Naked Science Forum
General Science => Question of the Week => Topic started by: thedoc on 16/01/2008 11:18:31
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My bicycling club has been having a debate. All other things being equal, who goes downhill faster? A fat bicyclist or a skinny bicyclist?
Asked by Jennifer, Chicago
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This question was answered by Dr Jos Darling, Dept Engineering, University of Bath.
That’s a tricky one. It’s been thought about for a long time really because Aristotle was the first bloke that thought about object falling due to gravity. At that time he decided that heavy object fell more quickly than light objects. Later on people like Newton decided that with gravity objects fall at the same rate. Strictly speaking that’s only true if you’re in a vacuum. On a bike you’re far from it. The big issue with the bike is the aerodynamic drag.
If there were no aerodynamic drag then the fat person or a thin person would end up accelerating down a hill at the same rate. The point is that with the fat person, assuming that they’re not incredible wide, the aerodynamic drag is going to be less significant in terms of their falling down the hill than for the thin person. Ultimately, a thin person’s going to end up going slower than a fat person. So if you’re in a race then you want to minimise that aerodynamic drag and of course the downside to being fat is that there’s always going to be a hill on the other side of the downhill, meaning that you’ve got to put a lot of work in to get up the other side. There’s always a catch!
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The problem here is the assumption that fat is the same as heavy.
It also depends on the efficiency of the cycle.
In a theoretically friction free cycle, all objects, whatever their weight, will fall at the same speed.
Where you have to overcome frictional forces (whether aerodynamic drag, or rolling resistance, or friction in the wheel hubs), then the greater weight would be better at overcoming the frictional forces.
On the other hand, greater size will increase all of the frictional effects, not least, the aerodynamic drag.
The more interesting question might be to compare a short fat cyclist to a tall skinny cyclist, both of the same weight, and the same density (the latter point is a little artificial, since actual fat will generally be lower density than muscle or bone). In that case, the tall skinny person has a higher surface area, so if sitting upright would have higher drag, but if lying prone could reduce his aerodynamic drag to a lower level than the short fat guy.
The aerodynamic issues can also be offset by putting fairing on the bicycle, in which case the major difference in frictional effects would be in slightly greater rolling resistance to carry the heavier (not necessarily equating to the fatter) cyclist. Whether the rolling resistance increases more than the increase in mass would I suspect depend on the gradient.
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The maximum speed freewheeling downhill is limited by the air resistance.
Air resistance is generally considered to go up in proportion to the area intercepted which is the square of the linear dimensions of an object whereas mass goes up as the cube of the linear dimensions so all things being equal heavy cyclists should go downhill faster freewheeling but then if the cyclists were pedalling and had high enough gears it could depend on the extra force that the cyclist could put in. Now without toeclips this would also depend on the weight of the cyclist but with toeclips where a cyclist can use his own energy to add more to the upstroke a fit thin cyclist might win because air resistance also goes up as the square of the speed.
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Now without toeclips this would also depend on the weight of the cyclist
I'm not sure that is quite true, why not change gear and pedal faster?
It is true that light cyclists are generally better climbers so you would suspect the reverse is true.
In the Tour de France, in years gone by, some light cyclists used to collect a bottle filled with the lead before they began a long decent and then threw it away when they reached the bottom. That trick doesn't seeme to be used anymore...probably due to the high price of lead.
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Now without toeclips this would also depend on the weight of the cyclist
I'm not sure that is quite true, why not change gear and pedal faster?
It is true that light cyclists are generally better climbers so you would suspect the reverse is true.
In the Tour de France, in years gone by, some light cyclists used to collect a bottle filled with the lead before they began a long decent and then threw it away when they reached the bottom. That trick doesn't seeme to be used anymore...probably due to the high price of lead.
Lead is not expensive at all and, however, you could give it to a friend at the end of the descent and reuse it. I think the problem could be it's not allowed (even if I don't know the rules).
However this situation is different from that of the OP because with lead it's obvious that you have more weight with the same air friction; with a fatter cyclist this is not clear at all; I would tend to agree with Soul Surfer however, so I would say a fat man goes down faster (everything else constant) than a skinny man.
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Air resistance is generally considered to go up in proportion to the area intercepted which is the square of the linear dimensions of an object whereas mass goes up as the cube of the linear dimensions so all things being equal heavy cyclists should go downhill faster freewheeling but then if the cyclists were pedalling and had high enough gears it could depend on the extra force that the cyclist could put in.
The main problem with this is that fat has a lower density than muscle, so someone who is fat (as in containing lots of fat, rather than simply of large girth) would not be proportionately heavier. Someone who has a lot of muscular bulk would generally be more consistent with your argument.
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So the skinny but more muscular person could be about the same weight as the fat person, in which case the greater drag on the latter should make the difference.....
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In a practical test while out cycling with my daughter we stopped on a slope of about 25 degrees then released our brakes at the same time and over a distance of about 200 metres without pedaling I was about 20 metres ahead, I am 12 stone my daughter is 9 stone. Although we are not fat I think that proves that weight wins.
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But were your bikes the same?
I used to annoy my kids by freewheeling past them on long downhill runs because my tyres were smoother and pumped up higher.
They could go better than me on muddy tracks, though.
