TL;DR - I think a 0.01-0.02 m^2 reduction in Cd*A due to leg shaving can be justified with relatively simple physical arguments.
I’m a fairly experienced runner but novice triathlete, and after a few good races this summer I’m thinking about getting more serious about the sport. Cycling aerodynamics seems to be a big place where a novice triathlete can gain ground, and I came across some old threads here with links to the Specialized “win tunnel” study showing that shaving legs leads to a decrease in Cd*A of about 0.015-0.02 m^2. This seems like a massive free speed boost, and I was somewhat incredulous – as many others seemed to be! On the other hand I feel like I do notice a drag reduction (or speed increase on the same route at similar exertion) from wearing tights vs bike shorts, which would be a manifestation of similar aerodynamics.
I’m wondering 1) if there have been follow-ups to that study that have reproduced its results, and 2) if anyone has insights as to why such a seemingly minor change leads to such large results. I have some ideas about how to make a back-of-the-envelope argument for the size of the aero effect, but wasn’t able to find anything similar here or elsewhere. Two speculative arguments follow below, and I’d appreciate any feedback or pointers to other ideas/interpretations.
Two rough estimates of the aero effect from shaving legs:
Assume legs are cylinders with hair increasing their effective width. If leg hairs increase calf width by ~1 cm on each side, and unsocked lower legs up through knee are ~40 cm long, that’s (0.01 m width)(0.4 m length)(2 legs)(2 sides per leg) = 0.016 m^2 increase in frontal area. Cd~1 for cylinders (calves) for the relevant Reynolds #~10^5 so that would be about a 0.016 increase in CdA with leg hair vs. without. Likely an overestimate of the added frontal area from hair rather than an underestimate; I got the ~1 cm number from estimating the decay length of hair density from the sides of my legs but the hair 1 cm from the calf is not all that dense.
Assume that hairs are cylinders and estimate their collective frontal area and drag. Using data from: https://www.sciencedirect.com/...ii/S0022202X15306291 - we have 14 calf hairs per cm^2, each of which is ~40 microns in diameter and ~2 cm in length (last number is my estimate). Each hair thus has a surface area of pi240e-4 ~ 0.025 cm^2, or a frontal area of 0.008 cm^2 if oriented perpendicular to the flow. On calves up to knees, 40 cm in length, 10 cm in diameter, this means that collected hairs have a surface area of: (40pi10 cm^2 leg area)(14 hairs per cm^2 leg area)(2 legs)(frontal area per hair) = 35000 hairs0.008 cm^2/hair = 281 cm^2 = 0.028 m^2. If we divide this by 2 to only count the hairs on the front half of the leg, this would be reduced to ~0.014 m^2. With diameters of only 40 microns, though, the Reynolds number for leg hairs is only ~40 (at a flow speed of 10 m/s) and thus Cd is closer to 1.5 than 1, so this would give us a reduction in Cd*A of ~0.02 m^2 by shaving legs. This again seems more likely an overestimate than an underestimate since hairs are not all oriented perpendicular to the flow; assuming random orientation would reduce the collective frontal area by about a factor of 2, but this still puts us in the ballpark of a 0.01 m^2 reduction from leg shaving, which depending on baseline aerodynamics is likely at least a few % of drag.
Some further speculative aero thinking about lower legs:
1) Humans may underestimate how much surface area there is near the perimeter of objects (I thought this was a well-documented perceptual bias but I'm failing to find anything on it...).
2) Lower legs seem really bad from an aero standpoint -- nearly always normal to the flow (and non-negotiably so!), cylinders (which have a substantially higher Cd than the spherical / prolate spheroidal head+torso), AND in a Reynolds number range where the boundary layer near the leg may not be turbulent and thus has a bigger wake/larger Cd.
3) Lower legs aren't shielding much behind them, so frontal area saved doesn't end up being a loss elsewhere.
4) Interference drag with wheels and the lower frame may be significant -- e.g. adding frontal area to the lower leg may combine with the flow around the bike in such a way as to create more drag than either the leg or the bike would in isolation. No idea how to estimate the magnitude of this effect though, especially for a marginal change in leg width.
