The complex case of aerodynamics and weight in racing
Moderator: robbosmans
For some time, aerodynamics have been the big trend in cycling and with almost every gear nowadays being aerodynamically optimized in wind tunnels. Marketing is focusing much more on watts saved due to drag reduction, and while its true for a single cyclist riding or for a breakaway where the cyclists take turns, how important is aerodynamics for the cyclist in the middle of the pack? It's a complex case where drag is becoming 4050% lower for the cyclist in the pack, and where the airflow is even less clean, hence it's harder to get it to stick to the aerodynamic surfaces of wheels, helmets, etc. Can it be so that other forces become more relevant?
What we haven't seen nor discussed is how important the different forces acting on the cyclist within the pack are compared to each other.
The CdA (coefficient of drag times the frontal area) is defined as Fd = 1/2 * Cd * A * p * v^2, where Cd is the coefficient of drag, A is the surface area towards airflow, p is the density of air, and v is velocity. The Cd will change when being in the slipstream as the drag is lower while being in the pack. A can't change, nor can the density of air or velocity if held constant. If the drag decreases by 40 percent, the cyclist being in the pack will have a very low CdA which in turn means that the power to overcome the airflow is becoming much lower, right? So, what does this mean for the share of forces to overcome? The rolling resistance and weight become even more important. With a very low CdA, weight and rolling resistance will have a almost equal impact on the cyslist as the CdA even at grades of only a few percentages.
In the complex case of aerodynamics and weight in racing, weight and rolling resistance can't be negligated if you wan't to save energy until the end and will try to hide in the pack.
A good calculator that can visualise the forces can be found here. https://www.gribble.org/cycling/power_v_speed.html. Decrease the Cd and not the A and add 13 percentage and see what happens to the forces at different speeds.
Agree or disaggree?
Sources: https://www.researchgate.net/publicatio ... 0ifQ%3D%3D
What we haven't seen nor discussed is how important the different forces acting on the cyclist within the pack are compared to each other.
The CdA (coefficient of drag times the frontal area) is defined as Fd = 1/2 * Cd * A * p * v^2, where Cd is the coefficient of drag, A is the surface area towards airflow, p is the density of air, and v is velocity. The Cd will change when being in the slipstream as the drag is lower while being in the pack. A can't change, nor can the density of air or velocity if held constant. If the drag decreases by 40 percent, the cyclist being in the pack will have a very low CdA which in turn means that the power to overcome the airflow is becoming much lower, right? So, what does this mean for the share of forces to overcome? The rolling resistance and weight become even more important. With a very low CdA, weight and rolling resistance will have a almost equal impact on the cyslist as the CdA even at grades of only a few percentages.
In the complex case of aerodynamics and weight in racing, weight and rolling resistance can't be negligated if you wan't to save energy until the end and will try to hide in the pack.
A good calculator that can visualise the forces can be found here. https://www.gribble.org/cycling/power_v_speed.html. Decrease the Cd and not the A and add 13 percentage and see what happens to the forces at different speeds.
Agree or disaggree?
Sources: https://www.researchgate.net/publicatio ... 0ifQ%3D%3D
It depends a lot on the group. If it really is a grand tour type group and you're at the back, you're doing so little of anything on flat ground that there's not much energy to save.
If it's a paceline, you'll still be working when not on the front. Then it might be worth saving energy via aerodynamics. On the flat I'm not sure lighter bikes help at all.
Usually you lose a group because there was an acelleration up a hill that you didn't respond to in time. Or you let it go and it gets away. There a lighter bike will matter more than saving energy while it's easy.
In a big group you want to be moving forward most of the time. So there'll be occasional short harder efforts to get into a gap that's opened up.
Not sure if any of this answers your question tbh, but it's quite complicated how much different factors matter. Race experience trumps any watt saving.
If it's a paceline, you'll still be working when not on the front. Then it might be worth saving energy via aerodynamics. On the flat I'm not sure lighter bikes help at all.
