This page describes horsepower and torque and how they relate to each other. (Not all of it is my words, but I can't even remember whose work I plagiarised now. Sorry!)
Horsepower and Torque
Everyone knows race engines make big horsepower and torque, but what do those terms mean?
It doesn't take an engineer to know these engines are powerful. To measure the power in a
scientific way, the engineers use the dynamometer to quantify the two measurements that rate an
engine's ability. The dyno gives the engine shop the critical info needed to gauge the ability of
their engines in the form of torque and horsepower.
First, let's look at torque. Torque is a "turning or twisting force." In an internal combustion
engine, torque means the amount of combustion pressure the engine creates. This force turns the rear
wheel and propels the bike forward. Torque is measured in foot/pounds or kilogram/metres or newton/metres.
A simplified way of looking at torque is to say it is the amount of force from the engine that turns
the rear wheel in a turning motion.
After a dyno run is completed, the resulting readout shows the torque available throughout the rev
range. This is called a torque curve. The Holy Grail for an engine engineer is a perfectly flat torque
curve. If it existed, it would give useable and predictable power throughout the rev range. But port
efficiency, timing, carburetion, and exhaust limitations keep the perfectly flat torque curve from
existing. The engineers use the intake, exhaust, timing and carburetion systems to eliminate dips in
the torque curve.
Since the torque curve isn't a straight line, the point at which peak torque occurs is important.
A Gold Wing or Harley cruiser will have its peak lower in the rev range. This gives a feel of good
acceleration or useable power in the lower rpm registers, and make the machine easy to ride.
A stout Superbike will have its peak torque somewhere near the beginning of the last third of the rev
range.
But torque is only half the story. While torque is the force created, it doesn't account for the
importance of revs. Imagine trying to remove a wheel from a car with an inadequate tyre tool and all
the torque you could produce couldn't loosen the rusty lug nuts on the studs. While you applied lots
of force, i.e. torque, you couldn't generate any rpm. Therefore nothing was accomplished, despite your
cursing, crying and kicking.
Without rpm, torque is useless.
Two engines may make 75 foot/pounds of torque, but if one is turning at 5,000 rpm and another is
turning 10,000 rpm, the latter is doing more work than the former. Remember, torque measures force,
but it doesn't measure actual power produced.
To measure that total power output, we have horsepower. Horsepower is torque times rpm divided by
5252 (Torque x RPM / 5252). Through this formula, we can calculate torque and horsepower and see that
both are linked.
In the same example above, the engine running at 5,000 rpm and producing 75 feet/pounds of torque is
making 71.4 horsepower. The engine turning at 10,000 rpm makes 142.8 horsepower. The force (torque)
is the same, but since the latter engine is turning twice as fast, it makes twice the horsepower.
Which is more important, revs or torque? Neither, really. In the real world, high performance
engines need both.
Dremeltype tools are handy devices. Say one is advertised to turn in the neighborhood of 22,000 rpm,
a pretty astounding figure. However, it has little torque, so for some jobs you'll need a drill that
turns at a fraction of that speed, but has more turning force. On the other hand, the drill is
illsuited for other tasks like polishing because it can't rev fast enough.
The dyno gives engineers a horsepower curve in addition to the torque curve. They will always be
different shapes, and peak rpm will always occur later in the rev range than peak torque. Although
the torque curve will decline slightly after peaking, the revs are still increasing, and thus the
horsepower curve increases as well. This difference in the curves is very important to how the engines
perform on the track.
If we look at both curves, we can see where the power band lies. The rider wants to keep the engine
revving between peak torque and peak rpm. The gear ratios will be selected to keep the bike in this
"happy zone" when it accelerates.
Sometimes the engineers succumb to a disease called "dyno blindness". To get the numbers,
they will change the timing, port size and shape, exhaust and/or carburation to get a higher
horsepower, and in turn narrow the power band, or create dips in the horsepower or torque curves.
This can a big mistake. Sometimes more isn't necessarily better.
Tuners should first develop a good torque curve and horsepower, then increase the acceleration
rates. The acceleration rate is how fast the engine can run through the rev range.
To beat the best on a consistent basis, you need all three elements, torque, horsepower, and
acceleration. Then all three combine to make a useable and effective power band.
