Aerodynamics Pt. 2

A few days ago I sized myself up for some compression socks. As a triathlete, you see, I have a duty to be as sartorially challenged as possible. It should be clear from the photo below that I take this duty very seriously.

Anyhow, to determine the proper size sock for myself, I referred to a handy compression sock sizing chart. Men's size small corresponds to a calf diameter of 12.5 to 15 inches, medium to a 15 to 17.5 inch diameter, and large to a 17.5 to 20 inch diameter. "Hmm," I thought sarcastically to myself, "what size might I be?"

Just to be sure I didn't have to have to order women's socks, I decided to measure up my legs of steel. After pulling a shoe lace from a nearby pair of trainers, I wrapped a length of the lace around my calf and then measured that length. "13 inches," I exclaimed aloud to no one, "now I don't have to cross dress every time I want moderate pressure applied to my lower appendages!"

What do my supermodel (5'10" 115 lb. female supermodel, that is) sized calves have to do with aerodynamics? Well, yesterday when I posted the drag formula (~50g of drag = ~0.5s/km time saving = ~5W) I left off one aspect. An additional 50g of drag is also roughly equivalent to an increase of 0.005 m^2 of frontal area. This additional bit of info allows us to estimate with relative precision the aerodynamic advantage my calves offer relative to a typical male triathlete.

As illustrated in the figure below, my calves are each about 4 inches wide when viewed from the front (seriously, I just measured with a tape measure). We can also approximate a man's calves as extending 8 inches vertically.

As a result, each of my calves has a frontal area of 32 square inches, which can be converted to 0.0206 m^2 per calf.

Now, let's estimate the typical triathlete as having slightly beefy calves from copious amounts of cycling. An 18" diameter seems reasonable as a comparison. Approximating a calve as a round tube, we can estimate the width of the ordinary triathlete's calve to be 5.7 inches. 5.7" x 8" = 45.6 sq. inches = 0.0294 m^2 of frontal area per calf for the typical triathlete.

Now to calculate my calves' aerodynamic superiority:
2 calves * (0.0206 m^2 - 0.0294 m^2)/calve = -0.0176 m^2 (this is the frontal area of my calves relative to the ordinary triathlete's)
0.0176 m^2 * 5 W/0.005 m^2 = 17.6 W (power savings)
0.0176 m^2 * 50g/0.005 m^2 = 176 g drag (reduction in drag)

Amazing! My calves save almost twice the difference between a Cervelo P3C and a Kuota Kalibur! Who needs a P4/Shiv/Speed Concept when you've got legs like mine?