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