How many cyclists riding in tandem would be able to reach 100 mi/hr if one rider can reach 35 mi/hr
The velocity of racing shells varies as n^(1/9)
v1/v2 = (n1/n2)^(1/9)
Assume v2 is the speed of the single rower racer, then
v1=v2*(n1)^(1/9) = 1.26 v1. The eight man shell goes 26% faster
The time on course should be 26% shorter or time=7min/1.26 = 5.6 min.
For a 16 man shell, the speed should be v2(16)^(1/9) = 1.36 so the time on course, t = 7/1.36 = 5.1 minutes.
You get faster rather slowly with the number of rowers. The above analysis is born out by the speeds achieved by 1 and 8 man crews.
To go twice as fast, we would need lots of rowers.
v1=2*v2
so 2 = (n1)^(1/9) and n1 = 2^9 = 512. You would have to have 512
rowers with a similarly built shell to achieve twice the speed of a
single rower! No experiment has been done like this. Although the
Triems of ancient times used lots of rowers, the boats were of a much
heavier, clumsier, less fast make and so did not achieve such high speeds.
Better you should get a better power to weight ratio .... like internal
combustion engines!
For this analysis, I'm assuming that the cyclists are riding on a big bike one behind the other so that the air resistance is kept to a minimum. However, the air resistance probably does not scale so nicely as the resistance of a shell. The frontal area stays the same but the air going by the bodies increases with the no. of cyclists. This calculation is a rougher approximation than it is for the shell.
For the cyclists to go 100 mph in a similar fashion , this would be about 3X faster so it would take n1 = 3^9 = 19,683 cyclists riding in a similar bike... if you can imagine this. The obstacle is putting in enough power to overcome the power used up by air resistance. In fact, a cyclist following an air shield behind a very powerful and fast car has obtained >100mi/hr in a bike.
The time is about 0.2 seconds. This is determined mostly by the speed of the nerve impulse that travels from the brain to the forearm.
What is the highest speed obtained by a part of the human body in a routine sports motion? What is this speed? About how much kinetic energy does the body part have in this motion? What power was required to make this go so fast?
The highest speeds obtained by the hand is probably the speed of baseball pitchers. Their hands at the release must be the same speed as the ball which is in the vicinity of 90 mi/hr. Other speeds like a sprinters foot is much slower like 23 mi/hr.
For a 90mi/hr pitch, the energy given to the hand is the kinetic energy of the hand which is 1/2 mv^2 = 1/2 * .7 * (39)^2 = 536J
To determine the power, we must find the time of the action. From the study of videos of pitchers, we see that most of the action takes place in one click of the video [in stop action] which is 1/30 sec. this means that the power is Energy/time = 536/(1/30) = 16,000 watts!!!