Structure

The spacecraft structure carries and protects the spacecraft and payload equipment through the launch environment and during its lifetime from external conditions. The load-carrying structure of a spacecraft is primary structure, whereas brackets, closeout panels, and most deployable components are secondary structure.

We size primary structure based on the launch loads, with strength and stiffness dominating its design. The size of secondary structure depends on on-orbit factors rather than boost-phase loads. Secondary structure only has to survive but not function during boost, and we can usually cage and protect deployables throughout this phase. As a reference value, the structure of a satellite usually represents the 20% of the spacecraft total mass. Although we should also add approximately 25% for weight growth to account for program additions, underestimating, and inadequate understanding of requirements.

Design Philosophy

To develop a structure light enough for flight, and to keep spacecraft affordable, we must accept some risk of failure. Material strengths vary because of random, undetectable flaws and process variations, and loads depend on unpredictable environments. Because of loads uncertainty, we cannot accurately quantify the structural reliability of a spacecraft. We can approximate it, however, and we can develop design criteria that will provide acceptable reliability.

• Use a design-allowable load (the highest load that a structure or material can withstand without failure) for the selected material that we expect 99% of all specimens will equal or exceed.
• If possible, from available environmental data from previous missions, derive a design limit load (the maximum load expecting during the mission) equal to the mean value plus three standard deviations. This means there will be 99.87% probability that the limit load will not be exceeded during the mission.
• Multiply the design limit load by a factor of safety, then show that the stress level at this load does not exceed the corresponding allowable load.

Nowadays, resorting to prefabricated structures when designing nanosatellites or cubesatellites is the common practice. There are several possibilities in the industry and each one of them shall be analyzed to determine whether it is suitable for your mission. Preliminary analyses might be done using the formulas described below and combining some FEM model to ensure the proper functioning of the satellite until its end-of-life.

Design options

When designing a structure, we consider several materials, types of structure, and methods of construction. To select from these options, we compare each option analyzing its weight, cost, and risk.

A typical spacecraft structure contains metallic and nonmetallic materials. By far the most commonly used metal for spacecraft structure is aluminum alloy, of which there are many types and tempers. Aluminum is relatively lightweight, strong, readily available, easy to machine, and low in raw material cost. Nonmetals are usually formed with composites. Although aluminum and composites are widely used in satellite structures there are a lot of different options that shall be considered. The main advantages and disadvantages of some of them are summarized in Table 14.

Material	Advantages	Disadvantages
Aluminum	High strength vs weight Ductile and low density Easy to machine	Relatively low strenh vs volume Low hardness High coefficient of themal expansion
Steel	High strength Wide range of strength, hardness and ductility	High density Hard to machine Magnetic
Magnesium	Low density	Susceptible to corrosion Low stregth vs volume
Titanium	High strength vs weight Low coefficient of thermal expansion	Hard to machine Poor fracture toughness if treated and aged
Beryllium	High stiffness vs density	Low ductile and fracture toughness Low short transverse properties Toxic
Composite	High stiffness, strength and low thermal expansion coefficient Low density Good in tension	Expensive for low production volume Brittle Dependant strength; usually requires proof testing

Preliminary design

The launch vehicle is the most obvious source of structural requirements, dictating the spacecraft weight, geometry, rigidity, and strength. Each of the launch boosters provides maximum acceleration levels to be used for design. These acceleration levels or load factors are typically 6 g’s maximum axial acceleration and 3 g’s maximum lateral acceleration. The actual force is obtained multiplying these load factors (\(LF\)) by the satellite weight:

\[P_{ax} = mgLF_{ax}; \ \ \ P_{lat} = mg LF_{lat}.\]

To approximate the required thickness of the structure we can resort to simplified geometries and formulas. Regardless of the actual shape of the satellite, we can suppose it to be a hollow cantilevered cylinder with uniform thickness, \(t\), and height, \(L\). The transversal area, \(A\), and its moment of inertia, \(I\), are related to its internal radius, \(r\), and the mentioned thickness:

\[A = 2 \pi r t, \ \ \ I = \pi r^3 t.\]

