Just One Metre

In a 200 metre sprint finish, is it better to be on a Cervélo R5 or S5?

 Tyler Farrar header

Good question. First of all, most who know Cervélo, know that aerodynamics is important in timed events like time trial and triathlon. (See “Aerodynamics”, a Thinking & Processes presentation in the Engineering section of the Cervélo web site.) Secondly, if you’ve followed closely you know aerodynamics is also important in events with drafting, like road racing, even on hilly terrain. (See “Col de la Tipping Point”, also known as “Weight vs. Aero”.)

But what effect does an aero bike have on sprinting?

Of course, track sprinters race full aero these days, and in the recent Giro d’Italia the commentators mentioned Mark Cavendish’s small frontal area as a potential advantage in his road sprinting, so asking what role an aero bike might play in an all-out sprint is perfectly sensible.

Actual sprint finishes are chaotic enough that it’s hard to point to any individual effect (like bike frame aerodynamics) as a significant effect in a statistical kind of analysis over, say, a season. But no individual sprint win is a statistic – each individual sprinter wants the best chance to win each individual sprint. No, we need a different way to compare bikes in a sprint.

As engineers, we like to measure. As a consequence we have a lot of data, and it comes in handy when comparing bike performance. We also have a lot of simulation capabilities, from our in-house developed C-TOP structural analysis software used in Project California’s R5ca (and subsequent Cervélo models) to our own wind-tunnel-validated computational fluid dynamics (CFD) software used to develop the P5 and S5. So we decided to do a quick simulation to calculate the advantage an aero bike might bring to a sprint.

Simulation

Let’s simulate Tyler Farrar’s (Team Garmin-Sharp) final 200 metre dash to the line. We took our measured data (aero drag and weight of the two Cervélo bikes, R5 or S5) and combined it with some estimates about Tyler’s typical weight, power, speed and sprint distance.

Jim Martin’s seminal paper “Validation of a Mathematical Model of Cycling Power” captures the fundamental physics of powering a bike. This work is the basis of most math models of cycling, including much of the current work being done with field testing, both the traditional regression method and the newer virtual elevation method, and now with Alphamantis Technologies’ Aerostick, including the measurement of ambient wind.

One convenient application using Jim’s model is Tom Compton’s excellent web site, analyticcycling.com. A straight-up sprint comparison is simple enough to model, so we used his page simulating the Final Sprint. Tom set up this page to compare two identical riders on different wheels, but with the flexibility he’s built in to the input fields we can easily use it to compare two identical riders on different frames.

Just one metre fig 2

Figure 2: Screen shot showing analytic cycling’s “Final Sprint” page. We used the inputs listed in the table below.

To make the comparison, we’ve put Tyler as the “Standard Rider” on a Cervélo R5 and Tyler as the “Test Rider” on a Cervélo S5. Since the rider is the same for both cases, the only differences are aero drag and weight between the two Cervélo models (R5 and S5). These differences are listed in the top three rows of the input table below, namely, frontal area “A,” coefficient of drag “Cd,” and “Bike Weight.”

Aero drag: CdA

We know from our wind tunnel tests that a good sprinter has a CdA of about 0.333 metres squared. We also know from our wind tunnel tests that the Cervélo S5 with rider has about 0.013 metres squared less drag area than an R5. So as inputs for our analysis we'll use 0.333 metres squared for the R5 and 0.320 metres squared for the S5.

Bike Weight

Since the question is in reference to professional riders in a UCI sanctioned event, the R5 has been ballasted up to the UCI minimum of 6.8kg. (The UCI minimum weight may not apply to you; we’ll simulate a larger weight difference below.) And the S5 in the heaviest team build is typically no more than 7.0kg. So the difference in weight is 7.0 – 6.8 = 0.2 kilograms, or 200 grams.