There are no substitutes.
The following is a great read that can be found on the Micapeak FJR1300 site
here. A
a site for FJR1300 enthusiasts. The document is reproduced here in full with the kind permission of
the Author Tom Barber.
Five Popular Urban Myths about Torque and Power Debunked
by Tom Barber
Anyone who spends much time on motorcycle and car related Web forums
knows that there is a fair amount of debate on whether the torque or
the power of an engine is the true indicator of the vehicle's maximum
acceleration. Numerous Web sites offer genuine information on the
subject, but there are also a few that offer misinformation and that
propagate a few popular myths. This article endeavors to clear up
some of the misunderstandings and debunk a few of the myths. Along
the way, this article will give a usefully complete theoretical
treatment of torque, work, and power, and will offer insight into the
metrics of torque, work and power. It will present a theoretical
perspective of how dynamometers work and will explain how the two
basic types differ. It will even explain precisely how torque and
power each relate to acceleration.
Myth #1: Dynamometers only actually measure torque. Power is an
abstract quantity that can't be measured, and must be calculated from
the torque.
This belief is false and it will not be hard to show that. However,
it involves a discussion of how dynamometers actually work, and
before we can go there, we have to begin with a brief review of some
fundamental physics. I'll try to avoid equations as much as
possible, and instead I'll try to instill an intuitive understanding
of the basic concepts, which is something that classroom lectures and
textbooks often fail to accomplish for many people.
Isaac Newton taught us that any object having a mass M, has an
intrinsic resistance to changes in its present momentum when external
force is applied. The acceleration of the object is proportional to
the strength of the external force, and is inversely proportional to
the mass of the object. These observations are summed up succinctly
by the infamous equation: F = M x A. The true essence of force, mass
and acceleration is embodied in this equation, and this equation
tells us how force or mass can be detected and measured. When an
object's momentum is not constant, this indicates the existence of an
external force, and the strength and direction of that force can be
determined by investigating the acceleration. Conversely, if an
object is accelerated under the influence of a wellknown force, its
mass can be determined.
Whenever the aggregate force acting on an object is not directed
through the object's center of mass, the object is caused to rotate,
and this rotation will continue to accelerate as long as this
condition persists. The laws governing rotational motion parallel
the laws governing straightline motion. Torque replaces force, the
moment of inertia replaces the mass, and the angular acceleration
replaces straightline acceleration. Whereas velocity is measured in
terms of absolute distance in straightline motion, in angular motion
we measure velocity in terms of degrees of rotation per unit of time,
which we may call angular distance. Angular velocity is the
instantaneous rate at which angular distance is covered. Angular
acceleration is the instantaneous rate at which the angular velocity
is changing, and is proportional to the applied torque, and inversely
proportional to the moment of inertia. The torque that is associated
with an applied force is equal to the force (magnitude) multiplied by
the distance from the center of mass of the object to the line of
force (measured at right angles to the line of force). For an object
that is constrained to rotate about a fixed axis of rotation, i.e., a
wheel, the distance is measured from the axis of rotation to the line
of force. Two objects with identical mass will not in general have
the same moment of inertia. For example, if two perfect spheres of
identical mass are made of different materials having different
densities such that they are not the same size, the larger one will
have the greater moment of inertia. In the case of objects having
fixed axis of rotation, if two such objects have the same overall
diameter and density but differ in the radial distribution of the
mass, the one with the mass concentrated closer to the axis of
rotation will have a lower moment of inertia.
Work, in the case of linear motion, is the force multiplied by the
distance through which the force was exerted and the object was
moved. Work and energy are equivalent; it takes a specific quantity
of energy to move an object a given distance in opposition to a given
resistive force, and that amount of energy is the same no matter how
quickly the movement is performed. Power is simply the instantaneous
rate at which work is performed (or energy is expended), and is
therefore equal to the product of the force and the velocity. If you
measure the force required to move an object, the distance that it
moves, and the time interval required to move it that distance, then
you can calculate the average power that was applied throughout that
motion and over that interval of time. Note, though, that average
power is no more equivalent to power than average speed is equivalent
to speed.
