Origami-inspired bloom patterns improve spacecraft design

The universe often demands inventions that balance elegance with function. Engineers design spacecraft parts to be compact during launch yet expansive when deployed. Surprisingly, inspiration for this comes from origami, the Japanese art of paper folding.

A new class of origami patterns, called bloom patterns, could provide solutions for the design of space telescopes, antennas, and solar arrays.

Origami bloom patterns and engineering

Traditional origami patterns are valued in engineering for their ability to fold into tight packages. Yet they are often difficult to unfold reliably. A single error can cause an entire structure to fail.

This makes deployment risky, especially in space where repairs are nearly impossible to conduct.

Bloom pattern breakthrough

Larry Howell and colleagues at Brigham Young University introduced bloom patterns, which unfold smoothly into flower-like bowls.

“We’re able to make new things that have never been done before, but then, at the same time, we’re creating these beautiful shapes,” said Howell.

Unlike many earlier origami patterns, blooms expand without step-by-step sequences, reducing the risk of failure.

Defining bloom patterns

Researchers created two definitions of bloom patterns: generalized and standardized. The generalized form captures the broadest set of characteristics, ensuring that future discoveries can be included.

The standardized form narrows the criteria, requiring bloom patterns to be flat-foldable, developable, and radially constructed around a polygonal center. This framework allows systematic study and reliable construction of these shapes.

Wedges and symmetry

At the heart of bloom patterns lie wedges – repeated segments cut from tessellations. These wedges radiate around a central polygon, resembling the blades of an aperture.

Their rotational symmetry ensures smooth folding and unfolding. Unlike earlier designs, bloom patterns often combine rotational symmetry, flat-foldability, and developability all at once, which is a rare trio in origami engineering.

Mathematical order of patterns

Bloom patterns can be classified by geometry, symmetry, and partitioning of wedges. Each bloom’s complexity can be measured by a “complexity index,” tied to how the wedges are arranged.

Lower complexity often means more symmetry and simpler unfolding. This mathematical system allows engineers to predict how a bloom will behave before building it.

The helical model

One challenge in origami design is proving whether a fold is truly flat-foldable. The helical model provides that proof for bloom patterns.

It ensures that wedges do not overlap improperly when folded. By mapping wedges onto helical surfaces, researchers confirm that blooms can fold injectively, avoiding self-intersections. This theory strengthens confidence that blooms will deploy correctly in real systems.

“Everything has to go right. If there’s a weak link in the chain, the whole thing fails. When I watch these [bloom patterns] unfold, you can see that it doesn’t necessarily have to do one thing after another for it to reach its maximum deployment,” added Michael Bartlett at Virginia Tech. 

Categories of bloom patterns

Bloom patterns can be symmetric or asymmetric, cyclic or non-cyclic, regular or irregular. Some are inscribed, where their boundaries match the central polygon, while others extend outward.

They can also be homogeneous – made of repeating identical facets – or hybrids that combine different tessellations.

This classification not only enriches mathematical theory but also guides practical design choices for space applications.

Space-ready advantages

Telescopes in orbit usually rely on flat mirrors, but bloom patterns could create curved dishes that are similar to ground-based observatories, thus improving image precision. Their smooth unfolding also minimizes deployment risks.

“You can make a better prediction of what a potential invention could look like, or if it’s worth it, or if you should go in a different direction,” added Jamie Paik from the Swiss Federal Institute of Technology in Lausanne (EPFL).

Future uses of origami

The theory extends beyond telescopes. Rigid foldability and bistability studies suggest bloom patterns could be used for antennas, solar collectors, or even expandable domes.

Their ability to be stacked makes them attractive for modular spacecraft or compact satellites, like DiskSat that is being developed by The Aerospace Corporation with support from NASA. In constrained forms, they may even serve as lightweight fluid containers.

Bloom patterns bring together geometry, art, and engineering. They are radially expansive, mathematically predictable, and mechanically reliable.

Their flower-like unfolding may one day shape the future of space structures, proving that elegance and utility can bloom together in orbit.

The study is published in the journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Image credit: Wang, Lang & Howell, Royal Society Publishing.

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