The remaining parameters were set to identical values for both cases (same rider, same wheels, etc.). Here is our final list of inputs:

Input parameter

“Standard Rider” on R5

“Test Rider” on S5

Source

A*

1 m2

1 m2

See note*

Cd*

0.333

0.320

See note*

Bike Weight, without wheels

3.732 kg

3.932 kg

Team mechanic

Rider Weight

74 kg

Estimated

Front Wheel Weight

1.264 kg

Default

Front Wheel Inertia

0.0885 kg/m2

Default

Front Wheel Drag Coefficient

0.0491

Default

Front Wheel Radius

0.337 m

Default

Rear Wheel Weight

1.804 kg

Default

Rear Wheel Inertia

0.0967 kg/m2

Default

Rear Wheel Drag Coefficient

0.0491

Default

Rear Wheel Radius

0.337 m

Default

Rear Wheel Shelter

25 %

Default

Max Power

2000 W

Estimated

Average Power

1200 W

Estimated

Time at Max Power

3.7 s

Default

Time Period

25 s

Default

Air Density

1.226 kg/m3

Default

Coefficient of Rolling Resistance

0.004 (asphalt road)

Default

Slope

0.00 (flat sprint)

Default

Time at start

0 s

Default

Speed at start

18.0 m/s

Estimated

Distance at start

0 m

Default

Time at End

25 s

Default

Sprint Distance

200 m

Estimated

*Since the product CdA is measured in the wind tunnel, not Cd nor A separately, and since analyticcycling.com multiplies Cd and A together even when entered separately, we entered “1” for both riders’ “Effective Frontal Area” (the A in CdA) and entered each rider’s individual CdA as the “Drag Coefficient” (Cd).

 Table 1: Inputs for analytic cycling’s “Final Sprint” web based calculator.

 

Just One Metre…

After running the model we see that the rider on the S5 would cross the finish line 0.059 seconds or 1.127 metres ahead of the rider on the R5. 

 Figure3

Figure 3 Charts showing the distance advantage of the S5 over the R5 (left) and speed of each bike (right).

We can quickly see how the aerodynamic advantage of the S5 clearly outweighs the slight weight advantage of the R-series, in a 200 metre sprint situation.

Fun fact: S5 VWD

The S5 VWD is a lighter variant of the S5 (using higher grade carbon and a more complex layup). It weighs a little less than the R3, so would also be ballasted up to 6.8kg. Type in the same weight to see the S5 VWD would give a 1.145 metre advantage in a sprint. It’s easy to see from this small increase that in a flat sprint, aerodynamics plays a bigger role than weight.

No UCI limit?

What if you’re not constrained by the UCI weight limit? Then the R5 doesn’t need ballast and it can be lighter than 6.8 kg. To run those numbers, change the R5’s “Bike Weight” from 3.732 to 3.432kg (the R5 is approximately 500 grams lighter than the S5 frame, fork, seat post, etc.) and see that even with the greater weight savings the S5 still crosses the line 1.103 metres ahead. Even this somewhat large weight difference has a tiny effect compared to the aero difference.

Result

1.127, 1.145, 1.103 metres… Basically, in every case, the S5 rider comes to the line just over a metre ahead of the R5 rider.

Reality

Of course, bike racing’s not a math problem – the chaos of a field sprint is impossible to model completely, and there are many strategic factors in a race that have more influence on the result than the one metre difference between these two bikes. Caught behind a slowing rider? On the windward side of the bunch? Avoid the spectator’s camera in the turn? Naturally, a good sprinter maximises his chances by paying attention to all factors. And all else equal, the Cervélo S5 is a factor you can rely on to certainly give a surprisingly large one metre advantage that’s real, always there, independent of other strategic factors in the race, even in a sprint. Aero is always on.

Answered by David Killing and Damon Rinard



[1] “Drag area,” or CdA, is related to drag force by the drag equation: drag force = ½ ρ V2 CdA.

 

 

Comments (15)
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  • sausskross

    Hi Damon, the new S5 was worth waiting, no wishes left behind. The missing C doesn't matter on the road .. oSo >>

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  • Damon Rinard, Cervélo Engineer

    Hi 06/08/2013, Actually, for a given size, the R5 head tube is 6mm shorter than the S5. But that's because the R-series fork is 6mm longer. By design, the frame stack dimension is the same. So the riding position is also the same. Nevertheless, you are certainly right, the rider's position dominates. Adding frontal area has a big negative effect. It adds aerodynamic drag. Cheers, -Damon

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  • Damon Rinard, Cervélo Engineer

    Hi denz, Pros (even Garmin pros) are human, just like us. We all draw our own conclusions, based on many factors. Despite the objective results, the subjective riding experience is strong. Cheers, -Damon

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  • Hi Damon, interesting article. Perhaps I've missed it in the article, but the R5 also has a longer head tube than the S5, would this weigh a factor? I would have thought a longer head tube would increase frontal drag as the rider is positioned more upright?

