VOLLEY: an electromagnetic orbital CubeSat deployer

Numerical audit correction, 2026-08-03. I corrected the winding-thickness quadrature and propagated the rated point to 11.03 N per kA/m, 16.388 m/s, 10.53 g, 20.99% net efficiency, and 65.552 N s per shot. I also corrected A13's internal-momentum physics, replaced A6's fixed-shape covariance claim with a valid current-geometry slab bound, extended A12's stress plane, removed a 0.344 kg brake-fin double count, and corrected the fin thermal mass. Superseded values remain visible in their validation records and change log.

A magazine-fed electromagnetic deployer that ejects unmodified CubeSats from a host stage at programmable velocity, aimed at the unserved regime between spring deployers (~2 m/s) and propulsive orbital transfer vehicles (hundreds of m/s).

Status: design study, TRL 2-3. Phase I CAD is complete across 9 Fusion 360 documents in three generations, with Gen3 STEP exports committed. A provisional Gen4 open assembly exists in Fusion but has no rated operating point or repository export yet (status). Nine of eleven planned validations have run — two of them failed, one found a published number 37 % high, and one returned three rows that could not be evaluated at all. Nothing has been built and nothing has been measured at any scale. Read docs/PROVENANCE.md before citing anything here.

📄 One-page summary · 🧊 Frozen baseline · Gen4 status · 🗺 Roadmap · ⚠ Open problems · ✓ Validation · 🏗 Manufacturing · 📐 ADRs · 📚 Literature · 🎯 Research position · ⛔ Velocity ceiling · ☠ Kill criteria · 🏁 Phase I closure · 📦 Payload classes · 📈 Market

Repository	Role	You are here
VOLLEY	Flagship, authoritative engineering record, portfolio
VOLLEY-paper	IEEE companion, manuscript and reproducibility package (generated)
VOLLEY-thesis	Thesis companion, university submission (generated)
VOLLEY-lab	Phase II, research, redesign, deliberately unstable

Four repositories, one programme, see docs/PROGRAMME.md.

The idea

CubeSats flown as rideshare secondaries inherit the primary customer's orbit. The spring that ejects them adds 1-2 m/s, enough to drift clear, not enough to change an orbit. A satellite with no propulsion of its own is stuck there for life.

VOLLEY replaces the spring with an ironless double-sided Halbach linear synchronous motor driving a reusable magnetic sled along a 1.5 m track. Twelve 3U CubeSats feed from two transverse cassettes and are fired one at a time. The satellite is never modified, the magnets ride the sled, not the payload.

Interior. Track, stator belts, sled, and both cassettes with the enclosure open.	Exploded. The nine documents: track, stator, sled, cassettes, brake, ESPA interface, enclosure, payload.
Aft mounting. Ø460 mm ring flange, Ø400 mm bolt circle, 24 holes, four gussets.	Mid-stroke. Sled under thrust, payload still cradled, 158.6 ms from breech to release.

Spin it in the browser: cad/stl/EMOCD_Assembly_Gen3.stl and cad/stl/EMOCD_Sled_Gen3.stl, GitHub renders STL natively, so click either and drag. They are derived meshes; cad/step/gen3/ is the master geometry (why).

How a shot works

flowchart LR
    A["Cassette feed<br/>12 x 3U, two cassettes"] --> B["Retention gate<br/>preload into structure"]
    B --> C["Accelerate<br/>1.3 m, 10.5 g, 158.6 ms"]
    C --> D["Coast &amp; trim<br/>0.2 m"]
    D --> E["Release at 1500 mm<br/>16.39 m/s"]
    E --> F["Eddy brake<br/>1530-1740 mm"]
    F --> G["Sled recovered<br/>reusable, next shot"]
    E -.->|"payload departs"| H["Own orbit<br/>x1.62 lifetime"]

Loading

The satellite is never modified: the magnets ride the sled, not the payload. The sled leaves release carrying 1268 J; 240 mm of stator past that point takes 291 J of it back into the bank, and the eddy brake absorbs the remaining 935 J. Efficiency is quoted electrical-to-payload, net of that credit.

Headline results (all model outputs, not measurements)

The pulse-power chain does not close on purchasable cells

Found 2026-07-30, and stated here rather than left in the defect log. The supercapacitor bank is modelled at 12 mΩ. Commercial cells of this capacitance give 116 to 185 mΩ, and the shot stops completing above 65 mΩ: a source behind resistance R cannot deliver more than V²/4R, and this one is asked for 30 kW.

Exit velocity, stroke time and dispersion are unaffected and the mechanical design is not implicated. What is affected is that the rated point assumes a bank nobody can buy. Fixing it is a sizing decision, costed at four parallel strings in docs/PHASE_II.md PII-7, and it is not silently applied here. See P26.

