Aerodynamics

Okay, while I admit to reading Slowtwitch pretty regularly, I rarely post. However, I had an aerodynamics question that I was hoping one of the aero nerds on the forum would have some insight on. Here's my post reproduced:

Drag numbers, like those illustrated in the graph below, are typically reported for a wind speed of 30 mph, correct?


The question I want to explore is how the results change when drag is scaled to a more realistic speed for an Ironman. Let's make a few simplifications. First, we'll use Tom A.'s rough formula that at 30 mph wind speed ~50g of drag = ~0.5s/km time saving = ~5W power savings. Second, let's estimate the difference between, say, a Cervelo P3 and a Kuota Kalibur to be 100 g of drag (we're simplifying here because the difference varies with yaw angle, but for the sake of simplicity we'll just consider the case of a 100 g difference).

Computing the time savings of a P3 vs. the Kalibur over 180 km, we get 100g = 10 W = 1s/km = 3 minutes for 180 km. Great, I'd take a 3 minute savings for an IM.

However, that 3 minute time savings is calculated using a formula based on a 30 mph wind speed, and to get a more realistic estimate of the time savings from a P3 to a Kalibur we should scale down to a more realistic speed. One point I'm not sure that most people recognize is that drag is a function of the square of wind speed and power savings is a function of wind speed cubed (i.e., we can not linearly scale these numbers). To scale our results for 20 mph -- a much more realistic speed for most AGers -- we can multiply Tom A.'s drag numbers by (20/30)^2, or about 45%, and we can multiply the power savings by (20/30)^3, or about 30%. So scaling our numbers indicates that the difference between a P3 and Kalibur would be 45 g and the power savings would be 3 W at 20 mph. While I recognize that every watt saved is valuable, 3 W isn't much. (A note: I recognize that the speed one is traveling is not necessarily equal to wind speed relative to the frame -- sometimes the wind speed relative to the frame would be greater and sometimes it would be less depending on wind speed and direction.)

Additionally, I know Gerard at Cervelo has said that the slower one goes the greater the time savings. Yet it seems strange that 3 W could save more than 3 minutes over 180 km at 20 mph. I don't recall any formula for time savings from my fluid dynamics classes. Does anyone have any insight here?

Feel free to critique my reasoning, as I just whipped this out without thinking it through too much (that's what you're here for, ST aero nerds).
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And now for more over-analysis:

My point is that the graph above, taken at face value and not considered as advertising, exaggerates the differences between bikes for most people. Based on a 3 W power savings for a rider putting out 200 W, analyticcycling.com estimates a time savings of a bit under 2 minutes for an Ironman when switching from a "slow" bike (the Kalibur) to a "fast" bike (the P3). However, another estimate based on the assumption that the % of time savings stays relatively constant regardless of a rider's speed gives an estimated time savings of a bit under 4 minutes between the bikes. (I have no idea what the basis for this assumption is.)

Don't get me wrong, 2 minutes is a nice savings. But differences in comfort and handling between two bikes might be able to provide similar savings (note that I say "might", as this is pure speculation), only those differences aren't so easily quantifiable.

Plus, the entire discussion above requires that one take the drag differences between bikes as fact and disregard that the company promulgating these results is the same company that happens to be shown in the best light. (In Cervelo's defense, every other company in the industry seems to view Cervelo's bikes as the gold standard, so I don't mean to criticize Cervelo. Plus other companies release their own data that should also be questioned.) So many ads say shifters or pedals or sunglasses can result in several seconds time savings, and many of those ads look ridiculous.

I am thinking about this because many triathletes have had great success on "slow" bikes. Normann Stadler and Torbjorn Sinballe both had amazingly fast rides on bikes that would be considered slow. I would expect the differences in ability between world class athletes to be very small, so if the difference in bikes were as great as many people say then I wouldn't expect so many wins on slow bikes. Winning, after all, is what matters.