Math formula for HP estimation

[Schulmann]

There are a lot of formulas available to estimate HP from a 1/4mi result.
However I was looking for a formula to estimate HP from a given speed change.
Here are the inputs:

Start speed = 41 mph
End speed = 135 mph
Elapsed time = 8 sec
Viper weight = 3800 lb
Rev = 5500 rpm

Once I was good in physics but it was a long time ago.
Anybody can help me ?

 

[Blade Runner]

Well given the info it works out to 477.5 horse power. Mathematical argumentation below.



Note: 1 mph=1.467 ft/s
1lbf = 32.174 lb*ft/s^2
1HP = 550 ft*lbf/s

v=v0 + at
135mph - 41 mph = a (8 seconds)
94mph = a (8 sec)
137.87 ft/s / 8 s = a
a = 17.23 ft/s^2

F=m*a
F= 3800lb * 17.23 ft/s^2
F=65474 lb*ft/s^2
F=2035 lbf

X=X0 + (v0*t) + (1/2 * a * t^2)
X=0 + (41mph*8sec) + (1/2 * 17.23 ft/s^2 * 8 Sec ^2)
X= (60.12 ft/s * 8 sec) + 551.36 ft
X = 481.07 ft + 551.36 ft
X=1032.43 ft

HP = (1032.43 ft * 2035 lbf / 8 sec) / 550 ft * lbf / sec)
HP = 262624.38 ft*lbf/s / 550 ft*lbf/sec
HP = 477.5

 

[BruceW]

That result assumes constant torque (at the wheels) throughout the run.

 

[Schulmann]

yes, that's right. It is only an estimation to make comparaisons between runs.

 

[Shelby3]

Well given the info it works out to 477.5 horse power. Mathematical argumentation below.



Note: 1 mph=1.467 ft/s
1lbf = 32.174 lb*ft/s^2
1HP = 550 ft*lbf/s

v=v0 + at
135mph - 41 mph = a (8 seconds)
94mph = a (8 sec)
137.87 ft/s / 8 s = a
a = 17.23 ft/s^2

F=m*a
F= 3800lb * 17.23 ft/s^2
F=65474 lb*ft/s^2
F=2035 lbf

X=X0 + (v0*t) + (1/2 * a * t^2)
X=0 + (41mph*8sec) + (1/2 * 17.23 ft/s^2 * 8 Sec ^2)
X= (60.12 ft/s * 8 sec) + 551.36 ft
X = 481.07 ft + 551.36 ft
X=1032.43 ft

HP = (1032.43 ft * 2035 lbf / 8 sec) / 550 ft * lbf / sec)
HP = 262624.38 ft*lbf/s / 550 ft*lbf/sec
HP = 477.5

Yup, that's what I was gonna say but you beat me to it.

 

[VIPER BAZ UK]

yep i agree...

 

[HOdbleFman]

You are assuming a constant acceleration. You would actually have to find the acceleration as a function of time, which would be some type of non-linear curve, and integrate that function, from 0 to 8 s.

 

[Big Medicine]

If a horse moves 33,000 pounds for a distance of one foot in 60 seconds elapsed time, would we have to integrate?

 

[Blade Runner]

I was assuming constant acceleration. Since the car was in motion the curve will be much less pronounced that from a standing start.
Was actually fun since it wasn't for work.

 

[Schulmann]

Yes this formula is not perfect but it's a good start.
It under estimates the HP at higher rpms and over estimates HP at lower rpms.

I have this formula here:

HP = Torque x RPM / 5250

The best would be to calculate an average Torque from acceleration and estimate the HP from there.

Blade Runner, would you be able to do this calculation for us ?

 

[Blade Runner]

more stuff than you ever wanter to know about HP and torque
http://www.g-speed.com/pbh/torque-and-hp.html

 

[Schulmann]

Actually we don't need the RPM and Torque since we assumed that acceleration is constant. Thus from the integration the real HP is 1.5 times the HP calculated.

Then another very important factor is the AIR resistance that we have forgotten !I just compared an older Dynosheet with my present acceleration results and using these formula without air resistance we severely under estimated the HP.

With the real data I arrive around 534HP for my estimation.

Using the formulas on a previous dynosheet I get 501HP compared to 503 on the dynosheet. Isn't bad. Thank Blade Runner.

 

[Anaconda]

Well given the info it works out to 477.5 horse power. Mathematical argumentation below.



Note: 1 mph=1.467 ft/s
1lbf = 32.174 lb*ft/s^2
1HP = 550 ft*lbf/s

v=v0 + at
135mph - 41 mph = a (8 seconds)
94mph = a (8 sec)
137.87 ft/s / 8 s = a
a = 17.23 ft/s^2

F=m*a
F= 3800lb * 17.23 ft/s^2
F=65474 lb*ft/s^2
F=2035 lbf

X=X0 + (v0*t) + (1/2 * a * t^2)
X=0 + (41mph*8sec) + (1/2 * 17.23 ft/s^2 * 8 Sec ^2)
X= (60.12 ft/s * 8 sec) + 551.36 ft
X = 481.07 ft + 551.36 ft
X=1032.43 ft

HP = (1032.43 ft * 2035 lbf / 8 sec) / 550 ft * lbf / sec)
HP = 262624.38 ft*lbf/s / 550 ft*lbf/sec
HP = 477.5

"F= 3800lb"

Your car weighs 3800 pounds with you in it????