Usually you lose a group because there was an acelleration up a hill that you didn't respond to in time. Or you let it go and it gets away. There a lighter bike will matter more than saving energy while it's easy.
In a big group you want to be moving forward most of the time. So there'll be occasional short harder efforts to get into a gap that's opened up.
Not sure if any of this answers your question tbh, but it's quite complicated how much different factors matter. Race experience trumps any watt saving.
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 MarshMellow
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Last edited by MarshMellow on Thu Jan 19, 2023 2:12 pm, edited 1 time in total.
 MarshMellow
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It's because aero matters a lot more than slight increases in weight. Races are decided when the decisive move is made. And that's when everyone is going all out, so even on a climb the racers are pushing big watts, have a decent amount of speed, and there is significant aero drag unless it's a literal wall they're climbing. Maybe not enough to justify a full on aero bike pushing 9 kg, but something like a Tarmac sitting at just over 7 kg will be faster than something with round tubes sitting right on 6.8 kg on almost every single climb out there.

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Worth noting that no world tour aero bike is pushing 9kg. The largest sizes of the SystemSix might be a little over 8kg.
With real world aero data collection starting to be more and more in reach of race teams, frame designs will evolve in a way where the weight vs. aero discussion around the frame itselt will become less relevant. I think we will see less of an emphasis put on aero shapes if it compromises the ability for a rider to acheive and sustain a "Remco like" fit.
I think that future bikes will continue to the have the front end optimized for aero with narrow handlebars, low stack numbers, deep headtubes and downtubes, but also increasingly use comfort features on the rear of the bike. They will also be optimized around a 2830mm tire rather than simply have capacity for those widths, and have their handling dialed to run the deeper wheels needed to mitigate the aero penalties of those wider tires.
Pretty much saying that I think Trek's Domane RSL+the new narrow/flared barstem from the Madone is going to be what future race bikes look like.
I think that future bikes will continue to the have the front end optimized for aero with narrow handlebars, low stack numbers, deep headtubes and downtubes, but also increasingly use comfort features on the rear of the bike. They will also be optimized around a 2830mm tire rather than simply have capacity for those widths, and have their handling dialed to run the deeper wheels needed to mitigate the aero penalties of those wider tires.
Pretty much saying that I think Trek's Domane RSL+the new narrow/flared barstem from the Madone is going to be what future race bikes look like.

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You're not wrong, but for many decades prior to about 1984, nearly all racers cared about weight exclusively; drillium was the way to go fast, most believed. So "for some time" is nearly 40 years. (Though I concede that the focus on aerodynamic frames picked up steam in the aughts—the Cervelo Soloist was introduced in 2002—and has only intensified since).
Frame and wheel aerodynamics aren't very important for riders in the middle of the pack. But if those riders aspire to any glory at all, they'll have to leave the middle and go to the front of the pack. That's how the officials decide who wins, right? At the front of the field, in a break, on a moderate climb and definitely in a sprint, aerodynamics are pretty much everything.
It's not nearly as complex as you might think. Laminar flow is a pretty rare phenomenon even for a rider in a solo break, which is why that paper spends significant time discussing turbulence models. But that's a red herring—aerodynamic drag dominates efforts at nearly all critical moments in a bicycle race. Mass becomes a significant factor only on the steepest slopes—this is well established. But if you're breaking away, sprinting or simply taking a pull at the front, aero drag consumes nearly all of your watts. Rolling resistance and mass are tertiary.handler wrote: ↑Thu Jan 19, 2023 10:57 amIt's a complex case where drag is becoming 4050% lower for the cyclist in the pack, and where the airflow is even less clean, hence it's harder to get it to stick to the aerodynamic surfaces of wheels, helmets, etc. Can it be so that other forces become more relevant?
