   Your recommended brake solution technique seems unnecessarily artificial. Why do I have to first assume a dummy brake actuation before working everything out on that basis then finally scaling ?
When I have to find the maximum torque that a brake can develop given that the average pressure over the lining   p_m must not exceed a certain value, why can't I just go straight to ( 9) and work out the corresponding   p_o which I can then use in all further calcs ( 5b) ( 6b) etc ?

Answer
Your suggested approach can too easily lead to complications because of the different actuation constants of the two shoes.
Think of the physical sequence of cause-and-effect :

1. the operator first applies the BRAKE actuation,   P_o
2. which is altered by a shoe's actuation mechanism to furnish the SHOE actuation,   P
3. on which depend all the parameters for that shoe - shoe torque, mean lining pressure etc.
4. which are combined for the two shoes where relevant ( eg. torques ) to give the overall brake parameters.

If you're into maths and enjoy a challenge then there's nothing to stop you trying the recommended solution route with an algebraic rather than dummy   P_o, then solving for   P_o when appropriate. But I'm sure you'll conclude that the "dummy for dummies" recommendation is much less hassle.
Incidentally the foregoing does not apply if the actuation constants are initially unknown and have to be selected. In this case one may consider the two shoes individually and tailor the actuating mechanism to suit.