Aero Drag/Power

[frenchyge]

Folks, I need some help here. I'm in the process of building up my new TT bike, and have been doing some reading on aero drag, etc. I've seen John Cobb's name on enough legitimate stuff to trust that he knows what he's doing, but I just can't seem to replicate the numbers in his article here:
http://www.slowtwitch.com/Tech/The_Aerodynamics_of_hand_height_131.html

I'm not familiar with grams of force, but I'm assuming that refers to the weight of a gram on earth (ie, .001 Newtons), right? Now this part seems wrong to me:

Our base position starting point was an average drag of 10.38 lbs. or 4715 grams of drag. This means that every square inch of exposed surface is “feeling” a pressure of 10.38 lbs.

...as I would expect the 4715 grams represents the total drag force, and not something that needs to be multiplied by the surface area, as the bolded portion would imply. Anyway, here's what's got me flumoxed:

Our base position starting point was an average drag of 10.38 lbs. or 4715 grams of drag. This means that every square inch of exposed surface is “feeling” a pressure of 10.38 lbs. While this particular rider is easily capable of producing very high watts, I have used a number to figure the time differences of 200 watts average. Our base line time for a 40k, or roughly 25mile event would be 1:17:45 @19.17 mph.

Power = Force x velocity, so I multiply 4715 grams (force) times 8.57 m/s (19.17 mph) and divide by 1000g per kg to get the power in watts, right? I get 40.4 as an answer, as opposed to the 200w that John shows.

I know I can't ride 19.17mph on 40w, but what am I missing? Likewise, I can't match any of his other numbers, nor are my answers off by a certain factor from his:

This resulted in a drag of 9.176 lbs or 4165 grams. This gave a 40k time of 1:14:55 @19.9mp Next we closed the zipper. This dropped the drag to 8.804lbs or 3997 grams, or 1:13:59 @20.16mph (so, close up those zippers).

Am I supposed to multiply by an assumed surface area, air density, or the gravitational constant or something? Seems pretty freakin' simple.

 

[daveryanwyoming]

...I'm not familiar with grams of force, but I'm assuming that refers to the weight of a gram on earth (ie, .001 Newtons), right?...

grams or kg force is common and from an engineering standpoint sloppy. It really messes with keeping your dimensions straight. It's basically the same as the conventional kg = lbs/2.205. It sorta works if we assume everybody is on earth at sea level but it's a conversion from force to mass with an implied gravitational acceleration. That comes back to bite you when you try to use it as you did below.

So that 4715 grams of mass is really 4.715kg*9.8m/s^2 = 46.207 newtons of force. Multiply that by forward speed in m/s and you get power.

That satisfies the dimensional analysis, but I'm with you it doesn't explain his findings.

One tricky point is that he's frozen the drag force with 30 mph head/yaw winds. That basically transforms areodynamic drag forces into static linear forces like rolling resistance or bearing drag which provides more test consistency as he points out in the article, but it's weird from a real world perspective since for that constant 200 watts power output the speed changes but of course the drag force is fixed by the 30 mph test chamber head/yaw wind. Your math should work fine with that static linear drag force with the appropriate conversion from mass to force given above, but obviously it doesn't

4.715*9.8*8.57 = ~396 watts or roughly double the fixed 200 watts used to predict speed with the fixed drag force.

I can't make his other examples work either. But like you observed the difference between the linear math we're using and his results aren't constant. I'm wondering if he somehow scaled the drag force for the reduced speed (V/30mph^0.5) or something like that but it seems to defeat the purpose of fixing the aero drag as a fixed linear term. Maybe Andy or Alex or someone who's done tunnel time can explain how this is typically approached.

BTW, I think his "every square inch" comment is just linguistically sloppy and it's more accurately the integrated force over every square inch or the total drag experienced by the entire bike/rider combo. It's the only way to make sense out of that statement or the total drag force would be on the order of tons

Anyway, it's late and I'm gonna crash but somethin' don't make sense here and I expect it's some sort of testing/analysis convention that isn't obvious but typical in his trade.

-Dave

 

[Alex Simmons]

grams I don't get and haven't bothered to try and work out. I probably should but haven't really had the need.

Give me CdA (and changes to CdA) any day. That way I know my maths works.

