The structure of VASCAT is designed with adequate surface area for body mounted solar cells and adequate volume to house all components including the MAPS instrument. The structure of the VASCAT is 0.67 m in major diameter and 1 m high. Figure 4 is an illustration of the VASCAT. The satellite’s dimensions are small enough to allow for 0.85 m on each side in the payload fairing.
Figure 4: VASCAT external configuration
2.2.1 Requirements
Design and analysis of primary structural components necessitates the derivation of structural requirements. Table 4 lists all requirements relevant to this preliminary design. Mass and size of the structure are limited by the launch vehicle selected, and the size and mass of the primary payload, should this satellite be a hitchhiker. The launch vehicle selected also sets requirements on the strength of the structure. The orbit altitude desired, and therefore the launch vehicle, restricts the mass of the structure. All primary and secondary structural components should meet the predetermined mass allocation (see Table 3).^{16}
Table 4: Structural requirements^{16}
Requirement

Description

Required information

General shape and purpose

Provides load paths between supported components and launch vehicle; fits inside payload fairing

Configuration, spacecraft component level layout

Strength

Survives loads induced during launch; withstands onorbit loads, cyclic over lifetime

Load factors from launch vehicle; mass properties of spacecraft

Stiffness

Meets launch vehicle fundamental frequency requirement

Dynamic envelope of launch vehicle environment; mass properties of spacecraft

Mechanical interface

Meets launch vehicle flatness requirements; adaptable to launch vehicle attachment interface

Interface requirements inside payload fairing

Mass

Meets target mass allotment; meets launch vehicle mass limitation

Allocated mass

2.2.2 Launch vehicle selection
Since the launch of this satellite is uncertain, no launch vehicle is desired more than another. The VASCAT can either launch on the Space Shuttle as a hitchhiker payload, or as a secondary payload on any other launch vehicle. The structure is designed based on a worst case launch environment scenario. The Athena I launch vehicle is therefore chosen for structural analysis due to its relatively high launch loads. The Athena I is produced by Lockheed Martin. It has a payload fairing diameter of 2.36 m and a height of 8.81 m, and is capable of carrying up to 794 kg to LEO.^{10}
2.2.3 Bus structure
Configuration and component layout guides the sizing of all primary structures. However, these dimensions change with strength requirements placed on the satellite. The challenge is to design a system to house all components, survive the launch environment, and withstand cyclic onorbit loads.^{15} This section describes the process used to define dimensions of the VASCAT’s primary structure.
The International Reference Guide to Space Launch Systems states that the Athena I environment’s limit load factors are 8.1g’s axially and 1.8g’s laterally. A factor of safety of 2 is used during static calculations to ensure that the structure withstands these loads during launch. ^{20} The fundamental frequency of the VASCAT must be above 15 Hz laterally and 30 Hz longitudinally. The type of structure is chosen during dynamic calculations to ensure that the natural frequency of the satellite meets this stiffness requirement.
The mechanical interface is chosen for integration with the launch vehicle such that it meets the payload fairing’s flatness requirement and coincides with its bolt hole patterns and other attachment restrictions.^{ 20} The VASCAT mass budget (Table 3) allows for the structure to be approximately 30% of the total mass of the satellite.
2.2.3.1 Ultimate loads
An ultimate load for the bus structure is calculated for tensile strength sizing.
Table 5: Limiting loads on structure during launch
Type of Load

Weight, N

Distance, m

Load factor

Limit load, N

Axial

359



8.1

2908

Lateral

359



1.8

646

Moment

359

0.45

1.8

291

The equivalent axial load, P_{eq}, is calculated by:

21

In Equation 21 P_{axial} is the axial limit load taken from Table 5: Limiting loads on structure during launch, M is the bending moment limit load taken from the same table, and R is the moment arm taken as half the length of the structure. The ultimate load for the structure, P_{ult}, is then found by multiplying P_{eq} by the factor of safety.^{ 20} The equivalent axial load on the structure is 4,201 N, giving an ultimate load of 8,403 N.
2.2.3.2 Tensile strength
Axial stress is used to size the structures for tensile strength, and is given by:

22

In Equation 22 is the axial stress and A is the necessary crosssectional area. By solving for A from Equation 22, an adequate thickness to maintain tensile strength during launch is t = 0.01 mm.^{ 20}
2.2.3.3 Buckling analysis
To further define the crosssectional thickness of the bus structure, some buckling analysis is performed. The critical load, or buckling load, F_{cr}, is approximated to find a thickness to withstand buckling under the axial loading of the launch environment. For this analysis, the buckling load is approximated as the ultimate load.

23


24

In Equation 23 t is the thickness of the plate, b is the width of the plate, and E is Young’s Modulus of the material. In Equation 24 k is a constant corresponding to the boundary conditions imposed on the plate and is Poisson’s ratio for the material. To model the buckling of the flat side panels that make up each structure, the fixedfixed configuration is assumed, corresponding to a value of k’ = 6.42.^{15} Thickness to withstand buckling during launch is t = 0.046 mm.
2.2.3.4 Dynamic analysis
In addition to static survival, the bus structure is sized to survive dynamic loading and meet the launch vehicle minimum natural frequency requirements. The following cases are considered to estimate the natural frequencies and deflections for the uniform beam in both lateral and axial dynamic loading.
Case A, lateral:

25


26

Case B, axial:

27


28

In Equations 25 through 28, is beam deflection, m = 36.7 kg uniformly distributed mass, l = 1 m is the length of the beam, and f_{nat} is the natural frequency requirement from the launch vehicle. Solving for A from Equation 28, a thickness of t = 0.004 mm satisfies axial natural frequency requirements and gives = 0.0026 m at the minimum frequency of 30 Hz. This thickness gives a moment of inertia, I_{x}, for the crosssection of 3.06 × 10^{4} m^{4}. Substituting this value into Equation 26 gives a lateral natural frequency of 428 Hz, which is above the minimum allowed value of 15 Hz.^{20}
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