# Origami and its applications in modern spacecrafts

There has been a large growth in interest in origami in recent years within the scientific community. The ancient Japanese art of folding paper actually has applications to many branches of modern physics. However, here I will be focusing on the way in which origami has been incorporated in the design of spacecrafts. Most objects we put into space have shapes are very awkward to store and pack inside rockets including long solar panels, communication arrays and in the case of the James Web Space Telescope (JWST), large reflecting mirrors and sun shields. So, the problem of packing has always played a large role in the design of these objects. In recent years the methods and techniques of origami are being investigated scientifically in much greater depth with this problem in mind, designing equipment in a way that it can be folded into smaller more regularly shaped volumes for transport out of the Earth’s atmosphere.

Famously JWST incorporated the principles of origami in the way its large reflector mirror and sun shield were folded away during transport.

Crease pattern of JWST’s reflector mirror.

Much of the mathematics of origami has actually already been developed so it is actually only a matter of understanding how it works and applying it to the concept of spacecraft design. Knowing a few simple definitions can actually bring us a long way to implementing origami in the design of spacecraft components. In origami maths a fold is characterised in one of two ways, either a mountain or a valley. There is no fundamental difference between the two only their orientation relative to each other on the paper or other material. It also turns out that at any vertex where folds intersect the number of mountain and valley folds coming out of the vertex will always differ by two. Now just knowing this we can create flat 2D crease patterns that represent complex 3D origami shapes. Figure 1 actually shows the crease pattern that NASA used to design the reflector mirror of the JWST. The two different fold types are marked and you can count the fold types at the vertexes if you want to verify for yourself.

Now trying to design the folds of these components manually would be exhaustive work so we want to find a way for computers to automate the process and simulate potential designs for us. If we can conceptualise a fold as a rotation about a line then the fold mathematically can be described by a rotation matrix and following from this complex 3D structures can be represented by simple matrix multiplications which is very easy for computers to do. In this way computer would easily be able to simulate and test potential designs based on certain human defined criteria that can speed up the whole process.

However, in doing this we have to make sure that our models are physically valid and reasonable. The way many people think about paper and folding is to neglect effects of the thickness entirely and have situation where pieces of paper can be folded 50 times and reach the Moon. There is actually a physical limit on the number of times you can fold something as there is a certain amount of material needed to traverse between layers in a fold that become “lost” and not available in future folds.

This physical limit is described by the loss function for folds which was derived in 2001 by Britney Galivan who was an American High School student at the time. It simply states what the minimum possible length (L) of material with thickness (t) you would need to fold the material n times in a given direction.

Finally, we can incorporate all this knowledge that we have gathered and apply it to our spacecrafts. All Satellite and telescopes that we put into space use solar panels as a source of energy but as we all know solar panels need large area to collect solar radiation which don’t easily fit into rockets. So, we want to fold these large flat sheets away as efficiently as possible for transport. When thinking of ways to fold large flat sheets our minds might immediately jump to the way we fold up large paper maps. However, there is a problem with the conventional orthogonally folded maps we are most used to. They take a lot a movement to open up which would require more expensive equipment to be attached to the satellite to unfold the solar panel that immediately become redundant upon deployable. Anyone who has use a paper map knows that they are prone to buckling along the creases and they start to tear at the vertexes where a large amount of stress in experience as the paper is forced to be folded through “lost” material as discussed above. These problems were recognised by Japanese Astrophysicist Koryo Miura and Masamori Sakamaki from Tokyo University’s Institute of Space and Aeronautical Science. They developed a better design specifically for use in solar panels that they based off of map crease patterns found in a map from ancient Egypt.

Crease pattern of a Mirua-Ori map design

They’re Miura-Ori design can be unfolded and refolded in one motion due to the interdependence of the folds which means that movement along any fold creates movement along another which is much more efficient. The angle of the folds at the vertexes also reduces the stress making the very expensive satellite components less prone to breaking.

So, this ancient art of origami has a big role to play in the modern world of space exploration. Understanding the physics of folding materials will allow us to push the current limitations of space craft and rocket design.

This content is adapted from information I presented as part of the “Origami: A game changer in space travel” presentation that I presented with Nathan Besch and Brice Cordier.

https://boundlessbrilliance.org/brilliant-blog/foldingpapertothemoon

https://mathworld.wolfram.com/Folding.html

https://web.archive.org/web/20051125174630/http://www.isas.jaxa.jp/e/enterp/missions/complate/sfu/2dsa.shtml

https://www.britishorigami.org/cp-resource/the-miura-ori-map/

Folding a New Tomorrow: Origami meets Math and Science, A lecture by Thomas Hull,

Images:

https://webb.nasa.gov/content/features/assets/documents/origami1.pdf

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