Hello Rasker4 and All,

Do you want to guess?



It might help to put a metric on it and compare those values ............ go here:

http://www.analyticcycling.com/ForcesPower_Page.html

Run the default model and note the Wattage.
then vary only the drag coefficient from 0.5 to some other value .... like 0.4 and run the model again with the other default values
Note the wattage required at the new drag coefficient.

This also gives you a feeling for whether you are talking about developing a large value or a small one depending on data you submit to the models.

Keep in mind that these values would need to be validated in a wind tunnel or with some other real world testing for better accuracy.

You may find that small drag changes result in small wattage changes that are not worth the discomfort or difficulty or expense of the drag reduction.

There are other models for Speed etc. that are interesting.

If you know your values for frontal area and drag and rolling resistance ...............input those for approximate real world values that describe you.

Cheers,

Neal

+1 mph Faster

Hi Flac,

From http://www.cervelo.com/...-vs-fast-riders.html

SLOW VS. FAST RIDERS
Slow Riders vs. Fast Riders: who gets more benefit from aerodynamics?



Everyone knows aerodynamic drag increases the faster you go, so an aero bike is important for fast rider. But what about the reat of us?



Let's take a fast rider who can ride an hour record of 40 km/h. If we give him an aero advantage (wheel, frame, helmet) that gives him a 2 km/h speed advantage. When we give the same advantage to a slower rider, he gains 1.392km/h. So the slow rider gains less speed from the aero improvement. This is as expected, based on the drag equation where drag force goes up as speed goes up.


However, usually we race a fixed distance, not a fixed time. So let's look at the SAME graph, but let's compute how long it takes to ride a 20k TT distance.





Simple math; to get the finishing time, simply divide the distance by the speed. For example, if our fast rider goes 40km in one hour, it takes 30min to ride 20km.


Likewise, if you ride 42km/h, it takes 20km / 42 km/h times 60min equals 28min 34sec.


Do the same for the two speeds of the slower rider and the result?


Baseline equipment: 20km / 30 km/h = 2/3rds hr, or 40 minutes.
Aero advantage: 20km / 31.392 km/h times 60min = 38min 13sec.
The faster rider saves 1:26, while the slower rider saves 1:47. The slower rider saves more time!


If you agreed with the graph before, you agree with this. We didn't change anything! The reason is that the rider saves less per second, but is on the course for more seconds so saves more time overall.


Cheers,

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Damon Rinard
Engineering Manager,
CSG Road Engineering Department
Cannondale & GT Bicycles
(ex-Cervelo, ex-Trek, ex-Velomax, ex-Kestrel)

In response to JackMott earlier


Also a disc cover typically will be better at higher yaws as well, which you will see more often as a slower rider (typically).

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Founder: BestBikeSplit
Amazonian

The math for this is pretty simple actually:

t=d/(2*P/(rho*Cd*A))^(1/3)

where:
t=time
d=distance of the course
P=power output
rho=air density
Cd=drag coefficient
A=frontal area

If you plug in some numbers you can see that the amount of time one can save is inversely proportional to how fast they're going. So someone going around 15mph will save about twice as much time as someone going around 30mph if they both reduce their drag by the same amount. The percent change for the two riders is exactly the same, though. If one rider saves five percent (of time) then a rider at a different speed will also save five percent. This obviously doesn't account for the fact that the coefficient of drag is yaw angle (and therefore velocity) dependent, but for small differences in velocity it's pretty accurate.

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Zach McCormick
Catalyst Cycling
http://www.catalyst.bike

Hi Zach,

Fantastic (and simple!) way to illustrate the relationship.

Another way to intuit it:
If it were not true, and in fact faster riders saved more time, then faster and faster riders would save more and more time, until you have to ask: how fast would a rider have to go, to finish before they started?

Cheers,

---

Damon Rinard
Engineering Manager,
CSG Road Engineering Department
Cannondale & GT Bicycles
(ex-Cervelo, ex-Trek, ex-Velomax, ex-Kestrel)

Time machine!

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AndyF
bike geek

I have been wondering about this related question: a rider who, without any aero improvements can ride 40k at exactly 60 min. at a fixed wattage, has 3 possible aero improvements he can apply (and we'll assume that these 3 aero improvements that have zero aero interaction between them).

If this theoretical rider applies "aero improvement A" only, he saves 1 min. (same 40k course, same conditions, same fixed wattage).
If he applies "aero improvement B" only, he saves 2 min.
If he applies "aero improvement C" only, he saves 3 min.

Is there a way to mathematically show that if the rider applies all the aero improvements (A, B, plus C) at the same time in a single ride (also same 40k distance, same course, same conditions, same fixed wattage), the combined time savings will not equal 6 min. (i.e., 1 + 2 + 3 minutes), instead the time savings with be considerably less than 6 min?

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Advanced Aero TopTube Storage for Road, Gravel, & Tri...ZeroSlip & Direct-mount, made in the USA.
DarkSpeedWorks.com.....Reviews.....Insta.....Facebook
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The "additivity" of aero gains is dependent on how much aero interaction there is in the flow of each gain.

For instance, if you save 1 minute from booties and 2 minutes from a helmet, the combined aero gains might come very close to being 3 minutes. It's not quite that additive, because aero gain 2 is now working with a 59minute baseline, so it might be the extra 2min gain might only be 2*59/60 = 1.9666 minutes.

Conversely, if you're working with armpad width and skinsuit gains, they might really not be very additive.

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AndyF
bike geek

Sure, but what about the additivity of a rear disc wheel and, say, using aerobars (vs conventional drop bars, standard road rider position)? With those two, it seems that there is nearly zero flow interaction.