 

[rmur17]

re that article, I pointed out the error to them some time ago (just after the article was published) but I guess it has never been revised. lb-f is indeed one way to measure/record aero drag but it definitely doesn't correspond to psi!!!!!!!!!!!

Gram-force are commonly reported for places like the LSWT in San Diego as I know that's the direct unit of measure on the balance.

All in all, Newtons would make more sense to me :-0)

 

[frenchyge]

Thanks for the look guys. Hopefully someone can point out the error of our ways.

4.715*9.8*8.57 = ~396 watts or roughly double the fixed 200 watts used to predict speed with the fixed drag force.

I definitely tried that too. The frustrating part is that I know the right answer (ie, riding on the tops at 20mph is much closer to 200w than 400w), but can't get the maths to support it when starting from grams of drag. As you guys have said, I expected gmf was an informal unit created to make it easy on the metric-ly challenged among us who are more used to lbf. Is it possible that it's been bastardized even further by including the conversion to kph rather than m/s? I couldn't find a good engineering explanation for it, although it's a very common term in describing aero drag.

A little more background for my dilemma is that this started from seeing gmf on the websites for HED, Zipp, Cervelo, etc. to describe the performance of their aero goodies, and I wanted to convert to watts. Since Cobb shows a few example calculations, I was hoping to use his article to make sure my methodology was correct, but it appears that I am not.

Another interesting thing is that an example run on www.analyticcycling.com at a CdA of .42, Crr .006 at 8.57 m/s on a flat surface shows total power of 199.9w and a "Wind Resistance" term of 18.9 kg-m/s^2.

There must be something else in that grams of drag term.

 

[rmur17]

Thanks for the look guys. Hopefully someone can point out the error of our ways.


I definitely tried that too. The frustrating part is that I know the right answer (ie, riding on the tops at 20mph is much closer to 200w than 400w), but can't get the maths to support it when starting from grams of drag. As you guys have said, I expected gmf was an informal unit created to make it easy on the metric-ly challenged among us who are more used to lbf. Is it possible that it's been bastardized even further by including the conversion to kph rather than m/s? I couldn't find a good engineering explanation for it, although it's a very common term in describing aero drag.

A little more background for my dilemma is that this started from seeing gmf on the websites for HED, Zipp, Cervelo, etc. to describe the performance of their aero goodies, and I wanted to convert to watts. Since Cobb shows a few example calculations, I was hoping to use his article to make sure my methodology was correct, but it appears that I am not.

Another interesting thing is that an example run on www.analyticcycling.com at a CdA of .42, Crr .006 at 8.57 m/s on a flat surface shows total power of 199.9w and a "Wind Resistance" term of 18.9 kg-m/s^2.

There must be something else in that grams of drag term.

just from scratch: aero drag = 0.5* rho*CdA*v^2 (Newtons)

rho = air density (kg/m3 std. 1.226 typical 1.20)
CdA = CdA (m2)
v= airspeed (m/s, ground speed with any ambient wind taken into account)

If you want to express aero drag in gf, use Aero drag = 0.5*1000/9.806* rho*CdA or 50.99*rho*CdA*v^2

Std. air temp, pressure, humidity rho is 1.226 kg/m3 so that further simplifies:

Aero drag (gf) = 62.51*CdA*v^2

In all cases, to convert you need to know the speed at which for example tunnel data listed in g-f was generated. That's often not stated for some stupid reason. NA tunnel generally are at 30mph or 25mph -- then convert to m/s. Metric is much easier!

 

[frenchyge]

just from scratch: aero drag = 0.5* rho*CdA*v^2 (Newtons)

rho = air density (kg/m3 std. 1.226 typical 1.20)
CdA = CdA (m2)
v= airspeed (m/s, ground speed with any ambient wind taken into account)

If you want to express aero drag in gf, use Aero drag = 0.5*1000/9.806* rho*CdA or 50.99*rho*CdA*v^2

Std. air temp, pressure, humidity rho is 1.226 kg/m3 so that further simplifies:

Aero drag (gf) = 62.51*CdA*v^2

In all cases, to convert you need to know the speed at which for example tunnel data listed in g-f was generated. That's often not stated for some stupid reason. NA tunnel generally are at 30mph or 25mph -- then convert to m/s. Metric is much easier!

Excellent, thanks Rick!