In the case of rotational motion, work is the torque multiplied by
the angular distance through which the object is rotated. The
parallel with linear motion is again applicable: it takes a specific
quantity of energy to rotate an object a given angular distance, and
that quantity of energy is the same no matter how quickly the
rotation is performed. Each time an object undergoes one complete
rotation, a fixed amount of work will have been performed. It
follows that the amount of work performed in a given interval of time
will depend on the angular distance covered in that time interval,
and the rate at which the work is performed will therefore depend on
the angular velocity. In rotational motion, power is equal to the
product of the torque and the angular velocity, which may be measured
in revolutions per minute or rpm.
Let's reiterate the important rules discussed thus far:
Straightline motion:
 Force = Mass x Acceleration
 Work = Force x Distance
 Power = Force x Velocity
Rotational motion:
Torque is measured by taking the rightangle distance from the line of force to the axis of rotation, and multiplying the force by that distance.
 Torque = Moment of Inertia x Angular Acceleration
 Work = Torque x Angular Distance
 Power = Torque x Angular Velocity
We should note that these equations are of the type of equation known as "identities". As opposed to stating conditions on the value of a variable, they simply state that the quantities on the two sides of
the equal sign are identical quantities.
Torque Multiplication
There is one more important theoretical concept that we have to
discuss, that being an important consequence of the relationship
among power, torque, and angular velocity as given in the last
equation above.
If you use a gearbox to achieve a different rotational rate at the
wheel as compared to the engine, the torque at the wheel will not be
the same as the torque at the engine crankshaft, even if there are no
frictional losses. The reason that this is so is that the rate at
which work is done must be constant throughout the system (excepting
only for the loss of energy within the system due to friction), and
because power is the product of the torque and the angular velocity.
Analogies between mechanical systems and electrical systems are often
insightful, so I'll ask you to indulge me for a moment while I
digress and talk about electrical transformers. The voltage
transformer is the electrical equivalent of the mechanical gearbox.
A voltage transformer (which, by the way, only works for alternating
current) takes advantage of the inductive coupling between the
primary and secondary windings to transform the voltage. In
electricity, power is the product of the voltage and the current.
Because the rate at which work is performed must be constant
throughout the system, the product of the voltage and the current in
the secondary must be the same as the product of the voltage and the
current in the primary ? at least in the case of an ideal
transformer where there is no loss to heat. If the voltage is
reduced or increased by a factor of N, the current will be inversely
changed in that same proportion.
Okay, back to mechanics. Because power is the product of the torque
and the rotational speed, and because the power must be constant
throughout the system, the transmission increases the torque in the
same proportion by which it reduces the rotational speed. If you
measure the torque at the rear wheel, you have to use the overall
reduction ratio to calculate the engine torque. At a given engine
speed, the rearwheel torque will depend on what gear is selected.
Any dynamometer chart that shows torque must be engine torque or else
it would be applicable only to a specific gear and the chart would
have to specify the gear, which would not be especially useful.
Note, however, that if the torque is measured at the rear wheel and
then the overall reduction ratio is used to calculate the engine
torque, the result will not be the same as the result that you would
get if you rigged the dynamometer directly to the crankshaft, because
the measured rearwheel torque is subject to power train losses.
Nevertheless, any dynamometer chart that shows torque and that does
not specify the gear is most definitely the engine torque, albeit
adjusted for drive train losses.
Metrics of torque and power; dynamometer theory
Okay, at last we're ready to talk about the metrics of torque and
power, and about how dynamometers work. Contrary to what the urban
myth says, there is no fundamental physical reason by which it is
impossible to measure work or power directly on a dynamometer, i.e.,
without deriving the power through the torque measurement.
Furthermore, even if it were true that the only way to measure power
is by derivation through the measured torque, that fact would have no
bearing on the significance of power.
In fact, measuring power on an inertial dynamometer is no more
difficult than measuring torque, and is not predicated on the
measurement of torque. Whenever the work performed goes to increase
the kinetic energy of an object, power is the instantaneous rate of
change of the kinetic energy. It is a trivial matter to calculate
the kinetic energy of a moving drum if its rotational speed and
moment of inertia are known. The rate of change of the kinetic
energy can be determined in a manner essentially identical to the
traditional method used to determine the angular acceleration of the
drum, which is needed in order to calculate the torque.
