Racing shells are very narrow, causing the water drag to be predominantly frictional. A typical eight-rower (plus coxswain) shell has a length at the waterline of 16.9 m and a wetted area of 9.41 m². A competitive speed for a men's eight in international competition is 6 m/s. You are asked to estimate the power each rower must generate to maintain that speed, and to check your estimate by comparing it with the power well-conditioned athletes have been found to generate.

(a) Confirm that, if the water boundary layer is similar to that on a flat plate, it will be very thin compared with the hull dimensions. This supports the idea of “unwrapping” the wetted surface into an equivalent flat plate.

(b) Estimate the water drag. Assume that the results for flat plates are applicable, based on the gradual taper of the hull and the thinness of the boundary layer.

(c) Estimate the air drag. You may assume that the lead rower experiences most of it, the others “drafting” behind him. A rower's sitting height and width are roughly 1.0 and 0.5 m, respectively. Based on results for other bluff objects (spheres, disks, cylinders), what is a reasonable value for C_D?

(d) Use the total drag to estimate the power (in W) each rower must provide. Exercise physiologists have found that elite oarsmen can average 390 W over 6 min (Hagerman, 1984), the approximate time for a 2000 m race. However, not all of the energy expended propels the boat. There are losses associated with the motion of the oar, the rower's body, and the sliding seat in the shell. The mechanical efficiency, defined as the propulsion power relative to the rower's total output, is thought to be about 60%. In light of that, is your power estimate reasonable?