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  • denz

    Hi Damon, great topic. Assuming the Garmin team would have access to all this type of data and more, it'd be interesting know why Tyler always chooses an R bike on sprint stages?

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  • sausskross

    Hi Damon, thank you for your reply. For sure I can't feel the handlebar getting warm (from the down & headtube :-) but I can feel that I can push harder and have more variance when the frontend is giving less back from the sprint explosion during these cadences. By the way, it's so much fun to ride my bike as a rouleur & to talk to the engineers who are creating my next one .. sCa >> Cheers, -sausskross

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  • Damon Rinard, Cervélo Engineer

    Hi g.barkerking, Great question, considering Dan Martin just won a fantastic victory under just those riding conditions. Shouldn't take us long to run those numbers. Cheers, -Damon

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  • Damon Rinard, Cervélo Engineer

    Hi sausskross, Thanks for your comment. Hm, stiffness to transfer power - I think you answered your own question with the "not lost as heat" comment. :-) And for feelings? You're going to love the next Ask the Engineers question. I'm writing the answer now, and it's right in your area of interest! Cheers, -Damon

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  • Damon Rinard, Cervélo Engineer

    Hi sausskross, Thanks for your comment. Hm, stiffness to transfer power - I think you answered your own question with the "not lost as heat" comment. :-) And for feelings? You're going to love the next Ask the Engineers question. I'm writing the answer now, and it's right in your area of interest! Cheers, -Damon

    Report this comment.
  • g.barkerking

    Nice article What happens when you take those bikes and send it up hill? Dan Martin (R5) vs. Dan Martin (S5) 1k uphill on a 6% grade? I would like to see that.

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  • sausskross

    Hi David & Damon, another meter for the acceleration thrill could be a more rigid frontend to transfer all explosiv power in the wanted direction for the rider + bike system. I guess the bottom bracket gives all power back during a cadence what is not becoming heat. If machines can't measure it? Great, give me a call, I can feel it :-) .. sCa >> Cheers, -sausskross, Cervélo Rider

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  • Damon Rinard, Cervélo Engineer

    Hi Jim, Definitely agree with you! Aiming solely at light weight doesn't automatically produce the best bike. As we often say, the right carbon in the right spot is better than simply the lowest weight. In addition to weight, other parameters affect performance too: aerodynamics (as highlighted in this article), stiffness, comfort and simplicity are others. Cheers, -Damon Rinard, Cervelo Engineer

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  • jim_c

    Hi Damon. Good article. Thanks. I've felt for quite some time that manufacturers are over-emphasizing weight (or lack there of). I feel that a bike with 200+ grams of extra carbon that has been strategically allocated to specific regions (head tube, non drive side BB, etc) could actually be a better bike. I'm not saying that making a bike as light as possible is not a good intention. What I'm saying is that through testing a multitude of frames, component, wheel, and accessory combinations the lightest setup is more often than not, NOT fastest. In short: I feel that it's not about how much carbon can a company remove from a frame...but rather it's where are they placing the carbon that matters.

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  • Damon Rinard, Cervélo Engineer

    Hi Brad, The simulation doesn't take into account differences in frame stiffness because there's no engineering basis by which to do so - no one's been able to measure significant power loss related to frame flex. Crazy, I know. We've tried measuring power lost in frame flex but do not have sensitive enough power meters (crank & hub) to find a loss, if there is one. Also, Dr. Martin's validated math model accounts for 96% of the power required to drive the bike, even without a flex term. So any power lost in frame flex must be less than 4%, and it's potentially zero. So for now, frame flex, as long as nothing's rubbing, appears to make no difference. Cheers, -Damon Rinard, Cervelo Engineer

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  • bradchristian

    I notice the simulation doesn't take into account differences in efficiency of power transfer (stiffness) between the frames. Any way to measure/account for this? I always enjoy the articles, keep them coming!

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