A script to calculate human-usable living space of SpaceX's ITS ship. After watching some of Elon Musk's presentation, I could quite wrap my head around 100 people on that ship. So here's the math and some perspective. Turns out 100 people may not be unreasonable.

spacex_its_volume.m

% SpaceX ITS Volumetric Capacity
% spacex_its_volume.m
% 
% Josh Kaplan
% contact@joshkaplan.org
%
% SpaceX claims that the spaceship that sits atop ITS can carry 100+ people
% per ship.
%
% The ship is slightly larger than the Saturn V, which carried 3 people.
% 
% Data is from Elon Musk's presentation slides:
% http://www.spacex.com/sites/spacex/files/mars_presentation.pdf
%
close all; clear all; clc;

%% Data

length = 49.5;          % length of ship        [m]
diameter = 17;          % diameter of ship      [m]
radius = diameter / 2;  % radius of the ship    [m]

%% Calculated Values
area = pi*(radius)^2;   % cross-sectional area  [m^2]

% SpaceX diagram shows roughly half the ship taken up by fuel tanks.
% So we'll only count half the length as human usable space.
% The ship's diameter also decreases, but we'll ignore that detail for a
% moment.
real_len = length / 2;  % human-usable length   [m]

%% Volume Calculation
vol = area * real_len;  % human-usable volume   [m^3]

fprintf('Volume of ITS:   %10.2f m^3\n', vol);


%% Let's compare it to my house for reference

% If you want to try this with your house, change this value
% to the square footage of your house.
sq_ft = 1400;

% My house is 1400 sq. ft. which equates to 130 m^2
area = sq_ft * 0.092903;     
height = 3;     % we'll approximate the ceiling height at 3m, close enough.
V = area * height;
fprintf('Volume of House: %10.2f m^3\n', V);

% Let's compare what this would be like in my house.
equivalent = round(100/(vol/V));
fprintf('It would be like having %d people in my house\n', equivalent)