In an inertial dynamometer, the engine is allowed to accelerate an
inertial drum as quickly as it is able. Newer inertial dynamometers
use an inertial accelerometer to give the measure of the angular
acceleration continuously. With the traditional method, however,
each time the drum rotates through a fixed number of degrees, an
electrical pulse is generated which triggers the recording of the
elapsed time. >From those data points, the average angular velocity
can be computed for each of the individual time intervals between
adjacent points, by dividing the fixed angular distance by each of
the time intervals. Then an average acceleration is calculated for
each adjacent pair of average angular velocity values, by dividing
the difference in the adjacent average angular velocity values by the
corresponding time difference. For each average acceleration value,
the average torque over the corresponding time interval is then found
by multiplying the average acceleration by the moment of inertia of
the drum.
On an inertial dynamometer, the average rate of change of kinetic
energy for each time interval can be determined using a method that
is essentially identical to the traditional method used to determine
the acceleration. The average kinetic energy for a given time
interval can be calculated from the average angular velocity over the
interval, using the formula: K.E. = ½M x V². (It is necessary to
factor in a standard correction to account for the fact that the
square of an average is not the same as the average of the squares.)
If the difference between the average kinetic energies for two
adjacent time intervals is divided by the corresponding time
difference, the result will be the average power for that time
interval. I want to emphasize that this is not in any way an
impractical, farfetched approach. It is for all intents and
purposes identical to the ubiquitous, traditional method used to
determine the acceleration and the torque on an inertial dynamometer.
It is also possible to measure power independently of torque on an
inertial dynamometer that is equipped with an accelerometer. A
computational technique known as numerical integration can be used to
derive the angular velocity at many closely spaced points, from the
accelerometer readings. The kinetic energy can then be calculated at
each of those points. The average rate of change of the kinetic
energy between each of those points can then be calculated the same
as with a traditional inertial dynamometer, by dividing adjacent
pairs of kinetic energy values by the corresponding time differences.
Inertial dynamometers vs. brake dynamometers
With an inertial dynamometer, the engine is allowed to spin up as
quickly as it can, accelerating the drum as quickly as possible.
Consequently, the measured results reflect the engine's ability to
increase its work output rapidly, which ability is more greatly
influenced by the engine's own internal inertia than is a measurement
of steadystate work output. This factor is treated less rigorously
than it could be: there is generally no attempt to quantify the
effect that the engine's reluctance to rapidly increase its output
has on the measured results, and the measured results are not
carefully distinguished from a measurement of steadystate output
such as would be obtained on a brake dynamometer. Be that as it may,
an inertial dynamometer is a more realistic test of an engine's
ability to accelerate a vehicle, whereas a brake dynamometer is at
least as realistic when the question at hand is an engine's ability
to climb a steep hill at steady speed. Turbine engines have a very
high thrust to weight ratio, but due to the combined moments of
inertia of all of the turbine blades, they are slow to speed up and
slow to slow down. Jay Leno's turbinepowered motorcycle would fare
much better on a brake dynamometer than it would on an inertial
dynamometer.
With a brake dynamometer, the engine speed is increased in small
steps and held steady at each step in order that the braking torque
that is required to hold the drum at a steady rotational rate
("dynamic equilibrium") can be read. The throttle is kept fully
open, but closedloop feedback using the drum's motion sensors is
used to regulate the braking force in order to hold the drum's
angular velocity constant. Several different types of brakes are
used, but regardless the principle of using feedback to hold the drum
velocity and the engine rpm constant is the same. Depending on the
type of brake used, transducers will be used to take measurements of
force, or hydraulic pressure, or hydraulic flow, or electric voltage,
or current, etc. Calibration factors and formulae will be applied,
all in order to determine the opposing torque that is applied via the
brake to the drum in order to maintain the drum at dynamic
equilibrium.
To summarize, with an inertial dynamometer, the drum is allowed to
accelerate as rapidly as the engine can make it accelerate, and the
torque that the wheel exerts on the drum is determined using the data
from the drum's motion sensors and simple mathematical methods to
obtain average rates of change over small time intervals. With a
brake dynamometer, the torque that the wheel applies to the drum is
found more directly by applying a regulated countertorque, using
transducers to measure the braking force, which must be calibrated
and which can be a significant source of error if not done properly
with a good understanding of metric processes.
