**by Rod Heilfron**

I've been
reading car and motorcycle magazines for more than 36 of my 52 years and I've
always seen articles about Torque vs. Horsepower but I've never seen one that
does the subject justice. So I'm going to try to tell you just what is Torque
and what is Horsepower. As a note, I’m not going to go into heavy math and
rocket science, like how you magnetize a spider in a super magnetic field and
suspend it in the air. I’m am going to discuss things just like any backyard
mechanic would, with simple math and a good understanding of the laws of
physics. I will be simplifying things a bit and I’m not going to go into
detail explanations for everything I say. You’ll just have to trust me,
honest.

Engine
Torque is a measure of the LOAD on a rotating part. As far as motorcycles are
concerned it is the load imposed on the primary drive's drive gear, the one
attached to the crankshaft. If you over-torque the head of a bolt, you’ll
break the head off. If you built an engine with too much torque you’d break
the crankshaft or sheer the teeth off of the primary’s drive gear (or some
weaker part farther down in the drive train). When you increase the torque of
an engine on a pre-made bike you increase all the loads on the clutch,
transmission gears, drive chain or belt or shaft and, of course, the rear
tire. But when you're designing an engine from scratch all the gear ratios are
undetermined and you can't even calculate the load on the clutch from Engine
Torque alone because the load on the clutch is equal to Engine Torque times
Primary Gear Ratio. As an example, lets make a test bike, with a 1.5:1 primary
ratio, a 3.0:1 first gear and a 3.0:1 final drive ratio. If the test engine
produced 80 ft lbs of torque the clutch has to handle 120 ft lbs of torque (80
ft lbs times 1.5 primary drive ratio). The output from the transmission in
first gear is 120 x 3.0 or 360 ft lbs. The torque is further multiplied by the
3.0 final drive ratio to 1080 ft lbs. Let's say that we loose 20% of our
torque do to "transmission losses", we end up with 864 ft lbs of torque at the
rear wheel. This is the maximum amount of torque at the rear wheel of our test
bike in first gear and will only be available at one rpm, peak torque’s rpm.
At all other rpms the torque will be less. Actually, if you rev the engine
with the clutch in, then let the clutch out, you’ll have much more torque
available for a drag racing launch because the energy stored in the rotating
crank, flywheel, clutch, etc. is released as they slow down. The heavier these
parts are, the more load you put on the clutch, transmission, drive chain or
belt or shaft, the rear wheel spokes, and rear tire. It feels like you have
more power but what you’ve done is store a lot of energy in rotating masses
and then applied it to the bike all at once. Once the engine and rear tire are
running in sync only the engine torque will accelerate you and the extra mass
of the flywheel will actually slow you down. It’s impossible to tell the
difference between low end torque and heavy flywheel effect when you rev the
engine and release the clutch from a stop. Now, to make rear wheel torque
useful for calculating acceleration we must convert it into lbs of force at
the rear tire’s contact patch by dividing the rear wheel torque by the rear
tire radius. So 864 ft lbs divided by 1.0425ft (12.5" radius for a 25"
diameter tire) is 829 lbs of forward thrust at the rear tire. If our bike
weights in at 500 lbs plus a 200 lb load for fuel and rider, that's 700 lbs of
weight. From one of Newton's laws of motion: f = ma or more useful for us: a =
f/m. a = 829/700 = 1.18 g's. Now, this means that if the rear tire can handle
it at one point during the acceleration in first gear the bike will reach a
little over 1g acceleration, kind of like taking a step of off a building's
roof, very scary. If we have a 1:1 gear ratio in 5th gear our maximum
acceleration will be 80 x 1.5 x 1 x 3.0 / 1.042 x 80% / 700 = .39g's.
That's: Engine Torque x Primary Gear Ratio x Transmission Ratio x Final Gear
Ratio / Tire Radius x (100% - Transmission Loose) / Weight . And all the gears
2 though 4 will be somewhere in between. Now, in the real world, the maximum
acceleration will be much less because we've got to fight the wind. In
reality, we’ll get about .8g's in first and .15 to .20g's in high gear,
depending on what rpm (and therefore what wind speed) the engine produces that
maximum torque figure. Actually, the maximum acceleration will occur at a
speed just below maximum torque since lowering the rpms reduces the torque
just a little but the reduction in speed reduces the wind resistance by a lot.

