Thanks again, Bert, for jumping in and explaining a lot of the physics. I've always marveled and wondered about the flying patterns of birds and it's interesting to make the connection between those principles and the ones you are exploring with cycling drag. Keep up the good work!
I am an absolute fan of CFD whenever that technology can be applied. There seem to be countless areas where answers to perplexing problems can be solved by its proper application. I had absolutely no idea for the reasons behind the "V" formation. I find this to be fascinating and Bert, I really appreciate you indicating the reason(s). This article is one more reason every practicing engineer needs to read Design News on a daily basis. Great work Ann.
Back in 1970 and 1971 we did some experiments with drafting and also with touching bike wheels as a result of being close. It is possible to survive a wheel "touch" even with a few inches of deflection, but probably not from the minimum drag stance that these guys ride in. Of course it is also mandatory that both riders be concentrating on riding and holding the bike in an upright position, two things that are probably quite foriegn to that racing crowd.
Hi Rob. The lead bird is indeed the one doing most of the hard work. All others behind him take advantage of the wingtip vortex. This wingtip vortex is very effective, and every duck except the first makes sure to fly in the upwash flow that is caused by this wingtip vortex of the duck in front of it. It is (much) more effective than the effect of just flying straight behind each other. The V-shape can reduce drag by up to 60 to 70%, which is much more than the 30% drag reduction effect that cyclists have on each other. For a more streamlined creature such as a bird, just flying behind each other will lead to even less than 30% reduction in drag. That's why birds of the same species will almost never fly straight behind each other. The V-shape and the very large drag reduction is crucial for birds to be able to perform their very long migration routes. They also alternate in cycles. Interestingly, they are even known to help weaker members of their group by not forcing them to take the lead. However, the lead bird would indeed have more advantage if the second bird would fly straight behind him/her - because of the same overpressure-underpressure effect as with cyclists. But overall, the group would not benefit from this. Mathematical models have been developed to assess the optimum flight configurations for birds, which are surprisingly similar to their actual flight behavior. A similar and very nice exercise for cycling races was done by Tim Olds, in 1982, who has actually provided mathematical models for cyclists to be successful (or not) in a break-away. The reference is:
Olds, T., 1998. The mathematics of breaking away and chasing in cycling. Eur. J. Appl. Physiology 77: 492-497.
This is all correct, except for the comparison with the ducks. Birds fly in V-shape, and not straight behind each other, even if there is no wind, because they want to benefit from the tip vortex shed from the wing of the one in front of them. It's a different mechanism than the overpressure-underpressure effect with drafting cyclists (or cars). But indeed for cyclists, the effect is surely larger for the fourth rider than for the second one, as indeed the wake widens.
This slug thing is most interesting. So a bottle can't catch up to the slug. There must be some air bouncing backwark as the weight of the slug increases preventing a trailing bottle from catching up. I'd like to hear more explanations and how it might relate to cycling.
Practicality from engineer and cyclist... Cycling teams have invested in drag reduction studies, foil shaped tubing, internal cabling, optimized rider positions, rider skin suits, aero helmets (even with golf ball dimples), for quite some time now. Any single cyclist drag reduction is a benefit to all in the group. NASCAR is one of the more prominent displays of aero effects (bricks at very high speed) and it is well known that a lead car needs a second car to hook up behind him to let them both go faster. It still applies at slower speeds but to much less effect. When you're drafting on a bike you can definitely feel that 30% benefit, and being the fourth rider is noticeably easier than even being the second rider. In the real world you're also subject to different wind directions, hence cyclists angled into an echelon (migrating ducks). For a cycling team of nine or less they're best off single file, but with a larger peloton group there's even more benefit as the group widens out. The danger in all this is if cyclists get too close and touch wheels – the guy with his front wheel touched usually goes down – hence the carnage we're seeing in this year's Tour de France.
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