If aerobars save you 3 min off a 60 min 40k time, and a disc wheel (tested separately) saves you 2 min off the same time/course, can you really just add the predicted time savings together with simple addition?

Years ago, I read an interesting analysis about 'diminishing returns' with the more aero improvements added. IIRC, you could not just apply addition to aero time gains, even when there were not aero interactions. But I could be mistaken.

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Advanced Aero TopTube Storage for Road, Gravel, & Tri...ZeroSlip & Direct-mount, made in the USA.
DarkSpeedWorks.com.....Reviews.....Insta.....Facebook
--

We've been through this before in another thread :)

Perhaps someone can explain to me where I am going wrong, if I am, because I can't see it. I have a spreadsheet model containing the cycling equation of motion and it gives the following results for what happens if I keep saving 0.01 CdA at 400W, starting at 0.20 CdA:

CdA.....10 mile time.....saving
0.20......19:01.3............N/A
0.19......18:42.8............18.5
0.18......18:23.6............19.2
0.17......18:03.7............19.9
0.16......17:43.1............20.6

However, if I use a different starting point, with a 300W rider, the first two rows become
CdA.....10 mile time.....saving
0.20......21:07.8............N/A
0.19......20:47.5............20.3

The 300W rider saves more time than the 400W rider. But as the 400W rider gets faster, each 0.01 CdA reduction saves him more time than the last. By the time his CdA is down to 0.17 and he is covering 10 miles in 17:43, reducing his CdA by 0.01 actually saves him more time than the same CdA reduction applied to the 300W/0.20 CdA/21:07 rider.

So I agree that there are some situations where a slower rider saves more time than a faster rider, but there also seem to be situations where a faster rider saves more time than a slower rider if both reduce their CdA by 0.01. Damon's time warp paradox doesn't happen, though, because the time saving never becomes large enough. These are the bottom few rows for the 400W rider's drag getting close to zero:
CdA.........10 mile time.....saving
0.03..........10:30.6............N/A
0.02..........09:17.7............1:12.9
0.01..........07:34.2............1:43.5
0.0001.......02:42.1............4:52.1 (338W of the 400W is consumed by rolling resistance at this speed, 357kph)

CdA reduction is CdA reduction (if there are truly no interactions), so the absolute drag changes would be linear with those changes.

BUT, you now need to plug those changes of CdA into the equation of motion of a cyclist and solve for the speed for a given power, and thus the time savings over a fixed distance. See the equation by zachmccormack above.

I think the problem you discuss is probably because people are taking a simplified ROT and using it beyond its intended purpose ;-)

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http://bikeblather.blogspot.com/

nawwww BMC aint that fast

Lot of posts, lot of information, lot of emotions.
Re-reading your original post, you appear to be asking if the reduction of aero benefit due to slower speed is made up by being on the course longer, and if this is the case are the effects equal or unequal.

If that's what you're asking, this might help. Aero benefits lead to reduction in drag, and are typically stated for a specific speed. If you go slower, the reduction in drag is NOT linear, it is exponential. Therefore, the loss of benefit from aero equipment is also exponential. But time on the course is linear with speed, not exponential. Therefore, at slower speed, aero stuff does you less good overall. There is a regain from being on the course longer but it is only a partial offset because that's a linear effect and the aero loss is exponential.

Bottom line: you still should select aero components based on cost/benefit. Drag gain at any standard speed vs dollars. But the faster you go, the more it matters, and time on course is an offset but only partial.

Go train! And thanks for the thought-provoking question.

That's because lowering CdA from .17 to .16 is a larger percent change than lowering it from .20 to .19, so it makes more of a difference. With that said, when bike companies talk about time savings between faster riders and slower riders, I think they're assuming that the faster rider is faster because he has a higher power output, not because his CdA is already lower. In reality it would probably be a mix of both, but power outputs between different riders vary much more than drag areas do, so this is a fair assumption. Using this assumption you get that slower riders save more time than faster riders. If, instead you say the faster rider is faster because he has a lower drag area to begin with, then, like you said, he will save more time than the slower rider. It all depends on what simplifying assumptions are made.

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Zach McCormick
Catalyst Cycling
http://www.catalyst.bike

lol!

Flac, here's the thing you seem to be struggling with: Reducing aerodynamic drag allows you to either ride faster at the same power (watts) resulting in a shorter ride time, or if you're like a lot of triathletes who have over biked in the past, hold the same speed as previously, but at a power level that is within your abilities then run better instead of blowing up like you did in the past. This is true for everyone, regardless of how fast or slow they are, but when the theories and math are applied to a slower rider, the total amount of time saved is usually greater than the total amount of time saved by a faster rider.

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____________________________________________
Don Larkin
Reach For More
http://www.reachformore.fit/
USAT Lvl1 Coach, NSCA-CPT, NASM-CPT, BS Exercise Science

It's an interesting question - admittedly I only quickly looked for a single example, but I took the Strava segment for a TT course where I knew I had the KOM and had a look to see how far down I could go and still find people outputting more power than me:
http://app.strava.com/segments/892764
Me 18:38 304W
142nd place 22:38 312W
My experience is that CdA varies a LOT from rider to rider.

Still, it doesn't change the fundamental truth that aero gains are relevant to riders of all speeds, it doesn't really matter whether the time savings are a teeny bit larger or a teeny bit smaller for a slower rider, everyone should be looking for ways to shave off their next 0.01 CdA.

This is all over my head...
Could someone please dumb it down for me? If someone rides say 18 mph on a training ride, what would the expected ave speed be in a race over the same distance with the same effort and conditions if you throw on the 808 race wheels, aero helmet, and tri suit (as opposed to basic dry fit t-shirt) and strip off excess bottle cages? Thanks.