# Cd & Frontal Area...

Discussion in 'Power Training' started by robmf, Jul 25, 2005.

1. ### robmf New Member

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Hi there.
I've been playing around at analyticcycling.com, and I was wondering what values people use for parameters such as:
- Frontal Area
- Drag coefficient

I have looked around a bit, and found some stuff(I currently use 0.5 for Cd, and 0.7 for A) but was wondering if there was more information out there.

As these values affect the Power calculations substantially, I want to get them right. Any good methods to determine them from test WITHOUT a wind tunnel, or power meter (i.e. coast down a known grade, observe max speed, calculate CdA for 0 power, or something similar)???

Cheers,
Rob

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2. ### rmur17 New Member

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Cd x A or simply CdA as only the product of the two matter, is a function primarily of: body size, bike position and aero kit employed.

A small cyclist with an excellent aero position and employing all the aero kit may have Cda < 0.20. A large cyclist on a road bike on the tops may be around 0.40. That's a 2:1 range ...

The gold standard for testing one's Cda is wind-tunnel testing. Failing that, controlled testing on flat road surfaces in calm conditions (multiple test runs) have been shown to obtain excellent results as well.

So, it depends

rick

3. ### rikoshea New Member

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I think rmur17 effectively answered your question if not in a generic sense.

As a matter of interest, can you provide values for:
height
weight
bike position (eg tribar, drops)
difference between saddle height and stem height [cm],
do you have an aero bike ?
do you have aero wheels (disk, tri-spoke) ?
do you have aero helmet, skin suit, skin overshoes ?

4. ### robmf New Member

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thanks rik & rmur.

I'm 183cm, 71 kg, drops, unsure (can check), nothing specially aerodynamic about the bike, wheels, clothing or helmet.

My CdA will definately be in the higher end of the range (hence using 0.35 currently).

rmur: how woulld you conduct such testing on the flat road? i.e. test setup, equipment, data gathered, etc...

cheers,
rob

5. ### rikoshea New Member

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Given the data supplied I would use a starting estimate for CdA of 0.3396
m^2 (~0.34). For a person of your size this corresponds to an effective frontal area of 0.4033 m^2 (which corresponds to 21% of you body surface area). Separating out the Cd value indicates a value of 0.842.

Given this CdA to ride at 40 km/h on a flat smooth road under calm conditions would require ~ 330 W.

To perform a test to try and validate these findings on a flat road (an indoor velodrome would be best) for a set distance
you need to record power, time (time & distance provide average velocity).

To calculate the air density, you need to know the values for air pressure, air temperature, humidity (this parameter less important than the former two).

6. ### antiram New Member

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Hello,

there is a program to calculate the CdA in relation to type of bike and body size:
http://www.kreuzotter.de/english/espeed.htm

for roll resistance of MTB tubes i am using:
0.0065 for race
0.008 for tour
0.0093 for enduro
and multiply this value with a factor for the ground:
0.82 for very good asphalt
1 for normal asphalt
1.15 for raw asphalt
1.47 for good gravel path
1.8 for normal gravel path

cheers

7. ### DannoXYZ New Member

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While you can work backwards and figure out total Cda by doing on-road testing and measuring speed vs. power-output, it would be even more helpful to fully separate Cd from A. That's because there are various mods that you can do to your position which doesn't change A much, but makes a difference in lowering Cd.

Measuring A could be as easily as taking a photograph head-on. Place the rider in position, either stationary or riding next to an object of known size, like a 4x8' sheet of plywood standing up facing the camera fully. Make a print of the picture with the rider next to the plywood. Trim out the profile of the rider and the plywood and weigh the pieces on a sensitive scale. The ratio of the weights will then represent the ratio of the cross-sectional surface-area of the rider versus a known area, that of the 4x8' piece of plywood. Once you've got A, then playing with Cd is easier.

8. ### acoggan Member

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Even if you know A, you must measure CdA to calculate Cd. I therefore see absolutely no advantage to taking frontal photographs if you've quantified your CdA via wind tunnel or field testing.

9. ### DannoXYZ New Member

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CdA is an integral funtion of power & speed. You can measure power-output and you can measure the resultant speed... you calculate CdA from that...

10. ### whoawhoa New Member

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A little off topic but is there a way to find out what time savings I could expect over a 20k tt by dropping my position 2 inches? At the last tt I did I used aero bars but I was way too high up.