Edit: for those following along at home, I still tripped myself up even after Rick explained that answer above. Here's how:

It seems pretty simple to take an aero drag figure from a website, multiply by speed in m/s, divide by 1000 and multiply by 9.806 to find watts..... unfortunately, that's still wrong unless you're planning to ride at the same speed that was used in the test (ie, 30 mph typical). If you want to use drag figures from HED, Zipp, etc. in your real world example then you need to dig back into the advertised drag figure as follows:

Advertised website drag in grams = 1000 gmf (@ 30mph)
Real world scenario speed = 22 mph

Real world drag = [Advertised drag / (tested speed)^2] x (real speed)^2 = [1000 / 30^2]*22^2 = 537.8 gmf at real world speeds

So, real world power required at 22mph (9.83 m/s) is 537.8 gmf * 9.83 m/s * 9.806/1000 = 51.8 watts

In some cases, the websites have already converted the wind tunnel testing speeds back to real world speeds, but not always. Drag differences at real speeds can be *much* lower, so buyer beware!

 

[acoggan]

To add to Rick's explanations: most wind tunnels actually don't operate at a constant speed - instead, the speed is varied (via a feedback loop system) to achieve a constant dynamic pressure (q). This automatically takes into account differences in air density, e.g., if the tunnel heats up significantly between runs then the resultant reduction in air density and hence q is sensed and compensated for by an increase in tunnel speed. This makes the drag force measurements directly comparable between runs, or at least more so than if speed were held constant. Of course, there is still some post-processing of the data to correct for minor variations in q, the balance tare, etc. As well, the drag data for cyclists must be corrected (using simple trig) to the "body axis" as opposed to "balance axis" in which it is measured.

EDIT: Here is a link to additional information about the wind tunnel at Texas A&M that may be useful:

http://lswt.tamu.edu/info.htm

 

[swampy1970]

After reading all the good stuff by Chester Kyle years ago in Cycling Science, I always wanted to get me position checked in a wind tunnel. However, if I went anytime soon, I'd plug the windtunnel and the huge propellers would stall....

 

[Alex Simmons]

After reading all the good stuff by Chester Kyle years ago in Cycling Science, I always wanted to get me position checked in a wind tunnel. However, if I went anytime soon, I'd plug the windtunnel and the huge propellers would stall....

Just put you mouth up close to the fan, it might clear out your lungs

 

[velomanct]

Wow, and I thought I was overly analytical.

 

[Steve_B]

Wow, and I thought I was overly analytical.

When have you ever been analytical?

 

[swampy1970]

Just put you mouth up close to the fan, it might clear out your lungs

... some might say that I'm full of hot air as it is.

 

[acoggan]

Wow, and I thought I was overly analytical.

Thanks in part to our overly analytical natures, John Verheul and I have our names in the USA Cycling record book. I'm just sayin'...

 

[Steve_B]

Thanks for the background info to get me thinking about this stuff. I'm going into A2WT soon and it will be good to be able to at least have a semi-intelligent conversation with them. (I do microamperes and microwatts for a living. I don't think about Reynolds numbers too often. )

BTW - anybody have any suggestions on maximizing my time in the tunnel? I've got two hours and I'm mostly concerned with positional stuff, probably less on the equipment side. I expect to go in there with a plan of positional stuff that I want to try but I will be open to their suggestions. Any other suggestions? Rick?

 

[rmur17]

Thanks for the background info to get me thinking about this stuff. I'm going into A2WT soon and it will be good to be able to at least have a semi-intelligent conversation with them. (I do microamperes and microwatts for a living. I don't think about Reynolds numbers too often. )

BTW - anybody have any suggestions on maximizing my time in the tunnel? I've got two hours and I'm mostly concerned with positional stuff, probably less on the equipment side. I expect to go in there with a plan of positional stuff that I want to try but I will be open to their suggestions. Any other suggestions? Rick?

2-hrs sounds cool. I've love to get back into a tunnel as I figure I honestly didn't get *that* much o/o my 1st vist. Having an experienced, trusted aero bloke to guide you thru is key I reckon ... and IMHO more important than a super-detailed plan. I figure you should think about what's important for you to get a handle on ... starting with the biggest typical item(s). If you're already well set-up wrt. to saddle height, fore-aft position and the like, I assume getting a good handle on drag as a function of drop would be 1st priority (I managed to get part of that but foolishly forgot about going higher than my baseline).