Maybe you haven't seen or discussed this. But among others, Dutch professor Bert Blocken has been working on this for some time:
https://www.iawe.org/Proceedings/EACWE2 ... locken.pdf
https://www.sciencedirect.com/science/a ... via%3Dihub
https://asmedigitalcollection.asme.org/ ... ofCyclist
You'll notice that Blocken is also the first author on the paper you cited. But he's not the only one; I'm pretty sure that Josh Poertner and Damon Rinard have both given this subject a lot of thought, and Robert Chung's elegant analysis framework ("the Chung method") is an extraordinary tool that allows one to evaluate drag in a finegrained way. I'm a little dubious of Aerocoach's RR testing, but they address the aero/RR optimization question directly, at least for tires.
The work of those mentioned above is directly relevant, even when it doesn't mention rolling resistance or weight. A rider's power is obviously consumed by many things including (but not limited to) aerodynamics, rolling resistance, bearing drag and (on climbs) mass. Aerodynamics dwarfs everything else in most situations, especially for a solo rider. By quantifying the aero drag, we can subtract it from total drag and thereby get at these other forces that you're concerned about.
Eh...a rider deep in the field is essentially riding within a "bubble" of entrained air, which could be understood (to a first approximation) as a constant CdA with a much lower air velocity than one would experience at the front. But this is a semantic distinction, so let's not fixate on it—your point stands regardless.
You're not wrong about this, but it's not as compelling as it might seem at first. The paper you cited shows that a rider at the front can have ten times the drag of one deep in the field. When a domestique at the front generates, say, 550 watts at 50 kph, that rider's team leader is only putting out maybe 150 watts while deep in the field. (To be clear, these are entirely madeup numbers...see the paper if you want realistic ones).handler wrote: ↑Thu Jan 19, 2023 10:57 amwhich in turn means that the power to overcome the airflow is becoming much lower, right? So, what does this mean for the share of forces to overcome? The rolling resistance and weight become even more important. With a very low CdA, weight and rolling resistance will have a almost equal impact on the cyslist as the CdA even at grades of only a few percentages.
You're right that of those 150 watts, rolling resistance is maybe 35 watts or so with good tires. That's 23% of the total power, which sounds like a lot—but there are a couple of reasons why it isn't:
1) Everyone is on pretty good tires, so that 35 watts is pretty much the same for everyone.
2) Tires are pretty fast these days, and Conti and Michelin have massive research programs aimed at reducing rolling resistance for cars (where the money is). You'd better believe that the tiny bike divisions at those companies take advantage of that research. You're simply not going to cut tire rolling resistance in half, no matter what. And even if you did, you're only saving 1718 watts. Some may want to shout "marginal gains!", as 17 watts sounds like a lot. But again: barring extraordinary advances that would absolutely show up in automotive tires first, that reduction simply isn't available.
3) If you're a pro in the Tour with an FTP pushing 6 w/kg, 150 watts is very much an easy spin. If you could knock that down to 125 watts, it's simply not much easier. Yes, you'll save a little muscle glycogen; yes, when you're burning matches, each one counts. But this isn't burning a match; watts matter the most when you're approaching your limits, and a male pro at 150 watts is nowhere near his limit.
Marginal gains matter, but diminishing returns suck resources that could be applied to juicier fruit, so to speak. Everyone has already accumulated nearly all of the marginal gains of lowRR tires and (ugh) ceramic bearings. The power required in a field is already very low, and there's not much one can do to lower it.
Okay, mass: I'll be buying a highend aero road bike sometime in the next five years, and it galls me a little that many of them are in the 8kilo range. But if you and I both weigh 70 kilos and my bike is 8.8 kilos while yours is 6.8, my system weighs merely 2.6% more than yours. If we're racing up a 10% slope (5.71 degrees), then the "drag" due to mass is 0.26% more for me. If we're competing for mountain points and both putting out 500 watts, your weight advantage means you have to put out a whopping 1.3 watts less than I do. Saving 1.3 watts at 500 watts? It's a difference, but an extremely small difference.
