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## Shell Hydrodynamics

Computational Models
The utility of a reasonably good computational model of any system is not that it can produce perfect absolute results but that it can produce good relative results. In no other way can changes in a variable of interest be evaluated while all others are held constant. With ROWING I would be unwilling to predict individual race results for any collection of boats and crews. But, because ROWING considers every significant variable, I have confidence in ROWING's ability to predict an advantage for a difference between one mode of rowing and another.

Hull Form
The Vespoli "B" forms the basis for the shell hull (for Eights as defined in ROWING) for which Scragg defines the waterline length (Lw) and beam (Bw), draft (D), weight displacement and wetted surface area (S) along with other values of the same parameters for some other hulls considered in his studies. Basing volume displacement (V) on fresh water at 60 F I estimate a block coefficient, Cb = V /(Lw Bw D), and a prismatic coefficient, Cp = S /(Lw (2D +Bw)) for application to convert the envelope of Lw, Bw, and D dimensions to estimates for wetted area and displacement volume for other shells with but modest deviations in form from Scragg. ROWING's factor values for his various hulls lead to values varying only by about 0.5 percent or less from his values giving confidence that ROWING fairly models hull shapes representative of the Vespoli "B" as wetted length and displacement vary by small amounts.

These two coefficients permit reasonable extrapolation of the effect on shell resistance of variation in displacement and wetted surface with variation in boat, coxswain, and rower weight.

I have been unable to find block and prismatic coefficients for hulls other than the Eights. A request for information from many boat makers has produced no result whatever. ROWING's current assumption is that the smaller shells have forms geometrically sufficiently similar to the Eights to have very similar block and prismatic coefficients.

Shell Frictional Resistance, Water
For a calculated volume displacement (V, at density (d) for water at 60 F) and a defined saxboard beam (Bs) ROWING finds the wetted length (Lw) (and estimates length overall), the wetted beam (Bw) (based on a semi-circular hull cross section centered in the saxboard plane), the draft (D), and the wetted surface area (S).

Using the instantaneous shell speed ROWING calculates an instantaneous Lw Reynolds' number and finds the skin friction coefficient, Cf, for turbulent flow (Re > 1,000,000) according to the ITTC-63 line. ROWING then adds an allowance for wave resistance (Cf *0.0002), and an allowance for form resistance based on an assumed 1/2 bow angle. ROWING then converts Cf to a resistance coefficient (Kw = Cf d S/2g). Unfortunately values for Cb and Cp are not generally available for hulls in general and so:

Alternatively ROWING will accept a "hard" value of Kw, independent of shell speed or displacement. I have published values of Kw only for fully seated eights. It would be relatively easy to estimate Kw = R/V^2 by weighing the towing line resistance (R) of other seated shells, at the same time knowing V.

ROWING does not consider the effects of pitch and water depth.

Shell Frictional Resistance, Air
Work on the frictional resistance of seated shells to the flow of air has not come to my attention as yet and I can only guess at values to use in ROWING. I estimate an air drag factor, Ka = Ra /V^2, as roughly one tenth of the water resistance allowing for boat, rowers, oars, riggers, etc. in air. In the future seated and sea-anchored shells should undergo the simple weighing of their longitudinal resistance in various airs as I can find no published data in this regard.

Shell Speed
ROWING produces a detailed table from which accurately to plot the speed and acceleration vs. time curves--closely resembling published curves produced by data from instrumented shells. Figure 4-1 illustrates a shell speed curve for a single closely matching that of an instrumented boat (with an added curve for the system center of mass).