# How can `tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)` be proved. I have a relation for back drive efficiency given by `e_b = (1/tan lambda)*(cos phi_n*tan lambda- mu)/(cos...

How can `tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)` be proved. I have a relation for back drive efficiency given by `e_b = (1/tan lambda)*(cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)`

Refer the equation 11 for lead angle back drive efficiency at:

*print*Print*list*Cite

### 2 Answers

The given relation ` tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda) ` cannot be proved.

As seen from the link provided in the question the back drive efficiency is given by `e_b = (1/tan lambda)*(cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)` where `mu` is the coefficient of friction. As all the values in the expression are dimensionless, the back drive efficiency is also a dimensionless scalar. This does not mean that `tan lambda = (cos phi_n*tan lambda- mu)/(cos phi_n + mu*tan lambda)`. All the values on the right are scalars that when multiplied, subtracted, added and divided together give a scalar that is the value on the left.

the equation 10 and 11 is derived from one equation Torque drive.

how to trace back equation 10 and 11, to their origin formula

revert back to their ancestor ?