Why Real-Life Science is Messy

For the past three weeks, we’ve talked about a bicycle racer and his bicycle. Last week, I suggested we could modify our experiment and measure force or torque directly in the next iteration of the experiment. If we had done that, we would have discovered this measured value was much greater than what we had predicted. Today we’re going to talk about why.

In our bicycle experiment, we made a bunch of assumptions. We assumed that the bicycler was traveling across a level surface, so gravity was neither speeding up nor slowing down his translational motion. We assumed the gear ratio was one-to-one. We used an estimate for the number of rotations of the pedals. We also implicitly assumed that the frictional forces associated with the bicycle-bicycler system were negligible. Were these all reasonable assumptions?

Let’s talk more about the frictional forces. There are multiple sources of friction in a bicycle-bicycler system. There are frictional forces associated with the movement of the mechanical parts of the bicycle, and the rolling of the tires across a surface. It turns out that these frictional forces are pretty small, so we’ll stop worrying about them.

However, aerodynamic drag introduces a lot of frictional forces into the bicycle-bicycler system. This aerodynamic resistance includes things like the density of the air, the wind velocity, the coefficient of wind resistance, and the frontal surface area of the bicycler and his bicycle.

The published results of other scientist’s experiments tell us that that aerodynamic forces on a bicycle-bicycler system can account for 70 – 90% of the resistance felt. How can we confirm these results using the scientific method?

Let’s design a new experiment. In order for it to be considered a controlled experiment, we’re going to make it as much like the previous experiment (the original race) as possible, with one notable exception. The same bicycler will complete the 1000-meter race on the same bicycle, but this time the bicycle is mounted to a smart bicycle machine designed for indoor training. Under these conditions, there will be no aerodynamic drag on the bicycle-bicycler system. The machine can measure all sorts of things, so we can have it measure time (to compare with the previous race) and the pedal force directly. This will give us insight into the “hidden” force of aerodynamic drag we encountered in the race. What should we expect this force to be?

Let’s do a quick back-of-the-envelope calculation. The force we naively calculated for the race was actually the total bicycle-bicycler system force minus the force of aerodynamic drag:

F(race) = F(total) – F(drag) –> F(total) = F(race) + F(drag)

So the bicycle-bicycler system actually exerted more total force than we originally measured! If we assume that the 70-90% of the total force was spent overcoming drag, then we can estimate the total pedal force from the calculated pedal force of 96 Newtons:

Lower bound: .3 * F(total) = F(race) –> F(total) = 96 * 10/3 = 320 N
Upper bound: .1 * F(total) = F(race) –> F(total) = 96 *10/1 = 960 N

We can now run our experiment, and see how the empirical data align with our estimates. If the results are as predicted, great. If not, well, we’ll have to think about a new experimental scenario to investigate the discrepancies.

In subsequent trials, we could use the bicycle trainer to measure other things. For example, we could measure the number of revolutions of the pedals over the course of the race, which would allow us to replace our original revolution estimate with an empirical value. We might even be able to modify our experimental set-up to be able to draw some conclusions about of the gears and gear ratios being used over the course of the race! Remember, using the bicycle trainer has removed the confounding effects of aerodynamic friction altogether, so we don’t have to worry about drag in any of these experiments now.

What we’ve learned here is that doing science can be pretty complicated. Even for the simple bicycle-bicycler system, we have to make some simplifying assumptions to get any traction on the problem. Each experiment allows us to learn more and more about the system by confirming/refuting hypotheses along the way, and refining/enhancing our set-up for the next experiment. Such adventures in discovery are, in fact, the essence of science.