What causes the push you back suddenly into your seat feeling when you accelerate cars?
Solution 1
There's acceleration and then there's also "jerk." Jerk is the rate at which the acceleration changes i.e. da/dt. A car that goes, say, 0 to 60 in four seconds can do so in many different ways such as a constant acceleration throughout or a big jump in acceleration at the beginning. So you're right that it's not just acceleration. It's also the rate of change of acceleration. I don't know how that relates to the engine characteristics.
Solution 2
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.
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Nicholas Davis
Updated on October 01, 2020Comments

Nicholas Davis over 2 years
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 pushyoubackinyourseat factor. It's not just acceleration.
http://www.citydata.com/forum/automotive/1977660howgetpinnedpushedintoseat.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.

d_b over 2 yearsWhat makes you say it's not just acceleration? Naively, the larger the acceleration, the more normal force you will feel from the seat back. If you can help explain why acceleration doesn't capture the effect you're talking about, it could help us determine exactly what does capture it.

Nicholas Davis over 2 yearsFor example, the car I drove has a 060 acceleration of around 5 seconds. Yet it didn't push me back in the seat like say a car with a less linear power curve would. To be specific a 2010 Ford Sho supposedly pushes you back in your seat way more than a Lexus IS 350, yet they both have a 060 of 5 seconds. Explanations for this include more lowend (low RPM) torque from the Ford SHO, and that the Lexus has a relatively linear Power Curve (power over RPM).

Nicholas Davis over 2 yearsTo comment further, most Lexus' don't "feel" fast despite having high acceleration. I guess I'm leaning towards the fact the 2nd derivative of power by time is 0 or approaching 0, making you not "feel" it even though perhaps the force is greater. So maybe my answer is that as the 2nd derivative of power by time approaches 0 the less of a push you feel in a car, and the converse is also true.

Bill N over 2 yearsCheck out these Tesla videos: youtube.com/watch?v=y1bYcetcufw and youtube.com/watch?v=I5mZ1IK7SuU


Philip Wood over 2 yearsThe motionrelated quantity is indeed simply acceleration. I'll just add seat design to the other factors BowlofRed has suggested in the second paragraph above.