Thrust and uE tradeoffs with mass flow to 550 AU SGL distance

gamma is mDot/m0, around 1e-6 in this example.

%---------------------------------------------------------------------
%  Copyright 2017 Princeton Satellite Systems, Inc.
%  All rights reserved.
%---------------------------------------------------------------------

year = 86400*365.25;

% Parameters
m0 = 10000;
mDot = 0.01*1e-3; % g/s
uE = [100 500 1000]; % km/s
t = [5:1:20]*year;

% Calculations
gamma = mDot/m0;
tMax = 1/gamma;
fprintf('tMax is %g yr\n',tMax/year)
thrust = uE*1e3*mDot;

d = [];
for k = 1:length(uE)
  for j = 1:length(t)
    d(j,k) = uE(k)/gamma*( (1-gamma*t(j))*log(1-gamma*t(j)) + gamma*t(j) );
  end
end
year = 86400*365.25;
au = Constant('au');
Plot2D(t/year,d/au,'Time (yr)','Distance (au)','Distance for Fixed mDot')
for k = 1:length(uE)
  text(t(end)/year,d(end,k)/au,sprintf('%g N\n%g km/s',thrust(k),uE(k)));
end

% Gamma is mDot/m0, so gamma*t is also mFuel/m0!
fact = 0.01:0.01:0.99;
func = (1-fact).*log(1-fact)+fact;
Plot2D(fact,func,'gamma * t','Factor')

thrust = linspace(0,100); % thrust (N)
dF = 550*Constant('au');  % desired distance
m0 = 20000;               % kg
uEMin = sqrt(dF*thrust*1e-3/m0);
Plot2D(thrust,uEMin,'Thrust (N)','Minimum uE (km/s)','Minimum Exhaust Velocity for 550 AU')


%--------------------------------------

% $Id: 1cdc4a8c5997b6162694178ea0dae538969fcc52 $

tMax is 31.6881 yr

Published with MATLAB® R2024a