[That said, please check my math either by hand or with a power/speed calculator. I'm taking a break to write this from work, and I need to get back to it—I don't have time now to doublecheck. To wit: 2.6% less mass * sin(deg(5.71)) = 0.00259, or 0.26%]
In contrast, let's say you buy a new frame or helmet or wheelset—it doesn't matter what—and independent testing convincingly shows that, compared to your current setup, a solo rider with the new gear will save 60 seconds over 40k at 50 kph.
That's 1.5 seconds per kilometer. Let's further assume that I'm slow and sprint at 50 kph/31 mph/13.9 m/s. In a 200m sprint, that saves 0.3 seconds. That doesn't sound like much, but 0.3 seconds is worth a whopping 4.2 meters at that speed. That's the difference between taking second place and wiping the floor with second place.
But that assumes a dragrace sprint from 200m (no drafting). If you slingshot past your opponents with a mere 100m to go, you'll only win by half as much—a mere two meters, or more than a bike length. I'm a dyedinthewool weight weenie, but I find that compelling.
It's not all that complex, really, once you've taken aerodynamics mostly out of the equation by sitting deep in a pack. Weight and rolling resistance do matter, but trivially. The former is trivial because bike weight differences are trivial compared to bike/rider mass; the latter is less trivial in absolute terms, but the overwhelming majority of the Tour field is equipped with tires that are within 13 watts of each other. Any gains to be had are exceedingly marginal in relative terms, which are the only ones that matter. And tires aren't going to get radically faster anytime soon, so it's hard to find a real advantage relative to the competition unless they love slow tires.
I'm not sure what you're asking us to agree or disagree with, exactly.
If you're asking whether nonaero drag forces deserve more attention from the engineering community, I'd disagree with that for the reasons I've articulated here. If someone comes up with a radial bike tire that cuts rolling resistance in half while retaining adequate torsional stiffness, I'll change my answer—but due to physics, I'm not holding my breath.
If you're asking whether your reasoning is sound, I'd say it is—this is worth considering. But I don't see that your reasoning supports the conclusion that we should spend a lot of effort to reduce nonaero drag—mostly because there's not much to reduce, and a big reduction would require materials and processes that don't actually exist right now.
Like I said, I love a light bicycle. But I did too much math in grad school to accept low weight over low drag.
Please let me know if I've misunderstood your post in any way or if you find a mistake in my math.
Last edited by youngs_modulus on Thu Jan 19, 2023 11:05 pm, edited 1 time in total.

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I should acknowledge that other posters beat me to the punch with a couple of these points. Well played, other posters!
It doesn't seem to be an either/or choice these days. One could have an aero bike, with the lowest rolling resistance tires, and that is still at the UCI weight limit.
Last edited by AJS914 on Fri Jan 20, 2023 1:05 am, edited 1 time in total.
You've done that wrong. Power into climbing is linear with mass (as I think you know, that's not your issue here). Presumably you chose 10% grade to assume the majority of power output is going into climbing. Let's say 80% of it. Then 80% of output is linear with a 2.6% mass gain. 0.8*2.6%=2.08%. Then, 2.08%*500w= 10.4Wyoungs_modulus wrote: ↑Thu Jan 19, 2023 8:17 pm[That said, please check my math either by hand or with a power/speed calculator. I'm taking a break to write this from work, and I need to get back to it—I don't have time now to doublecheck. To wit: 2.6% less mass * sin(deg(5.71)) = 0.00259, or 0.26%]
You don't mulitiply by the sine of the angle.
A more precise analysis would be to work out on a 10% grade what proportion of power DOES go into climbing. Requires solving the other sinks of power.

