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Automotive Calculating HP from time/distance

  1. Jul 27, 2016 #1
    Well, I ran my truck down the 1/8th mile track over the weekend, and with a bunch of the online conversion calculators it told me that my truck is about 487hp.

    So I plugged in the old kinematics formulas, and i got quite a discrepancy between them.. Did I do the math right?

    Time = 10.055s
    Speed (from trap speed) = 75 mph = 33.5 m/s
    Distance =1/8th mile, 201.2m
    Mass = 7370 lbs = 3350kg
    Ke = 1/2 mv2 = 1883 KJ
    P = 1883/10.055 = 187 KW
    P = 187/.745 = 251 hp...
    Yes, that's perfect world, no friction, wind resistance, and doesn't include Ke left in the drivetrain

    that's pretty much half of what the online calculators come up with

    Now if I shifted 3 gears (manual) and each shift takes .75 seconds (that's optimistic on a truck), would I be correct in deducting that time from the elapsed time?
    P = 1883 / (10.055-(3*.75)) = 241KW = 323hp
  2. jcsd
  3. Jul 29, 2016 #2
    Yes, because you are calculating a change in kinetic energy = 0.5m(v^2-v0^2) over change in time t-t0
    Furthermore, you are probably dropping one or two mph at each gear change.
  4. Jul 30, 2016 #3
    Kinetic energy can be calculated between each gear shift [(v1^2-v0^2)/(t1-t0), (v2^2-v1^2)/(t2-t1), etc] to give average power for each, perhaps somebody can help take the measurements as you drive.
    Instantaneous power is obtained as t2-t1 approaches zero, and the primary influence is the engine rpm as described by a Power / rpm curve. For a small truck 'peak power' might be at around 4500 - 5500rpm. This is where you get the most acceleration for a particular gear.
  5. Jul 30, 2016 #4


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    For a particular gear, peak acceleration occurs at peak torque.

    I tried this online calculator and got different results for the time and for the speed.

  6. Jul 31, 2016 #5


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    True, but for a particular speed, max acceleration occurs in the gear such that the engine is making the peak horsepower.

    As for that calculator, the HP calculated by mph is way above the HP calculated by ET, which indicates that the vehicle had poor traction off the line, but likely has horsepower more in line with the high number (mph based calculations are usually more representative). This calculator gives 483, which is right in line with the numbers other calculators are apparently giving.

    As for the discrepancy between that number and your calculated value, that's likely drivetrain loss, rolling resistance, and aerodynamic drag. 434 horsepower at the wheels compared to ~330 actually going towards increasing your KE indicates a loss of about 100hp, which isn't unreasonable for a large, heavy truck.
  7. Aug 6, 2016 #6
    The online calculators leave a lot to be desired... Something as simple as automatic/manual transmission can make a big difference, as well as the different torque curves of naturally aspirated (most calculators use this), nitrous, super and turbocharged engines.. Turbocharged vehicles with large turbos that take a long time to get going will often have a poor (relatively) ET but a high trap speed, the shorter the track, the more pronounced this is.

    One thing I can say for certain is that by 75mph I'm probably pushing air to the tune of 50hp

    If anyone's curious.. here's a couple videos

    I think peak torque is around 2300 RPM, peak power around 3300 RPM which is where I was shifting
  8. Aug 8, 2016 #7
    Nice Vids ... adds some perspective!

    Wind Power:
    Cd = Drag Coefficient, 0.8 - 1 for full frontal truck
    A = Area, say 1.6m^2
    P = Wind pressure = 1/2 rho V^2 = 1/2 x 1.25 x[ (75mph x 0.447 m/s / mph)]^2 = 702Pa
    F= Wind Force = A x P x Cd ~ 1800N
    Wind Power = Work per Second = Wind Force x Distance travelled per second = 1800 x (75mph x 0.447 m/s / mph)
    ~ 60kN/s (81.5 hp)

    That should be about right ... once you get to about 45mph, with a drag coefficient of 1, the wind drag becomes the biggest thing to slow you down. Note: I got 45mph by just saying that half of the 100hp loss above is 50hp so 75mph x 50hp / 81.5hp = 45mph.
  9. Aug 23, 2016 #8
    actually , mostly true.. however, the greatest acceleration will alwways occure at max torque in any one gear, HOWEVER, the max acceleration at any given speed (velocity) will happen at max HP.
    Hp is the rate of doing work or the rate of change of KE. so, if you ask, how is what i said possible if the greatest acceleration is found in any one gear at max torque of the engine levels? because through gearing, you can run at a higher HP level of the engine, and produce more rear wheel forces even though the engine torque is less.

    a great example of this is a same weight viper vs 911GT3. both have 500hp , but the viper has 600lb-ft of torque and the porsche only 250lb-ft of torque. both accelerate the same at any speed, and why? because the rear wheel forces are the same because the HP is the same.

    HP is the capacity of a car to accelerate (based on its weight and frictional forces), much like the rule that says that energy is the capacity to do work.
  10. Aug 23, 2016 #9
    you want to shift well beyond max HP if you want to maximize HP. always you want to shift past max HP. you want to maximize usable HP, and that becomes looking at the average HP you take advantage of. so, shifting past max HP willl always yield more average HP which equals more acceleration potential.

    an interesting way to calcuate Hp required or used, is to use the fact that HP is the rate of change of KE

    example if you have a 1,000,000J of KE (KE=1/2mv^2 and mass in Kg, velocity in m/s) to go from 60mph to 80mph and it took 2 seconds, then thats 1340hp-seconds (because there is 746joules per HP and a jouile is a watt-second).. this means the car or truck needs 670HP to acceerate at that rate of 60 -80mph in 2 seconds.
  11. Jul 2, 2017 #10
    Thought I'd update this.. I had my truck on a dynamometer in December, and found out a few things.. like my fuel pressure drops dramatically and I have to do some upgrades there.. it also led to an interesting dyno graph.. There were also some other little problems.. like when they make the dyno learn engine RPM from wheel speed, they weren't very accurate about it which throws the torque/RPM numbers off.. I believe the RPM on the graph is about 10% below actual, inflating the torque number (I know the truck revved to 3000+ RPM).
    You can also see where the limit of the fuel delivery is.. right at 436 hp, it just stays flat and really doesn't drop at all like most dyno charts, this suggests to me that the truck could easily achieve much higher power levels with adequate fuel... The existing system was able to deliver 436 hp worth of fuel, and that was it


    Meanwhile, since the trap speed equations said 487 hp and the dyno says 437, the trap speed equation may be adjusted to provide engine output, rather than wheel HP, and then it would actually be pretty close.
    I also know that my truck with a manual transmission shifts SLOW, and that with an automatic I could have saved a lot of time and gained several MPH... Since then, I've changed the rear end gear ratio to 3.54 from 4.10, and put a 6 speed manual instead of the 5 speed.. the gears may help me, but the 6 speed will not.. at least not on the track, but it's MUCH better for driving and towing, which is the real job of this vehicle
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