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So the skinny but more muscular person could be about the same weight as the fat person, in which case the greater drag on the latter should make the difference.....
I don't think the difference in density is enough for making the skinny win.
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Really? Shame- go skinnies go!
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i have an addition to this - me and a friend used to go rollerblading down this hill near my house, we both had the same rollerblade (Bauer FX1's incase you're interested) and both used to use pledge on them to keep the friction to a minimum...starting at the top we would just freefall down the hill, now, she was around 11 stone, i was around 6and a half, and every time she would hit the bottom first (unless i cheated and pushed myself forward when she wasnt looking)
i know its a little different than a bike but....i wonder if swapping our skates would have made a difference. hers were 2 shoe sizes bigger...who knows.
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i have an addition to this - me and a friend used to go rollerblading down this hill near my house, we both had the same rollerblade (Bauer FX1's incase you're interested) and both used to use pledge on them to keep the friction to a minimum...starting at the top we would just freefall down the hill, now, she was around 11 stone, i was around 6and a half, and every time she would hit the bottom first (unless i cheated and pushed myself forward when she wasnt looking)
i know its a little different than a bike but....i wonder if swapping our skates would have made a difference. hers were 2 shoe sizes bigger...who knows.
Interesting. You are approximately the same height?
(P.S. what kind of weight unit is "stone"?)
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Interesting. You are approximately the same height?
(P.S. what kind of weight unit is "stone"?)
sorry, i should have used more international units..
one inch or so of a difference in height, not much though,
one stone is 14 pounds, or 6.35 kilograms (i.e: 11 stone=70 kilograms, 6.5stone=41.3kg)
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In 2002 I cycled through Tasmania, and this was the subject of many discussions...
I don't think we came to a conclusion there either :)
In a practical test while out cycling with my daughter we stopped on a slope of about 25 degrees then released our brakes at the same time and over a distance of about 200 metres without pedaling I was about 20 metres ahead, I am 12 stone my daughter is 9 stone. Although we are not fat I think that proves that weight wins.
this was more probable.
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Generally Speaking in the ideal world mass does not have any bearing only gravity and the angle of the slope... in the real world there are other factors as well as gravity....
As pointed out, air resistance and friction (from bike parts) are factors... Being a cyclist and a bit, OK more heavier than other cyclists [;D] I have to keep hitting the breaks when free wheeling down hill to stay next to riders next to me, most of them riding better bikes than me.
The main factor, assuming that the bikes are identical is momentum as in nature not wanting to change state. The bigger the mass (OK the heavier the rider) momentum is higher. Air resistance and friction is slowing cyclist down, momentum is keeping the speed. The bigger the difference between momentum and resistance the slower a bike will loose its speed. Hence the difference for a heavier rider is bigger than the difference for a lighter rider so the lighter rider will slow down more than the heavier one.
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As a regular cyclist, I can tell you that the tyre-pressure (rolling resistance) has a significant effect on the speed at which I can cycle (higher pressure = faster). Wind resistance is also a huge factor, with cycling being notably harder in a winter jacket and baggy trousers than in summer shorts and T-shirt. Cycling into or away from the wind makes a big difference.
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I have a small amount of experimental evidence to add to this discussion. I am a 60-pounds overweight cyclist. When I ride with others of similar fitness and experience, the lighter people pass me easily on the uphills and I zoom past them on the downhills. The only way I can keep up in a fit group of riders is to pass others on the downhills, then they catch up on the uphills etc.
The wind resistance component mentioned is interesting ie. the idea that a fat cyclist may have more wind resistance. The mitigating factor here is that many fat cyclists (I'm one of them!) carry their weight in their bellies which jut out in front and don't necessarily provide that much wind resistance...I may be heavy, but I am only a little bit wider than other cyclists. Also, when going downhill, cyclists often drop down onto the lowest run of their handlebars, called the drops, significantly reducing their wind resistance.
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If the cyclist is heavy enough friction within the bike can increase (pressing down on the tires flattens them out and increases drag on the ground)
I think it is fair to say that there are enough variables, that several reasonable scenarios could be devised in which either fat or skinny could be the clear victor, depending on which variable were set as what.
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If you have a short fat cyclist and tall thin one of the same weight, there will be no difference from the tyres as they have the same weight pressing on them (ignoring aerodynamic lift if the shapes of the riders generate different amounts - you'd have to select ones with the same component of lift). The tall thin cyclist should win out every time (unless you add other aspects of shaping to slow the thin one down).
In normal situations out on the road, of course, the fat riders are heavier than the thin ones, and they are faster downhill. On a CTC run, I was once pedalling flat out down a steep hill on my road racing bike and a freewheeling woman overtook me. (She wasn't actually fat, but I was at that time close to the minimum healthy weight for a racing cyclist of average height who specialised in climbing, so she didn't have to be fat to be faster.)
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Are there any mathematical calculations that could be used to prove what you have stated in your article?
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I am an engineer. Sosjay is correct. Air friction will not slow the heavier ride as rapidly as the light rider. Both have the same acceleration due to gravity, g, but the more massive person has a greater force F = mass X g. This greater force is significant in overcoming frictional resistance (counter force) from air. Aerodynamics can help reduce friction but mass will always trump aerodynamics on down hill slopes where air resistance persists (notwithstanding terminal velocity etc.).