5) A minor effect that makes added calf frontal area extra bad is that lower legs bear an additional aero burden because of their bike-relative forwards-backwards motion during the pedal stroke. I think this effect is minor since the bike-relative motion of the lower leg is small relative to forward cycling speed, but maybe notable in some situations.
Thanks for running the math! I’m inclined to use the first estimate, since the second can’t account for all the interactive effects between the “hairflow” (we’re more like a sheep than a hedgehog).
On a qualitative level, compare the frontal area of two lower legs to that of an aero bike frame (even neglecting the much lower Cd of airfoil tubes) and it’s easy to see why there is such a difference.
A bigger aero penalty could come from certain hairstyles and certain helmets
Like, In a good helmet, air flows in through a vent and travels unimpeded over your head for cooling and out the exhaust port(s) with next to nothing resistance
if your hair volume is clogging your vents and hence the internal airflow of the helmet … Then you basically convert your aero helmet into a drag chute on your head while also reducing the cooling effect
Also if your hair is short but bristles forward into the airflow, it will grip the fluid air as it tries to pass through like a cats tongue and milk… You might as well have a brake rubbing
…Also if your hair is short but bristles forward into the airflow, it will grip the fluid air as it tries to pass through like a cats tongue and milk… You might as well have a brake rubbing???
Not so much. When you find yourself using words like “grip” when talking about airflow, something is generally out of whack.
Unless you’re going so fast you need to consider compressible flow, I don’t think this theory is going to hold much water, milk or any other fluid.
Interesting and useful analogy! Is there a thread here you had in mind? This review paper: https://onlinelibrary.wiley.com/doi/pdf/10.1002/jst.11 seems to suggest that the drag coefficient of tennis balls first increases and then decreases with usage, as the fuzz first gets pulled outwards a bit but then wears off with further use.
Also, perhaps more importantly, it shows that a fuzzy sphere has a much higher Cd than a smooth sphere by about 20%, and also lacks a critical Reynolds number where the drag coefficient drops dramatically (as the boundary layer becomes turbulent, point of separation moves backwards, and the wake narrows). So it seems like decreases in Cd*A with shaving might also be explained by tennis ball experiments purely as a consequence of Cd reduction, though it would be interesting to see if anyone has done calculations or experiments with fuzzy cylinders.
Idk if there’s ever been or ever will be a follow up. Most racers out there seem to be in agreement the data seems at worst acceptable and leg shaving is essentially free, and takes me at least no more than 5 minutes (old school safety razor demolishes hair) additionally speed isn’t the ONLY reason we shave. There’s also the occasional wrapping bandages, easier sunscreen application, and lets be honest there’s a certain vanity to it feeling nice and plenty of peer pressure.
All that combined it doesn’t seem worth the effort just to “reaffirm†what everyone already accepts. Regardless since it’s so cheap and effortless I’ll keep shaving.
Also, perhaps more importantly, it shows that a fuzzy sphere has a much higher Cd than a smooth sphere by about 20%, and also lacks a critical Reynolds number where the drag coefficient drops dramatically (as the boundary layer becomes turbulent, point of separation moves backwards, and the wake narrows).
Reynolds number is a function of test length, velocity, and fluid kinematic viscosity (or fluid density, test length, velocity, and fluid dynamic viscosity, depending which information you have available)–so a statement like “this sphere lacks a critical Reynolds number” is meaningless without specifying its size and velocity. There might be analogous drag mechanisms between an unshaven lower leg and a fuzzy tennis ball, but you’ll need calculations or experimentation to show that; otherwise we’re just shooting from the hip here.
The first thing I would like to see: another wind tunnel test showing a difference in drag force between shaven and unshaven legs. As far as I know, we have just the one claim.
Second - I don’t shave legs, never have, but I do typically now wear calf sleeves (Mad Calf Disease while running) so perhaps that is the aero equivalent of shaving?
Lastly - tights (and calf sleeves) are still slightly larger circumference than hairless legs, so it’s clearly more than just reducing that measurement.
