HP Calculations and other formulas - The Unofficial BMW M5 Messageboard (m5board.com)

Bart Carter · 3rd November 2001, 20:19

Over the years I have gathered many formulas for the calculation of HP. I have put many of these to the test and have found that this formula is by far the best for a car's HP:

HP = (the weight of the car plus driver) times ((the MPH in the quarter mile divided by 234)cubed)

For an example, lets say we have a car that weighs 4,100 lbs with driver, fuel, etc., that does the quarter mile at 107 MPH.

So,
Weight = 4100
MPH/234 = 0.457265, cubed = 0.09561
4100*0.09561 = 392 HP

A simular formula for the ET in a quarter mile can be also calculated, but THIS FORMULA ASSUMES MAXIMUM TRACTION AND GEARING.

ET = (the cube root of weight/HP) times 5.825

So,
Weight = 4100
HP = 392
Cube root of weight/HP = 2.1869
2.1869*5.825 = 12.74 second ET

Please note that there are other factors that may affect results. For example wind resistance goes up as the square of speed, not linear. So over 100 MPH the HP needed to overcome wind resistance begins to become a factor.

EBMCS03 · 4th November 2001, 10:11

Very Interesting Bart... Thanks for posting!

tfung · 5th November 2001, 13:31

Bart,
great post... can any of our software engineers make a program using these formulas, so we can just plug numbers in and get the result.. sort of like the gear ratio vs speed calculator on e31.net?
Thanks!

johann · 5th November 2001, 15:52

No need to re-write.

http://www.prestage.com/carmath/

Bart, HP was RWHP, right?

Cheers,
/Johan

Bart Carter · 5th November 2001, 19:02

Johan,

Actually these formulas work for net advertised HP. In the example I used an M5. If you compare my results with published data, it is real close.

I have followed test results for many years. The HP formula is very accurate. Most manufacturers publish the correct HP.

There are some cases where I have found manufacturers fudge up their HP claims. And even a few where the manufacturer underrates the HP, for instance the high HP Camero/Firebird, for insurance reasons.

tfung.

I have all my formulas in a spreadsheet. If you have Excel or Lotus they are very easy to plug in from what I've given you. If you have any trouble, I would be happy to e-mail you a spreadsheet.

johann · 5th November 2001, 19:08

Bart,

That assumes that drive train losses are virtually similar, which they in fact are not. Still it seems like the differences are not big enough to influence it.

Cheers,
/Johan

Bart Carter · 5th November 2001, 19:43

Johan,

I have about 5 different formulas for HP calculations from respected sources. What I did is take all the formulas and compare them against actual road tests. This involved figuring out the real test weight, among other things, trying to keep apples to apples. I'll have to look, but I think I have at least 100 tests.

Then I looked for patterns and similarities. Of course there is a bell shaped curve, but the overwhelming evidence was for the formula I have given. The cars that fell outside of the predictions tended to be some cars that seemed to need more HP on paper to be more competitive and the insurance problem cars on the other end. For instance Ford had a 427 they rated at 425 HP and everyone knew that it was well over 500.

I have never analyzed why this formula works so well universally. Probably as you said, "it seems like the differences are not big enough to influence it."

2001's X5/Z8 · 2nd April 2002, 08:36

anyone know the % used to determine the loss between the crank and the rear end????

Bart Carter · 2nd April 2002, 20:49

As far as I am concerned, this has always been a number of convenience for people that want come up with actual HP.

I have seen the percent vary from 12 to 22. I have seen flat figures, like 40 HP.

The only work that I have seen that makes sense is measuring road HP using a stopwatch through a gear. You measure acceleration and coastdown times. The coastdown information is taken at various times so you can get drag and mechanical losses.

Then everything is calculated and plotted to get real HP.

A lot of time and effort, but you can get HP over your entire RPM range. And it is neat to see what your real drag and mechanical losses are.

Apples · 1st March 2003, 21:07

Bart is there a sheet for working out speeds V's gears for other cars?? apart from the M5?? I have a M3 track car (no speedo) and all l can see is the taco at the best of times, so l would like to know what speeds l'm doing around the track . I have the ratios for the 5 speed M3 box...it has 645mm total height on the rear tire and it's running a 3:73 rear end
So to be simple the tires are very much the same as the M5's in height and 5th in the M5 is the same as the M3 (1:00) so the olny difference is that the M5 has a 3:15 rear compared to the M3's 3:73.....
My numbers seem to work out at...
3rd (1:66) @7,000 = 85mph
4th (1:24) @ 7,000 = 113mph
5th (1:00) @ 7,000 = 140mph
This sound right.?????
APPLES

Bart Carter · 4th March 2003, 04:02

Apples,

What is the actual diameter of your tire, not the height?

What are your gear ratios in 1st and 2nd?

I have an easy-to-use spreadsheet.

I will work the numbers and post.

Do you have Lotus 1-2-3?

Do you have adobe acrobat reader?

I can send you a full chart with each gear at RPM differentials.

Let me know.

Bart