Quantity	Value	Source
Thrust constant	11.03 N per kA/m, ±0.99 % ripple, independently computed by FEM to 0.03 %	analysis/motor_model.py, A1
Exit velocity, 3U	16.39 m/s at 10.5 g	analysis/motor_model.py
Electrical to payload efficiency	21.0 % (2.56 kJ net of regeneration, 537 J delivered)	analysis/motor_model.py
Closed-loop dispersion	0.027 m/s (3σ) at a 16.2 m/s setpoint to ±0.10 km apogee	analysis/motor_model.py
Orbital lifetime multiplier	x1.62 at mean activity, not invariant, see P16	analysis/astro.py
Constellation seeding	30° in 1.4-6.9 days vs 25 days by differential drag	analysis/astro.py
Dry / loaded mass	76.5 kg / 124.5 kg	analysis/mass_properties.py
Recoil per shot	65.6 N·s	analysis/astro.py
Track first mode	109 Hz fixed-fixed (target >70)	analysis/sizing.py
Energy closure	100.0 % accounted	analysis/sizing.py

These numbers moved on 2026-07-29, downward

The headline used to read 20.37 m/s at 16.3 g, computed against a 4.86 kg parametric sled. Exact solid volumes from the Gen3 CAD give 9.445 kg: the plates are drawn solid, with no pocketing (P15).

That was not resolved by picking a number. validation/A4_sled_structural.md fixed the consequence of each outcome before the structural analysis ran:

Measured mass	Declared consequence
≤ 5.35 kg	parametric model stands, 20.37 m/s holds
5.35-6.80 kg	neither estimate right
≥ 6.80 kg	the headline changes and the paper changes materially

A4 has since run, the drawn plate passes all three structural bands, so nothing forces a lighter chassis, and the CAD result landed in the third branch. The scripts moved first, then the paper. Writing the rule down in advance is what made that a procedure rather than a preference.

What this costs and does not cost. Exit velocity is down 19 % and efficiency from 32 % to 20 %, and to 19 % after the ESR correction of 2026-07-30 (P24); regeneration has then took it to 21.2 % (A11); the corrected quadrature now gives 21.0 %. The lifetime multiplier is down only 10 %, x1.80 to x1.62, because lifetime is a weak function of Δv, the mission case survives better than the machine spec does. 9.445 kg is the as-drawn, unpocketed geometry, and A4 reports a 17x stress margin, so a rib-stiffened chassis would recover mass. Nobody has designed one (docs/ROADMAP.md).

Ways to recover the velocity, pocketing, sheet current, stroke length, a two-layer stator, and a momentum-transfer release that buys it all back for 1.6 % of the shot energy, are costed in docs/DESIGN_OPTIONS_exit_velocity.md.

Three results have independent cross-checks: the Halbach field model (analytic vs magpylib, agreeing to three digits, and again vs a meshed magnetostatic FEM, a PDE solve rather than another superposition, agreeing on the corrected thrust constant to 0.03 %), and orbital decay (orbit-averaged vs Cowell RK4, 99.4 %). Everything else is single-sourced.

Reproducing

pip install -r requirements.txt
cd analysis
python3 verify_field.py && python3 mass_properties.py && python3 motor_model.py && python3 sizing.py && python3 astro.py

Results land in analysis/results/*.json.

The analysis layer needs nothing but requirements.txt. The validation layer needs external solvers, gmsh and scikit-fem for the magnetostatic FEM, GetDP, CalculiX, ngspice, and a LaTeX install for the manuscript. tools/env-setup.sh installs all of them on a Debian/Ubuntu machine and verifies each one before exiting.

The shot. Force, velocity and current through the 158.6 ms stroke (motor_model.py).

Lifetime. Boosted vs unboosted decay, the x1.62 multiplier at mean activity is the current model result, not the absolute years (astro.py).

Validation

docs/VALIDATION_REPORT.md: every claim, independently checked where possible. Four analyses were actually run; three could not be.

• Reproducibility holds exactly: 173 values re-computed from clean, 173 identical.
• GMAT falsified the invariance claim. It reproduced the old x1.80 multiplier at mean and high solar activity but gave 2.074 at low, an 18.5 % spread against a ≤5 % band. astro.py varies solar activity by scaling density uniformly, and ballistic coefficient enters the same multiplicative slot, so both halves of that claim were tested by a sweep that could not have detected a problem (P16).
• CalculiX cleared the chassis on all three structural bands, which is what settled the sled mass at the CAD-derived 9.445 kg and moved the headline to 16.54 m/s (P15), before the quadrature correction moved it to 16.39 m/s.
• ngspice reproduced the then-current shot model to 0.03 % and then, re-run at the then-current operating point, found a loss the analytic model had no term for at all: the bank's own series resistance, 86 J a shot (P24). Corrected, the two methods agree on peak current to 0.01 %. It also found the quoted bank sag is state-of-charge, not the terminal voltage the drive sees.
• A1 and A10--A13 have been propagated to the corrected point. A5 and the ngspice A8 run predate it (P19) and needs re-running. A4 survives, its load being magnetostatic and velocity-independent.
• A1 has run (2026-07-29). A meshed 2-D magnetostatic FEM gives K_t = 11.026 N per kA/m against the model's 11.03, ratio 0.9997, ripple 0.97 % against 0.99 %. The number every headline descends from is no longer checked only analytic-against-analytic. Two of seven bands missed, both with identified causes and neither a model error (P20, P21).
• Not run: A6, A7, A9.

