Contents

Delta-V limits for a selected mission

See also: Straight2DStructure, DVLimit, DVForTime, Plot2D

%--------------------------------------------------------------------------
%	Copyright (c) 2018 Princeton Satellite Systems, Inc.
% All rights reserved.
%--------------------------------------------------------------------------

d = Straight2DStructure;
d.sigma = 1000; % W/kg
d.eta = 0.5;
d.f = 0.1;

DV limit

tFs = [1 5 10];
uEs = linspace(5,500);
DVmax = [];
dVstar = [];
massFrac = [];

for k = 1:length(tFs)
  tF = tFs(k)*365.25*86400;
  d.tF = tF;
  DVmax(k,:) = DVLimit( tF, uEs, d.sigma, d.eta, d.f );
  dVstar(k) = fminbnd( @(x) -DVLimit( tF(1), x, d.sigma, d.eta, d.f ), uEs(1), uEs(end) );
  massFrac(k,:) = exp(-DVmax(k,:)./uEs);
end
Plot2D(uEs,DVmax,'Exhaust Velocity (km/s)','Max DV (km/s)','Delta-V Limit')
yy = axis;
hold on;
plot(linspace(yy(1),yy(2)),linspace(yy(1),yy(2)),'k--')
plot(linspace(yy(1),yy(2)),linspace(yy(1),yy(2))*log((1+d.f)/d.f),'m--')
axis(yy)
legs = cellstr(num2str(tFs'));
ll = legend([legs(:)',{'DV=uE'},{'Limit'}]);
ll.Title.String = 'Years';
text(300,200,sprintf('sigma = %g kW/kg\neta = %g\nf = %g',...
    d.sigma*1e-3,d.eta,d.f),'fontsize',12)

Plot2D(uEs,massFrac,'Exhaust Velocity (km/s)','Mass Fraction (m_f/m_0)','Final Mass Fraction')
ll = legend(num2str(tFs'));
ll.Title.String = 'Years';

With exhaust velocity and power

d.tF = 1*365.25*86400;

uEs = [50 100 120 150 200 500];
powers = linspace(0.5,10);
limit = [];
DVs   = [];

for j = 1:length(uEs)
  d.uE = uEs(j);
  for k = 1:length(powers)
    DVs(j,k) = DVForTime(powers(k)*1e6, d);
  end
  [~,limit(j)] = DVForTime(powers(k)*1e6, d);
end
Plot2D(powers,DVs,'Power (MW)','DV (km/s)','Delta-V per Fixed Time')
ll = legend(num2str(uEs'));
ll.Title.String = 'uE';

With specific power and fixed uE

d.uE = 100;
d.eta = 0.4;
sigmas = [500 750 1000 1250 1500];
powers = linspace(0.5,10);
limit = [];
DVs   = [];

for j = 1:length(sigmas)
  d.sigma = sigmas(j);
  for k = 1:length(powers)
    DVs(j,k) = DVForTime(powers(k)*1e6, d);
  end
  [~,limit(j)] = DVForTime(powers(k)*1e6, d);
end
titleS = sprintf('Delta-V per Fixed Time, %g Years',d.tF/86400/365.25);
Plot2D(powers,DVs,'Power (MW)','DV (km/s)',titleS)
ll = legend(num2str(sigmas'));
ll.Title.String = 'Sigma';
limit = d.uE*log(d.f/1+d.f);

% array of durations
sigmas = linspace(0.5,2)*1e3;
DVmax = [];
massFrac = [];
for k = 1:length(tFs)
  tF = tFs(k)*365.25*86400;
  % DVLimit
  numL = (d.uE*1e3)^2/2/d.eta./sigmas + (1+d.f)*tF;
  denL = (d.uE*1e3)^2/2/d.eta./sigmas + d.f*tF;
  ff = log(numL./denL);
  DVmax(k,:) = d.uE*ff;
  massFrac(k,:) = exp(-DVmax(k,:)./d.uE);
end
titleS = sprintf('DV Limit, uE = %g km/s',d.uE);
Plot2D(sigmas,DVmax,'Specific Power','Max DV (km/s)',titleS)
ll = legend(num2str(tFs'));
ll.Title.String = 'Years';


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% $Id: 815e8d39854b519a87b9d9987ba88ce01b1d6c85 $

Published with MATLAB® R2024a