Max Power rpm

It occurred to me while I was reading the book – ‘Fundamentals of Vehicle Dynamics’ by Thomas Gillespie.

I have been using torque for all calculations or trying to explain everything based on torque. It was like I almost forgot the ‘power’ of an engine. I never did use power for any calculations. And I dint see the relevance of it, and was like ‘power = torque times angular velocity’ – at a particular torque conditions the engine rotates at a particular angular velocity and the product is taken.

I dint think why the power curve was given importance, one reason being it can be constructed from a torque. MY Negligence.

In the book, it was given ‘Power = Force X Velocity’ – it was a revelation, though I knew the formula. ‘I was not using this simple formula.’ Tractive force times velocity equals the power at the wheels (engine power – losses). ‘Oh! shame on me’.

The maximum traction at any given velocity is at the point when the power at the wheels is highest or if we assume the losses is not substantial then the rpm at which engine produces the peak power.

The book clearly says that if we have a transmission with infinite ratios(without slippage) then we can keep the engine revving at max power rpm to get the maximum traction force.

It took me some time to digest that. Because traction is due to torque and hence was thinking that the maximum traction should be at that rpm where we get the maximum torque. So did I go wrong?? No, I can’t be.

But the calculations in the book and the calculations I did, were getting the same answers. That instilled some confidence in me. So I started re-checking everything including basics. Then to check whether what the book said is correct I tried with some graphs. That gave me another ‘revelation’. The velocity depends on the ratio of Gearboxes, the multiplication of torque, the division of rpm, but the final force – traction force – will be higher for the max power rpm at a particular vehicle speed. So I did go wrong? Many people say that I am a very stubborn kind of a guy – true, only in cases where my common sense says it can’t be the other way round.

Now it came to me ‘where I was wrong (or true)’
I was considering same ratio for comparing max power rpm and max torque rpm. Or I was considering at a particular ‘gear’. The velocity of the vehicle will be different in both cases. Though I will be getting more traction at peak torque rpm, the velocity of vehicle is lower.


That page was mentioning something about the gearboxes and traction. I found out that what I guessed was correct. Or what was wrong.

Now it said the manual transmission gearbox ratios are selected to get maximum traction within the constraint of the size of gearbox.
The traction at a particular gear is found out from the torque curve.

May be – MY Guesses

To find the optimum gear ratios for maximum traction and hence maximum acceleration.

The final gear will reflect the maximum speed that the vehicle can travel (Also depends on the torque/power of engine – power should be more than the losses at that speed).

The first gear will depend on the load the vehicle has got to carry (for CVs).

The graph showing the force vs speed is given from the book.
As clearly stated the maximum traction force at any vehicle speed(not any gear – not constant ratio in transmission line) corresponds to the max power line.

Also shown in the picture, the torque curves multiplied by arbitrary gear ratios.

The equation of the ‘constant engine power’ is that of a rectangular hyperbola, the equation being xy = k.
If we can get the equation of the engine torque, then the equation of the curves.

Now optimizing for the gear ratios – lesser the area between the ‘constant power curve’ and the torque curves, better the performance.

Though the theory can be written easily like that the evaluation is quite difficult. Also the equation for torque curve over engine/vehicle speeds, it seems ‘ridiculous’ for me. But I guess can be done like that.

A word from the book – the best gear ratios usually fall close to a geometric progression. – well I don’t know why?

Please do throw some light if you have some idea.