Engine horsepower calculation

[cranetruck]

In my MVM article on engine braking and downhill driving (#108, April 2005), I showed how to calculate the approximate engine HP based on the grade, speed and vehicle weight.

I have often played with those numbers after recording my own driving experiences and feel that the formula is fairly accurate.

This is how it works using my latest drive up the I-77 NC to VA grade, which is 5%:

The wheel rpm was 33 MPH x 484 revs/mile divided by 60 = 266 rpm (1100-20 tires)

The force "along the hill" was 29,000 lb x 5% = 1,450 lb

The amount of torque needed to overcome this force is 1,450 x the "lever" (loaded radius of the wheel) = 1,450 x 1.75 ft = 2,537 ft-lb

Horsepower = (2,537 x 266) divided by 5,252 = 128 HP

Adding about 10% drivetrain losses would bring the needed HP output from the engine to about 141 HP.

Ryan (rmgill) provided some numbers from his run up the same mountain:

Wheel rpm = 215 (25 MPH with 900-20 tires)
Force "along the grade" = 26,000 x 5% = 1,300 lb
Torque = 1,300 x 1.58 (900-20 radius) = 2,054 ft-lb
Horsepower = 2,054 x 215 divided by 5,252 = 84 HP

Adding 10% for losses yields 92 HP.

I know I was holding back a little during my drive, the boost was about 8 psi and the EGT was about 1,100°F. Apparently Ryan was holding back too since his HP output seems a little low.

BTW, I didn't have any biodiesel left coming home and the uphill drive was done on regular diesel.

Bottom line is that if you want to figure out how much HP your engine is putting out, find a hill with a known grade and keep track of the numbers.

 

[cranetruck]

Using the same formula, a previous drive shown in the image here yields a engine horsepower output of about 123HP for 52 MPH with the empty 16,000 lb deuce (w/crane).

 

[Recovry4x4]

Interesting. Much too complicated for my simple mind but interesting none the less. Next time I'm grade bound I'll have to record the numbers. Would this be rear wheel HP and does gear selection play any part on the calculation?

 

[FSBruva]

Then send them to bjorn for analysis?

matt

 

[cranetruck]

Kenny, gear selection/rpm doesn't matter, but you should keep the engine from lugging of course, make it run as efficiently as possible.

The data you need is:
1) Grade of the hill (%)
2) Weight of vehicle
3) Max speed you can drive up the hill
4) Tire size matters for the calculation (loaded radius)

 

[Recovry4x4]

Gotcha! Thanks

 

[houdel]

Nice, but the hard part of the equation is the "known grade". Bjorn - any links for a dash mounted gradometer/inclinometer? I've seen pics of them but have no idea where to find one. Seems like a neat thing to have, especially for a frequent off-roader.

And what engine PRM would you suggest? Theoretical HP peak, Torque peak, Brake-Specific minumum fuel consumption rate?

 

[cranetruck]

Lee, the interstate grades are probably all listed somewhere, just go ogling it.
If you need an inclinometer like the one shown below go to westmarine.com, about $20....