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This spreadsheet shows why torque and gearing are the important factors in vehicle performance. Many people think horsepower
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is the important factor.
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All the formulas are visible in the cells, they are all straight high school physics. As is generally the case in examples like this, we
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are assuming zero mechanical and aerodynamic drag. (You can plug different numbers in for stuff, but be careful not to mess up formulas. If you do you can just make a new copy).
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We have a motorcycle with the gear ratios, weight and drive wheel radius listed. We know that when accelerating at WOT the
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engine produces 50 foot-pounds of torque at 5,000 RPM. Let's see what's happening at the rear wheel in different gears.
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First, how much horsepower does 50 ft-lbs of torque at 5,000 RPM represent?
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HP = torque * RPM / 5,252, and 50 * 5,000 / 5,252 = 47.6 HP. That's the short formula. There's some stuff simplified in there.
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The "real" formula looks like this:
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HP (ft-lbf/min) = {torque (ft-lbf) * (rev/min) * (2 * Pi) (rad/rev)} / [33,000 {(ft-lbf/min)/(HP)}]
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Let's look at acceleration potential in each gear at 5,000 RPM, WOT.
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Rear wheel torque "on the ground"
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Foot pounds force
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Gear ratiosGearOverall RPMTorqueHorsepower123456
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Primary2.09RatioRatio5,00050.047.6771.0556.9432.6378.5301.2266.8
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First2.4615.4215.42
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Second1.7811.1411.14Acceleration, foot/second^2
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Third1.388.658.6538.227.621.418.714.913.2
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Fourth1.217.577.57
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Fifth0.966.026.02
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Sixth0.855.345.34
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Final3.00Overall ratio includes drive wheel radius
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Vehicle weight =650.0poundsIncludes rider
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Drive wheel radius =12.0inches
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What is the HP "on the ground" in each of the gears at this time? Using HP = torque * RPM / 5,252 we can calculate HP.
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The RPM of the rear wheel is (engine RPM / (gear ratio)* (12 / drive wheel radius) (corrects torque for the wheel radius).
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Rear wheel HP in gear
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123456
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47.647.647.647.647.647.6
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The HP is the same in all six cases, identically engine horsepower. So calculating acceleration from HP is not possible without first
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converting HP to force (in this case, torque).
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Here is a torque/HP graph that further illustrates the lack of relationship between HP and acceleration. It's the same vehicle above
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with an unusual engine that makes a constant torque. Let's look at first gear acceleration.
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RPMTorqueHPAcceleration
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1000509.538.2
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20005019.038.2
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30005028.638.2
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40005038.138.2
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50005047.638.2
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60005057.138.2
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70005066.638.2
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80005076.238.2
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90005085.738.2
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100005095.238.2
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HP continuously increases, torque remains constant, acceleration remains constant.
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Here's another example with a "special" engine. In this case HP remains constant.
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RPMTorqueHPAcceleration
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1000131.325.0100.3
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200065.725.050.2
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300043.825.033.4
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400032.825.025.1
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500026.325.020.1
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600021.925.016.7
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700018.825.014.3
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800016.425.012.5
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900014.625.011.1
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1000013.125.010.0
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Torque and acceleration are again proportional, HP again is not related to acceleration.
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In this example torque (and so acceleration) decreases. Horsepower increases.
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RPMTorqueHPAcceleration
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100050.09.538.2
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200048.018.336.7
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300046.026.335.1
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400044.033.533.6
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500042.040.032.1
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600040.045.730.6
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700038.050.629.0
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800036.054.827.5