This page describes the physics and design basis of the standard-gauge splinky guideway. It states the governing equations and the assumptions behind every quoted figure, so that the design can be checked and its limits pushed. SI units are used throughout; vacuum permeability is μ₀ = 4π × 10⁻⁷ T·m·A⁻¹.

Principle of operation#

A splinky is built from strands — contiguous series of coaxial superconducting rings — anchored at their ends and junctions by terminals, which hold each strand to the habitat structure and act as its power source and sink. Within a strand the rings perform three functions with one set of magnetic elements:

1. Standoff and station-keeping. The rings carry no physical connection to one another. Each senses its position relative to its neighbours and modulates its current to hold station: coaxial rings repel when their currents oppose and attract when they align, so by biasing toward repulsion and trimming about that point a strand behaves as a chain of free-flying rings held in formation by an actively controlled magnetic spring. (Earnshaw’s theorem forbids doing this with fixed fields, so the spacing is a closed-loop control problem.)
2. Levitation and guidance. A vehicle collar encloses a short run of the lattice and floats in the rings’ field. Because magnetic levitation has no stable equilibrium under static fields (Earnshaw’s theorem), the lateral position is held actively: each ring’s flux can be displaced sideways by redistributing current among internal conducting paths, generating a restoring force.
3. Propulsion. The alternating ring polarities present a periodic field along the track. The collar carries windings that, energised in phase with the passing poles, push against the rings — a linear synchronous motor whose stator is the guideway itself.

Reference geometry and design basis#

All worked figures below use the standard-gauge parameter set. These are design choices, not derived constants; the scaling relations that follow show how the performance moves when they change.

The choice Jₑ = 1000 A·mm⁻² at 40–60 K and multi-tesla field is the principal materials assumption: it is roughly an order of magnitude beyond early rare-earth-barium-copper-oxide tape but is the design point assumed for the high-temperature superconductor used in mature autopoietic-industry production. The main-winding cross-section follows directly: A_w = NI / Jₑ = 4.0 × 10⁶ / 1.0 × 10⁹ = 4.0 × 10⁻³ m².

The ring-centre field is the standard single-loop result,

B₀ = μ₀ NI / (2a) = (4π × 10⁻⁷ × 4.0 × 10⁶) / (2 × 0.50) ≈ 5.0 T.

Per-ring mass is taken as ≈ 150 kg (winding ≈ 90 kg at a composite-tape density of ≈ 7000 kg·m⁻³ over the 2πa ≈ 3.14 m circumference, plus ≈ 60 kg of cryostat, former, and shield). At 4 rings·m⁻¹ this gives λ ≈ 600 kg·m⁻¹, the figure used for all span calculations.

Active station-keeping#

The rings are joined by no physical member; each holds its place by modulating its own current in response to its measured spacing from its neighbours. Two coaxial rings attract when their currents run in the same sense and repel when opposed, so each ring has a signed axial force available in either direction. Biasing every gap toward repulsion gives the lattice its nominal “slinky” standoff; trimming the bias about that point — repelling harder as a gap closes, easing or reversing toward attraction as it opens — makes each gap a bidirectional spring. Because a chain of pure repulsion is unstable in extension, and a static field has no stable equilibrium at all (Earnshaw’s theorem), the spacing is held by closed-loop control: the same active principle used for lateral guidance, extended to the axial degree of freedom.

The force available to each gap sets the stiffness of that spring, and is estimated from the magnetic pressure across the rings’ facing annulus. The magnetic pressure of a field B is

P = B² / (2μ₀).

Taking an effective inter-ring field B_gap ≈ 3 T (below B₀ because the opposed axial fields partly cancel on the midplane, leaving the strong fields localised near the conductors) and a facing annulus A_face ≈ 2πa·w = 2π × 0.50 × 0.06 ≈ 0.19 m², the force one ring can exert on a neighbour is

F_ring ≈ (B_gap² / 2μ₀) · A_face ≈ 3.6 × 10⁶ × 0.19 ≈ 0.68 MN.

So each ring commands of order 0.7 MN of axial authority — the force that both holds the strand in formation and reacts vehicle loads into the lattice. The hoop stress on a ring from its own field, ≈ B₀²/2μ₀ ≈ 10 MPa, is two orders of magnitude below the composite former’s strength, so the rings are not stress-limited at standard gauge. Station-keeping runs as a fast distributed control loop; a bandwidth of order 1 kHz, well within solid-state flux-pump switching rates, holds the gaps against vehicle passage, vibration, and — in spin gravity — Coriolis and tidal loads.

