OK, I mentioned in an other thread that I would post my findings about how to calculate whp from your 1/4 mile times and the weight of the vehicle. The following info is based upon what I could remember from physics classes taken 15-20 years ago. I was a bit rusty to say the least, and couldn't figure it out. I was missing a crucial step. Finally I stumbled upon a document from Earle McCaul from the 1970's which not only filled in my missing step, but confirmed my other analysis. That document is attached.
Now, on to the goods.
Short version:
This equation gives the GUARANTEED MINIMUM amount of whp that your car had to lay down in order to get the ET you posted. (Provided the track accurately measured your ET, and you have an accurate measure of the weight of your car - including driver)
WHP = (Weight * 196.93) / ET^3
The ^3 means "to the power of 3" or cubed. (in other words ET * ET * ET)
This number does NOT factor in the roll resistance of your tires or air resistance.
Long version:
The above mentions a "GUARANTEED MINIMUM" whp measure from ET and weight. How? Well, it is a physical fact that is takes a certain amount of power to move a certain mass a certain distance in a certain amount of time. Well, we know the distance (1/4 mile) and we know the time (your ET) and we should know the mass (mass = weight/32.174) so we should be able to quickly calulate the power required.
There are several advantages to this approach. In this approach we aren't worrying about friction (roll resistance) or air resistance, or even drive train loss. It is simply how much power to move ANY object that far in that time. It doesn't matter if we're talking about a 3240 pound brick or a Crossfire SRT-6 - the physics of motion and power remain the same. We could attempt to calculate the power lost to roll resistance and to air resistance, but the calculations become very complex, and would require a lot more information, some of which is hard to get. Since the power losses due to roll resistance and air resistance are small (not insignificant) we can use the number given from the above equation as a minimum, knowing that you actually laid down more power, which was lost to roll resistance and air resistance.
It is also important to note that this is horsepower as measured at the wheel, NOT crank horsepower. To consider crank horsepower, we would have to know the precise drivetrain loss for your car.
Now back to how we figured this out. We start out with the definition of Power.
Power = work / time
Which begs the question what is work?
Work = force times distance
So what is force?
Force = mass times acceleration
How does mass relate to weight?
Mass = weight / 32.174 (32.174 is the acceleration due to gravity)
So how do we know what the acceleration of the car was? Well, short answer is that we don't. Are we at a dead end here? No. We can use the tools of physics to replace acceleration in this equation with something else. This uses physics kinematic equations. From kinematics we know that distance equals initial velocity times time plus one half acceleration times time squared.
distance = Vi * t + 1/2 * a * t^2
Well, we know that in this instance that the initial velocity of the car is 0, because all 1/4 races are done from a standing start. So we can eliminate the "Vi * t" portion of the equation, because anything times 0 is 0. That leaves:
distance = 1/2 * a * t^2
We want to solve the equation for a, which is acceleration, so that we can substitute it into our force equation. Solving it for a yeilds:
a = (2 * distance) / t^2
Since we know the distance (1/4 mile) we can replace distance with 1320 feet (a quarter mile). That gives us:
a = 2640 / t^2
Now we can replace acceleration in our force equation above:
F = m * a
F = m * 2640 / t^2
We can also replace mass in that equation with our weight calculation, giving us:
F = (weight / 32.174) * 2640 / t^2
Which simplifies to:
F = 82.058 * weight / t^2
Now we can substitute our force equation into our work equation.
Work = F * distance
Work = (82.058 * weight / t^2) * distance
Work = (82.058 * weight / t^2) * 1320
Work = 108311 * weight / t^2
And we can now substitute our work equation into our power equation.
Power = work / t
Power = ( 108311 * weight / t^2 ) / t
Power = 108311 * weight / t^3
Now we have to consider units. These equations use standard units of measure, which is why we used 1320 feet for the distance, not .25 miles. Feet are standard measure, not miles - at least as far as physics equations go. The standard English (not metric) power unit in physics is the watt, not horsepower. So we need to include a conversion between watts and horsepower. 1 horsepower = 550 watts. So we need to divide the 108311 by 550 in our equation, weilding:
Horsepower = 196.93 * weight / t^3
Putting it in more familiar terms:
WHP = 196.93 * Weight / ET^3
Keep in mind that the weight in the equation includes the driver. A Crossfire SRT-6 Coupe weighs 3240 pounds. So if the driver weighs 200 pounds (for a total of 3440), and you ran a 13.550 ET, then you have laid down at least 272.30 whp. Of course, your car would have had more whp than that if you wasted some of it spinning out at the start line. Also you lost some power to air resistance and roll resistance. But you definitely laid down that 272.30 hp to the ground.