## Sunday, January 10, 2010

### closing a gap with head down

I did a quick calculation of the effect of the head position on closing a gap. Suppose I'm chasing a group riding @ 40 kph and I can ride with the head up at 45 kph. I can't sustain that pace for too long, so the clock's ticking. I have to close that gap as quickly as possible.

I'll do an first-order analysis, which means I assume a starting condition then apply a first-order correction for the small change. In this case the head position change is a small fraction of total wind drag, so the linear analysis should do fairly well. It wouldn't do well, for example, were I to swap my bike for a recumbent... an interesting thought.

Furthermore, I neglect drivetrain losses. Calculated powers are "PowerTap" equivalent. I assume drivetrain losses are proportional to transmitted power.

Baseline condition:

CdA = 0.32 m²
M = 65 kg
ρ = 1.1 kg/m³ (air density)
g = 9.81 m/s²
Crr = 0.5% (rolling resistance coefficient)

Then I get 40 watts dissipated in rolling resistance, 343 watts dissipated to wind resistance. So 343/383 watts goes into wind resistance: 90%. Fabian Cancellara closing a gap to San Remo in 2008 (Graham Watson)

I previously calculated the effect of power on speed: a fractional improvement of power results in a fractional improvement of speed in a ratio of (1 + 2f):1, where f is the fraction of power going into wind resistance. In this case, that ratio is 2.8:1. In other words, it takes around a 0.28% increase in power to increase speed by 0.1%.

In this case, a fractional reduction in power required is equivalent to the same fractional increase in power produced (since I'm doing linear analysis). 6.7 watts out of 383 watts is 1.75%. So the effect on speed is 0.62%. At 45 kph that's 0.28 kph.

So I said I was riding 45 kph and chasing a group riding at 40 kph. That's a difference of 5 kph. I put my head down, and I'm now closing @ 5.28 kph. That's a 5.6% reduction in the amount of time it takes to close the gap.

So for example instead of chasing for 5 minutes, I'd have to chase for 4:43. 17 seconds in hell saved.

Huge big deal? I'm not sure, but it's free. This is as big a fractional advantage as is claimed for aerodynamic road frames like the Cervelo S, Felt AR, or Ridley Noah. People pay big bucks for these. Putting your head down doesn't cost anything.