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Horsepower and Torque: A Practical Explanation

This may be the most highly debated question in all automotive internet forums.  It's not that the definitions are in doubt.  They're obviously objective.  The controversy centers around which is more important.

Force

Force is the pressure of one mass against another, and is one of the primary units in all of physics.  In the metric system, force is calculated in "Newtons".  Gravity is an easy example of a natural force and is written in the English system as "pounds".  So we also use pounds as the basic unit of force.

Work

Work is defined as force over distance and is calculated as Work= Force * Distance.  In other words, work is achieved when force causes an object to move.  The force placed on the object and the distance it moves are calculated as the work done.

Power

Power was originally defined by the engineer James Watt as the amount of work that can be done in a certain amount of time.  So its function is Power = Work / Time.

Torque

Torque is defined as the force at any one point on the edge of a circle in the exact direction of the rotation multiplied by the radius (distance from the center).  This comes from the calculus/geometry concept of a "tangent", a line which touches exactly one point of the edge of a circle.

tangent.jpg (8172 bytes)

In the metric system, force is calculated in newtons, and distance is in meters, so the standard torque unit is Newton-Meters or N-M.  In the Standard/English system, force is calculated in pounds and distance in feet.  So the torque unit is lb-ft, usually pronounced as "Foot-pounds" and sometimes written as "ft/lb".

Horsepower

Horsepower is a unit of power.  It can be defined in many ways.  In its basic sense, it's defined as work done in a straight line as described above under "Power".  But when the work is not done in a straight line, it must be defined in a different way: torque.

Horsepower = Torque X RPM
5252

Now although horsepower in this instance is defined by rotational forces, it is no different than straight-line horsepower.  For instance, if you wrapped a rope around the circle and allowed the torque to pull the rope, the force on the rope would now be exactly as defined above.

Gearing and Towing

Now when it comes to just about any type of racing known to mankind, besides engine output, gearing is the single most contributor to acceleration.  It will make or break any car and the right gear selection can and will mean the difference between winning and losing a race.

How important is gearing?  Gearing nearly makes torque obsolete.  Yes, it's that important.  In a perfect environment with no limiting factors such as size and weight, the actual peak torque output of an engine would be totally meaningless because of gearing.

How's that possible?  It's simple.  Gearing multiplies peak torque to the wheels to any amount desired.  Increasing the ratio increases torque.

The limiting factors are the biggest problem with this ideal setup.  Torque is multiplied through gear ratios, but the higher the gear ratio, the larger the gear and the more space it takes up.  Unfortunately, in the real world, there's only so much space for a gear to occupy.  It's this space limit that contributes to the "torque = towing capacity" philosophy.  If space were unlimited and we could make the ratios anything we wanted, then towing capacity would be limitless since we could easily just utilize a higher ratio gear.

But since the car world doesn't operate like that, there is generally a maximum amount of torque that can be generated at the wheels.  It's this maximum which defines the towing capacity of the vehicle.  If you start with an engine that already generates a great deal of torque, then the towing capacity will be easier to manipulate to higher levels.

Horsepower and Torque "At the Wheels"

Now when we're talking about automobiles, the amount of horsepower or torque generated at the flywheel is not very useful when determining acceleration.  What is useful, however, is horsepower and torque "at the wheels".  The problem here is that drivetrains cannot be perfectly efficient and pass 100% of the power of the engine through its components to the wheels.  Some of the power is lost for several reasons.  Generally 15-25% of engine power never makes it to the wheels.  Different types of drivetrains will have different levels of efficiency.  Generally, drivetrains with more weight and those with more components will be less efficient.

Let's use my own car for some sample calculations.  In stock form, it has 165 hp @ 5600 RPM and 166 lb-ft @ 4000 RPM.

Dyno results have shown that the car has around 127 peak hp at the wheels.  That's a 23.03% loss.  Note that this is higher than most cars because of the heavy and sophisticated all-wheel-drive system.

Here's a chart to show how the power and torque change before they reach the wheels.  Although, the efficiency loss is difference for each gear, we'll assume that 127 peak hp is attainable in every gear.  At 5600 RPM, the flywheel torque calculates as 154.7 lb-ft.  Calculating the same efficiency loss (23.03%) as horsepower, this would come out to 119.1 lb-ft.

Engine RPM = 5600

Gear Gear Ratio Axle Ratio Total Ratio Flywheel Horsepower Wheel Horsepower Flywheel Torque Wheel Torque after loss
1 3.545 4.11 14.57 165 127 154.7 1735
2 2.110 4.11 8.67 165 127 154.7 1033
3 1.448 4.11 5.95 165 127 154.7 707
4 1.088 4.11 4.47 165 127 154.7 532
5 0.780 4.11 3.21 165 127 154.7 382

To prove the accuracy of the wheel torque numbers, let's look at the example of 1st gear.  Using the Speed/RPM Calculator, we can determine that the vehicle will be traveling at approximately 27.5 mph in 1st gear at 5600 RPM.  Using the Tire Size Calculator, we can determine that the circumference of the tire is approximately 78.16 inches.  Let's calculate the RPM of the tire:

27.5 mph = 145,200 ft/hour
145,200 ft/hour = 1,742,400 in/hour
1,742,400 in/hour = 22,294 revs/hour
22,294 revs/hour = 372 RPM

Now we know that there is 127 hp generated at the wheels.  If we use the horsepower formula above:

127 HP = (Torque * 372 RPM) / 5252
667,004 = Torque * 372
Torque = 1793 lb-ft

Notice the difference between 1793 and 1735.  This is caused by the reduction of the tire's size when fitted onto the vehicle.  To help explain this, please read "Why isn't it perfectly accurate?"