HP, Torque, and other Calculations
Where I post answers I find to those oddball questions.

Whether 4x4 or motorcycle, I always hear the HP vs Torque comparisons.  What does it mean?  I thought I would write up the ultimate definition....but then I noticed that others already had.  So here's the short version instead, with references.

Calculating Shift Points....aka There's Torque then there's Torque.
A great demonstration all the torque/HP talk  is calculating shift points for a vehicle.  If you have the torque at a certain RPM, gear ratios, and a tire size, you can calculate/plot a variety of useful interesting information, including:
• Radius and diameter of a tire
• Torque and HP vs RPM
• Torque and HP vs MPH
• RPM vs MPH in each gear
• Torque at the wheel for various Gears, RPM, and MPH

Where this actually becomes useful is calculating the rear wheel torque (RWT) vs MPH.  Where RWT lines cross each other are the natural shift points for a vehicle; providing a smooth transfer of power.  You can read about it, including how to do it, at:
http://www.micapeak.com/bike/ST1300/Horsepower.html
This page also shows power and torque curves for many different bikes.

You can also download the following spreadsheet and follow along.  I've calculated the points for the 94-2003 Honda Magna (same engine/drivetrain), 1340 CA Big Twin Harley, and the 1993 Isuzu Amigo 4x4 (4EZ1 2.6 liter engine, in 2-wheel HI gear)
• Torque_HP_Shift_Calc.xls  (150k)

Torque vs HP
First, to settle it, Torque is measured, HP is calculated.  I know people will debate this to the end of time (or until a torque wrench hits someone's head), it will be pointed out that formulas go both ways, but the simpler (fundamental) measurement is torque, as the units will explain.

Force:  Take a socket wrench and try to remove a bolt from the alternator.  You push and push on that wrench handle handle....and nothing happens.  You are applying a force.  But you're not doing anything.  That is force--you apply it.  Nothing has to happen if the counter force is stronger.  You can carefully put a vehicle with automatic transmission up against a wall, put it in drive, let it run (slowly!)--and nothing happens.  You're burning energy and pushing forward--and you'll run out of gas.  The wall isn't moving, the car isn't moving--the bumper is applying a force, but no work is being done. (Relative to the car-wall relationship.)

Torque:  A a rotational (twisting) force. Force applied at a 90 degree angle, usually with a lever....like with a socket wrench.  Torque = Direct Force * Length of arm.  The example most people are familiar with is busting a nut.  You apply a force to the end of the socket wrench and can't bust that nut.  What do you do?  You can't get stronger without months in the gym, and you need to bust that nut off now.  So you grab a 12 inch pipe or breaker bar and slip it over the end of the wrench.  You're not any stronger....but you have a longer arm, and therefore more torque.

There's a cost/tradeoff, however.....the longer arm gives you more leverage on the nut, but you have to move the end of bar farther to rotate once around.  With that breaker bar on there, you're spinning your arm like a windmill to get that nut unscrewed.  Once you break the nut loose, you remove the breaker bar extension (shorten the arm length) and use just the wrench with the short arm to remove the nut.  The bar gave you more torque--it was a force multiplier.  But it was a distance multiplier as well.

This is similar to shifting to a lower (physically bigger) gear; you get more power in the lower gears to climb hills, but the wheel has to spin more to go the same distance as the higher (physically smaller) gears.  

Horsepower:  You apply a force.  You multiply it by a lever arm to get torque, a rotational force.  But you haven't actually done anything--just changed your force.  Horsepower is an application of force over time.  It's a measurement of work done with the direct force (pushing) or rotational force (torque).  HP is a summation of all the individual times you applied force.  For example, a generator with a crank.  At the top of the crank circle, you are applying a force to the push the generator handle away from you.  Good for you, it moves.  Then at the bottom, you are pulling the handle towards you.  Again, more work, opposite direction.  Each instant you are applying a torque (rotational force) and changing direction.  Sum all these millions of Torque/direction changes up.....and the generator is putting out 1 horsepower.  You're as strong as a horse! 

