A double$-$strand no$.60$ roller chain is used to transmit power between a $13-$tooth driving sprocket rotating at $\backslash (300\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash )$ and a $52-$tooth driven sprocket.

$($a$)$ What is the allowable horsepower of this drive?

$($b$)$ Estimate the center$-$to$-$center distance if the chain length is $82$ pitches.

$($c$)$ Estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is $30$ percent less than the corrected $($allowable$)$ power.