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.
In the metric system, force is calculated in
newtons, and distance is in meters, so the standard torque unit is
NewtonMeters or NM. In the Standard/English system, force is
calculated in pounds and distance in feet. So the torque unit is
lbft, usually pronounced as "Footpounds" 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 straightline
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 1525% 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 lbft
@ 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
allwheeldrive 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
lbft. Calculating the same efficiency loss (23.03%) as horsepower,
this would come out to 119.1 lbft.
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 lbft
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?"