Supposing that the center of mass location is at the cylinder mid-length (\(L/2\)), we can find the equivalent axial load taking into account that the lateral acceleration will produce a momentum on the base of the structure (in the interface with the launcher). This momentum will increase the axial equivalent force:

\[P_{eq} = P_{axial} + \frac{2 M}{r} = P_{axial} + \frac{2 P_{lat} L}{2r}\]

Now the structure shall be checked for ultimate and yield conditions. \(P_{eq}\) is multiplied by a factor of safety, \(f\), which has a value of 1.25 for ultimate conditions and 1.1 for yield and then compared with the material allowable stress. The thickness must be capable of resisting the axial loads:

\[\frac{P_{eq}f_{u}}{A} < \sigma_{u}; \ \ \ \frac{P_{eq}f_{y}}{A} < \sigma_{y},\]

where \(\sigma_{u}\) and \(\sigma_{y}\) represent the material allowable stress for ultimate and yield conditions, respectively. To see different materials \(\sigma_{u}\) and \(\sigma_{y}\) refer to Table 11-52 in [WL99].

Furthermore, a launch-vehicle structure has certain natural frequencies that respond to forces from both internal (engine oscillations) and external (aerodynamic effects) sources. The launch vehicle contractor lists known natural frequencies for each launch vehicle. The spacecraft structure tailored to avoid the launch vehicle natural frequencies will experience much lower loads and this is one of the most important requirements when designing the spacecraft structure.

With the launcher frequencies (axial and lateral) known, we can find a value of the thickness for which the natural frequencies of the structure will be larger than the launcher frequencies. For axial natural frequency we have:

\[f_{ax} = \frac{1}{2\pi} \sqrt{\frac{EA}{mL}} = \frac{1}{2\pi} \sqrt{\frac{2 E \pi r t}{mL}},\]

and for the lateral natural frequency

\[f_{lat} = \frac{1}{2\pi}\sqrt{\frac{3EI}{mL}} = \frac{1}{2\pi}\sqrt{\frac{3E\pi r^3 t}{mL}}.\]

The final thickness will be the more conservative value of the ones obtained before (combining the values obtained in the equivalent loads and frequency analyses).

Although the previous formulas can provide an approximated value for the structure thickness, the actual analysis of a spacecraft structure is much more complex. It possesses a lot of internal elements which will affect to the natural frequencies of the structure. Moreover, there are more requirements to meet caused by different perturbation sources. For example, random vibration from engines and other sources is a critical source of load as well. It must be proved that the satellite is capable of resisting these kind of loads (and any other). In actual design, this is proved by means of some numerical result using FEM tools and then checked during the test campaign.

[DRDF12]

Anton H De Ruiter, Christopher Damaren, and James R Forbes. Spacecraft dynamics and control: an introduction. John Wiley & Sons, 2012.

[MB14]

Malcolm Macdonald and Viorel Badescu. The international handbook of space technology. Springer, 2014.

[SB16]

George P Sutton and Oscar Biblarz. Rocket propulsion elements. John Wiley & Sons, 2016.

[Uni07]

California Polytechnic State University. Poly Picosatellite Orbital Deployer Mk. III Rev. E User Guide. The CubeSat Program, Cal Poly SLO, 2007.

[WEP11]

James R Wertz, David F Everett, and Jeffery J Puschell. Space mission engineering: the new SMAD. Microcosm Press, 2011.

[WL99]

James R Wertz and Wiley J Larson. Space Mission Analysis and Design, Space Technology Library. Microcosm Press and Kluwer Academic Publishers, El Segundo, CA, USA, 1999.

[Wer78]

James R. Wertz, editor. Spacecraft Attitude Determination and Control. Springer Netherlands, 1978. URL: https://doi.org/10.1007/978-94-009-9907-7, doi:10.1007/978-94-009-9907-7.