Myth #2: Engine torque is the same as the dynamometer drum torque.
Peculiar though it is that anyone with any real knowledge of the
subject could be this misinformed, it is apparent that many of the
same people who believe that dynamometers can't measure power,
believe this as well. Regardless, the true nature of the
relationship between engine torque and dynamometer drum torque is
sufficiently important such that I would be remiss if I were to omit
that subject from this article.
Regardless of which type of dynamometer is used, the dynamometer
measures the torque that is applied to the drum by the wheel, which
is applied by way of a longitudinal, frictional force between the
wheel and the drum. That longitudinal force can be found by dividing
the measured drum torque by the drum's radius. The rear wheel torque
can then be found by multiplying the longitudinal force by the
wheel's radius. Of course, the longitudinal force is not usually of
interest unless perhaps you wish to calculate the theoretical
acceleration of your vehicle. To get the rear wheel torque more
directly, you divide the drum torque by the drum radius and multiply
by the wheel radius. To convert the rear wheel torque to engine
torque, you divide the rear wheel torque by the overall reduction
ratio. The overall reduction ratio is found by multiplying together
the primary reduction ratio between the crankshaft and the
transmission's input shaft, the final reduction ratio between the
transmission's output shaft and the rear wheel, and the transmission
ratio that depends on the specific gear that was used during the
dynamometer run.
Myth #3: Acceleration will be greatest when the engine speed matches
the engine speed where the torque peak occurs.
Myth #4: Power is an abstract, derived quantity that is meaningless
insofar as concerns the goal of selecting shift points that yield the
greatest acceleration.
In accordance with the well known relationship among force, mass and
acceleration given by Newton's wellknown F = M x A, the acceleration
of the vehicle is proportional to the longitudinal force at the tire
contact patch. (We can ignore the fact that some of the force goes
to angular acceleration of the wheels; this will not alter the
validity of the analysis or the conclusions.) If the engine torque
(adjusted for power train losses) is known for a given engine speed,
the corresponding longitudinal force at the contact patch can be
calculated by multiplying that torque by the overall reduction ratio
and then dividing by the rear wheel radius. So long as the reduction
ratio remains fixed at a given gear, the wheel torque, the
longitudinal force and the acceleration will all have their maximum
values at the engine speed where the torque has its maximum value.
That is fine and good, and obvious, but it bears little on the
question of how the maximum rear wheel torque and acceleration are
determined and maximized when you can use gear selection to alter the
engine speed at a given wheel speed.
When you use gear selection to change the relationship between the
engine speed and the wheel speed, two things happen. First, the
change to the engine speed generally alters the engine torque.
Second, the change to the overall reduction ratio changes the torque
multiplication between the engine and the rear wheel.
The vehicle will have greatest acceleration at a given wheel speed
when the gear selected results in the greatest rear wheel torque. If
a gear is selected that puts the engine speed somewhat higher than
the engine speed at which the engine torque peak occurs, that
numerically lower gear will result in greater torque multiplication
and the rear wheel torque will be greater even though the engine
torque will be somewhat less than its maximum value. This will be
true so long as the torque curve remains reasonably flat above its
peak value. Even with engines that have a pronounced peak in the
torque curve, the torque curve will be essentially flat for some
distance near the peak. If the gear ratios are properly matched to
that torque curve and the wheel speed is within the normal operating
range, it will always be true that the acceleration will be greatest
when the engine speed is higher than the engine speed at which the
torque peak occurs.
This begs the question of how the acceleration is related to the
power. That relationship is slightly complicated by the coupling of
several facts. Power is the rate of change of the kinetic energy,
kinetic energy depends on the square of the velocity, and it is not
intuitively obvious whether the velocity should change most rapidly
at the same engine speed where the square of the velocity changes
most rapidly. However, by combining two of the identities
(equations) that were presented near the beginning of this article,
we can derive an identity that describes acceleration as a function
of power, velocity and mass.
Combining the two identities: Power = Force x Velocity; Force = Mass
x Acceleration, we get another useful identity: Power = Mass x
Acceleration x Velocity. Rearranging the terms to isolate
acceleration, we get an identity that describes acceleration as a
function of power, velocity and mass:
 Acceleration = Power / (Mass x Velocity)
This formula provides us with a couple of useful facts. For one, it
tells us that for a given power and mass, the acceleration decreases
as the velocity increases, which is consistent with the fact that
kinetic energy increases as the square of the velocity.