Holding station this way costs continuous control power and fails actively (see Power and energy and Design assumptions and known limits). A passive safety tether — a thin tension fibre threading the rings — is an option on crewed lines and on the longest free spans: it does not set the spacing but provides a failsafe backbone and adds global tension stiffness. It is a variant, not part of the standard strand.

Assumption flagged for refinement. F_ring depends on B_gap and A_face, both estimated rather than computed from the full mutual-inductance field. A parallel-wire near-field estimate runs roughly an order of magnitude higher; a dipole far-field estimate diverges because the pitch is below the gauge radius. The pressure-over-annulus value above is the conservative one, and is the single quantity most worth replacing with a detailed field solution, because station-keeping stiffness, reaction capacity, and span all scale with it.

Levitation and load capacity#

The collar floats on the same magnetic pressure. With a collar interaction field of B_c ≈ 2 T across the 25 mm gap, the lift pressure is

P_lift = B_c² / (2μ₀) = (2.0)² / (2 × 4π × 10⁻⁷) ≈ 1.6 × 10⁶ Pa.

A collar two metres long presents an interaction area A_collar ≈ 2πa · 2 m ≈ 6.3 m², giving an available lift of P_lift · A_collar ≈ 1.0 × 10⁷ N — about 10³ tonnes-force in one gravity. A loaded car of 30 t (≈ 3 × 10⁵ N) requires only ≈ 0.2 m² of interaction area. The splinky is not lift-limited. The binding constraints are guidance stability, self-support over a span, and propulsion power, treated below.

Because no static field configuration is laterally stable, this lift must be actively centred. The mechanism is flux steering.

Lateral guidance by flux steering#

Each ring is wound so that its magnetic flux can be displaced transversely under control. The main winding is a closed, persistent loop that needs no power to maintain lift. Two further trim saddle windings, wound as orthogonal transverse-dipole pairs, are superimposed on it; driving a current through one saddle adds a transverse field component that shifts the ring’s effective magnetic centre sideways by a controllable offset, in any direction in the cross-plane. Each saddle is energised by an integrated flux pump, so the steering topology is also fully closed and persistent and dissipates only switching losses.

A lateral offset δx of the field centre produces a restoring force on the collar of order

F_x ≈ k_lat · δx, with stiffness k_lat ≈ P_lift · A_collar / g_c.

At standard gauge k_lat ≈ 1.0 × 10⁷ / 0.025 ≈ 4 × 10⁸ N·m⁻¹, so millimetre-scale flux displacement commands meganewton restoring forces — ample authority. The control loop must run faster than the open-loop instability it is correcting; a bandwidth of order 1 kHz is sufficient for the gap dynamics and is well within solid-state flux-pump switching rates.

This authority also absorbs the Coriolis loads of travel inside a spinning gyrealm. For a habitat of rim radius R at one gravity, the spin rate is ω = √(g/R); in Coriopolis (R = 10 km), ω ≈ 0.031 rad·s⁻¹. A vehicle moving circumferentially at v = 100 m·s⁻¹ feels a lateral Coriolis acceleration

a_Cor = 2ωv ≈ 2 × 0.031 × 100 ≈ 6.3 m·s⁻² ≈ 0.64 g,

which the guidance supplies as a steady transverse bias. Travel along the spin axis is parallel to ω and feels no Coriolis force; axial splinky lines are therefore the smoothest routes, and most long interior runs are laid axially for this reason.

Self-support and spanning#

A strand has no tension member, so between its terminals it carries its own weight as an actively stiffened beam: the station-keeping loop commands a differential force across each ring — harder on the lower side, easing on the upper — which sums to a restoring bending moment. The moment one gap can supply is bounded by the per-ring force authority acting across the gauge radius,

M_max ≈ F_ring · a ≈ 0.68 × 10⁶ × 0.5 ≈ 0.34 MN·m.

Equating this to the peak bending moment of a uniformly loaded span between supports, M = w_lin L² / 8, and solving,

L ≈ √(8 M_max / w_lin).

In one gravity w_lin = λg = 600 × 9.81 ≈ 5.9 × 10³ N·m⁻¹, so

L ≈ √(8 × 0.34 × 10⁶ / 5.9 × 10³) ≈ 21 m.

A strand thus self-supports over about twenty metres in one gravity before a terminal must take the weight; deflection over that span is actively nulled within the control gap rather than allowed to sag. Interior splinkies are carried on terminals — which double as supports and power nodes — spaced at that interval, giving operationally a magnetic-levitation rail with no moving parts and no tension cable. This limit is a force-authority (strength) limit, not a stiffness one: the control nulls deflection up to the point where a gap saturates its available moment.

