The heart of all our vehicles is
the engine. We know that it burns fuel to get us moving and over
obstacles. We know that torque and power are some kind of metrics
to characterize the engine. Much confusion exists over what torque
and horsepower are and how they relate. In this article, we try to
disspell the confusion. In the next article, we will explain how we
put the power to the ground and get things moving via gear
reduction.
The Basics
Let's start with some basics.
Velocity is speed. It tells how far something moves in a given
about of time, e.g. miles per hour. It is a ratio of distance to
time: miles/hour or feet/sec.
Acceleration
is what causes the speed to change. It is a ratio of velocity to
time: (feet/sec)/sec. It tells us how much the velocity changes in
a given amount of time.
Every object has
mass. To get an object to move, we must accelerate it somehow to
give it velocity. For example, we push on it. Now moving an
elephant is much harder than moving a rock. We have to push harder
to move the elephant. We quantify this using force. Force = Mass *
Acceleration. We see that if we push harder on an object, the
acceleration must increase. Something moving at a constant speed
has no acceleration, hence needs no force. The metric unit of force
is the Newton (N), N=kg*m/s/s. In the US, we use the pound (lb or
lbs).
If we exert a force over a given
distance, we have done work. Common units are the Joule (J),
Calorie (cal), or pound-feet (lb-ft). We can think of work as
energy. Power is how fast we can do work or how fast we can deliver
energy, measured by work/time or force*velocity. Common units are
the Watt (W = 1 J/s), lb-ft/s, or horsepower (hp = 550
lb-ft/s).
Imagine an elevator with 1000 lbs
of load going up 10 stories. If it takes 1 minute or 10 minutes, it
takes the same about of energy or work to move the load. Since
power is work/time or energy/time, it takes more power to move the
load in 1 minute instead of 10 minutes.
Torque
In the automotive world, lots of
things move in circles rather than in straight lines. Think of the
wheels or engine. Some of the above concepts behave differently and
use different names. However, they relate to one another in the
same way.
Distance is no longer feet or
meters, it is revolutions measured in radians. Speed is revolutions
(or radians) over time instead of distance over time, for example,
revolutions/minute (RPM) or radians/sec. Mass is called inertia. We
still need some kind of "push" to get something spinning. Instead
of force, we have torque which is "twisting" force so to speak.
Like force, torque must be applied to get something to spin faster
or slower (accelerate).
Torque is measured
by the amout of force applied tangentially at a given distance and
is given units of force * distance. In the metric system, we would
use Newton*meter (N*m). In the US, we would use pound*feet
(lbs*ft). For some strange reason we usually say "foot pound"
instead of "pound feet" but use both lbs*ft and ft*lbs. Think of a
wrench. We pull on the handle to turn the bolt. The longer the
wrench, the more torque exert on the bolt with the same amount of
force.
Rotational
Work and
Power
As mentioned above, work is
force*distance. The major source of confusion about torque comes
from the units. Torque in lbs*ft or N*m has the same units as work.
Work is energy, torque is a force.
Work in
the rotational world is still basically force*distance. Torque is
our force and distance is our revolutions in radians (1 revolution
= 6.28 radians roughly). We use the same units such as lb*ft, N*m,
or J. The reason the units do not change is that the distance
(radians) is a dimensionless quantity. Don't worry about it. Just
know that you have to say x lbs*ft of torque or x lbs*ft of work or
energy to differentiate them.
Similarly,
power is work/time or force*velocity. Since work in the rotational
world has the same units as in the linear world, power has the same
units also. We would use lbs*ft/s, J/s, W, or hp for
example.
Engines,
Torque, and
Power
To get our vehicles moving, we use
some kind of engine to convert chemical energy (fuel) into useful
work. In an internal combustion engine, the fuel in the combustion
chamber is ignited by a spark (gasoline) or from compression
(diesel), creating high pressure gasses that press down on the
pistons. Via the connecting rods, this force pushes the crankshaft
throws or arms. Bearings control the crankshaft, allowing it to
only rotate. Since each crank arm is offset from the centerline of
the crankshaft (the rotational axis), we have torque. Voila.
So far we have been kind of simple. The combustion
gases develop pressure right away and continue while the crank is
turning. Hence, sometimes the force along the connecting rod is not
tangential to the crank rotation; it is that way only
instantaneously. To further complicate matters, the crank turns at
varying rates (engine rpm), different amounts of gasses expanding
(throttle), etc. The bottom line is that engines develop differing
amounts of torque during operation which is hard to predict.
However, we can easily measure it.
If we
assume that we want maximum torque figures, we assume maximum
throttle. All we then worry about is how much torque at what rpm.
We end up with a curve. Engine design, fuel systems, etc all change
the shape of the torque curve. Note that in most cases, torque
rises to some peak value and then decreases.
So what about power? If we remember from above,
power is torque*distance/time or is torque*velocity. For this
discussion, we want to take torque in lbs*ft and speed in
revs/minute and calculate horsepower:
In the first line, torque is in lbs*ft, speed in
revs/minute. The third term just converts RPM to revs/s. The fourth
term converts revs to radians. The last term is the conversion
factor from lbs*ft/s to horsepower. The second equation just
multiplies out the constants to make life easy.
Using the above equation, we can add a horsepower curve to our
torque graph. Note that the horsepower peak is at a higher rpm than
the torque peak.
Torque and horsepower are very closely related. We can see that a
high revving motor does not need to produce much torque to get lots
of horsepower. Similarly, a high torque engine may not develop lots
of horsepower.
Load
One thing that should be
considered is that the torque and power graphs illustrate the
maximum levels possible. An engine can develop less than that
amount at a given rpm. The throttle controls the amount of fuel to
the motor and, hence, the torque and power produced.
Earlier, we said that force and torque cause
acceleration. If we are at a constant speed, how come we continue
to need power or torque? The answer is friction or drag. The drag
torque tries to slow us down so we add an opposite torque to
prevent the deceleration. So in the case of steady speeds, we only
need the engine to produce enough torque to compensate for the drag
torque.
When idling, all the power goes to
overcome the drag from friction (assuming no accessories). You can
barely touch the throttle to rev the motor 2000 rpm. However, when
cruising down the highway at 2,000, you are using much more power
to overcome friction, rolling resistance, wind drag, etc. At top
speed, 100% of the torque goes to overcome drag.
Continued
In the next article, we will talk
about what the torque and horsepower curves mean to us, and how we
make them do what we want go get us up and over rocks and down the
trail.
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