Charts

Full set in docs/RESULTS.md: all drawn by GitHub from text, no image files. Two that carry the argument:

pie showData
    title Energy per shot (J) - sizing.py energy_closure
    "Sled KE to the eddy brake" : 935
    "Payload KE, the useful output" : 537
    "Copper loss, shot + regen" : 850
    "Converter loss" : 111
    "Bank ESR loss" : 91
    "Auxiliary" : 35

Loading

537 J reaches the payload out of a net 2560 J: 2851 J leaves the bank and 291 J returns. That is the 21.0 %. Efficiency fell with the heavier sled twice over, because more of the same mechanical work goes into a mass that is then braked away and the longer 159 ms pulse accrues more copper loss at unchanged current density. Regeneration is the first thing that has moved it the other way.

This page said "no regeneration credit" until 2026-07-31, on the strength of a 2025 decision that argued the motor cannot arrest the sled. It cannot, and the brake stays. It was never shown that no energy could be recovered, and validation/A11_regen_braking.md found 23.0 % of the sled's energy available inside the existing envelope at the existing current rating.

The 86 J ESR slice was not here until 2026-07-30. No script modelled the bank's series resistance, so the loss existed in the hardware and nowhere in the accounting. A circuit simulation found it (P24).

xychart-beta
    title "Minimum approach vs ejection velocity - not a robust quantity"
    x-axis "Ejection velocity (m/s)" [20.00, 20.37, 20.50, 20.65, 21.00]
    y-axis "Minimum approach (km)" 0 --> 70
    line [37.5, 4.6, 56.1, 45.3, 63.4]

Loading

A ±2.5 % velocity change moves the conjunction minimum from 4.6 km to 63.4 km. That is why the paper's safety claim rests on the realignment period, now 9.9 days at the current operating point, instead of a single distance (P1). The sweep above was computed at the superseded 20.37 m/s point and is kept as the evidence for P1; the fragility it demonstrates is a property of the beat geometry, not of any one velocity.

Validation status

Each analysis has its acceptance band declared before the run, in validation/. A5 has now been run under GMAT; the rest have not, a cross-check whose target is chosen after seeing the answer proves nothing.

Analysis	Tool	Closes	Status
A1 airgap field	FEMM	E1 (2-D half), E2	specified
A4 sled chassis	CalculiX ccx 2.21	P5, P8	run: as-drawn plate passes; mass unchanged
A5 lifetime & seeding	GMAT R2022a	E6	run: see docs/RESULTS.md
A6 conjunction Pc	NASA CARA	P1	specified
A7 separation & tip-off	Project Chrono	E7	specified
A8 pulse-power chain	ngspice 42	E17	run: bands met, 2 findings

Host integration, worked against real vehicles

The interface asks four things of any host: mass and control authority, a 150-300 W recharge feed, a serial command link, and an authorized firing window. Two Indian candidates are worked as examples in the paper because both exist today.

ISRO's POEM is the flown precedent, a spent PS4 stage operated as a three-axis-stabilized hosted platform with solar power, NavIC navigation and helium attitude thrusters, retired by controlled reentry. It supplies everything the attached variant borrows, and its zero-debris closeout is the regulatory template.

Skyroot Aerospace's Vikram-1 carries a restartable liquid Orbit Adjustment Module, one Raman-2 engine, four Raman Mini thrusters, eight cold-gas thrusters, stage-tested through more than a thousand pulses, whose stated multi-orbit deployment role is functionally the PS4's. Against the vehicle's published 350 kg LEO capacity, a loaded VOLLEY is 34 %, falling to 22 % and 13 % on the announced 550 kg and 900 kg family members. Early flights are therefore dedicated demonstrations and later ones ordinary manifest items.

One integration quantity cannot be closed from public data: the OAM's mass and control authority are undisclosed, which is why the recoil budget is parametric. Obtaining stage mass, thruster impulse budget and coast duration is the single data exchange that converts this analysis from parametric to specific, for any candidate vehicle, Indian or otherwise.

