Power Available Constraints

List of Symbols

E          Energy (joules)

r             Packing Factor (cell area/entire side area)

h             Solar Cell Efficiency (per cell)

S          Solar Constant 1367 W/m2 or 0.8819 W/in2

A         Effective Area (area normal to the sun)

P          Period of Orbit (seconds)

f           Fraction of orbital period in sun

At         Total area for a side

q          Angle of incidence (angle between sun vector and vector normal to area surface)

w         Angular velocity of satellite (rad/s)

t          Period of one revolution of satellite (s)

Orbit

The satellite will be delivered to a 492 km. altitude orbit.  From the calculations in Appendix A (1.1):

Event                            Time                 Percent of Orbit

Length of orbit:             5670 s              100%

Eclipse:                         2150 s              38%

Sun:                              3520 s              62%

Table 1. Orbit Times

(These are based on worst case eclipse occurring twice yearly)

The energy equation for a solar cell is:

The packing factor and the cell efficiency are based on the type of cell used.  The effective area is based on the number of sides facing the sun and their orientation.

The effective area is based on the entire cross section of the satellite facing the sun in one of two possible cases.

Orientation

Case 1 provides the maximum effective area at 666.3 in2.  This is the most optimistic scenario, but unlikely in that the satellite would have to be in a torque-free configuration and have no rotation about its major axis so that it would have to remain at precisely the attitude indicated in Figure 1.

The worst-case scenario would be for the satellite to orbit with its end always facing the sun.  No cells would be facing the sun to generate power.  This event is unlikely for the same reasons as the satellite remaining in a Case 1 attitude.

The satellite will most likely tumble in orbit, and not be stuck in any one orientation.  The effective area will vary as the satellite rotates.  Case 2 provides an effective area of 615.6 in2.  Rotation about the major axis, with that axis perpendicular to the sun vector yields the minimum average power.

Figure 1. Effective Area

The effective area will oscillate between zero for the end-on orientation, and either Case 2 for the side-on orientation.  The energy for one rotation about the major axis was calculated to be:

When computed over the length of an entire orbit, the angular velocity of rotation cancels out and:

Case 1 Orientation Factor:        2.6

Case 2 Orientation Factor:        2.4

Rotation Factor:                        (2/pi)

The following tables compare the trade-offs associated with packing factor and power/energy produced for several common efficiencies of solar cells.

 Average Power (W) Efficiency Silicon GaAs Packing Factor 0.12 0.14 0.16 0.19 0.21 0.23 0.25 0.26 0.27 0.28 0.20 5.1 5.9 6.8 8.1 8.9 9.8 10.6 11.0 11.5 11.9 0.25 6.4 7.4 8.5 10.1 11.2 12.2 13.3 13.8 14.3 14.9 0.30 7.7 8.9 10.2 12.1 13.4 14.7 16.0 16.6 17.2 17.9 0.35 8.9 10.4 11.9 14.1 15.6 17.1 18.6 19.3 20.1 20.8 0.40 10.2 11.9 13.6 16.1 17.8 19.5 21.2 22.1 22.9 23.8 0.45 11.5 13.4 15.3 18.2 20.1 22.0 23.9 24.9 25.8 26.8 0.50 12.7 14.9 17.0 20.2 22.3 24.4 26.6 27.6 28.7 29.7 0.55 14.0 16.4 18.7 22.2 24.5 26.9 29.2 30.4 31.6 32.7 0.60 15.3 17.8 20.4 24.2 26.8 29.3 31.9 33.1 34.4 35.7 0.65 16.6 19.3 22.1 26.2 29.0 31.8 34.5 35.9 37.3 38.7 0.70 17.8 20.8 23.8 28.3 31.2 34.2 37.2 38.7 40.2 41.6 0.75 19.1 22.3 25.5 30.3 33.5 36.7 39.8 41.4 43.0 44.6 0.80 20.4 23.8 27.2 32.3 35.7 39.1 42.5 44.2 45.9 47.6 0.85 21.7 25.3 28.9 34.3 37.9 41.5 45.2 47.0 48.8 50.6

Table 2. Average Power

 Energy (J) Efficiency Silicon GaAs Packing Factor 0.12 0.14 0.16 0.19 0.21 0.23 0.25 0.26 0.27 0.28 0.20 29,000 34,000 39,000 46,000 51,000 55,000 60,000 63,000 65,000 67,000 0.25 36,000 42,000 48,000 57,000 63,000 69,000 75,000 78,000 81,000 84,000 0.30 43,000 51,000 58,000 69,000 76,000 83,000 90,000 94,000 98,000 101,000 0.35 51,000 59,000 67,000 80,000 89,000 97,000 105,000 110,000 114,000 118,000 0.40 58,000 67,000 77,000 92,000 101,000 111,000 120,000 125,000 130,000 135,000 0.45 65,000 76,000 87,000 103,000 114,000 125,000 135,000 141,000 146,000 152,000 0.50 72,000 84,000 96,000 114,000 126,000 138,000 151,000 157,000 163,000 169,000 0.55 79,000 93,000 106,000 126,000 139,000 152,000 166,000 172,000 179,000 185,000 0.60 87,000 101,000 116,000 137,000 152,000 166,000 181,000 188,000 195,000 202,000 0.65 94,000 110,000 125,000 149,000 164,000 180,000 196,000 204,000 211,000 219,000 0.70 101,000 118,000 135,000 160,000 177,000 194,000 211,000 219,000 228,000 236,000 0.75 108,000 126,000 145,000 172,000 190,000 208,000 226,000 235,000 244,000 253,000 0.80 116,000 135,000 154,000 183,000 202,000 222,000 241,000 250,000 260,000 270,000 0.85 123,000 143,000 164,000 194,000 215,000 235,000 256,000 266,000 276,000 287,000

Table 3. Energy

Table 2 and Table 3 were calculated based on rotation about the major axis, a Case 2 effective area, and AM0 industry standard solar conditions  (solar constant equal to 0.873 W/in2 or 1560 W/m2).