Simple car acceleration formula?

[jpsa]

is there a simple formula to get the theoretical acceleration and top speed of a car given power, mass and drag?

 

[ray b]

MAYBE

but in the real world drag racers
use a box called a G-teck to get instant answers
gear ratio and tyre traction are also big factors as is driver skill

 

[chroot]

F = ma.

And ray, the Gtech sucks.

- Warren

 

[Cliff_J]

You would also need to know the average power applied as a function of time (unless you have a CVT) and drivetrain losses.

The tire/traction point is an interesting one as well, the typical understanding of analyzing 1/4 mile tests is to use the MPH as more an indication of power:weight and the 60ft and ET to determine how large a component the launch played in the run down the track.

There were some approimation formulas published in Hot Rod magazine a few years back, maybe someone has posted something similar online.

Cliff

 

[Pergatory]

Originally posted by Cliff_J
You would also need to know the average power applied as a function of time (unless you have a CVT) and drivetrain losses.

The tire/traction point is an interesting one as well, the typical understanding of analyzing 1/4 mile tests is to use the MPH as more an indication of power:weight and the 60ft and ET to determine how large a component the launch played in the run down the track.

There were some approimation formulas published in Hot Rod magazine a few years back, maybe someone has posted something similar online.

Cliff

Good point. A car's power is not constant, if you have ever seen dynamometer results, the power generally increases as RPM increases, except with turbocharged engines which are more dependent on the RPM of the turbo itself. Anyway, in addition to that, you can only apply as much power as your tires have traction, which increases as weight/downforce increases. As we know, downforce increases as the car's speed increases, and more weight is transferred to the rear as the car accelerates faster (or to the front as it slows its acceleration such as during shifting). Speaking of shifting, you must also add the time it takes to shift, which is different for every driver. So as you can see, acceleration is far from linear, which is why drag racing is a sport and not a study. ;) Don't let me mislead you though, if you think drag racing is complicated, try drifting!

 

[krab]

Originally posted by jpsa
is there a simple formula to get the theoretical acceleration and top speed of a car given power, mass and drag?

Acceleration is complicated, as it depends upon speed, drag and power and weight. Top speed is easy, as it depends only on drag and power. Top speed is achieved when drag equals driving force. But driving force is power over speed and drag is a constant times speed squared. Therefore,

$${P\over v_\infty}= \mbox{constant }\times v_\infty^2$$

or

$$v_\infty=\mbox{constant }\times P^{1/3}$$

For example, for a small aerodynamic car, top speed in mph is 25 times the cube root of the horsepower.