Recoil is the satellite's momentum only, 65.6 N·s per shot, nulled by a few grams of cold gas. Comparison against fielded deployers and transfer vehicles, including Dhruva Space's flown DSOD, is in docs/LANDSCAPE.md.

Repository layout

• analysis/, current scripts; these reproduce the numbers above
• analysis/femm/, FEMM magnetostatics package: emocd_cross_section.dxf + FEMM_RUN_SHEET.md (analysis A1, not yet run)
• cad/, Fusion 360 CAD: parameters.json (geometry source of truth, 9 documents), step/gen1|gen2|gen3/ exports (Gen3 current), stl/ (browser-viewable meshes), renders/, CHANGELOG_CAD.md (generation history and per-file defect list)
• legacy/, superseded scripts, kept for history, do not cite
• paper/, IEEE conference paper (LaTeX source, figures, PDF)
• validation/, independent cross-check plan (FEMM, CalculiX, Orekit, CARA, Chrono), each with an acceptance band declared before the run; nothing run yet
• docs/, computation notes, FEMM run sheet, related work and comparator sources
• docs/PROJECT_NOTES.md, working context: ground rules, layout, locked decisions
• docs/LANDSCAPE.md, how this compares with deployers that actually fly
• docs/DESIGN_OPTIONS_exit_velocity.md, options for the P15 velocity shortfall, costed
• docs/INVENTORY.md, complete indexed catalogue of every calculation, decision and artifact
• docs/DECISION_LOG.md, why each design change happened, including two self-corrections
• docs/PROVENANCE.md, what came from where, and what was never verified
• OPEN_PROBLEMS.md, known errors in the paper, and unsolved engineering
• docs/PROGRAMME.md, the four repositories and how they relate
• docs/BASELINE.md, the frozen Phase I baseline (generated) and its change-control rule
• docs/GEN4_STATUS.md, provisional open-assembly geometry and the export/performance gate
• docs/HISTORY.md, project timeline since 2021, and how the git history was reconstructed
• docs/programme/, the governing dossier, adopted verbatim, plus its amendment record
• docs/adr/, nineteen architecture decision records
• docs/PHASE_II.md, deferred work and the gate it must clear to return
• docs/MANUFACTURING.md, tolerance stack, assembly hazard, make-vs-buy
• docs/CROSS_INDUSTRY.md, which open items are actually solved elsewhere
• docs/QUALIFICATION_PLAN.md, environmental and qualification campaign, specified not run
• docs/BENCHTOP_TESTS.md, four cheap sub-scale experiments, bands declared in advance
• analysis/cost.py, parametric BOM; every price assumed, structure is the deliverable

Known issues

The published paper previously contained four numbers its own scripts did not reproduce (conjunction minimum, peak current, far-field stray values, brake fin temperature rise), all found by reconstructing the analysis from scratch. All four were corrected in paper/paper.tex on 2026-07-23 to match the scripts, and the conjunction claim was additionally reframed because that minimum is not a robust quantity. Note that paper/archive/EMOCD_submission_uncorrected.pdf still carries the uncorrected values, whether that build is the one that was submitted is open (OPEN_PROBLEMS.md P11). Full record with cause, before/after, and references is in CHANGELOG.md; the original defects remain documented in OPEN_PROBLEMS.md P1, P4 for the audit trail.

Two issues are live rather than historical, and both sit in the paper:

• P16, the invariance claim in the abstract is falsified. GMAT reproduces the x1.80 lifetime multiplier at mean and high solar activity but gives x2.074 at low, an 18.5 % spread against a ≤5 % band. The reason is that astro.py varies solar activity by scaling density uniformly, which preserves a ratio by construction, and the ballistic-coefficient half of the same sentence is the identical construction, since scale and 1/BC occupy the same slot in the drag term. Neither half of that claim was ever tested by a method capable of falsifying it. paper/paper.tex still asserts it in five places, including the abstract, because there is no TeX engine here and editing the source without rebuilding the PDF would split the two.
• P11, which build was actually submitted is unresolved. Until that is answered, it is not known whether the version of record carries P1, P4 and the falsified abstract claim.

Newest entries: P26 (the supercapacitor bank cannot source the shot on purchasable cells), P28 (the regeneration stator and the eddy fin do not both fit the arrest section) and P29 (the paper says the winding is segmented; the model charges copper for all 1.3 m). Most recently closed: P17, the inter-array attraction feeding the A4 FEA, 37 % high — resolved by A12, which also found that P17's explanation of its own finding was backwards.

Author

Adityavardhan Mishra: Department of Mechanical Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune. Project begun April 2021.

📧 adityavardhanmishr@gmail.com

Questions, corrections and reproduction attempts are all welcome, particularly reproduction attempts. If a number in this repository does not reproduce for you, that is a defect and I want to know. See docs/CONTRIBUTING.md.