SINGLE SCULLS

In this example, we have used a popular Empacher single hull which is used by many first class rowers. This hull has a design displacement volume of D=0.1035 m³; the underwater portion has length L=7.925 m, draft T=0.101 m, and beam B=0.274 m. Offsets for this hull were digitised from lines drawings supplied by Graeme King of King Boatworks, Putney, Vermont. The offsets of the hull were then scaled to nominal displacements for the various classes. Obviously this is not entirely satisfactory but it is not practical to collect the offsets of hulls used by the actual rowers.

The following table shows the dimensions of the underwater portion of the hulls used for each class. Abbreviations for the various classes are: LW for lightweight women, HW for heavyweight women; LM and HM are the lightweight and heavyweight men's classes, respectively. For all cases, we have assumed that the hull and other deadweight weighs m_B=20 kg. Nominal average rowers' weights are m₁=57 kgs for LW, m₁=75 kg for HW, m₁=72 kgs for LM, and m₁=95 kg for HM.

The following table shows the sectional times for the various classes obtained by averaging results from three recent world championship events, namely, Aiguebelette 1997; Lucerne 1997, and Paris 1997. (Source: Rowers Resource...) Note that some slower 'outliers' were omitted prior to averaging due to the possibility that they were wind-affected. Also shown are the sectional times estimated using the present mathematical model and the peak force (to the nearest Newton) required to achieve the same finishing time as the (averaged) race results.

The peak forces required to achieve world class times seem in reasonable accord with published results. Millward (1987) estimated that a lightweight male would need to exert a peak force of 308 N to finish the 2000 metre race in 440.5 seconds at a constant stroke rate of r=30. It is difficult to compare this with our result for lightweight males, as our sculler is slightly heavier, and presumably more powerful than Millward's 70 kg sculler. Our lighweight males finish the race roughly 20 seconds faster than Millward's and so it is not surprising that at 332N, our peak force is greater than Millward's estimate of 308N. On the other hand, the Heavyweight Women's class time of 445 seconds is closer to Millward's (male) sculler's time of 440.5 seconds as is the required peak force of 305 N.

The table also shows that the time for the initial 500 metres of the race is also predicted reasonably well by the mathematical model. The graph below shows the predicted mean boat speed for the first 100 seconds.

The curves reach their respective maxima at about 10 to 12 seconds, with the larger and more powerful (male) rowers reaching maximum speed earlier than the lighter rowers. This is in agreement with observations, however as we have not found published times for the first few hundred metres of top class events, we are not in a position to comment on whether the maximum speeds attained are reasonable or not.

The following graph shows the mean power during the first 100 seconds.

The 'steady-state' average power for the various classes seems close to power outputs for other sports. Jackson (1995) estimated an average power requirement of 440 Watts for (81 kg) male rowers in the 1000 metre K1, K2 and K4 Olympic kayak classes. For (65 kg) women he estimated that 300 Watts on average would be required.

The maxima of the the power curves are more difficult to interpret as we know of no published data for comparisons. Although the values seem to be far in excess of the power that could be sustained by top class athletes for an entire 2000 metre race, the duration of the peak power requirement is quite short. Charlton et al. (1987) reproduce a graph from Whitt and Wilson (1982) that shows long duration human power output. For first class (presumably male) athletes, the power available is approximately 400 Watts for 7 minutes. For short durations of around 30 seconds, about 800 Watts is available. Whitt and Wilson's graph is quite small and the scale is such that accurate interpolations are not possible, however our results seem reasonable.

The following graph shows the mean power during a stroke as a function of mean boatspeed.

For each of the four classes, power increases smoothly to a maximum, then decreases to the final 'steady-state' value. For the higher speeds, power is not a unique function of boatspeed. This is, of course, because of the higher stroke rates employed at the start of the race.

The variation of speed during one 'steady-state' rowing stoke is shown in the following graph.

The fluctuation of the boat velocity can greatly affect the work performed during a rowing stroke and is therefore a very important factor in determining performance. In general, a small difference beween the maximum and minimum speeds is indicative of a efficient rowing technique. Dal Monte and Komor (1989) reported that the difference between the maximum and minimum speeds is about 2.4 ms^-1 for single sculls. Our results show differences of 2.03, 2.33, 2.31 and 2.63 ms^-1 for the LW, HW, LM, and HM classes, respectively.