PEP hulls have Parabolic waterlines, Elliptical cross-sections and Parabolic keellines. PER hulls are similar but have Rectangular keellines. The PP variant is clearly superior with respect to total resistance. This is as expected. The PP ship drafts are deeper than the hulls of the corresponding RR ships.
W increases rapidly.
In other words, the optimum trimarans and catamarans are essentially separate, infinitely-spaced ships. The effect of keelline shape on the optimal overall length Figure 7 shows the overall lengths of the ships.