Compare the solar pressure force for flat and billowed circular sails.

Since version 7.
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See also SailMesh, HCircularBillow, SolarPressureForce, PolygonProps,
Figui, NewFig, Plot2D, Dot, Mag, Unit, SolarFlx, CP1Props
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Contents

%-------------------------------------------------------------------------------
%	 Copyright 2009 Princeton Satellite Systems, Inc.
%-------------------------------------------------------------------------------

% These sails have a nominal front normal of [0;0;1], +Z.

Circular sail perimeter

%------------------------
theta = linspace(0,2*pi,20);
theta = theta(1:end-1);
rSail = 60;  % m
x = rSail*cos(theta);
y = rSail*sin(theta);
b = [0; 0.2; 0.4; 0.6];

CP1 properties - 90% specular

%------------------------------
[optical, infrared, thermal] = CP1Props;

Solar flux at 1 AU

%--------------------
flux = SolarFlx( 1.0 );

Create a vector of incidence angles in x/z plane

%-------------------------------------------------
theta = linspace(0,pi/2);
nPts  = length(theta);
uSun  = [sin(theta);zeros(size(theta));cos(theta)];

fElements = cell(1,4);
fTotal = cell(1,4);
coneAngle = zeros(4,nPts);
centerAngle = zeros(4,nPts);
Tavg = [];

for k = 1:4

  dBillow = struct('b',b(k),'r',rSail);
  [v,f] = SailMesh( x, y, 'HCircularBillow', dBillow, 3 );
  [a, n, r] = PolygonProps( v, f );

  NewFig(['Sail Mesh ' num2str(k)]);
  patch('vertices',v,'faces',f,...
      'facevertexcdata',v(:,3),'CDataMapping','scaled',...
      'facecolor','interp','edgecolor',[0 0 0]);
  axis equal;
  grid on;
  view(3);
  colorbar

  nEl = length(a);
  % display the total membrane area for each sail
  area = sum(a);
  title(sprintf('Area: %.4f m^2',area))

  fSail = zeros(3,nPts);

  % Compute the force and temperature of each element
  %--------------------------------------------------
  for j = 1:nPts
    [fEl, T, fT] = SolarPressureForce( a', n', uSun(:,j), flux, ...
                                           optical, thermal.emissivity );
    if j == 1
      fElements{k} = fEl;
      Tavg(k,:) = T;
    end

    fSail(:,j) = fT;
  end

  coneAngle(k,:) = acos(Dot(Unit(fSail),-uSun));
  centerAngle(k,:) = acos(Dot(Unit(fSail),-[0;0;1]));
  fTotal{k} = fSail;

end

Plot the element forces for incidence angle of zero

----------------------------------------------------

sailLabl = {'Flat', '0.2 Billow', '0.4 Billow', '0.6 Billow'};
Plot2D(1:nEl, fElements{2}, 'Element', {'x','y','z'}, 'Element Forces (mN)');
subplot(3,1,1)
hold on
plot(1:nEl, fElements{3}(1,:), 'g');
plot(1:nEl, fElements{4}(1,:), 'r');
subplot(3,1,2)
hold on
plot(1:nEl, fElements{3}(2,:), 'g');
plot(1:nEl, fElements{4}(2,:), 'r');
subplot(3,1,3)
hold on
plot(1:nEl, fElements{3}(3,:), 'g');
plot(1:nEl, fElements{4}(3,:), 'r');
legend(sailLabl{2:4})

Plot the results

%-----------------
angles = theta*180/pi;
aLabl = 'Sun Incidence Angle (deg)';
Plot2D(angles, [fTotal{2}([1 3],:);Mag(fTotal{2})]*1000, aLabl,{'Fx','Fz','|F|'},'Sail Performance (force in mN)');
subplot(3,1,1)
hold on
plot(angles, fTotal{3}(1,:)*1000, 'g');
plot(angles, fTotal{4}(1,:)*1000, 'r');
subplot(3,1,2)
hold on
plot(angles, fTotal{3}(3,:)*1000, 'g');
plot(angles, fTotal{4}(3,:)*1000, 'r');
subplot(3,1,3)
hold on
plot(angles, Mag(fTotal{3})*1000, 'g');
plot(angles, Mag(fTotal{4})*1000, 'r');
legend(sailLabl{2:4})

% Force magnitude alone on big plot
Plot2D(angles, [Mag(fTotal{1});Mag(fTotal{2});Mag(fTotal{3});Mag(fTotal{4})], ...
    aLabl,'Force Magnitude (N)','Sail Performance');
legend(sailLabl{:});

% CONE angle
Plot2D(angles, coneAngle*180/pi, aLabl,'Cone Angle (deg)','Sail Cone Angle');
legend(sailLabl{:},'location','NorthWest');
% add ideal sail relationship - linear
y = axis;
hold on
plot(linspace(0,y(4)),linspace(0,y(4)),'k--')

% CENTERLINE angle
Plot2D(angles, centerAngle*180/pi,...
  aLabl,'Centerline Angle (deg)','Sail Centerline Angle');

Figui;

%--------------------------------------
% PSS internal file version information
%--------------------------------------

Published with MATLAB® R2020a