# Laws of Physics

Posted by: Jan Heine

## Laws of Physics

In the last issue of Bicycle Quarterly, we compared the performance of a 17-pound titanium racing bike and of a 26-pound steel randonneur bike. We were surprised when both bikes climbed at the same speed in a set of controlled experiments. Others shared our surprise, but added: “That cannot be true. Physics require that the heavier bike climbs slower.”
Having ridden the bikes myself, I know that their performance was evenly matched. And as a scientist, I also know that this result does not contradict the laws of physics.
Our critics assume a constant power output. If we always put out 600 Watts during these climbs, then any added weight will slow us down, all other things being equal. And an extra 9 pounds is significant enough that it should be measurable. There is little disagreement on this.
And yet the two bikes did climb at the same speed, despite their different weights. It’s clear then that our power output was not constant. On one bike, we were able to put out slightly more power than on the other – just enough extra power to equalize the weight handicap.
It should not come as a surprise that one frame performed better than another. We documented the same effect in Bicycle Quarterly’s double-blind test of frame stiffness. There, we sprinted up a hill five times, side-by-side, on two bikes. The frames had different frame tubes, but otherwise, the bikes were identical. They even weighed the same.
We switched bikes after each run. We used a PowerTap to measure power output without the rider being able to see the numbers. We found that one frame consistently was faster than the other – no matter who rode it. It wasn’t for lack of trying – as most racers know, nothing makes you ride harder than another rider pulling away.
When we downloaded the numbers from the power meter, we found that our power output was higher on the faster frame – not just a little bit, but about 5% for Mark, and 2% for me. And these were relatively similar frames, both made from lightweight, standard-diameter steel tubing.
Why did we put out more power on some frames than on others? In the above-mentioned double-blind test, we found that frame stiffness and how the frame works with our pedal strokes influences our power output. Here is how we think this works: There are different factors that limit our power output on a bike. Our hearts beat at their maximum, we are gasping for air, our legs start burning…
Our absolute maximum probably is determined by our maximum heart rate. As anybody who has trained with a heart rate monitor knows, it often is impossible to reach one’s maximum heart rate. (I used to reach ultra-high heart rates during runs that I could not achieve on my bike.)
Why can’t we always reach our maximum heart rate? The limiting factor is our muscles. If the muscles aren’t able to use the oxygen our heart pumps to them, then there is no use for our hearts to beat faster. And if one bike frame leads to more rapid muscle fatigue than the other, then our power output will be lower on that frame. (In running, I may use more muscle groups, so the cumulative oxygen use is higher, hence the higher heart rate.)
This straightforward explanation does not require invalidating the laws of physics. The simple fact is that the human body is a complex machine, and doesn’t have a constant power output.
Most cyclists have experienced inexpensive bikes that simply were “dogs” and did not perform well. We often try to explain that lack of performance with extra weight or other factors, but these bikes don’t perform well even on the flats, so one has to look for other reasons. And most of these inexpensive bikes have heavy, stiff frames that may fatigue our muscles prematurely.
Now none of the titanium bikes we tested for the Winter 2012 issue of Bicycle Quarterly were “dogs.”  They all offered awesome performance and were great fun to ride, but even near the absolute top, there were some slight, but noticeable differences in how these bikes performed for us.