After that's done, I'd pick a new baseline drop and start the semi-science, semi-art process of making a dozen small changes that could add up to 10% if you're lucky and have the right person guiding the process. i think you need to let experience guide that process vs. being too smart and pre-selecting everything you want to try and in what order. The tunnel can be a cruel task-master!

I'd leave messing with wheels, bars etc .. much further down the list if at all for your 1st visit.

In general, make it as easy as possible to change the front-end of your bike: take off cables etc if need be. Time goes quickly in the tunnel. If I had my time back, I'd have dumb cowhorns and simple adjustable (front to back, and side to side) clip-ons + adjustable drop stem on the bike. DON'T worry too much about getting an absolute CdA with your race setup (as I reckon I did) -- try and improve as much as possible!

Sorry for the order in which I'm writing this (so says Yoda)!!

I suppose I should have asked whether you can or want to test at multiple yaw angles? In some tunnels it's not possible or takes up a lot of time. 2hrs may be short depending on starting point, # of yaw angles and if you need to test kit along the way. If there was one piece of kit to test, it'd be aero helmets.

How much for 4hrs Steve?? Hey if you want to sponsor me, I'm willing to help you thru a session and get in some funky testing of my own .

In any case, I defer 100% to Dr.AC on this one ..

 

[acoggan]

2-hrs sounds cool. I've love to get back into a tunnel as I figure I honestly didn't get *that* much o/o my 1st vist. Having an experienced, trusted aero bloke to guide you thru is key I reckon ... and IMHO more important than a super-detailed plan. I figure you should think about what's important for you to get a handle on ... starting with the biggest typical item(s). If you're already well set-up wrt. to saddle height, fore-aft position and the like, I assume getting a good handle on drag as a function of drop would be 1st priority (I managed to get part of that but foolishly forgot about going higher than my baseline).

After that's done, I'd pick a new baseline drop and start the semi-science, semi-art process of making a dozen small changes that could add up to 10% if you're lucky and have the right person guiding the process. i think you need to let experience guide that process vs. being too smart and pre-selecting everything you want to try and in what order. The tunnel can be a cruel task-master!

I'd leave messing with wheels, bars etc .. much further down the list if at all for your 1st visit.

In general, make it as easy as possible to change the front-end of your bike: take off cables etc if need be. Time goes quickly in the tunnel. If I had my time back, I'd have dumb cowhorns and simple adjustable (front to back, and side to side) clip-ons + adjustable drop stem on the bike. DON'T worry too much about getting an absolute CdA with your race setup (as I reckon I did) -- try and improve as much as possible!

Sorry for the order in which I'm writing this (so says Yoda)!!

I suppose I should have asked whether you can or want to test at multiple yaw angles? In some tunnels it's not possible or takes up a lot of time. 2hrs may be short depending on starting point, # of yaw angles and if you need to test kit along the way. If there was one piece of kit to test, it'd be aero helmets.

How much for 4hrs Steve?? Hey if you want to sponsor me, I'm willing to help you thru a session and get in some funky testing of my own .

In any case, I defer 100% to Dr.AC on this one ..

I definitely think you hit the high points (which I bolded) in your answer. As for the time/yaw angle question, I'm not sufficiently familiar with the A2 facility to comment in detail...but what happens at yaw is clearly very important.

(FWIW, when Angie went to TAMU in 2007 we got in 15 runs covering the 0 -> 2.5 -> 5 -> 10 -> 5 -> 2.5 -> 0 deg of yaw "loop" in about 2 h, and that included some wheel swaps as well as a brief time-out for, um, "lunch" for our then-still-infant son. The TAMU bike mount is on built into the tunnel's turntable, though, so that saves a lot of time vs. facilities where you have to shut down the tunnel and manually reposition the mount.)

 

[rmur17]

I definitely think you hit the high points (which I bolded) in your answer. As for the time/yaw angle question, I'm not sufficiently familiar with the A2 facility to comment in detail...but what happens at yaw is clearly very important.

(FWIW, when Angie went to TAMU in 2007 we got in 15 runs covering the 0 -> 2.5 -> 5 -> 10 -> 5 -> 2.5 -> 0 deg of yaw "loop" in about 2 h, and that included some wheel swaps as well as a brief time-out for, um, "lunch" for our then-still-infant son. The TAMU bike mount is on built into the tunnel's turntable, though, so that saves a lot of time vs. facilities where you have to shut down the tunnel and manually reposition the mount.)

