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So,no matter what gear ratio 'i' I choose, P_out=P_in, since the gear ratio 'i' term would get cancelled at the numerator and denominator.

$$P_{eng}= ω_{eng} M_{eng}= i . ω_{out} \frac{M_{out}}{i}$$

hence P_in=P_out

But, what is the drivetrain efficiency a function of? Is it a function of gear ratio and engine speed and engine torque? Or is it a constant always?

2.And why is the drivetrain efficiency of automatic transmissions 10% lesser than manual? [source page 417:Advanced Direct Injection Combustion Engine Technologies and Development ...

edited by H Zhao]