Contents

Mass calculation demo

Demonstrates SolenoidStructuralMass

%--------------------------------------------------------------------------
% See also: EllipsoidalSolenoid, PFRCSolenoid, CocentricCoils
%--------------------------------------------------------------------------

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

Tapered coils, titanium alloy

sigma   = 900e6; % titanium
rho     = 4500;  % titanium
nu      = 1/3;
z       = [-1.15 -0.75 -0.45 -0.15 0.15 0.45 0.75 1.15];
a       = EllipsoidalSolenoid( 0.35, 0.5, z );
bAxial	= 5;
i       = PFRCSolenoid( a, z, bAxial,[],[],0.5  );
n       = length(z);
bA      = 5*ones(1,n);
bB      = zeros(1,n);
b       = 1.2*a;
w       = 0.2*(z(2)-z(1))*ones(1,n);

SolenoidStructuralMass( a, b, w, z, bA, bB, i, nu, sigma, rho );
[massA, massC, massT] = SolenoidStructuralMass( a, b, w, z, bA, bB, i, nu, sigma, rho )
f =
  Columns 1 through 6
   1.3456e-10    9.619e-11   1.0675e-10  -5.2134e-10  -5.6628e-10   1.1738e-10
  -9.0427e-11   2.8022e-11   4.1669e-10  -2.1761e-11  -1.6471e-11   4.9795e-10
  -5.7148e+05  -1.2694e+06  -1.2907e+06  -6.2403e+05   6.2403e+05   1.2907e+06
  Columns 7 through 8
    7.016e-11   1.2708e-10
  -4.1138e-12  -8.8646e-11
   1.2694e+06   5.7148e+05
deltaF =
  Columns 1 through 6
   6.9795e+05        21272  -6.6667e+05  -1.2481e+06  -6.6667e+05        21272
  Column 7
   6.9795e+05
ans =
  Columns 1 through 6
     0.027848    0.0048616     0.027217     0.037239     0.027217    0.0048616
  Column 7
     0.027848
fM =
  Columns 1 through 6
            0   2.2128e+05   1.4882e+05   1.0009e+05        57603        27717
  -2.2128e+05            0    6.558e+05   4.3173e+05   2.3693e+05   1.0799e+05
  -1.4882e+05   -6.558e+05            0   1.0973e+06   5.9795e+05    2.644e+05
  -1.0009e+05  -4.3173e+05  -1.0973e+06            0   1.3606e+06   5.9795e+05
       -57603  -2.3693e+05  -5.9795e+05  -1.3606e+06            0   1.0973e+06
       -27717  -1.0799e+05   -2.644e+05  -5.9795e+05  -1.0973e+06            0
       -12400       -45856  -1.0799e+05  -2.3693e+05  -4.3173e+05   -6.558e+05
        -3566       -12400       -27717       -57603  -1.0009e+05  -1.4882e+05
  Columns 7 through 8
        12400         3566
        45856        12400
   1.0799e+05        27717
   2.3693e+05        57603
   4.3173e+05   1.0009e+05
    6.558e+05   1.4882e+05
            0   2.2128e+05
  -2.2128e+05            0
Axial Masses:
  Columns 1 through 6
       1.3959     0.031907            1       1.8721            1     0.031907
  Column 7
       1.3959
Circumferential Masses:
  Columns 1 through 6
       9.2141       19.835       29.347       38.033       38.033       29.347
  Columns 7 through 8
       19.835       9.2141
f =
  Columns 1 through 6
   1.3456e-10    9.619e-11   1.0675e-10  -5.2134e-10  -5.6628e-10   1.1738e-10
  -9.0427e-11   2.8022e-11   4.1669e-10  -2.1761e-11  -1.6471e-11   4.9795e-10
  -5.7148e+05  -1.2694e+06  -1.2907e+06  -6.2403e+05   6.2403e+05   1.2907e+06
  Columns 7 through 8
    7.016e-11   1.2708e-10
  -4.1138e-12  -8.8646e-11
   1.2694e+06   5.7148e+05
deltaF =
  Columns 1 through 6
   6.9795e+05        21272  -6.6667e+05  -1.2481e+06  -6.6667e+05        21272
  Column 7
   6.9795e+05
ans =
  Columns 1 through 6
     0.027848    0.0048616     0.027217     0.037239     0.027217    0.0048616
  Column 7
     0.027848
fM =
  Columns 1 through 6
            0   2.2128e+05   1.4882e+05   1.0009e+05        57603        27717
  -2.2128e+05            0    6.558e+05   4.3173e+05   2.3693e+05   1.0799e+05
  -1.4882e+05   -6.558e+05            0   1.0973e+06   5.9795e+05    2.644e+05
  -1.0009e+05  -4.3173e+05  -1.0973e+06            0   1.3606e+06   5.9795e+05
       -57603  -2.3693e+05  -5.9795e+05  -1.3606e+06            0   1.0973e+06
       -27717  -1.0799e+05   -2.644e+05  -5.9795e+05  -1.0973e+06            0
       -12400       -45856  -1.0799e+05  -2.3693e+05  -4.3173e+05   -6.558e+05
        -3566       -12400       -27717       -57603  -1.0009e+05  -1.4882e+05
  Columns 7 through 8
        12400         3566
        45856        12400
   1.0799e+05        27717
   2.3693e+05        57603
   4.3173e+05   1.0009e+05
    6.558e+05   1.4882e+05
            0   2.2128e+05
  -2.2128e+05            0
massA =
  Columns 1 through 6
       1.3959     0.031907            1       1.8721            1     0.031907
  Column 7
       1.3959
massC =
  Columns 1 through 6
       9.2141       19.835       29.347       38.033       38.033       29.347
  Columns 7 through 8
       19.835       9.2141
massT =
       199.59

