Chargermal wrote:(The formula I derived from physics says average wheel hp = 197*weight/et^3 and plugging in 11 flat and 3500 lbs that gives 518 average wheel hp so if the Moroso says 520 hp it gives wheel hp, not flywheel/engine hp.)
Sorry to be blunt, but where did you get the "197" constant?
I ask because a "constant" for RWHP CANNOT BE DETERMINED, due to varying factors as Widowmaker has explained...
The accepted formulas for FWHP are:
Hale - HP = (mph/234)cubed x weight (lbs)
Fox - HP = (mph/230)cubed x weight (lbs)
Both the 'constants" (234 and 230) were arrived at by simply taking the results of counltess strip runs using the empirical data. (see link below)
The same CAN'T be done for RWHP, becuase the inertial losses vary to a FAR greater extent for every drivetrain. ITs IMPOSSIBLE to generate an accurate "constant".
Go here for a LOT more reading.
http://www.stealth316.com/2-calc-hp-et-mph.htm
Sorry to be slow answering but work, well, it's been work
. The 197 in the formula I posted comes from converting kilograms, meters, and watts into pounds, feet, and hp. It does not represent any kind of empirical fudging or correction, just unit conversions. If you know the weight of an object, the distance, the time to cover that distance, and assume constant acceleration, you can derive the formula that I posted. It gives the net power used to accelerate the object, or in other words, the power applied to the track by the driven wheels. It says nothing about drivetrain losses and nothing about engine flywheel hp, it tells how much power must reach the track to get the object to cover that distance in that time. The assumption of constant acceleration sounds poor given how fast a car will accelerate in first gear compared to high gear, but it greatly simplifies the math and gives the lowest possible hp estimate. Any other acceleration assumption will require a higher peak hp because some of the time the accleration and thus the hp will be less, so it is a conservative lower bound. Now, the formula is in terms of et, and we all know that et really depends critically on traction so it is not a very accurate number to plug into the hp formula; the mph is much more reproducible. Again, using constant acceleration the et and mph are inversely related: et = a constant / mph and mph = the same constant / et. I used a bunch of et-mph pairs from a turbo regal website because that's the kind of car I have, and I found that for cars running 7's up to 13.50 the best constant was 1356, and for cars slower than 13.50 a more accurate constant was 1370. You can also derive this constant from phyics and you get something like 1450, which tells us that constant acceleration isn't really that great an assumption but again, it's simple and it ain't bad. The "best" number will be different for every different car shape because we are totally ignoring wind resistance, too. Now, if you take the hp formula I gave, hp = 197 * weight / et^3, and substitute 1362/mph (using 1362 instead of my 1356, a slight tweak I'm sure due to using different cars to get the number) for the et, hp = 197 * weight / (1362/mph)^3, and do the algebra you get hp = (mph/234)^3 * weight which is your "Hale" equation. Using my 1356 would give 233 instead of 234 in the same formula, again because I wanted the most accurate numbers for turbo regals. That also shows that your Hale formula is giving wheel hp and not flywheel hp, by the way. Using this formula does involve an empirical constant, the 1362, whereas the one using et does not, but I think it is a net win given how much easier it is to reproduce mph compared to et. Oh, I guess I should say that the uncertainty using et=1356/mph for the regals was +/- .5 sec or so, and my guess is that for a manual trans car the drivetrain losses are small enough that they are probably buried in the "noise" of trying to make identical runs anyway, so the difference between rwhp and flywheel hp is going to be small enough that the formula could be said to give both or either. However, with an automatic trans the apparent losses will be much greater so that's where it should be obvious that the formula is giving wheel hp and not flywheel hp.
You state that "a "constant" for RWHP CANNOT BE DETERMINED" but I think that in the most practical sense you have it backwards. It is the actual power applied to the track through the tires that moves the car (and that is what we really care about), and we can directly measure the result (the et and mph), so we can directly measure the "net" or driven wheel hp. What we cannot easily get a handle on is all the drivetrain losses, and so we cannot easily or accurately use the wheel hp to calculate the engine or flywheel hp. The way you phrase it, you are saying that we can accurately measure the flywheel hp (which is true, with an engine dyno, but that's not convenient or easy for most people), but that we cannot accurately turn that into rwhp. That may be true in the strictest sense but we can easily get the rwhp so to me it is much more relevant that we cannot accurately and easily turn that rwhp into flywheel hp. That's why I said nothing about flywheel hp in my first post, and that's why I cranked through the physics in the first place to make sure that the formula I was using gave wheel hp and not flywheel hp based on someone's estimate of drivetrain losses.
Oh, hsutton is right that the mph in the formula is the instanteous mph as the car crosses the finish line, and that isn't quite what the time slip gives, but I chose to ignore that
. Also, Barry Burch's formula uses 0.0426 which is 1/234.7, probably a result of some roundoff in starting with 1/234, and the 0.0426 need to be cubed as well: (0.0426*mph)^3.
I haven't gone and read the Am J Phys article but most of the info on the link you posted really involves determining the empirical constant in the equation et=constant/mph for different kinds of cars. The basic derivation of hp =197 * weight / et^3 barely qualifies as a college physics quiz question and contains no empirical constants.