Bicycle efficiency and power -- or, why bikes have gears.

When you try to determine how fast a bike can go, what you do is you match the power available against the power required, at a given speed. This energy budget indicates whether you can go faster, or whether you can even hold your current speed.

Power available:

A human engine has a torque curve similar to that of a steam engine, more or less, which is to say that it is flat until a certain critical rpm, at which point it begins to drop off, because the energy used in accelerating and decelerating massy components (legs) begins to take up all the energy produced.

Power produced is the product of torque times rpm. (a quick digression: your torque is a product of your leg length, your crankarm length, your wheel size, your gear ratio -- what we're talking about here, though, is torque measured at the crank itself. So the only things that are of issue are leg geometry, crankarm length, the rider's weight, and, most of all -- the rider's leg strength.)

So if we revisit the previous graph to show POWER produced, it will look like this:

This is just the torque curve above, with each point multiplied by the matching rpm. One thing to notice here in comparing this to the previous graph is that your power is still rising even after you've passed the torque peak. You can actually feel this when you're pedalling really fast up a hill -- you feel like you almost can't push on the pedals because you don't have time to, but you're still going like anything.

So we can make a graph showing three different riders and their power curves, like so:

This shows three cyclists: the lowermost curve is the power curve for a beginning cyclist; the middle one for a fairly serious recreational cyclist, and the top one for a track racer. Notice that there isn't much difference in the force they can exert (I'm making some assumptions here -- a beginning cyclist can push 120 lb-feet and peaks at 90 rpm, whereas a serious track racer like Marty Northstein can generate 160 lb-feet at over 175 rpm.)

The point here is that strength is less important than smooth, fast pedalling.

Power Required:

Now, the next subject is: where does the power go?

There are two places: friction and air resistance.

Friction:

Friction losses are from bearings, from the viscosity of grease, from the chain, from the tire squishing against the pavement. Knobby tires are rougher; soft tires smoosh more; heavy grease or badly-maintained and corroded bearings take more force to move.

Estimates of friction losses are between 15% of total power, for a Huffy moutainbike that has had little maintenance, to maybe 0.5% for an Olympic track bike. (The friction losses in powertrains for bicycles are the lowest of any machine, because the speeds are low and the power is low.)

The power required to overcome friction rises linearly with speed.

On this graph, the upper line is an old mountain bike; lower is a nice track bike.

Then there is the huge one, that serious cyclists spend most of their time fighting: