87 8787 87792010-03-11 18:21:53 / rev 41072188e694+4.4.2 SwimmingA previous section’s analysis of cycling helps predict the world-recordspeed for swimming.vmax∼PathleteρA1/3.To evaluate the maximum speed for swimming, one could put in a newρ and A directly into that formula. However, that method replicates thework of multiplying, dividing, and cube-rooting the various values.Instead it is instructive to scale the numerical result for cycling by look-ing at how the maximum speed depends on the parameters of the sit-uation. In other words, I’ll use the formula for vmaxto work out theratio vswimmer/vcyclist, and then use that ratio along with vcyclistto work outvswimmer.The speed vmaxisvmax∼PathleteρA1/3.So the ratio of swimming and cycling speeds isvswimmervcyclist∼PswimmerPcyclist1/3×ρswimmerρcyclist−1/3×AswimmerAcyclist−1/3.Estimate each factor in turn. The first factor accounts for the relative ath-letic prowess of swimmers and cyclists. Let’s assume that they generateequal amounts of power; then the first factor is unity. The second factoraccounts for the differing density of the mediums in which each athletemoves. Roughly, water is 1000 times denser than air. So the second factorcontributes a factor of 0.1 to the speed ratio. If the only factors were thefirst two, then the swimming world record would be about 1 m s−1.Let’s compare with reality. The actual world record for a 1500-m freestyle(in a 50-m pool) is 14m34.56s set in July 2001 by Grant Hackett. Thatspeed is 1.713 m s−1, significantly higher than the prediction of 1 m s−1.The third factor comes to the rescue by accounting for the relative profileof a cyclist and a swimmer. A swimmer and a cyclist probably have thesame width, but the swimmer’s height (depth in the water) is perhaps87 8787 87792010-03-11 18:21:53 / rev 41072188e694+4.4.2 SwimmingA previous section’s analysis of cycling helps predict the world-recordspeed for swimming.vmax∼PathleteρA1/3.To evaluate the maximum speed for swimming, one could put in a newρ and A directly into that formula. However, that method replicates thework of multiplying, dividing, and cube-rooting the various values.Instead it is instructive to scale the numerical result for cycling by look-ing at how the maximum speed depends on the parameters of the sit-uation. In other words, I’ll use the formula for vmaxto work out theratio vswimmer/vcyclist, and then use that ratio along with vcyclistto work outvswimmer.The speed vmaxisvmax∼PathleteρA1/3.So the ratio of swimming and cycling speeds isvswimmervcyclist∼PswimmerPcyclist1/3×ρswimmerρcyclist−1/3×AswimmerAcyclist−1/3.Estimate each factor in turn. The first factor accounts for the relative ath-letic prowess of swimmers and cyclists. Let’s assume that they generateequal amounts of power; then the first factor is unity. The second factoraccounts for the differing density of the mediums in which each athletemoves. Roughly, water is 1000 times denser than air. So the second factorcontributes a factor of 0.1 to the speed ratio. If the only factors were thefirst two, then the swimming world record would be about 1 m s−1.Let’s compare with reality. The actual world record for a 1500-m freestyle(in a 50-m pool) is 14m34.56s set in July 2001 by Grant Hackett. Thatspeed is 1.713 m s−1, significantly higher than the prediction of 1 m s−1.The third factor comes to the rescue by accounting for the relative profileof a cyclist and a swimmer. A swimmer and a cyclist probably have thesame width, but the swimmer’s height (depth in the water) is perhapsGlobal comments 1Global commentsWhat is A in this section? Not sure what this Area is in reference too, maybe i’ll referback to the previous reading.It’s the cross-sectional area. I should add a subscript to indicate that.How did you make that conversion?I am really enjoying this section. It’s really cool to just use a ratio with something that isknown to find something that is not.87 8787 87792010-03-11 18:21:53 / rev 41072188e694+4.4.2 SwimmingA previous section’s analysis of cycling helps predict the world-recordspeed for swimming.vmax∼PathleteρA1/3.To evaluate the maximum speed for swimming, one could put in a newρ and A directly into that formula. However, that method replicates thework of multiplying, dividing, and cube-rooting the various values.Instead it is instructive to scale the numerical result for cycling by look-ing at how the maximum speed depends on the parameters of the sit-uation. In other words, I’ll use the formula for vmaxto work out theratio vswimmer/vcyclist, and then use that ratio along with vcyclistto work outvswimmer.The speed vmaxisvmax∼PathleteρA1/3.So the ratio of swimming and cycling speeds isvswimmervcyclist∼PswimmerPcyclist1/3×ρswimmerρcyclist−1/3×AswimmerAcyclist−1/3.Estimate each factor in turn. The first factor accounts for the relative ath-letic prowess of swimmers and cyclists. Let’s assume that they generateequal amounts of power; then the first factor is unity. The second factoraccounts for the differing density of the mediums in which each athletemoves. Roughly, water is 1000 times denser than air. So the second factorcontributes a factor of 0.1 to the speed ratio. If the only factors were thefirst two, then the swimming world record would be about 1 m s−1.Let’s compare with reality. The actual world record for a 1500-m freestyle(in a 50-m pool) is 14m34.56s set in July 2001 by Grant Hackett. Thatspeed is 1.713 m s−1, significantly higher than the prediction of 1 m s−1.The third factor comes to the rescue by accounting for the relative profileof a cyclist and a swimmer. A swimmer and a cyclist probably have thesame width, but the swimmer’s height (depth in the water) is perhaps87 8787 87792010-03-11 18:21:53 / rev 41072188e694+4.4.2 SwimmingA previous section’s analysis of cycling helps predict the world-recordspeed for swimming.vmax∼PathleteρA1/3.To evaluate the maximum speed for swimming, one could put in a newρ and A directly into that formula. However, that method replicates thework of multiplying, dividing, and cube-rooting the various values.Instead it is instructive to scale the numerical result for cycling by look-ing at how the maximum speed depends on the parameters of the sit-uation. In other words, I’ll use the formula for vmaxto work out theratio