HBPF-1 Project Design

Hexagonal Bellows Accordion Photonic Funnel-Tube

The following project develops the concept in stages: first, a testable single module with a 1.73 m entrance aperture; then a multi-module honeycomb array; and finally a 60 m-class system. This approach is consistent with the existing development direction of lightweight composite deployable booms and metallized thin-film membranes for space deployment. [1][2]

Project Objective

HBPF-1 is a lightweight, modular photonic funnel-tube demonstrator that is compact during launch, expands in orbit in a bellows/accordion configuration, and uses an internal smooth metallized membrane to reflect, direct, or concentrate sunlight.

The principal objectives are:

• Demonstrate reliable vacuum deployment of a hexagonal bellows structure.
• Lock the deployed structure and verify resistance to bending and torsion.
• Tension the internal optical membrane without unacceptable wrinkling.
• Demonstrate an optical concentration ratio between 4:1 and 9:1.
• Demonstrate reliable opening and safe closure of the front and rear covers.
• Monitor temperature, structural strain, position, and optical alignment using sensors.
• Establish scalability from one module to a honeycomb assembly of multiple modules.

System Definition

HBPF-1: A hexagonal-section, bellows-deployable, reflective-membrane-lined photonic funnel-tube module designed for solar-light redirection and low-to-medium optical concentration.

The system operates in three modes:

Mode	Purpose	Geometry
Protection / launch mode	Protect optical surfaces, mechanisms, and electronics	Fully compressed bellows; covers closed
Reflective tube mode	Direct sunlight toward a target or transmit it with low loss	Entrance and exit have equal dimensions
Concentrator funnel mode	Direct sunlight toward a rear thermal receiver	Wide entrance and reduced exit

HBPF-1 Baseline Dimensions

The following dimensions are proposed for the initial engineering prototype.

Parameter	Value
Cross-sectional shape	Regular hexagon
Entrance side length	1.00 m
Entrance flat-to-flat width	1.732 m
Entrance corner-to-corner width	2.000 m
Entrance area	2.598 m²
Exit side length	0.50 m
Exit flat-to-flat width	0.866 m
Exit corner-to-corner width	1.000 m
Exit area	0.650 m²
Geometric concentration ratio	4:1
Deployed length	2.40 m
Stowed length	0.30 m
Number of bellows segments	8
Deployed length per segment	0.30 m
Stowed length per segment	0.0375 m
External structural diameter	Approximately 2.1 m
Target dry mass	12–18 kg
Target optical efficiency	70–80%

For a regular hexagon:

$$
A_{\text{hexagon}}=\frac{3\sqrt{3}}{2}s^2
$$

For the entrance, where $$s=1.00\ \text{m}$$:

$$
A_{\text{entrance}}=
\frac{3\sqrt{3}}{2}(1)^2
\approx2.598\ \text{m}^2
$$

For the exit, where $$s=0.50\ \text{m}$$:

$$
A_{\text{exit}}=
\frac{3\sqrt{3}}{2}(0.5)^2
\approx0.650\ \text{m}^2
$$

Therefore:

$$
C_g=
\frac{A_{\text{entrance}}}{A_{\text{exit}}}
\approx4.0
$$

A 4:1 ratio is a prudent first-demonstrator choice. Higher concentration ratios make the system substantially more sensitive to optical errors, membrane wrinkling, scattering, and multiple-reflection losses.

Optical Geometry

Initial Design: 4:1 Funnel

HBPF-1 should not initially be designed as a fully ideal classical CPC. It should be developed as a short, hexagonal, stepped-conical reflector with actively controlled alignment. Classical CPC geometry involves a trade-off between acceptance angle and concentration ratio; as concentration rises, the acceptance angle narrows and pointing tolerance decreases. [3]

The proposed optical parameters are:

Parameter	Value
Entrance flat-to-flat width	1.732 m
Exit flat-to-flat width	0.866 m
Length	2.40 m
Average sidewall slope	Approximately 10.2°
Micro-adjustment range per internal panel	±5°
Number of internal reflective surfaces	6
Optical surface type	Tensioned segmented metallized membrane
Target acceptance half-angle	±20–25°
Illumination source	Solar input with active Sun tracking

The half-width difference is:

$$
\Delta r=
\frac{1.732-0.866}{2}

0.433\ \text{m}
$$

The nominal conical slope is:

$$
\alpha=
\tan^{-1}
\left(
\frac{0.433}{2.40}
\right)
\approx10.2^\circ
$$

Because the spacecraft will use Sun sensors and star trackers for active pointing, the system does not require the broad passive acceptance angle of a stationary terrestrial CPC.

Structural Architecture

The module consists of two separate layers: an external deployable bellows structure and an internal smooth optical surface.

Subsystem	Function	Proposed implementation
External bellows shell	Deployment, stowage, mechanical protection	CFRP-reinforced thin thermoplastic composite
Hexagonal ring frames	Preserve cross-sectional geometry	Eight CFRP or titanium-aluminum rings
Axial deployment system	Extend the bellows	Six tape-spring CFRP booms or central cable-driven spool
Locking system	Provide deployed rigidity	Positive mechanical latches at each hexagonal corner
Internal optical membrane	Direct or concentrate sunlight	Aluminized CP1 or PEN film
Tension network	Reduce wrinkling	Aramid/CFRP tension cords at six vertices
Front cover	Launch protection and entrance control	Six-leaf iris cover
Rear cover	Receiver protection and exit control	Hinged hexagonal exit cover
Central receiver	Absorb concentrated energy in thermal mode	Black ceramic-coated thermal receiver
Control electronics	Deployment, sensing, and communication	Radiation-tolerant compact electronics board

NASA’s deployable composite boom technology provides a relevant starting architecture: lightweight carbon-fiber-reinforced polymer structures can be compactly stowed and deployed in space. ACS3 uses this general approach for solar-sail support structures. [1][4]

Material Package

Reference material configuration

Component	Material	Function
Internal front optical surface	80–120 nm aluminum	High reflectance with low mass
Optical membrane substrate	2–5 $$\mu\text{m}$$ CP1 or PEN	Flexibility and low areal density
Rear thermal layer	10–20 nm chromium	Increased infrared emission
Optical protective layer	10–30 nm Al₂O₃ or SiO₂	UV and surface-durability protection
External bellows shell	CFRP with high-temperature polymer matrix	Low mass and structural strength
Ring and hinge reinforcement	CFRP, titanium, or Al-Li alloy	Load transfer and mechanical locking
Tension cords	Zylon/PBO, aramid, or CFRP	Lightweight tensile support
Thermal receiver coating	SiC, Al₂O₃, or black ceramic	High-temperature solar absorption
Electrical pathways	Kapton flexible circuits with gold-plated copper conductors	Sensor and actuator interconnection

ACS3 uses an approximately 2 $$\mu\text{m}$$ PEN substrate with an approximately 100 nm aluminum reflective layer and a thin chromium layer on the reverse side to enhance thermal emission. This is a realistic material reference for HBPF-1. [2]

Cover Mechanism

Front iris cover

The entrance aperture includes six rhombus-shaped or trapezoidal leaves.

Feature	Design
Number of leaves	6
Opening range	0–110°
Closed configuration	Protects the optical membrane during launch, transfer, and non-operational states
Open configuration	Each leaf may serve as supplementary reflective surface
Actuation	Shape-memory-alloy wire with spring return, or miniature electric motor
Safety	Dual independent locking paths and mechanical travel stops
Failure configuration	Closed, optically passive, safe state

Rear exit cover

The rear cover protects the thermal receiver. It opens in concentrator mode; in reflector mode, it may be partially opened or repositioned according to the desired target direction.

Energy and Thermal Calculations

Mars-orbit case

Mean solar irradiance near Mars is approximately 590 W/m². [5]

The ideal collected power at the HBPF-1 entrance is:

$$
P_{\text{incident}}

590\times2.598
\approx1.533\ \text{kW}
$$

At 75% net optical efficiency:

$$
P_{\text{output}}

1.533\times0.75
\approx1.15\ \text{kW}
$$

The average flux at the exit aperture is:

$$
q_{\text{exit}}

\frac{1.15\ \text{kW}}{0.650\ \text{m}^2}
\approx1.77\ \text{kW/m}^2
$$

This is suitable for thermal control, small receiver heating, low-to-medium-temperature experiments, and structural/optical validation. It is not, by itself, a high-temperature industrial furnace.

Earth-orbit case

At approximately 1,361 W/m² near Earth:

$$
P_{\text{incident}}

1.361\times2.598
\approx3.54\ \text{kW}
$$

$$
P_{\text{output}}
\approx2.65\ \text{kW}
$$

The first orbital demonstrator should therefore operate in Earth orbit, where higher solar irradiance, communications access, operational simplicity, and lower mission cost improve validation opportunities.

Control System

Sensor or actuator	Quantity	Function
Sun sensors	2	Determine solar direction
Temperature sensors	12	Monitor internal surfaces and critical mechanisms
Strain sensors	6	Monitor bellows and tension-system loads
Deployment encoders	8	Confirm open/closed state of each bellows segment
Optical-alignment photodiodes	3	Measure light centering at the exit
Micro-actuators	6	Adjust the inclination of each internal surface
Main deployment actuator	1–2	Extend the bellows axially
Cover actuators	2	Control front and rear covers
Flight computer	1	Autonomous sequencing, fault response, and telemetry

Deployment sequence

1. Confirm launch-lock release.
2. Confirm spacecraft safe orientation toward the Sun.
3. Open the front cover to 20%.
4. Extend bellows to 25%; check strain and temperature.
5. Extend bellows progressively to full length.
6. Engage corner latches.
7. Tension the internal membrane.
8. Use optical-alignment sensors for micro-angle adjustments.
9. Activate thermal or reflective operating mode.
10. Move to safe mode if excessive temperature, membrane damage, loss of attitude, or mechanical fault is detected.