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Well, I don't think your planned position change is addressed specifically, but Jim Martin has done some pretty good work on all the attributes that contribute to time savings in TTs. Position is, of course, the biggest single contributor. http://www.cervelo.com/tech/articles/article5.html I think Kraig Willett has done some testing on hand positions but I don't have that link handy.

12. ### acoggan Member

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Or you can measure drag force directly in a wind tunnel, and calculate CdA based on the air density and speed...but in any case, I don't understand how this addresses my point? All that matters to the individual rider is their CdA; estimating* A so that you can calculate Cd doesn't really tell you anything of value.

*I say "estimating" because the projected frontal area of a person on a bicycle is a bit of a nebulous concept. For example, when viewed directly from the front the seat tube is largely if not completely hidden by the front wheel and head tube, yet air obviously still strikes the seat tube, adding to the drag. Similarly, the thighs are are partially hidden behind the arms, but nonetheless contribute significantly to the overall drag. IOW, even if you have a good frontal photograph, you'll still only have a proxy of the true frontal area, such that Cd will be overestimated (since Cd = CdA/A, and A is underestimated).

13. ### acoggan Member

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The only way to make an accurate prediction would be to measure your CdA in both positions. However, the article on the Cervelo website by Jim Martin that RapDaddyo linked to might give you a crude approximation.

FWIW, I just finished a series of aero field tests addressing this specific question...what I found was the same as I'd previously learned from getting in the wind tunnel, i.e., Jim is right: once my torso is essentially horizontal, there's nothing to be gained by getting lower.

14. ### DannoXYZ New Member

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"For example, when viewed directly from the front the seat tube is largely if not completely hidden by the front wheel and head tube, yet air obviously still strikes the seat tube, adding to the drag. Similarly, the thighs are are partially hidden behind the arms, but nonetheless contribute significantly to the overall drag."

What the seat-tube affects the Cd even though it's not even included in the A. Aero seat-tubes lowers the Cd even though they don't affect A in any way. Another way to look at is that A is the particle-model of light and Cd is the wave-model. Combining them gives you a closer match to modeling the real thing.

"Or you can measure drag force directly in a wind tunnel, and calculate CdA based on the air density and speed...but in any case, I don't understand how this addresses my point? All that matters to the individual rider is their CdA; estimating* A so that you can calculate Cd doesn't really tell you anything of value."

Well that's what rob is trying to figure out. Without the data at all, we have to way to determine if it's of value or not. By getting as much data as possible, the measured road power-output vs. speed, the calculated/measured Cd, A values, maybe even the wind-tunnel tests, but I don't think he has access to that. One you've collected enough data, you can start coming up with ways of analyzing and forming it into ways that may be helpful.

Like that one guy that graphed time-saved in time-trials based upon the vertical position of the forearms alone. The front-area certainly has not changed one bit, but there IS a difference in speed. Being able to quantify the data and putting a Cd to different configurations will help you make what-if predictions and maybe come up with a new set-up that you've haven't ever tried before. After all not everyone has a wind-tunnel for testing. And even those who use wind-tunnel testing, like auto- and aircraft makers, use it at the end to verify their calculations as a proof-of-concept confirmation. But where are you gonna get the numbers to plug into your calculations to begin with?

15. ### rmur17 New Member

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you mean we are not cylinders?
rmur

16. ### rikoshea New Member

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Yes, I'd agree for pure practical purposes, as in this case, all that really matters is the CdA value or drag force at a particular velocity. However on a more academic level trying to understand "why" certain positions are more aerodynamic than others (i.e. is it through a reduction in frontal area or an improvement in drag coefficient) it would be benefical to separate Cd and A, although attempting to do so is a difficult process.

17. ### acoggan Member

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Agreed - I'm speaking from a purely practical perspective (which is why I specified "for a given individual").

18. ### acoggan Member

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But your original position was that it is useful to be able to separate Cd and A when you already know the product. My argument is that, for a given individual, all that matters is the product, since that's what you wish to minimize. Being able to separate the two and, e.g., come up with prediction equations (several of which already exist) is an interesting academic exercise that may (or may not) contribute to our understanding of the determinants of cycling aerodynamics, as Rik O'Shea suggests. For an athlete who is simply interested in going faster, though, taking frontal photographs is only useful if you can't determine CdA via wind tunnel or field testing (e.g., due to lack of an appropriate venue).

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