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If you've been around motorized vehicles for any length of time, you have probably been exposed to the great torque vs. power debate at some point. If not, it goes like this:
"Torque is what makes a bike accelerate, not power."
Torque and power are inescapably linked by the fact that horsepower equals torque (in ft-pounds) times RPM divided by 5250, so people who talk as if they are independent are full of it. If you have a given torque curve for an engine, you have the horsepower curve also. Knowing how these two numbers work with each other lets you can poke through some of the BS you might read.
First, as usual, a few definitions.
Torque is a twisting force applied to an object, like a wheel or a crankshaft. Note that motion is not required for torque to exist! If you stand on a lug wrench that is on a frozen lug bolt, you are applying a torque to that bolt even though there may be no movement. For our purposes, we will consider that torque is measured in pounds-force feet (lbf-ft) meaning the equivalent of a given force, in pounds, acting on the end of a lever of length in feet. For example, standing with 180 pounds body weight on a lug wrench one foot long yields 180 lbf-ft of torque. A child of 90 pounds standing on a two-foot lug wrench applies the same torque.
Work is the application of force over a distance. Unfortunately, the units used are the same (pounds times feet) but we write this as ft-lb just to distinguish it. The real difference is that in this case, the "feet" part means feet of movement. If you push on a car with 100 pounds of force and maintain that for 30 feet, you have done 3000 ft-lb of work. An easier example is lifting a weight (in pounds) a given distance (in feet). If you use some sort of mechanical advantage, like a winch, you will do the same amount of work because by halving the effort required, you will have to double the distance through which you apply the force to achive the same objective.
Power is the application of work within a finite time. 550 ft-lb of work in one second is one horsepower.
So, let's first go through the numbers to get from torque to horsepower. Pushing with 87.5 pounds (force) on the end of our 1-foot lug wrench applies a torque of 87.5 lbf-ft. No motion yet, so no work and no power. But now let's say the lug bolt loosens slightly and starts to turn, but that same 87.5 pounds of force is needed to keep the wrench turning. For every revolution of the wrench, you are applying 87.5 pounds of force over a distance of (2 * pi * 1 foot) or 6.28 feet, the circumference of the circle that your hand is making, for a total of 550 ft-lb of work. It's only when this system is actually moving that work is being performed. From here, it's a quick step to say that if you work fast enough to turn that wrench once per second, then you are doing 550 ft-lb of work per second, which means you are applying one horsepower.
By the definitions we can see that HP is directly proportional to torque and RPM. "Directly proportional" means there may be a multiplyer involved, so let's find it using our example numbers, remembering that 1 revolution per second is 60 RPM:
torque * RPM * constant = hp
87.5 lbf-ft * 60 rev/min * X = 1 hp
X = 1 / (60 * 87.5) = 1/5250
torque * RPM * 1/5250 = hp
hp = (torque * RPM) / 5250
For internal combustion engines, torque is always given at a certain RPM because they can't generate any torque when they aren't moving. Once they are running fast enough to sustain their own operation, the force that they are exerting against a load can be measured, and the speed at which they are turning can be measured, so the torque (and therefore power) numbers become known.
So, if there is such a fixed relationship between torque and power, why do some people say that a certain engine has lots of power, but no torque? Remember that the connection between torque and power is rotational speed. A sportbike motor might generate 150hp at 14,000 RPM but the torque at that RPM is very small; about 53 ft-lbs. In comparison, a large-displacement twin might peak at 100 hp at 7000 RPM. The torque applied at the twin's 7000 rpm, 75 ft-lbs, is greater than the torque applied at the sport bike's 14,000 rpm but the sport bike makes up for it with a lot more engine speed and ends up with more horsepower.
The street, though, complicates things because the sport bike will probably not be ridden at 14,000 RPM. At 5000 RPM, the twin would likely have more power. This is an artificial handicap; the sport bike wasn't meant to be ridden at that speed since it generates its power by sending the RPM part of the equation sky-high. For street riding, the twin is easier to ride, less prone to stalling as you pull away from a light, and you get that satisfying "oomph" when you twist the throttle. But as the RPM increases, the twin runs out of breath and the race bike, although the torque is low and probably getting lower, continues to make more and more power until it hits its peak at 14000.
[Insert dyno charts for comparison showing less torque but more power for sportbikes at high RPM]
Engines are designed for their intended use. Our twins are designed to yield fairly high torque values at low RPM, because this makes them easy to ride in day-to-day life, and Harley-Davidsons have their torque concentrated even lower in the RPM range than BMWs do. Low-end torque is accomplished by several design traits, one being small valves and intake tubes which create high air velocity into the cylinder for good fuel mix at low speed.
Those effects tend to become a restriction at high RPM, which means that engines intended for high RPM end up with larger valves, larger air intakes, smaller cylinders and other things that let them continue to breathe when other engines start to gasp. Race bike engines have fairly small displacement, which limits the torque that can be produced at the crank. They apply that torque at much higher speeds to get high horsepower (and who can argue that those bikes don't accelerate quickly?).
To a lesser extent, BMW varies these techniques for different bikes. The GS series has narrower intake tubes to give a faster intake charge, giving better fuel/air mixing and better torque at low RPM. Since this becomes a bottleneck at higher RPM, the "power" engine in the RS and RT bikes have larger intake tubes. Swapping the GS tubes into an RS or RT is a common retrofit, as it makes the bike torquier at low RPM where most of us ride. Newer technology in cars, like variable valve timing and variable intake tract length, can give motors the best of both worlds by increasing torque at higher RPM without giving it up at low RPM. Incidentally, Honda has variable valve timing on a motorcycle now.
But to get back to the main point, it is power that moves our bikes down the road. Yes, torque provides the pushing force through the drivetrain, but it needs to happen at some given speed, and those two factors define "power."
Why does torque drop after a certain RPM?
Torque starts to decrease because the engine cannot breathe as well. Due to the speed, the cylinder does not fill with air as well. A designer can get around this problem with "tuned intake" which sets up a resonance to pack the cylinder with air, but it only happens at a certain RPM. The next evolution of design is to make a variable system which packs the cylinders with air at all RPM; this is usually called "variable tuned intake runners" or something like that and involves valves which open and close to create a different size for the airbox and manifold.
Why does power continue to increase after torque decreases?
Remember that the power is essentially the product of the RPM and the torque. When the torque peaks at a certain RPM and starts to drop off, the decrease is small and is not enough to offset the increasing RPM, so the overall product still increases. Eventually the decrease in torque becomes large enough that it outweighs the increase in RPM and we see the power start to drop. Because of this, the power peak will always be after the torque peak.
A few other well-writen articles illustrate these concepts, although many can be found by entering "torque horsepower" into Google: