01Intro
Spacecraft sunlit
Drag to look around
A deployable solar array for a 3U CubeSat

Miura-Ori

Folded for launch. Opened for power.
Scroll
Overview

One fold.
Four ideas.

An origami array that packs flat into a side pocket and opens into a wing.

01 Structure Measured

The Miura cell

A 2 × 2 unit driven by one angle
  • Facet edges a, b85 mm, 45 mm
  • Sector angle γ72°
  • Substrate1 mm Al 7075-T6
  • Cell area14 551 mm², constant
02 Spacecraft Modelled

3U, two rows

One wing on each side face
  • Sunlit power, two faces—
  • Stowed stack per side—
  • Wing reach at 5°—
  • Substrate mass—
03 Study Simulated

Nine fold angles

From 5° deployed to 88° stowed
  • SolverCOMSOL 6.3, shell
  • Mesh4 mm, 2348 elements
  • Loads20 g on three axes
  • ModesFirst six
04 Finding Simulated

Folding stiffens bending

Torsion stays at the flat-plate level
  • Bending gain vs flat plate3.5× → 6.8×
  • Torsional gain0.99 → 0.73
  • First mode, all anglesTorsion
  • f₁ range176 – 323 Hz
Mission

Sunlight
to shadow.

One orbit of a 3U CubeSat, 500 km above the Earth.

Orbit Illustrative

500 km · 97.4°

Sun-synchronous, circular

Two-body orbit with a fixed Sun direction. The orbit is an assumed input, not a mission plan.

Period Modelled

—

One revolution
  • T = 2π√(r³/μ)—
  • Orbital speed—
Eclipse Modelled

—

Longest pass through shadow

Cylindrical Earth shadow, Sun in the orbit plane (β = 0). Array output is zero in shadow.

Power Modelled

—

Sunlit, two wings

1361 W/m² × cell area × 0.29 × 0.85, beginning of life, Sun normal to the cells. Output = P₀ · cos θ · cos(incidence).

Scene not to scale: the spacecraft is enlarged; planet sizes and distances are compressed.

Deployment

Pocket
to wing.

88.0°
Fold angle θ
5° deployed88° stowed
Wing reach—
Fold height—
Modelled
Recessed pocket—
Modelled
Scroll here to fold · scroll elsewhere for the next section
01 θ = 88°

Stowed

Held flat in the side pocket

A hold-down keeps the array in the pocket, so the CubeSat, not the dispenser, restrains it (CDS Req. 2.2.4).

02 ≥ 30 min

Release

After ejection from the dispenser

Deployables wait at least 30 min after ejection (CDS Req. 2.4.4). A launch provider may set its own timing.

03 1 DOF

Unfold

One motion opens every facet

Root vertices swing in the face plane while the array grows outward along the face normal. A roller sits at each root vertex; the larger dark one with the white ring is the pivot, and a roller turns red if it would run past the end of the body. The shaded plane on each side face is the 6.5 mm stowed envelope, which turns red when the stack exceeds it.

04 θ = 5°

Latch

Root chain nearly straight

The root chain keeps a 7 mm zigzag and latches along the face, matching the clamped root of the finite element model.

Layouts

More rows,
more power.

Same cell, six bodies. Hover a card to swap the model.

3U · 2 rows

Values modelled. The fold study covers the single analysed cell; extra rows lengthen the cantilever beyond it.

Fold study · nine angles

The cell
at 5°

f₁ torsion—Hz
f₂ bending—Hz
Peak stress under 20 g · MPaSimulated
X
—
Y
—
Z
—

Scroll on this panel to step the angle. COMSOL 6.3 shell, fixed root chain. Mode shape schematic, amplitude exaggerated, playback 100× slower.

Mode 1

Torsion

Twist about the root-to-tip axis

The first mode at all nine angles: 176 Hz deployed, 323 Hz stowed.

Mode 2

Bending

Deflection along the facet normal

Rises from 227 Hz at 5° to 367 Hz at 80°. The ratio f₂/f₁ peaks at 1.78 at 70°.

Stiffness

Against a flat plate

Same footprint, thickness and root
  • k_bend3.48 → 6.77
  • k_tors0.99 → 0.73

Reported to 70°: the matched footprint degenerates near the stowed state.

Method

How the numbers
were made.

Every figure carries a label: Simulated Modelled Measured Illustrative

Geometry

Rigid-foldable

After Schenk and Guest
  • Ha sinθ sinγ
  • La √(1 − sin²θ sin²γ)
  • Vb / √(1 + cos²θ tan²γ)
  • Sb cosθ tanγ / √(1 + cos²θ tan²γ)

Area 14 551.24 mm² in SolidWorks against 14 551.16 mm² closed form (5.2 ppm).

Finite elements

COMSOL shell

One model, nine angles
  • MaterialE 71.7 GPa, ν 0.33
  • Thickness1 mm mid-surface
  • FoldsKnitted, full moment
  • RootBoth a-edges clamped
  • Mesh2348 el., 29 415 DOF
Verification

Mesh study

θ = 30°, 20 g on −Y
  • 8 mm · 624 el.180.10 / 265.32 Hz
  • 4 mm · 2348 el.179.92 / 265.50 Hz
  • 2 mm · 8772 el.179.66 / 265.48 Hz

Frequencies move less than 0.15 % from 4 to 2 mm. The flat reference plate matches Leissa within 0.7 %.

Limits

What it leaves out

Read before quoting a number
  • Nine fixed configurations, no deployment dynamics.
  • Clamped root and rigid folds: an upper bound on stiffness.
  • No contact, cells, adhesive or wiring in the model.
  • Thermal case is a prescribed 100 K input.
  • No physical test yet.
2026

Fold-Angle Dependence of the Structural, Modal and Thermomechanical Response of a Miura-Ori Deployable Solar-Array Structure

Geometry and finite element results are research outputs; the orbit and imagery are illustrative context. Planets, distances and the spacecraft are not to scale. Earth imagery: NASA Blue Marble and NASA Earth at Night. Star field: Tycho-2 catalogue sky box (CesiumJS, Apache 2.0). Planet maps: James Hastings-Trew. 3D rendering: three.js (MIT).