Top fuel facts

[capitlj]

Zach that kind of arguement is not going to get this on mythbusters, step it up guy.

[thrash]

the average velocity is nothing more than the change in velocity over the change in time. in the case of a standing start at t0, it's as simple as dividing trap speed by seconds.

here's a fun experiment! supposing that i need to go 1320 feet, and i do it in 4.5 seconds, what is my average velocity?

1320 / 4.5 = 293.333

293.333 is a funny number in a funny unit - its in feet per second.

so we figure there are 5280 ft in a mile and 3600 seconds in an hour, and we see that to go from FPS to MPH we divide the FPS value by (5280/3600).

If you cut a 4.5 second quarter mile, your average speed was 293.33 fps or 200 MPH, dead on.

If you cut a 4.0 quarter mile, your average speed was 225 mph.
here are the values in seconds, fps, and mph, for the spread between a 4.0 ET and a 4.5 ET, in .1s increments:

4.0 - 330 - 225
4.1 - 321.9 - 219.5
4.2 - 314 - 214
4.3 - 306.9 - 209
4.4 - 300 - 204
4.5 - 293.333 - 200

if we know the time, and that we had a standing start, what can we say about the trap speed?

Well, we cannot say anything definitively. If the change in velocity were constant (ps: the change in velocity is acceleration, and the change in a function over time is known as its "derivative", thus acceleratoin is the derivative of velocity..), then the acceleration at t(x) would be a simple line. (when f'(x) is constant, f(x) is linear)

One would expect that at the half way point, the car would have instantaneously acheived its "average" velocity. It spent the first half of the run going slower than average, and will spend the final half of the run going faster than average.

So in the constant-acceleration case with a 200 mph average speed, the start speed is 0 and the trap speed must therefore be 400mph.

The ending velocity, in fps would be 586.6 fps, and it was acheived in 4.5S, for a constant acceleration of just over 130f feet per second "squared" (per second "squared" are the units of acceleration)

Acceleration due to earth Gravity in the FPS system is about 32 fps^2, and so the 4.5s constant-acceleration standing start run is 4.074Gs for its entire duration.

Since a top fuel car does not trap at 400mph, and it also finishes the run in under 4.5s, we can say that is average acceleration is actually higher than 4G. We can also say that it's average speed is higher than 200 mph, with the majority of the acceleration front-loaded into the first half of the run.

This intuitively makes sense -- every ground vehicle has higher acceleration at lower speeds than it does at higher speeds, if for no other reason than work-required to overcome aerodynamic drag increases with the square of velocity.

The short version is this:
if you finish the quarter in under 4.5 seconds, your average velocity was higher than 200mph, and your average acceleration was higher than 4 Gs. No exceptions.

[capitlj]

That's more like it.