Also, perhaps more importantly, it shows that a fuzzy sphere has a much higher Cd than a smooth sphere by about 20%, and also lacks a critical Reynolds number where the drag coefficient drops dramatically (as the boundary layer becomes turbulent, point of separation moves backwards, and the wake narrows).
Reynolds number is a function of test length, velocity, and fluid kinematic viscosity (or fluid density, test length, velocity, and fluid dynamic viscosity, depending which information you have available)–so a statement like “this sphere lacks a critical Reynolds number” is meaningless without specifying its size and velocity. There might be analogous drag mechanisms between an unshaven lower leg and a fuzzy tennis ball, but you’ll need calculations or experimentation to show that; otherwise we’re just shooting from the hip here.
The first thing I would like to see: another wind tunnel test showing a difference in drag force between shaven and unshaven legs. As far as I know, we have just the one claim.
I agree that it’s speculative to make the analogy between a tennis ball and an unshaven lower leg. But the Reynolds number (Re) should be all that matters for this sort of problem (for intensive measures like Cd), not the size and velocity of the object or the viscosity of the fluid – that’s the whole point of dynamic similarity. You would have to show that the leg has a similar Re to the experimental conditions for tennis balls, but this paper (https://onlinelibrary.wiley.com/doi/pdf/10.1002/jst.11) looks at values of Re from 50,000 to 150,000. If we take the lower leg as having characteristic dimension 10 cm in air with kinematic viscosity ~10^{-5} m^2/s, that would correspond to flow speeds around the leg of ~5-15 m/s or ~11-33 mph – pretty much the whole range we care about in terms of cycling drag.
Also agree that it would be nice to see more studies, I’m surprised there haven’t been any follow-ups that people widely know about in the last 5 years.
Second - I don’t shave legs, never have, but I do typically now wear calf sleeves (Mad Calf Disease while running) so perhaps that is the aero equivalent of shaving?
Lastly - tights (and calf sleeves) are still slightly larger circumference than hairless legs, so it’s clearly more than just reducing that measurement.
“So much” – 4-7% decrease in CdA across a set of 6 riders in the Specialized study – seems intuitively way out of proportion to the area taken up by leg hair.
I’m also interested in the compression sleeve effect, since I’m not particularly interested in shaving my legs, and I do sometimes get calf soreness with running. I’m not actually sure that they increase frontal area above that of hairless legs, since (for me at least) they seem to pull the sides of the calf muscles in a bit.
fwiw, I did a bunch of hill coastdown tests one cold, still evening. Compared hairy legs (about 7/10 on chewbacca scale) to smooth legwarmers. About a dozen tests, aabbaabb etc. Std dev CdA was about .003. No difference between them within that error. Average CdA for legwarmers was lower than for bare legs. Need to go back and repeat test for same legwarmers vs shaved legs.
I’m sure it’s because cda is less with shaved legs vs without. It also helps heat dispersion, which should theoretically keep you cooler and help you ride faster.
It’s directly correlated to the reason why there have been so many home runs in baseball this year. The leather is smoother and the overall ball is slightly smaller. In the kbo, they decided there were too many home runs (there were) so they simply raised the seams of the ball by like 2mm. Home runs went way down.
Interesting and useful analogy! Is there a thread here you had in mind? This review paper: https://onlinelibrary.wiley.com/doi/pdf/10.1002/jst.11 seems to suggest that the drag coefficient of tennis balls first increases and then decreases with usage, as the fuzz first gets pulled outwards a bit but then wears off with further use.
Also, perhaps more importantly, it shows that a fuzzy sphere has a much higher Cd than a smooth sphere by about 20%, and also lacks a critical Reynolds number where the drag coefficient drops dramatically (as the boundary layer becomes turbulent, point of separation moves backwards, and the wake narrows). So it seems like decreases in Cd*A with shaving might also be explained by tennis ball experiments purely as a consequence of Cd reduction, though it would be interesting to see if anyone has done calculations or experiments with fuzzy cylinders.
I can’t find the article, but there was an old publication looking at the aerodynamics of cylinder surface treatments. I can’t remember the actual value, but I think they found a 3-5% reduction in drag by shot-peaning the cylinder. That is a pretty good change for a minimal change in surface texture
