## Integrating the Spacecraft Design

10.5.1 Spacecraft Size

If we know the spacecraft's weight and power, we can estimate its size. Most spacecraft have a main body or equipment compartment Many also have solar panels which wrap around the compartment for launch and deploy outside the compartment on orbit.

Table 10-28 gives estimating relations based on analysis of the volume and dimensions of a number of spacecraft These spacecraft ranged from 135 kg to 3,625 kg and represent about 15% of the U.S. spacecraft launched between 1978 and 1984 [TRW Defense and Space Systems Group, 1980-1985]. Their density ranged from 20 kg/m3 to 172 kg/m3, with an average of 79 kg/m3. The spacecraft were all cylindrically symmetric, although the cross section varied from rectangular to circular. The ratio of base diameter to cube root of mass ranged from 0.16 m/kg1/3 to 0.31 m/kg1/3, with an average of 0.23 m/kg^3. The ratio of spacecraft height to cube root of mass ranged from 0.13 to 0.83, with an average of 0.39 m/kg1'3.

TABLE 10-28. Rules for Estimating Volume,. Dimension, Area, and Moments of Inertia.

M = spacecraft loaded mass in kg as defined in Table 10-10.

TABLE 10-28. Rules for Estimating Volume,. Dimension, Area, and Moments of Inertia.

M = spacecraft loaded mass in kg as defined in Table 10-10.

Characteristic |
Estimate |
Linear Dimension (m) Body Area (m2) Moment of Inertia (kg- m?) |
V=0.01 M 3=025^® Ab=s2 /=0.01 M»3 |
0.005 to 0.05 0.15 to 0.30 |

Section 10.4.6 presented relations for estimating the area of a solar array. Sometimes, the required array area is smaller than the spacecraft's body area, and the body can be oriented properly relative to the Sun. In this case, we can mount the solar cells directly on the body. But high-power spacecraft usually mount the solar cells on external panels, either off to one side or symmetrically on both sides of the equipment compartment. External solar arrays greatly increase the spacecraft's moment of inertia, particularly about the axes perpendicular to the array axis. Suppose the solar array consists of two square panels, one on each side of the spacecraft, and the center of each of these panels is La meters from the body's center. If so, the increase in moment of inertia is approximately La2Ma, where Ma is the solar array weight Table 10-29 gives an approximate expression for La in terms of the array area and the body dimension, s. It shows the solar array's moment of inertia relative to the spacecraft's center. External solar arrays also affect the total projected spacecraft area, which in turn influences aerodynamic drag and solar-radiation pressure. Table 10-29 summarizes estimating rules for solar-array moment of inertia and area offset Aais the total solar array area. We must add these inertias to the inertias of the central compartment assuming the latter to be equal to the values for the folded spacecraft computed above.

TABLE 10-29. Rules for Estimating Area Offset and Moment of Inertia of a Solar Array.

These should be added to the body values computed in Table 10-28. See text for definition of terms.

TABLE 10-29. Rules for Estimating Area Offset and Moment of Inertia of a Solar Array.

These should be added to the body values computed in Table 10-28. See text for definition of terms.

Solar Array Area Offset (m) |
I* |
= 1.5 s + 0.5 (Aal 2)1® |

Solar Array Moment of Inertia (kg 7m2) |

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