Horsepower is a measurement of applied force over time.  HP = Torque (ft-lb) * RPM / 5252
Notice that RPM is in there.  Power isn't just the explosive force * the piston arm length.  RPM is how many times you do it in a minute.

Common Sense Proof
Torque is a measure of force at any instant, not power.  Horsepower is a measure of work over time (specifically 550 pounds lifted one foot every second).  Using a time analogy, do you add up hours (HP) to equal a second (torque), or do you add  up seconds (torque) to equal on hour (HP)?  If you want to know more about torque and see an animation, try HowStuffWorks.com.  It also compares a 430 HP Caterpillar truck to a 437 HP Mustang Cobra to show how Torque and HP are two different creatures.

To elaborate on HowStuffWorks example of the 430 HP Caterpillar vs Cobra engines, let's detail the engines.  The diesel dump truck engine has a long stroke (the piston travels a long distance up and down).  This lets it generate a lot of torque (remember....longer lever arm = more torque) and thus a lot of HP at low RPM..  The Cobra, however, has a large-diameter piston and goes up and down a short distance.  This means it can turn faster (10k-15k RPM) and use that to crank out the same amount of HP as the diesel.  The gasoline engine is usually smaller and lighter per HP generated as well.  So why don't dump trucks use Formula 1 engines?

Simple--a Formula 1 race car has a lifetime measured in hours.  A diesel dump truck with the same HP runs at much lower RPM's and has a lifetime measured in decades.  You won't see a formula 1 dump drunk leaping off the starting line at the next Indy 500, but you will find a diesel work truck at the track that's lasted though 20 generations of race cars.  The bigger, slower turning engine lasts much longer.  All things being equal, think of each engine as having a lifetime of 10 million RPM.  It takes the lower RPM diesel engine longer to use up it's time.  In reality, higher RPM generates more heat, which makes the high RPM vehicle burn out even faster.

That additional heat also explains why Harley advertises that low-end torque is the most important characteristic.  They have to run low RPM to keep their air-cooled engine from burning up (and why their 1300 cc engines were only putting out 40 HP).  Strange how once the water cooled V-Rod came out, Harley got quiet on the torque issue and started talking horsepower..... 

HP = Torque (ft-lb) * RPM / 5252
From the formula you can see a general rule about making power. Generally, in order to make more power, you have to spin the engine faster.  Also, each time you shift gears, the torque gets divided by the same ratio that the rpm gets divided. So, to go fast, you want a motor where you don't have to shift gears as often. In fact, if two motorcycles  make the same peak torque - say, 80 foot pounds - the motor which makes the torque at a higher rpm can stay in lower gears longer and therefore accelerate faster. Wouldn't it be useful to have a single number which reported both the peak torque and the peak rpm?

There is just such as number: horsepower. Horsepower equals torque times rpm; thus an engine which makes 80 foot pounds of torque at 8000 rpm makes twice as many horsepower as another engine which makes the same 80 foot pounds at 4000 rpm. Although the two engines deliver the same amount of torque, and therefore the same amount of push, the first engine can go twice as fast in each gear. If you're racing a cruiser in 3rd gear producing your peak 80 foot-pounds of torque at 4000 RPM, you're getting blown away by a sport bike making the same peak 80 foot-lbs at 8000 RPM in 1st gear.

If all you care about is horsepower, get a crotch rocket or Corvette.   If what you're really interested in is power at low rpm, now you probably want a big cruiser or a big diesel pickup.  Riders/Drivers  who claim to prefer torque over horsepower really mean they prefer engines with more horse power at lower RPM, but this comes at the expense of high-end HP or top-end speeds. 

The general rule is to get your torque numbers as low in the RPM range as possible to improve stoplight acceleration and around town driving. Get torque numbers in the higher RPM range to increase performance in racing applications such as circle track and road courses.