sf 
% 
SHIP CALCULATIONS; DERIVATION AND ANALYSIS 
OF METHODS. 
By Navat Constructor T. G. Roperts, U. S. N., MEMBER. 
[Read at the eighteenth general meeting of the Society of Naval Architects and Marine Engineers, held in 
New York, November 16 and 17, 1911.] 
In presenting a paper dealing with the first elements of a subject so 
well known to naval architects, reliance is placed mainly upon the possi- 
bility of interesting those who may find in these notes a shorter or clearer 
method of teaching the subject comprehensively to the student, aside from 
the desire to put into the proceedings a presentation of the entire subject 
along the same general lines as practiced by the French, as nearly as my 
recollection permits. The formule used were pieced together by the writer 
several years ago while preparing for an examination for promotion, and 
the practical examples worked out at that time are herein included to make 
clearer the application of the formule. If this paper may serve to alleviate 
the efforts of some student searching diligently for the reasons why, which 
were not always clear to the writer, in the calculation tables, until he had 
dug out these formule for himself, I shall then feel justified in having 
prepared the paper. 
It is to be hoped the reader will not become discouraged at the displace- 
ment and incidental calculations at the start, as the subsequent matter is 
less complicated and more interesting. 
DISPLACEMENT. 
The symbols are used to indicate the following: 
= Water-line areas. 
Areas of sections. 
= Vertical interval between adjacent water-lines. 
Horizontal interval between adjacent sections. 
Volume of displacement. 
Displacement in salt water. 
Displacement in fresh water. 
Displacement in tons per inch of immersion. 
= Ordinates of water-lines and sections. 
N78 OA 
I tl Il 
| 
Ryo 
ll 
The volume of displacement may be obtained by summing up either 
the curve of water-line areas or the curve of sectional areas; thus 
V= f Adz= f Sdx @) 