Probably of greater interest to most readers is the fact that for a
given velocity and mass, the acceleration is directly proportional to
the power. There are two distinct and meaningful consequences of the
proportionality between acceleration and power. First, at a given
speed, the acceleration will be greatest when the gear selected is
such that the power at the associated engine speed is the greatest
among all the gears. Second, given any two vehicles with identical
mass (to include the mass of the rider), the one with the more
powerful engine will exhibit the greatest maximum acceleration,
regardless of which one produces the most torque. To be sure, the
power to weight ratio determines the vehicle's maximum acceleration,
which of course is why that ratio is frequently quoted.
The simplest way to assess what the acceleration can be at any given
wheel speed, is to convert that wheel speed to the equivalent engine
speed for each gear, and then look at the power curve to find which
of those engine speeds yields the most power. You can also answer
this question from the standpoint of rear wheel torque, but then
after looking up the engine torque for each of the engine speeds, you
have to turn back around and multiply those engine torque values by
their corresponding reduction ratios in order to find the rear wheel
torque for each gear. You'll get the same result either way; if you
don't, then at least one of the two graphs is in error. However, the
torque method requires more computational work as compared to simply
looking at the power curve, so why would anyone want to do that?
Just for grins, let's consider an actual example. The March, 2003
issue of Motorcycle Consumer News has a dynamometer chart for the
2003 FJR1300. The Yamaha shop manual gives the primary, secondary,
and gearspecific reduction ratios for the five gears. I want to
find the optimal road speed for shifting from 1st gear to 2nd gear.
I worked out the value of the multiplier for converting the road
speed in mph to engine speed in rpm. That multiplier is 60, and the
primary and secondary reduction ratios are already factored in to
that, but I still have to multiply by the gearspecific reduction
ratio. At 50 mph, the engine speed will be 7590 rpm in 1st gear
(more or less depending on the accuracy of my measurement of the
wheel radius), and looking at the dynamometer chart, I read about 120
hp for that engine speed. That's very close to the peak power, but
the peak is located a little higher, just shy of 8000 rpm.
Therefore, I expect that I should go beyond 50 mph in 1st gear before
shifting to 2nd gear.
At 60 mph, the engine speed will be 9104 rpm in 1st gear, which is
just off the chart because when you cross 9000 rpm you're into the
red zone, but I can visually extrapolate the curve and estimate 110
hp, well below the maximum hp. (The error in my measurement of the
wheel diameter might be the reason for the engine speed being in the
red zone at 60 mph in 1st gear, but that error won't effect the
essential comparative result, so I will ignore the red zone.) I can't
know whether I should shift to 2nd before reaching 60 mph, until I
check what the power will be in 2nd gear at 60 mph and confirm that
it is more than 110 hp. At 60 mph in 2nd gear, the engine speed will
be 6380 rpm, and the chart indicates about 105 hp, which is slightly
less than the 110 hp that I'll get at 60 mph if I remain in 1st gear.
Therefore, if this chart is correct and subject to the accuracy of
my measurement of the rear wheel diameter, the implication is that
for purposes of maximum acceleration, I should wait until I reach a
speed slightly higher than 60 mph before shifting from 1st to 2nd.
But what happens if I compare the engine torques? At 60 mph in 1st
gear, at 9104 rpm, the engine torque has dropped to about 60 lb.
ft., a value well below the peak value of about 87 lb. ft. At 60
mph in 2nd gear, at 6380 rpm, the engine torque is about 85 lb. ft.,
which is very close to the peak. If I were to believe that the
acceleration is greatest when the engine torque is greatest, then I
would conclude that I should shift well before I reach 60 mph,
probably somewhere in the neighborhood of 50 mph. But let's see what
happens when we convert those engine torque values to rear wheel
torque. When 60 lb. ft. is multiplied by the overall reduction
ratio for 1st gear, the rear wheel torque at 60 mph in 1st gear is
found to be about 658 lb. ft. When 85 lb. ft. is multiplied by
the overall reduction ratio for 2nd gear, the rear wheel torque is
found to be about 653 lb. ft. In other words, I have slightly more
rear wheel torque at 60 mph in 1st gear than I do in 2nd gear, which
suggests that I should wait until I reach a speed slightly higher
than 60 mph before shifting from 1st to 2nd, which agrees exactly
with the result that I got when I compared the power!
