Intro to Power

December 10, 2007

The first step in learning to use power data in your triathlon racing and training is to understand what “power” is. We tend to use terms such as “strength” and “force” and “power” rather loosely, and now is the time to become more exacting. We’ll move toward the precise definition of power in a few steps.

To move any object, you have to push on it. We measure how hard we push on something by determining the force that we apply to it. The harder we are pushing, the more force we apply. (Strength is a measure of the maximal force a person can apply to an object.) However, knowing how much force we apply to something doesn’t tell us much about the process of moving it, and moving ourselves down the road is what our sport is all about. After all, you can apply all the force you want to a brick wall and you won’t go anywhere.

The next key element is the distance you move the object. You push on something (with force), and you move it a certain distance. The force that you apply to something, times the distance that you moved it, is the work that you did:

Force x Distance = Work

You can see that, if you push on something and don’t go anywhere, you don’t do any mechanical work. The process of pushing on something and moving it – doing work – is the process of adding energy to the object. Work is measured in joules, or one Newton of force applied over one meter of movement. Note for the moment that time has not entered into the discussion of work.

Now we know that, in order to move something, we have to apply some force for a particular distance. In the simple case of lifting an object, it takes the same work to lift it a given height whether we take one second to lift it or an hour to lift it. Similarly, it takes you about the same total amount of work to ride your bike 40 kilometers whether you ride the course in an hour or two hours (ignoring wind resistance for the moment). In racing, we don’t care so much about the total work required to cover the distance. We care about how fast we can do that work.

Therefore, it is the rate at which we can do the work that counts. In physics, this is (not surprisingly) called the work rate. It is measured by dividing the amount of work we did by the time during which we did it. Again, work is measured in joules; time, of course, is measured in seconds. One joule of work done in one second is called a Watt. This is power.

Power = Work/Time = rate at which we do work.

In a human powered race of any kind, the winner is (all else equal) the one who can do the work required to complete the event in the smallest amount of time. This means that the fastest athlete is the one that generates the most power, whether on foot, on a bike or pulling water. Power wins races.

Here we have described power as the rate at which work is done: joules divided by seconds. If we do a little algebra and move some units around, we find another equivalent way to think about Power: Force times velocity.

Power = Force x Distance ÷ Time = Force x Velocity
(since Velocity = Distance ÷ Time)

So, the speed with which we apply force is another way to define the power output. This is a good way to think about how your muscles work. Your muscles aren’t really aware of how far you have moved a bike with each pedal stroke, and they don’t care. Your muscles only care about how hard they contract and how fast they contract. The harder they contract, and the faster they do it, the more power they produce. Harder; faster = higher work rate = more power. That’s what makes a faster athlete.

Whether on foot, on wheels or in the water, improving the power that you can produce for the duration of your chosen event is the path to advancement. While surely technique and economy matter (more in some sports than others), the purpose of conditioning and training is to improve your power output. Power wins races.

Power and the Human Animal

Skeletal muscles are pretty simple. They contract in one direction, and then they relax. Some other muscle stretches them back out so they can do it again. Repeat. In engineering terms, muscles are a reciprocating motor. Back and forth; back and forth. Some muscles are designed (intelligently or not) to contract a long distance; some are designed to contract rapidly; some forcefully; some delicately and precisely. Still, they all do the same basic thing. Upon some command from your brain, they get shorter. In doing so, they pull on a bone and start some sort of motion.

When your leg muscles (quads and glutes, mostly) contract, your leg extends and pushes down on the bike pedals. The pedals turn the cranks, which in turn rotate the bottom bracket spindle. The spindle turns the chainring, which pulls the chain across the rear cogs and turns the rear wheel. The outer edge of the rear tire grips and pushes against the road. The bike moves forward. All of the interim steps from muscle contraction to the tire pushing against the road are merely linkages. Linkages are passive elements of a system and cannot add to the power output (they can, however, subtract power due to friction). The power output is determined entirely by your muscles: how fast and how hard they contract. (This explains why you can’t improve your power output by changing to cranks that are a little longer or shorter.)

Remember that, in the power equation, force and speed are interchangeable. If you increase one by ten percent and decrease the other by ten percent, you end up with the same power. Linkages merely serve to make these exchanges. Human muscles are evolved to exert (a) highly forceful contractions, (b) over very short distances, (c) at low rates of speed. We need to convert short slow movements into long fast movements so we can get to the finish line while there is still pizza. The linkages of our bones and joints, combined with the gearing of our bicycles, do that very nicely.

Muscle Power = Short, Slow and Forceful is converted to:
Bike Power = Longer, Faster and not-so-Forceful

All the while, the total power is preserved (ignoring friction in the linkages).

On foot, our long legs and the construction of our feet allow our very strong, yet short and slow, muscles to propel us at high rates of speed when running and leaping. Leg muscles contracting over a total length of a few centimeters can propel Michael Jordan more than a meter into the air. Legs muscles contracting at a speed of a few centimeters per second can propel a bicycle at a thousand centimeters per second.

Remember, power is produced by your muscles. The rest of the apparatus – bones, joints, bike parts – only serves to transmit that power to the road or the water.