Fixed radius coils, titanium

a       = EllipsoidalSolenoid( 0.5, 0.5, z );
[~,i]   = ConcentricCoils( z, bAxial, a );
b       = 1.2*a;
SolenoidStructuralMass( a, b, w, z, bA, bB, i, nu, sigma, rho );
f =
  Columns 1 through 6
  -3.1136e-10   5.1802e-11   3.2858e-10   4.4612e-10   4.4612e-10   3.2858e-10
   7.6889e-10   2.2407e-10   6.7407e-10   1.5699e-10   1.5699e-10   6.7407e-10
  -4.0355e+06  -4.7195e+05   -2.554e+05       -37034        37034    2.554e+05
  Columns 7 through 8
   5.1802e-11  -3.1136e-10
   2.2407e-10   7.6889e-10
   4.7195e+05   4.0355e+06
deltaF =
  Columns 1 through 6
  -3.5636e+06  -2.1655e+05  -2.1837e+05       -74068  -2.1837e+05  -2.1655e+05
  Column 7
  -3.5636e+06
ans =
  Columns 1 through 6
     0.062925     0.015512     0.015577    0.0090718     0.015577     0.015512
  Column 7
     0.062925
fM =
  Columns 1 through 6
            0   1.6678e+06   9.9648e+05   5.2713e+05   3.1552e+05   2.1421e+05
  -1.6678e+06            0   9.6451e+05    4.924e+05   2.7662e+05   1.7521e+05
  -9.9648e+05  -9.6451e+05            0   9.7068e+05   5.3355e+05   3.2273e+05
  -5.2713e+05   -4.924e+05  -9.7068e+05            0   9.0153e+05   5.3355e+05
  -3.1552e+05  -2.7662e+05  -5.3355e+05  -9.0153e+05            0   9.7068e+05
  -2.1421e+05  -1.7521e+05  -3.2273e+05  -5.3355e+05  -9.7068e+05            0
  -1.3075e+05  -1.0023e+05  -1.7521e+05  -2.7662e+05   -4.924e+05  -9.6451e+05
  -1.8366e+05  -1.3075e+05  -2.1421e+05  -3.1552e+05  -5.2713e+05  -9.9648e+05
  Columns 7 through 8
   1.3075e+05   1.8366e+05
   1.0023e+05   1.3075e+05
   1.7521e+05   2.1421e+05
   2.7662e+05   3.1552e+05
    4.924e+05   5.2713e+05
   9.6451e+05   9.9648e+05
            0   1.6678e+06
  -1.6678e+06            0
Axial Masses:
  Columns 1 through 6
       7.1271      0.32482      0.32755       0.1111      0.32755      0.32482
  Column 7
       7.1271
Circumferential Masses:
  Columns 1 through 6
       71.695       30.631       33.241        30.83        30.83       33.241
  Columns 7 through 8
       30.631       71.695

Carbon-carbon

Use properties given in Santarius

sigma   = 1000e6; % carbon-carbon
rho     = 2500;  % km/m3
[massA, massC, massT] = SolenoidStructuralMass( a, b, w, z, bA, bB, i, nu, sigma, rho )


%--------------------------------------
f =
  Columns 1 through 6
  -3.1136e-10   5.1802e-11   3.2858e-10   4.4612e-10   4.4612e-10   3.2858e-10
   7.6889e-10   2.2407e-10   6.7407e-10   1.5699e-10   1.5699e-10   6.7407e-10
  -4.0355e+06  -4.7195e+05   -2.554e+05       -37034        37034    2.554e+05
  Columns 7 through 8
   5.1802e-11  -3.1136e-10
   2.2407e-10   7.6889e-10
   4.7195e+05   4.0355e+06
deltaF =
  Columns 1 through 6
  -3.5636e+06  -2.1655e+05  -2.1837e+05       -74068  -2.1837e+05  -2.1655e+05
  Column 7
  -3.5636e+06
ans =
  Columns 1 through 6
     0.059696     0.014716     0.014777    0.0086063     0.014777     0.014716
  Column 7
     0.059696
fM =
  Columns 1 through 6
            0   1.6678e+06   9.9648e+05   5.2713e+05   3.1552e+05   2.1421e+05
  -1.6678e+06            0   9.6451e+05    4.924e+05   2.7662e+05   1.7521e+05
  -9.9648e+05  -9.6451e+05            0   9.7068e+05   5.3355e+05   3.2273e+05
  -5.2713e+05   -4.924e+05  -9.7068e+05            0   9.0153e+05   5.3355e+05
  -3.1552e+05  -2.7662e+05  -5.3355e+05  -9.0153e+05            0   9.7068e+05
  -2.1421e+05  -1.7521e+05  -3.2273e+05  -5.3355e+05  -9.7068e+05            0
  -1.3075e+05  -1.0023e+05  -1.7521e+05  -2.7662e+05   -4.924e+05  -9.6451e+05
  -1.8366e+05  -1.3075e+05  -2.1421e+05  -3.1552e+05  -5.2713e+05  -9.9648e+05
  Columns 7 through 8
   1.3075e+05   1.8366e+05
   1.0023e+05   1.3075e+05
   1.7521e+05   2.1421e+05
   2.7662e+05   3.1552e+05
    4.924e+05   5.2713e+05
   9.6451e+05   9.9648e+05
            0   1.6678e+06
  -1.6678e+06            0
massA =
  Columns 1 through 6
       3.5636      0.16241      0.16378     0.055551      0.16378      0.16241
  Column 7
       3.5636
massC =
  Columns 1 through 6
       35.702       15.288       16.588       15.387       15.387       16.588
  Columns 7 through 8
       15.288       35.702
massT =
       173.77