Now lets
explore the acceleration due to Engine Torque a little more in depth. Lets say
we've got 2 identical cruisers with two riders that weigh the same. At 60 mph
both bikes make 75 ft lbs of torque and both accelerate around an 18 wheeler
at the same time. Now one of the riders believes that acceleration is caused
by torque and the more you have the better and he notes that his engine will
produce more torque as he accelerates from 2500 rpm if he keeps his bike in
5th gear. The other rider (me) believes that horsepower, not torque,
accelerates the bike and he down shifts into 3rd gear, revving to 3900 rpms
knowing that all the time he's accelerating, his torque will be decreasing.
The first bike accelerates at a pretty constant .2g's to .16g's while the
second bike accelerates at first at .3g's slowing to .2 g's as it reaches the
top speed available in 3rd gear. This second bike accelerates at a much higher
rate even though it’s torque is going down while the torque of the first bike
is going up! What's going on? Well, the people that say that Engine Torque is
what accelerates a bike forgot about the gear ratios. Rear Tire Force, not
Engine Torque, is what accelerates the bike and Rear Tire Force is Engine
Torque times all the gear ratios and then modified for the rear tire diameter.
Engine Torque only determines the load on the Primary Drive's drive gear,
that's all. It's the most misused property of an engine ever. Knowing the
torque that an engine produces only tells you it's displacement and nothing
about the bike's acceleration unless you know the gear ratios and rear tire
diameter. Oh, by the way, in the truck passing example the second bike was
able to pass the truck and pull in front of it about 100 feet before it's
competition on the first bike, who, unfortunately didn't have an extra 100
feet to spare and became a splat on the front of the 18 wheeler that was
coming the other way.

Magazine
articles that you've read that say they measured the torque at the rear wheel
and got 45 to 120 ft lbs are not telling you the truth. Rear Wheel Torque is
200 ft lbs to well over 1,000 ft lbs depending on what gear the bike was
tested in and can not even be measured on a rear wheel dyno. Rear wheel dynos
measure Horsepower not Torque, the Engine Torque is calculated from the
equation: Horsepower = Torque x RPM / 5252 or Torque = Horsepower x 5252 /
RPM. People that claim that horsepower is just the result of a calculation are
wrong, the equation just relates different aspects of the engine: Torque, RPM
and Horsepower. If you know any 2 of the aspect you can calculate the 3rd. For
example if you know the Horsepower and the Torque you can calculate the RPMs,
that doesn't make the RPMs just some calculated item. The math is just used to
calculate what ever you don't know, with an inertia dyno (rear wheel dyno)
you know the RPMs and the Horsepower and you calculate the Engine Torque, NOT
the REAR WHEEL Torque.

Engine
Torque is about as useless an attribute of a bike as can be. Two equal weight
bikes, both make a maximum of 70 ft lbs of torque, which one accelerates
faster? Why, the one with the most Horsepower! 70 ft lbs of torque at 5,000
rpms can't beat 70 ft lbs of torque at 10,000 rpms! Why? Because torque times
rpms equals horsepower and it is horsepower that moves your bike down the
road. You can gear a 10,000 rpm engine twice as low as a 5,000 rpm engine thus
doubling the Rear Wheel Torque and therefor the force at the tire contact
patch.

The
torque required to go a certain speed increases as the square of the speed, so
it would take 4 times as much torque to go 100mph as it does to go 50mph but
it would also require the engine to rev twice as high. And 4 times as much
torque revving twice as high is 8 times as much horsepower. Therefore the
horsepower required to go 100mph is 8 times as much as that required to go
50mph. So to figure how much horsepower is required to overcome the wind
resistance of a Harley sized bike at speed you multiply the cube root of the
horsepower by 30.2. This constant is approximate and changes do to the size of
the bike.

