I'm trying to buy a car that really feels fun to drive, and the one I test drove doesn't feel all that fun despite having high horsepower, torque, and acceleration. I'm trying to find a mathematical method for observing the car's push-you-back-in-your-seat factor. It's not just acceleration.
http://www.city-data.com/forum/automotive/1977660-how-get-pinned-pushed-into-seat.html
You can't just say horsepower or torque. Some cars with less horsepower and torque have given the push you back into your seat feeling more than cars with higher. It's about the rate of change in these. Some say the more linear the horsepower over RPM graph the less push you feel. Does that mean it's the second or first derivative of Horsepower/RPM? Rate of change of a curve sounds like second derivative. . d^2HP/d^2RPM. Does that have a certain term? Power = torque / angular speed, and in this case horsepower = torque / RPM. Therefore d^2(HP)/d^2(RPM) = d^2(torque*RPM)/d^2(RPM). Can this be simplified any further? Is this a correct interpretation of the sudden feeling of getting pushed back, and if so is there a term or some quantity that helps describe it instead of just the second derivative of HP/RPM?
And perhaps it's the rate of change of Torque/RPM instead of HP/RPM.. I'm not sure.
Best Answer
From a physics point of view, it's exactly acceleration. The larger the acceleration of the vehicle, the greater the force the seat is pushing on you to achieve it. (You could of course render acceleration as a function of mass and torque or power, but that's just complicating it)
That said, our bodies are not precision instruments, and our perception of "force" is not perfect. A smaller, louder, windier car may "feel speedier" than a big, quiet boat, even if the actual acceleration is smaller. But those perceptions are not easy to tie an equation to.