## Monday, September 14, 2009

### Old La Honda: iBike analysis

A friend of mine sent me data from his iBike, taken on a climb of Old La Honda on May 10 2009 at 8:47 am. Conditions on Skyline Blvd, the top of the climb, were cool and calm: pretty much ideal climbing weather.

The iBike records altitude, road grade, acceleration, and relative wind speed. It uses a coast-down test wherein, since applied power is zero, it calibrates wind resistance and rolling resistance to the rate the bike decelerates, wind resistance dominating initially, then rolling resistance taking over as the speed drops sufficiently. Given this calibration, it can then derive how much power is being applied to the pedals based on how the bike decelerates (or accelerates) relative to how it did so in the coast-down test, adjusting for the measured road grade. Fun stuff.

iBike

The iBike measures the altitude and road grade separately, but of course the road grade is derived from the derivative of the altitude with respect to distance. A direct measure of road grade is more accurate, but can be off slightly if the gradiometer is tilted. So the iBike calibrates a tilt offset to the altimeter over long time scales. I applied a small correction factor to the measured grades, such that the net altitude gain derived by integrating the grade over distance equaled the net altitude gain measured by the altimeter. Here's the result:

Old La Honda grade derived from iBike data

I integrated these data to generate a hill profile. Recall I'd calibrated the grade to match the total climbing with what was reported by the altimeter:

Old La Honda profile derived from iBike data

No surprises: although grade fluctuates about the mean of 7.3%, it fails to do so over any substantial length scale, so the profile is pretty much minor deviations from a straight line.

The primary point of this blog post, however, is the effect of wind speed. Plotted next is the measured bike and wind speeds. The wind speed sensor is the real novelty of the iBike (well, plus the offset-correcting gradiometer). Absolute wind speed is the difference of the two. Note the absolute wind speed is quite modest: only ±1 meter/second typical. That's ±2.2 miles/hr for the metrically challenged.

Wind speed and bike speed recorded by iBike on Old La Honda Road

Well, from the coast down data we know the relationship between relative wind speed, bike speed, and power due to air resistance. We further know total power as derived from the iBike. As was derived in this blog earlier, given these we can determine the effect of a fractional change in power on bike speed. The following plot shows two fractions:
• the fraction of power due to air resistance
• the fraction of speed change due to the absolute wind speed

Effect of wind on power and speed on Old La Honda, derived from iBike data

We normally think of climbing as being all due to overcoming the effect of gravity, not air. It's true the majority of power, in this case around 92% (if you believe the iBike's derivation of CdA and Crr), is divided between climbing power and rolling resistance power. Yet the effect of air resistance is still significant. The wind is fluctuating between a tailwind and headwind. This may be all real, or may be due to noise in the detector. But assuming the noise part averages out to zero, the effect of these fluctuations on speed should be quite small. For the purpose of this analysis, let's treat the wind signal as real.

It's simple enough to convert the a speed difference to a time difference. The final plot shows the deviation in climbing time due to the effect of the absolute wind speed:

Effect of wind on climbing time on Old La Honda Road, measured with an iBike

So over the whole climb, despite "calm conditions", the prevailing wind seemed to be responsible for around a 9 second reduction in the climbing time. Assuming this is typical, it goes to show that one shouldn't take differences in climbing time of on order 10 seconds too seriously. It could simply be a minor shift in the winds. Similar time differences may occur due to drafting behind other riders for a part of the climb. And if you have a good wheel to follow for the full distance, someone riding just a bit faster than you can sustain on your own, even bigger time advantages may be possible.