The
formula is: Top Speed = Constant x (Horsepower ^ 1/3)

Where
Constant = 30.2 for a large cruiser

31.79 for a medium sport bike

32.99 for a small sport bike

Examples:

Horsepower Harley Top Speed VFR750 Top Speed

------------------------------------------------------------------------------------------

20 hp 82mph 86mph

60 118 124

100 140 148

150 160 169

200 177 186

Now
you'll notice that I don't need to know what rpms the horsepower is at nor the
gearing of the bike in order to calculate it's top speed potential using
horsepower. When you build the bike, you have to put it on a dyno to find out
what rpm it reaches maximum horsepower at, then gear the bike accordingly. If
I used the engine's torque I'd have to use the amount of torque the engine
produced at maximum horsepower and the rpms at maximum horsepower to make the
calculation for top speed.

Engine
Horsepower is a measure of the engines ability to do work per unit time and
work per time is the moving of a weight some distance in a given amount of
time. The units of horsepower is Foot Pounds per Second. 1320 feet times 815
lbs divided by 13.6 seconds is equal to power. If you increase either the
weight or the distance while keeping the elapsed time the same you are making
more horsepower. If you can keep the distance and the weight the same and
decrease the time you are also making more horsepower. Of course, all of this
has to take into consideration wind resistance which increases as your speed
increases. So, 60 Hp in a 815 lb cruiser bike (stock Harley 88") gets you down
the 1/4 mile in 13.6 seconds at 98 mph but 83 Hp (from the same engine) gets
the same bike down the 1/4 mile in 12.9 seconds at 108.8 mph. Both bikes make
the same amount of Engine Torque but the faster bike makes more horsepower.
Horsepower is not related to engine displacement, Engine Torque is related to
engine displacement. Horsepower is related to the engine's piston area, or the
bore squared times the number of cylinders. This is easily seen from the
equation Horsepower = Torque x RPM (I'll be leaving out the constants from
now on since constants are only used to convert units of measurement) where
Displacement can be substituted for Torque. I'm not going to explain why,
you'll just have to take my word for it that if you double the displacement of
an engine you will double it's torque. Now, 1/Stroke can be substituted for
RPM because we want to keep the average piston speed the same in our engines.
Piston speed is the limiting factor in an engine's ability to rev and for our
purposes 4,000 ft/min will be used. This means that a 4" stroke Harley 88"
engine would have a redline of 6,000 rpm and a 1.9" Honda VFR750 would redline
at 12,500 rpms. Both can make about the same amount of horsepower, somewhere
in the low 90's, but the Harley makes about double the torque and revs about
1/2 as much. Now, making the substitutions in the formula we have:

Horsepower = Displacement x 1/Stroke

but

Displacement = Bore squared times number of cylinders times the Stroke,

therefor:

Horsepower = Bore squared times number of cylinders

which is
the piston area of the engine. The engine’s stroke has no affect on
horsepower, it simply determines the redline of the engine. If you doubled the
stroke of an engine, you’d double the torque but you must limit the redline to
1/2 of what it was to prevent the engine’s piston speed from exceeding what it
was with the stock stroke. Double the Torque and 1/2 the RPMs is the same
amount of Horsepower. If Displacement (and therefor Torque) ruled acceleration
then big twin motorcycles would be the fastest bikes on Earth but they are
about the slowest. The new big twin cruiser drag racing record set recently is
9.8 seconds at 133 mph on a highly modified twin cylinder Yamaha Road Warrior,
yet 20 years ago that was matched by a stock 4 cylinder engine Yamaha VMax.
Why? Because the piston area of the twin is about the same as the 4 cylinder
VMax and therefor the Horsepower is about the same yet the twin makes much,
much more torque than the 4 cylinder engine but isn't any faster. Piston Area,
not Displacement, determines how fast your bike is!

If you’d
like to guess what your bike will do in the 1/4 mile, the formula is:

1/4 mile Speed = Constant * (Horsepower ^ 1/3) / Weight

Where the
Constant = 20350 for a large cruiser

20800 for a small sport bike

This
constant is for the wind resistance of the bike, it gets smaller the bigger
the bike is.

The ET will
depend on how well you launch but the formula will be approximately:

1/4 mile ET = Constant / 1/4 mile Speed

Where the
Constant = 1340 if you launch well

1440 if you launch poorly

And any
number in between for a launch between well and poor.

