boatmath.m

% Estimating the length & beam of boats from their tonnage.
% Ian McDougall
% 25 July 2019

clear all, close all, nfig=0;

% The Thames Measurement (TM) estimates the tonnage of a ship given its length (LOA) and beam in feet. It is intended for yachts.
function tons = TM(LOA,beam)
  tons = ((LOA - beam).*beam.^2)/188;
endfunction

% The Builder's Old Measurement (BOM) estamtes the tonnage of a ship given its LOA and beam in feet. It is older than the Thames measurement.
function tons = BOM(LOA,beam)
  tons = ((LOA - 0.6*beam).*beam.^2)/188;
endfunction

% This rule-of-thumb (ROT) estimates the beam in feet, given the LOA.
function beam = ROT(LOA)
  beam = LOA.^(2/3) +1;
endfunction

% The hull speed is an early boat limitation in knots, given LWL in feet (length at the waterline)
function vhull = hull(LWL)
  vhull = 1.34.*LWL.^0.5;
endfunction

init_ft = 10;
tons = 0;
for i = 1:10
  tons = i
  length = fzero(@(LOA) BOM(LOA,ROT(LOA))-i,init_ft)
  vhull = hull(length)
  init_ft = length;
endfor