You know given the extra cost of travelling with bikes and all (at least with Air Canada who seem to love torturing folks w/o any options!), I'd be happy if a tunnel had a 'standard' bike in a size close enough to mine -- already setup with a clean/easy front-end, widely adjustable saddle height and setback, and a generic set of aero wheels. I wonder has anyone considered that?

What brought that to mind was pics of the A2WT I've seen with various aero bars/extensions and helmets on the wall (to try out I assume). At least for 1st time users, i reckon an aero bike and wheels are pretty much: an aero bike and wheels. For those getting into the 2nd/3rd round, I agree every little thing potentially matters.

Out at the LSWT in San Diego, the procedure re yaw 'was' to turn off air flow (or to idle perhaps), rotate the turntable, re-tare there I assume and bring the tunnel back up to stable Q. That wasn't fast -- I decided to test only my 'new baseline' position at 10 degrees yaw just to ensure I hadn't made a right mess o' things by changing based on zero yaw alone.

Anyhow, it's a great experience - just being a tunnel where some of the top Pro's and aero guru's have tread is pretty darned cool.

 

[Steve_B]

You know given the extra cost of travelling with bikes and all (at least with Air Canada who seem to love torturing folks w/o any options!), I'd be happy if a tunnel had a 'standard' bike in a size close enough to mine -- already setup with a clean/easy front-end, widely adjustable saddle height and setback, and a generic set of aero wheels. I wonder has anyone considered that?

I guess there's some value in that but at some point the specificity of your body on your bike with your wheels starts to matter. Where does that start? You know the answer to that one.

With me, I was going in to a tunnel for the first time but I was already "pretty aero" so having my stuff there was crucial. In the end, no huge gains (only 3%) but that's the way it goes when you're already "slick".

What brought that to mind was pics of the A2WT I've seen with various aero bars/extensions and helmets on the wall (to try out I assume). At least for 1st time users, i reckon an aero bike and wheels are pretty much: an aero bike and wheels. For those getting into the 2nd/3rd round, I agree every little thing potentially matters.

I was able to try out different helmets. In the end, the three other helmets I tried (besides my LAS) didn't matter - the difference was in the noise. See above for comment about "where does it matter?"

BTW - the stuff is there for use but it would take a while to patch in a new set of bars, of course. It was good to fit my arms in the top of the line bars and see how they adjust and fit. A2 has a great relationship with Hed and lots of stuff there. Oval...ummm...not so much. No stuff there. Their loss, I guess.

Out at the LSWT in San Diego, the procedure re yaw 'was' to turn off air flow (or to idle perhaps), rotate the turntable, re-tare there I assume and bring the tunnel back up to stable Q. That wasn't fast -- I decided to test only my 'new baseline' position at 10 degrees yaw just to ensure I hadn't made a right mess o' things by changing based on zero yaw alone.

It's the same at A2 - manual yaw adjustment. We tested my baseline at 0, 5 and 10 degrees but really didn't touch yaw again. We could have done my new position at yaw but I didn't think of it. We actually did 20 test runs in ~2 hours and quite frankly, I was kind of tired after all that anyway.

Mike, the bike manager at A2, feels that 99.9% of the time, investigatory work like what I was doing can be restricted to 0 degree yaw without a big penalty. If I go back, I would have a smaller subset of things to look at and yaw would be on the plate though. OTOH, we don't have a lot of wind around here so maybe it's less of a big deal.

Anyhow, it's a great experience - just being a tunnel where some of the top Pro's and aero guru's have tread is pretty darned cool.

I changed in the same bathroom that George Hincapie and Kristin Armstrong used! (presumably not simultaneously)

 

[J-V]

I was able to try out different helmets. In the end, the three other helmets I tried (besides my LAS) didn't matter - the difference was in the noise. See above for comment about "where does it matter?"

I'm curious to hear more about this statement. Are you suggesting that there was little measurable difference in drag between the helmets, but some were noisier than others?

I'm interested because my Advantage 2 is very noisy when down on my back, but if I look down just a bit, it gets much quieter. Not sure any conclusions can be drawn as to decreases in drag, but I just thought it an odd relationship.

Thanks,

J\V