You might
note some discrepancies between my figures and ones you calculate. That’s
because I use a computer program for my numbers which is a little more
accurate than these simple calculations.

It may
sound like I'm putting down torque and I'm all for rpms and horsepower but the
truth is I like having a low rpm, therefor high torque, engine to get the
horsepower needed, because rpms affect power bandwidth. I define an engine's
power bandwidth as the rpm range from below and above the peak torque where
the torque is 80% of the peak divided by the redline. So if your engine, an
88" Harley, makes 80 ft lbs of torque at 3100 rpms and it makes 64 ft lbs of
torque at 1000 and at 5000 rpms with a redline of 6000 you'd have "(5000 -
1000) / 6000", or a 67% power bandwidth. If on the other hand you have a Honda
VFR750 with 50 ft lbs of peak torque and 40 ft lbs at 5,600 and 11,700 with a
redline of 12,000 rpms you'd have a 51% power bandwidth. You'd have just as
much power at the top end but less at the low end (and top end and low end are
measured in mph not rpm when comparing bikes with different engine redlines
and different gearing). It's power bandwidth that makes a bike easy to drive,
keeps it from stalling when taking off in first gear and makes it unnecessary
to down shift in order to accelerate well. We rarely drive our bikes at peak
torque rpms, usually we are well below that. The lower the redline, the
broader the power bandwidth and the better the bike is to drive on the street.
So I hope that Yamaha builds the new VMax with a 2 litter engine and a 7500
rpm redline. It would make more than 150 rear wheel horsepower and have a very
broad power bandwidth. Then I'd have something to replace my current VMax
with. Think they will, well, probably not.

Now I'd
like to discuss horsepower and torque graphs and just how useless they are.
Have you ever tried to compare power graphs between two engines that have
different redlines? It's impossible to get anything useful out of the
comparison. Which bike accelerates best from 50 mph or from 80 mph? Which is
quicker in the 1/4 mile? You can't tell. Which bike accelerates best in 3rd
gear when passing an 18 wheeler? Again, you can't tell. Horsepower and torque
graphs are fine for tuning an engine but useless for comparing two different
types of engines. The only graph motorcycle magazines need to display is an
acceleration vs. speed, in each gear. Measuring performance vs. rpms is
useless, if I get my VMax going 7,000 rpms you can't even get a Harley to go
that fast, so we can't even have a roll-on test from a given rpm. So instead
we both start our roll-on acceleration test from 50 mph regardless of the rpms
the engines are turning. All acceleration test should be relative to mph, it's
meaningless to care about what rpms the engines are turning, just as
meaningless as horsepower vs. rpms is. Horsepower vs. mph is much more
meaningful but even that doesn't allow for different bike weights and
different wind resistances. So knowing the horsepower of a bike is useless,
only the actual acceleration, measured in g's, vs. mph is meaningful. I have
seen such a graph only in one British motorcycle magazine and I wish the
American magazines would change to it. It would really be nice if they were
printed on a transparent sheet and all were the same size with the same
maximums in both the X and Y directions, then you could cut them out and lay
them on top of each other to compare different bike's accelerations. Or make
them Online, like the stock market does with companies’ stock prices vs. time,
so you can compare any number of bikes on one graph. But I'm just dreaming,
aren't I? Will it happen in my lifetime, it would be nice, but who knows.

Well
that's it for now. Maybe next time I'll discuss the truth about how counter
steering works or why gyroscopic progression of the front wheel is
meaningless as far as motorcycle steering is concerned. Or perhaps why low
centers of gravity aren't the way to go for best handling. Or maybe how gear
ratios should be chosen for a street bike. Or why I don't like chain drives
(unless fully enclosed) for the street. Or what engine/transmission oil to use
and how often to change it. Or what effects changing the fork oil level has on
your bikes front end’s ride. Oh, there are so many things to talk about, I
can't wait till my next article!

Thanks for
listening,

Rod (over
384,000 miles of bike riding)

1981 Yamaha
XV920RH (65,000 miles) enclosed chain drive

2000 Yamaha
VMax (30,000 miles) shaft drive