Estimating Bike Rider Drag Coefficient

In response to my last post there was some facebook discussion (always goes well) about wheels and what not, I chimed in with a statement and someone proceeded to correct me on the difference between Frontal Area, CdA and just plain Cd…………….

Anyway.

So this is already implemented in the Wheel Selector so this is a bit of back tracking but I’d like to add explanation, even for my own personal record keeping. I originally thought that estimating the bike/rider system drag coefficients would be easy. I’d just grab a few values form some tables then BOOM done. Nope. Turns out when you’re trying to estimate Drag Coefficient Area you have two moving targets to track: Drag Coefficient and Frontal Area.

F_d\, =\, \tfrac12\, \rho\, v^2\, c_d\, A

So it’s really easy to measure what CdA is. You just plop a guy in a wind tunnel and factor it out. The problem is this method is great for one-of scenarios and is just on the slightly expensive side of things. I’d like to have it very easy to calculate given some pretty well known metrics: height and weight. This means I have to separate out my Cd and Frontal Area. While CdA is relatively easy to measure in a wind tunnel A must be done with 3d scanning, some photo software, or voodoo magic. You can’t actually measure Cd anywhere (i think?) you have to calculate it back out using CdA/Frontal Area.

So I’m going to say we have 4 positions to ride in: Tops, Hoods, Drops, and TT bars. The problem is that both your Frontal Area AND Drag Coefficient change when you change positions (never mind when you stick your fat knees out into the wind while pedaling).

There are a couple studies out there that try to estimate this. The problem is they’re sometimes quite complex. For instance the most accurate way to measure frontal area is to do a 3D scan and import it into a CAD software program. You can also take a front-on image and get your frontal area from the picture as done here. This adds some uncertainty, like having a directly front on image (can be remedied by scaling image), and having a point of scale (although a bike wheel’s always going to be the same size, so there’s that). The problem with both these methods is they’re both a huge pain in the ass.

The next step down in fidelity is taking body angle measurements and plug this into an equation (also huge pain in the ass).

All these methods are detailed in this paper which is a great summary of all the different attempts to calculate frontal area’s and Cd’s.

Highlights from that paper are as follows:

  • A Body Surface Area estimation is only really valid for cyclists 60kg to 80kg.
  • There’s a weak correlation between trunk angle and frontal area
  • Frontal Area’s the primary driver in a cyclists drag
  • There are a TON of formula out there to calculate Frontal Area
  • There’s no one “correct” formula due to the wide variation in body type and position

 

I’m going to go ahead and use the simplest method they detail, using Body Surface Area (BSA) since it only requires your height and weight. I’m sure this will not be super accurate, but then again I’m not looking for minute differences, just a general magnitude to compare to wheel aerodynamics.

BSA (m2) = 0.007184 x Height(cm)0.725 x Weight(kg)0.425

Olds_FA_Estimate

Where Ab is Body area Ap is total including bicycle (sorry about potato quality screen grab)

 

This will give us an estimate for Area in the TT position. Now the problem is your frontal area’s changing with your position. I.E. a position on your tops is going to have a larger frontal area than the frontal area you’re at in your drops (Just going to go ahead and ignore standing for now).

So this is a generalized starting point, remember I’m not SUPER concerned with accuracy, just general magnitude.

As far as getting Cd, a separate case all together, there’s not a lot of consensus. The paper I mentioned earlier has a pretty exhaustive list of data that’s collected from the accurate methods (CAD, 3d scan) to the totally weird methods (towing a rider behind a car with a cable that has a strain gauge). I’m going through those next to see if there’s any sort of pattern.

Also the cyclingpowerlab.com (which seems to be down at the moment) has a list from the Cycle Science Book (wilson 2004) that has another pretty complete table of Cd values, but it condenses down to this:

Tops: 1.15
Hoods: 1
Drops 0.88
TT Position: 0.77

So I now have Cd and A

Thus

Cd A!!!!!!!!!!!

(roughly estimated)

To Be continued

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