60 SOME MODEL BASIN INVESTIGATIONS OF THE INFLUENCE 
used and four different water-lines. The water-lines were largely the same 
for the two series. Each curve of sectional area being combined with each 
water-line resulted in 16 models. In addition the models of each series, 
which all had the same midship section, were made in halves so that each 
bow could be combined with each stern resulting in 256 possible combina- 
tions for each series. 
As will be explained later there were a number of different combinations 
made during the experiments, but not 256. Fig. 1, Plate 2, shows the 
separate curves of sectional area and water-lines used for Series No. 29 and 
Fig. 2, Plate 3, shows the same for Series No. 32. Figs. 3, 4, and 5, Plates 
4 and 5, show body plans and bow and stern profiles for selected models 
from Series No. 29, and Figs. 6, 7 and 8, Plates 5 and 6, show the same for 
three selected models from Series No. 32. The selected models for each 
series, shown in Figs. 3 to 8, Plates 4 to 6, give the extreme types of each 
series anda medium type. The actual curves of sectional area and the water- 
lines used as shown in Figs. 2 and 3, Plates 3 and 4, were calculated mathe- 
matically in each case. For present purposes it is sufficient to characterize 
them by the value of ¢ in Table I; ¢ being what we call the unit tangent at 
the extremity of the line. ‘That is to say, for water-line curves, for instance, 
if ¢=o the water-line is tangent to the center line at the extremity, and if 
t=1 the tangent at the extremity cuts the perpendicular at the center at a 
point one-half the beam out from the center line; if t=2 it cuts the per- 
pendicular at twice the half beam out, etc. 4 
For convenience and simplicity the stern profiles, as will be seen, are 
rectangular. The bow profiles are practically rectangular. ‘The curves of 
sectional area have a value at the bow or, in other words, the bow below 
water is of a simple bulbous form, as indicated. In each case half of the 
displacement was forward of the center and half of the displacement abaft 
of the center, the water-line, however, had a greater area abaft the center; 
the coefficient of the after half of the water-line of Series No. 29 being always 
five points greater than that of the forward half of the water-line. In each 
case of Series No. 32 the after water-line coefficient was ten points larger 
than the forward water-line coefficient. This was done to make the water- 
lines approach more closely average practice. 
The resistance being due partly to the surface and partly to the dis- 
turbance created, the first question to be investigated is the relative surfaces 
of the various models. 
Figs. 9 and 10, Plate 7, ‘show relative surfaces as affected by the shapes 
of sectional area and water-line coefficients. Contours for each sectional 
area curve are plotted upon water-line coefficient, the coefficient used being 
