ECONOMICAL CARGO SHIPS—SOME MODEL EXPERIMENTS. 47 
of midship section within the range adopted in cargo ships does not make any 
material difference in the resistance of the ship, and, as it was necessary to stand- 
ardize draught as well as form, the following method was employed. A slight modi- 
fication of the block model, generally known as Dr. Kirk’s analysis, was adopted 
wherein the breadth of the model was maintained equal to the breadth of the ship, 
and modification was made in the draught, this being such that the cross-sectional 
area of the model is the same as the midship section of the ship. This gives us an 
analysis draught equal to the product of draught of the vessel and coefficient of 
midship sectional area, and the angles of entrance and run are such that the plan 
of the block model contains exactly the same area as a curve of sectional areas of 
the ship. The fraction of the length of the vessel which would consist of entrance 
is equal to I minus prismatic coefficient of fore body. ‘The fraction of the length of 
the vessel represented by parallel middle body is equal to twice the prismatic 
coefficient of the whole ship minus 1, and the fraction of length of run is, of course, 
equal to I minus prismatic coefficient of after body. This block model, which is 
bounded by straight lines and contains a volume equal to the displacement of the 
ship, indicates the mean angle of entrance and mean angle of run of the vessel, as 
well as the analysis length of entrance and run; examples are shown on Figs. 5, 6, 
7 and 9g, Plates 19 to 22. 
In order to distinguish this analysis entrance from the ordinary length of en- 
trance, the Greek letter e has been used and for run the letter p has been adopted, 
the parallel middle body being represented by z and the ratio of entrance to run 
has been expressed as e/p throughout the paper. The analysis draught, when di- 
vided by breadth, gives the analysis draught ratio 6. (See Appendix I.) 
SERIES II07. 
Model 1107 is that of an ordinary cargo ship with plumb stem and counter 
stern raised well above the load waterline,and the length for displacement was 
taken as 98 per cent of the length between perpendiculars. The original model 
designated A had a curve of areas as shown in the lower part of Figs. 5 and 6, 
Plates 19 and 20, and was tested at Washington and Ann Arbor. The Ann Arbor 
model was then fined in two steps as shown, the resulting resistance curves being 
also shown. Cross curves of C values at different speeds are given in the left-hand 
end of each diagram plotted on ¢/p ratios, and a zero line, which required a certain 
amount of fairing, has been shown indicating the actual difference in C value 
for model A as tested and extended at Washington and at Ann Arbor. In Fig. 6 
the two modifications designated C and CX are identical with B and BX in Fig. 5 
as regards prismatic coefficient, but are straight in form and consequently easier 
at the after shoulder than the B curves. It will be noticed that the straight form 
generally produces the lower resistances but has not eliminated a curious crossing 
in the C curves around the region of a speed ratio of 0.50. 
A third comparison of resistances is shown in Fig. 7, Plate 21, BX and CX 
being plotted together with an intermediate curve identical in form with the 