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Hmmm. Are you familiar with vectors?Nereth wrote: ↑Thu Jan 19, 2023 11:26 pmYou've done that wrong.youngs_modulus wrote: ↑Thu Jan 19, 2023 8:17 pm[That said, please check my math either by hand or with a power/speed calculator. I'm taking a break to write this from work, and I need to get back to it—I don't have time now to doublecheck. To wit: 2.6% less mass * sin(deg(5.71)) = 0.00259, or 0.26%]
Nope. I chose a 10% grade because it's steep enough to be a significant climb but shallow enough that many people can find a 10% grade nearby. If I wanted a majority of the power to go to climbing, I'd assume a grade of >30°, as the sine of 30° is 0.5.
Regardless of the grade, for a given speed/slope, the power required to ascend isn't hard to calculate. Science is easiest to understand when it's relatable, I hear.
I'm sorry...what?
Respectfully, why on earth are you guessing about vector components? As math goes, vector decomposition is not very fancy.
If you're not guessing, please explain where you found that 80% number. Like the kids¹ say, extraordinary claims require extraordinary evidence.
For context, if 80% of your output were going to ascension, you'd be climbing a hill at an angle of roughly 53°, or 133%. You must have some steep hills chez toi.
Wow. I mean, that follows from your guess, but why on earth are you so confident in your guess?
The thing is, though, that you do multiply by the sine of the angle—if, that is, you're after what pedants refer to as "the right answer."
Again, this is just vector decomposition.
I didn't have time to check my work, so I thought I might have made an arithmetic² error. I don't think you've found one, though I've been wrong plenty of times before.
Can you explain why vector decomposition doesn't apply here?
Either way, I'll leave it to you to provide a considerably more precise analysis.
Solve for those other power sinks! I'll wait.
¹ What? Carl Sagan was a kid once!
² I'm obviously going full Jobst at this point—the post I'm responding to was a lot, and dude literally joined the forum yesterday.
That said, I really thought I might have made a math error; even so, I'm comfortable with my analytical approach. If anyone has mathbased or physicsbased objection to my original post, I'm definitely all ears. If anyone has a better answer than either of us, I'm excited to hear it!
Oh my god, slow your roll.
I've been familiar with vectors since doing them in highschool physics decades ago, and continuing with them through uni and my profession. But you don't use them the way you're using them here.
You've completely messed up your understanding of this maths. As proof by counterexample, note that your result is in conflict with established sources: go to any online cycling power calculator that shows a breakdown of power usage, type in a 10% slope for a 70kg bike and 810kg of frame, at 500W, you'll get 8090% of power into gravity depending on other inputs. Not the sine if the angle. Try: https://www.gribble.org/cycling/power_v_speed.html (my favourite).
As a proof on principle instead of counterexample, your method leads to a watt loss to gravity that is dependant only on power and grade, thus the proportion of power going into drag is fixed, thus an arbitrarily light rider would be able to go arbitrarily fast, with no increase in power available to fight drag. In reality, lighter rider, faster ground speed, more drag, the 80% proportion drops. Not reflected by your mass * sine of angle method
To teach you how to calculate the real proportions are beyond me right now, I'm typing with one hand with a broken collarbone. But this source looks good: https://www.omnicalculator.com/sports/cyclingwattage . Make your own calculator in excel and when it agrees with the online calculators you know you have it. With a username like "Young's Modulus" you should have that covered.
I've been familiar with vectors since doing them in highschool physics decades ago, and continuing with them through uni and my profession. But you don't use them the way you're using them here.
You've completely messed up your understanding of this maths. As proof by counterexample, note that your result is in conflict with established sources: go to any online cycling power calculator that shows a breakdown of power usage, type in a 10% slope for a 70kg bike and 810kg of frame, at 500W, you'll get 8090% of power into gravity depending on other inputs. Not the sine if the angle. Try: https://www.gribble.org/cycling/power_v_speed.html (my favourite).