Myth #5: The reason that longstroke, undersquare engines produce
more torque at low rpm than shortstroke, oversquare engines, is
because the longer crank throws are more distant from the axis of
rotation, and that causes the torque to be greater.
Let's consider the question of what determines the engine torque, and
in doing so, let's be careful to distinguish the instantaneous torque
from the average torque through a full rotation of the crank. The
instantaneous torque varies considerably throughout that rotation,
even within the ½ crank rotation corresponding to the power stroke.
The quantity of work done during one complete rotation of the crank
is fully determined by the integral of the instantaneous torque over
that complete rotation. The average torque over the rotation is the
integral of the instantaneous torque divided by the angular distance,
so it follows that the average torque over the crank rotation
effectively determines the quantity of work done over that crank
rotation. (I have of course simplified matters by adopting an engine
that has but a single cylinder.) Now, if it were possible to increase
the average torque over a crank rotation simply by lengthening the
stroke and the crank throw, then it would be possible to arbitrarily
increase the work, the power, and the acceleration simply by
lengthening the stroke! Talk about your free lunch!
The work performed by an engine during the movement of the piston
through a single power stroke is determined by the quantity of energy
released by the combustion of fuel and by the compression ratio (the
compression ratio determines the thermal efficiency). Any desired
compression ratio can be achieved for a given stroke, by shortening
the space between the piston face and the cylinder head. Since the
length of the stroke does not fundamentally determine either the
compression ratio or the amount of energy released in the combustion,
the quantity of work performed during a single crank rotation must be
independent of the length of the stroke. Since the average torque
over the rotation likewise determines the quantity of work performed,
it follows that the average torque over the rotation must also be
independent of the length of the stroke.
The torque applied to the crank depends on the force as well as the
crank throw distance. The force that the gas exerts on the piston
face is proportional to both the gas pressure and the area of the
piston face. As the stroke is make longer, for a given displacement,
the piston face area is made proportionally smaller, and the force
exerted on the piston face is made proportionally smaller. Thus, the
effect of increasing the stroke length is cancelled by the coupled
effect of reducing the piston face area. Here, we see that even the
maximum instantaneous torque applied to the crank will be independent
of the stroke if the stroke variation is subject to a constraint on
the displacement.
To the extent that a long stroke engine happens to produce more
engine torque at low engine speed as compared to a short stroke
engine, the reason for this is at best indirectly related to the
length of the stroke. Rather, it can only be due to a difference in
volumetric efficiency at that lower engine speed, i.e., design
characteristics such as valve lift/duration and the rate of
volumetric expansion of the combustion chamber on the intake stroke.
Instead of the long stroke causing the engine to produce more torque
at low engine speed, the truth of the matter is that the long stroke
and its associated greater piston speed and piston acceleration limit
the engine speed. As such, it only makes sense that the design
characteristics such as the valve lift and duration be optimized for
greatest volumetric efficiency at the lower engine speeds where that
engine will always be operated. Because of that specific
optimization, you would expect that such an engine should be capable
of producing more torque at those low engine speeds than an engine
that is not similarly optimized for low engine speed.
Whether or not an engine that by design produces its maximum torque
at a low rpm is a Good Thing™, is subjective. The power and
acceleration will come on a little sooner off the line, and this sort
of engine will be able to increase its output from low output to
maximum output more quickly, because the rpm range through which it
must be accelerated to reach its peak power will be smaller.
However, power determines acceleration, and power depends on the
engine speed, so an engine of this sort is inherently incapable of
achieving the same power or acceleration as compared to a high rpm
engine of similar displacement, at any road speed. Even "off the
line", if a short stroke, high rpm engine is mated to a gear box with
1st gear set adequately low, the short stroke, high rpm engine will
outaccelerate the long stroke, low rpm engine, anytime, anywhere.
Copyright © 2003, by Tom Barber. All rights reserved.
End of the article