Safety and Fault Tolerance

Risk	Potential result	Mitigation
Bellows fails to deploy	Mission loss	Dual deployment paths and spring-assisted passive deployment
Membrane wrinkling	Optical-efficiency loss	Tension cords and multi-point strain sensing
Cover jamming	Failure to activate optics	Redundant actuator and mechanical overtravel allowance
Excess temperature	Coating or polymer degradation	Sun-avoidance attitude, cover closure, radiative cooling surface
Micrometeoroid puncture	Local optical loss	Compartmentalized membrane and tear-arrest mesh
Electrical fault	Loss of active control	Passive safe closure and mechanical locking
Orbital debris impact	Puncture or structural damage	Protected initial orbit, tracking, and avoidance procedures

Thermal-vacuum testing is critical for verifying that space hardware remains functional under vacuum and extreme temperature cycling. [6] Qualification of deployable membranes also typically involves vibration, static-load, rapid depressurization, thermal-vacuum, and repeated deployment testing. [7]

Development Plan

Phase 0 — Design Validation

Duration: 3–6 months.

• Optical ray-tracing analysis.
• Folding kinematics and interference analysis.
• Structural finite-element analysis.
• Thermal analysis.
• Mechanism tolerance study.
• Reflective-coating sample testing.

Deliverable: HBPF-1 engineering-design package and manufacturing drawings.

Phase 1 — 0.5 m Laboratory Prototype

Duration: 4–6 months.

• 0.5 m entrance-aperture hexagonal module.
• Three or four bellows segments.
• Manual and motorized deployment testing.
• Optical-wrinkling measurement.
• At least 100 deployment cycles.
• Thermal testing under a solar simulator.

Success criterion: Greater than 95% deployment repeatability and greater than 60% optical transfer efficiency.

Phase 2 — HBPF-1 Engineering Model

Duration: 8–12 months.

• 1.732 m entrance flat-to-flat width.
• Eight bellows rings.
• Full covers, sensors, and actuator system.
• 500 deployment/stowage cycles.
• Thermal-vacuum qualification.
• Vibration and shock tests.
• Optical-efficiency measurement.
• Locking-system load tests.

Success criterion: Approximately 75% optical efficiency and mechanical stability within defined bending and torsional limits at 2.4 m deployed length.

Phase 3 — Orbital Demonstrator

Duration: 12–24 months.

• Low Earth orbit mission on a small satellite or hosted payload platform.
• Full deployment, cover operation, and telemetry.
• Sun-pointing and optical-alignment experiment.
• Six to twelve months of material-degradation monitoring.
• Measurement of photon-pressure and thermal-deformation effects.

Success criterion: Successful deployment, stable optical surface, thermal operation within limits, and safe closure.

Phase 4 — HBPF-7 and HBPF-61

System	Description	Approximate optical area	Objective
HBPF-7	First 7-module honeycomb cluster	18 m²	Inter-module mechanical and optical synchronization
HBPF-61	61-module honeycomb array	158 m²	Large-area funnel-tube network
HBPF-60	60 m-class expanded array	Approximately 2,500 m²	Mars light redirection, solar sailing, or solar-thermal power demonstration

Note: Sixty-one HBPF-1 modules produce only:

$$
61\times2.598
\approx158.5\ \text{m}^2
$$

of total entrance area. This is not a 60 m-diameter aperture. Reaching approximately 2,500 m² requires larger modules or a much larger number of smaller hexagonal modules.

60 m System Scaling

For a 60 m-class external aperture, each module should have an approximately 4 m hexagonal side length.

Parameter	HBPF-60 proposal
Number of modules	61
Entrance side length per module	4 m
Entrance area per module	41.57 m²
Total active area	Approximately 2,536 m²
Deployed length per module	8–10 m
Ideal solar power at Mars	Approximately 1.50 MW
Net optical delivery at 75%	Approximately 1.12 MW
Exit area per module at 4:1 concentration	Approximately 10.39 m²
Net output per module	Approximately 18.4 kW
Total net output	Approximately 1.12 MW

In this architecture, the light from each module should be directed to its own rear receiver rather than merged onto a single central receiver. Combining the output of many wide modules into one point creates unnecessary difficulty in alignment, shadowing, thermal concentration, and fault tolerance.

Final Design Statement

HBPF is not a single-piece glass mirror funnel. It is a modular space-optics tube formed by a hexagonal CFRP bellows structure, a tensioned internal metallized photonic membrane, protective covers, sensors, and active controls. Each module may direct sunlight to its own thermal receiver, or disable its funnel shape and operate as a broad-area reflective panel.

The first realistic milestone is the single-module HBPF-1, demonstrating deployment, locking, membrane tensioning, and 4:1 optical concentration. The concept can then scale through a seven-module honeycomb and a 61-module array, while Mars-directed illumination, asteroid thermal processing, and solar-sail applications should be evaluated only after this validation sequence.