As a proof on principle instead of counterexample, your method leads to a watt loss to gravity that is dependant only on power and grade, thus the proportion of power going into drag is fixed, thus an arbitrarily light rider would be able to go arbitrarily fast, with no increase in power available to fight drag. In reality, lighter rider, faster ground speed, more drag, the 80% proportion drops. Not reflected by your mass * sine of angle method
To teach you how to calculate the real proportions are beyond me right now, I'm typing with one hand with a broken collarbone. But this source looks good: https://www.omnicalculator.com/sports/cyclingwattage . Make your own calculator in excel and when it agrees with the online calculators you know you have it. With a username like "Young's Modulus" you should have that covered.
At 500 W and 10% slope, assuming a CdA of 0.25 m^2, 2% drivetrain loss, Crr = 0.005 and air density of 1.226 kg/m^3, you get the following speeds:
 21.02 kph at 76.8 kg total system mass (rider + bike)
 20.57 kph at 78.8 kg total system mass
Doing it backwards, to go 20 kph at 10% slope, you get the following Watts:
 472.9 W at 76.8 kg
 484.5 W at 78.8 kg
So a 2.6% difference in mass requires roughly an additional 2.5% in Watts when climbing something that steep.
 21.02 kph at 76.8 kg total system mass (rider + bike)
 20.57 kph at 78.8 kg total system mass
Doing it backwards, to go 20 kph at 10% slope, you get the following Watts:
 472.9 W at 76.8 kg
 484.5 W at 78.8 kg
So a 2.6% difference in mass requires roughly an additional 2.5% in Watts when climbing something that steep.
youngs_modulus wrote: ↑Thu Jan 19, 2023 8:17 pm
Okay, mass: I'll be buying a highend aero road bike sometime in the next five years, and it galls me a little that many of them are in the 8kilo range. But if you and I both weigh 70 kilos and my bike is 8.8 kilos while yours is 6.8, my system weighs merely 2.6% more than yours. If we're racing up a 10% slope (5.71 degrees), then the "drag" due to mass is 0.26% more for me. If we're competing for mountain points and both putting out 500 watts, your weight advantage means you have to put out a whopping 1.3 watts less than I do. Saving 1.3 watts at 500 watts? It's a difference, but an extremely small difference.
[That said, please check my math either by hand or with a power/speed calculator. I'm taking a break to write this from work, and I need to get back to it—I don't have time now to doublecheck. To wit: 2.6% less mass * sin(deg(5.71)) = 0.00259, or 0.26%]
Last edited by fa63 on Fri Jan 20, 2023 2:00 am, edited 1 time in total.
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Okay—this is substantial. I'll cogitate and respond in a few hours. Cheers!fa63 wrote: ↑Fri Jan 20, 2023 1:26 amAt 500 W and 10% slope, assuming a CdA of 0.25 m^2, 2% drivetrain loss and air density of 1.226 kg/m^3, you get the following speeds:
 21.02 kph at 76.8 kg total system mass (rider + bike)
 20.57 kph at 78.8 kg total system mass
Doing it backwards, to go 20 kph at 10% slope, you get the following Watts:
 472.9 W at 76.8 kg
 484.5 W at 78.8 kg
So a 2.6% difference in mass requires roughly an additional 2.5% in Watts when climbing something that steep.
youngs_modulus wrote: ↑Thu Jan 19, 2023 8:17 pm
Okay, mass: I'll be buying a highend aero road bike sometime in the next five years, and it galls me a little that many of them are in the 8kilo range. But if you and I both weigh 70 kilos and my bike is 8.8 kilos while yours is 6.8, my system weighs merely 2.6% more than yours. If we're racing up a 10% slope (5.71 degrees), then the "drag" due to mass is 0.26% more for me. If we're competing for mountain points and both putting out 500 watts, your weight advantage means you have to put out a whopping 1.3 watts less than I do. Saving 1.3 watts at 500 watts? It's a difference, but an extremely small difference.
[That said, please check my math either by hand or with a power/speed calculator. I'm taking a break to write this from work, and I need to get back to it—I don't have time now to doublecheck. To wit: 2.6% less mass * sin(deg(5.71)) = 0.00259, or 0.26%]