Friday, February 11, 2011

Too Much Booty in the Pants: A Scientific Examination of Its Value in Cycling

The most coveted wheel in the peleton: Stign Vandenbergh

Several riders in the local peleton are universally beloved for their large asses. This is not necessarily homoerotic or 40 ounce bounce-type love; this love is directed toward the supposed larger pocket of rarefied post-ass air they offer. I'd say a good 30% of conversations after races involve rating and debating the drafts offered by various asses. Of course, this conversation is much more common in the lower ranks, since large asses are rare in the higher categories with a few notable exceptions such as Johan Vansummeren, Stijn Vandenbergh and, a few years ago, Magnus Backstedt.






Boonen receives an unfair advantage drafting from Johan Vansummeren

I've always felt as if larger riders offered a significantly different draft, but I've never seen a study on exactly how many watts savings riding behind a six and half foot 250 pound rider gets you compared to, say, a five and a half foot 135 pounder. When Maggie Backstedt, at around 6'8", launched a break at Clarendon Cup several years ago, I couldn't help but feel he gave more draft than he got.

I brake for massive booty: Maggie Backstedt
Unfortunately, no study yet exists comparing the draft of different size asses. Ideally, I'd find test subjects and do the data collection myself with my own power meter. Unfortunately, this is not an option, since I don't have the nerve to put up an "ISO Wide Loads for test study" on the MABRA forum. Also, the government is presently unwilling to fund such a study.

Never fear. I believe through sheer brain power and confusing numbers games, I have come close to answering the question of how much bounce you can get per ounce. I will use data from two related studies to extrapolate (a big word meaning "to lie about") an exact answer to our question of whether what's in the trunk is just junk, or if it's actually useful.

Study 1: Watts Required to Sustain 20 mph behind (a) Car and (b) another Cyclist
The first study I charted the power output of a cyclist at 20 mph in four states--upright, on the drops, behind another cyclist, and behind a car.


Upright: 260 watts
Aero: 215
Drafting a cyclist: 180
Drafting a car: 120

The bigger the draft, the less power need to go 20 mph. This means that drafting behind a bigger thing is better than drafting behind a smaller thing. Uh, we knew this already.

What we want to know is when that size increase starts to really matter.

This requires that we turn away from booty, and focus on the frontal area, since that's what determines the size of the draft. We'll need to figure out the frontal surface area of a car and various-sized riders. From there, given our data, we can answer the question of whether big booty is as wonderful to ride as we make it out to be.

To find an estimate for frontal surface area (FSA) of different-sized riders, we turn to a second study.

Study 2: Frontal Surface Area of different sized ridersThis study gives us an idea of surface area of cyclists. Cyclists at 5'8" have a FSA of .379 meters. Cyclists around 5'10" have a FSA of .402.

This gives us a rough idea of the difference in surface area between riders: for every 2 inches of height, there is a .03 difference in FSA.

So, with a bicycle's FSA added in, the FSA of a 5'6" rider is .449 meters; a 6'6" rider comes in at .622 square meters. Compare that to The FSA of a car (a Mazda sedan, in this example) is about 7.763 meters.

We calculate the coefficient:
Difference in watts / difference in FSA = coefficient
(140-80) / (7.763-.449) = 8.203

This means that, assuming a constant coefficient, for every 1 meter increase in FSA in the object to be drafted, the rider gets an 8-watt savings.

We end up with a chart like this:



Drafting behind a normal-sized rider at 20 mph saves you 80 watts; drafting behind a 6'6" rider saves you 81.48 watts.

This is crude and assumes a lot of things remain constant.

Still, this suggests that drafting behind a larger person does save a small amount of energy. Over an hour or two, this adds up.

Also, at higher speeds, a big booty will offer even greater savings in power output. My guess (commoner for "extrapolation") is that at 30 mph, drafting behind a large person compared to a smaller one is probably at least a 20-30 watt advantage.

In summary, our data suggests that the condition commonly referred to as Too Much Booty in the Pants offers significant advantage to those who pursue it. For drafting purposes, naturally.

6 comments:

Marten said...

Although this assumes a linear relationship between height and FSA. FSA should be proportional to to the square of a cyclists height. A 10% taller person would also have a 10% wider waist (scaling up a cyclist proportionally).

The linear assumption over estimates the power savings for cyclists of different heights.

The functional dependence of different physiological parameters is interesting, check out Bicycling Science by Gordon Wilson for some interesting analysis. For example, bigger riders are at a physiological disadvantage for aerobic power/kg body mass, because volume (therefore mass) scales as height cubed, and lung surface area scales as height squared.

It is the same sort of size/surface area dependence that tells biological cells when to divide. The membranes get too small compared to the volume they enclose.

Good stuff, keep it up,
Marten

lifein360 said...

Can I relate to this. As a speedskater, I am often drafting men and women who are built like tiny birds. All arms and legs. No mass. Then there is me. Rugby player in spandex. I have to work twice as hard whether getting a draft or now. But those behind me are loving it! Skinny bastards

Anonymous said...

I got loads of (no pun intended) data of a big ass rider, as I raced some NRC at 200lbs last year...if you really want #s

Nick said...

between this and marten's comment, apparently i am screwed either way.

magnus, the viking that i aspire to be, is only 6'4", per wikipedia.

Calvini said...

@Marten: I do assume linearity, but only in the interval in size increase of rider-to-car. The ratio of watts saved / size of object drafting is not linear on the whole, since drafting behind a semi is probably only slightly better than drafting behind a Hummer. I'm simply assuming it's roughly linear for objects larger than cyclists and smaller than cars.

Also, I'm not convinced that being tall is a disadvantage. First, taller riders should put out more watts, meaning that while their w/kg may be lower than a short rider, their wattage will be more. This means that they'll be better as TT guys and on the flats. I also think taller riders can have a proportionally smaller frontal surface area (FSA) than shorter riders. If you compare the FSA of Gustav Larson, a tall TT specialist, to Levi Leipheimer (a short TT specialist), it's probably not that much different.

This is bourne out in the professiaonl ranks--tall riders like Boonen, Greg Rast, and Taylor Phinney have massive engines but struggle on hills. The kind of racing we do in MABRA, in fact, is perfect for big, strong, and tall riders.

Marten said...

Absolutely, I didn't mean to imply that bigger riders were at a disadvantage, only when the road is going up (and watts/kg trumps total watts). Most pure climbers are pretty small.

Personally, I'd trade a few W/kg for a few more W. At 135, I have a weak TT in my category (4), but can climb with the best around here. But as you mentioned, most races around here just don't feature big climbs.

Nick is obviously doing very well, it would take a pretty big mountain to give me any advantage!