Scaling. The span follows

L ∝ √(F_ring / w_lin) ∝ B_gap / √λ.

Raising the ring field increases per-ring force as F_ring ∝ B_gap², and lighter construction lowers w_lin. A high-field variant running B₀ ≈ 15 T (gap field ≈ 11 T, per-ring force ≈ 9 MN, still only ≈ 90 MPa of magnetic pressure on the rings) built at λ ≈ 300 kg·m⁻¹ reaches L ≈ 110 m between terminals. Span in one gravity is thus set by per-ring force authority and structural mass, not by any hard ceiling — the figures rise with material performance.

Microgravity. Where there is no weight to carry, w_lin → 0 and the static limit vanishes; free spans extend to hundreds of metres or kilometres, bounded instead by active bending stiffness, control bandwidth, and accumulated station-keeping error. Lacking a tension member, a very long free strand relies entirely on active stiffness, and so demands more control authority and bandwidth than a tensioned cable of equal length would — the honest cost of the tetherless design, and the case in which the optional safety tether is most attractive, since even a light fibre adds global tension stiffening. This is the regime in which the free-flying lattice is decisive: the kilometre-scale spans of dock and hub regions, and the axial crossing of the 2 km inter-section gap of Coriopolis routed near the low-gravity spin axis, are practical only because the strand carries little or no gravitational load there.

Propulsion and reaction#

The alternating ring polarities give a field that reverses every pitch, so its spatial wavelength is λ_f = 2p = 0.50 m. The collar drives itself as a linear synchronous motor: the synchronous speed is

v = f · λ_f,

so cruising at 100 m·s⁻¹ requires a drive frequency f = 200 Hz, and 150 m·s⁻¹ requires 300 Hz — both modest for solid-state drives. Thrust comes from the Maxwell shear stress between the collar’s travelling field and the ring poles,

τ ≈ B_n B_t / μ₀.

With normal and tangential components each of order 1 T, τ ≈ 8 × 10⁵ Pa; over the 6.3 m² collar this is ≈ 5 × 10⁶ N of available thrust. A 30 t car could in principle accelerate at over 15 g, so thrust is comfort-limited rather than force-limited: at a passenger-comfortable 0.15 g (≈ 1.5 m·s⁻²) the demand is ≈ 4.5 × 10⁴ N, drawing Fv ≈ 4.5 MW at 100 m·s⁻¹ during acceleration. Top speed is set by drive frequency, residual losses, and — in interior lines — aerodynamic drag, not by available thrust; long-haul splinkies therefore run in evacuated tubes.

Each thrust pulse pushes on the rings the collar is passing, which is the sense in which the lattice serves as reaction mass. The momentum is shared across the rings under the collar and routed through the station-keeping lattice into the nearest terminal, exactly as a conventional linear motor reacts against its mounting. In a long free strand the loaded rings recoil slightly and the control loop restores them, spreading the impulse over many rings before it reaches a terminal. Braking reverses the drive phase and is regenerative, returning kinetic energy to the line — where, as below, it can be stored in the rings themselves or drained at a terminal.

Strands, terminals, and reconfiguration#

A strand is a single contiguous series of rings under one station-keeping domain. Strands begin and end at terminals — structures that anchor the strand to the habitat (reacting its weight and the vehicles’ propulsive reaction into primary structure) and serve as its electrical source and sink. A route is assembled from strands meeting at terminals, which also act as the switches and junctions where a vehicle passes from one strand to the next.

Because the rings are not physically joined, a strand is reconfigurable while live. Individual rings can be ejected and incorporated: a ring that quenches, drifts out of tolerance, or fails mechanically is commanded out of the line — the lattice opens a gap and walks it to the strand edge — while its neighbours close ranks and re-establish the field pattern across the gap, and a replacement is inserted and brought up to current the same way. A strand survives the loss of any single ring as a local stiffness notch rather than a collapse. The same mechanism reconfigures a route: strands can be lengthened, shortened, split, merged, or re-anchored to different terminals by adding, removing, or handing off rings, with no cable to cut or splice. This live reconfigurability is the chief operational advantage of the tetherless strand over a tethered backbone.

Power and energy#

Each ring is a persistent superconducting loop and therefore an energy store: its magnetic energy is E = ½ L I², of order a few megajoules at standard gauge (the field energy B²/2μ₀ integrated over the bore and near field). A strand of a few hundred rings holds of order a gigajoule, distributed along its length.

Power is moved without a separate conductor. Adjacent rings are inductively coupled, so energy is ratcheted from ring to ring by the same flux pumps that trim the fields — charging, discharging, or shifting current along and between rings by modulating the coupling. Power injected at a terminal propagates down the strand as a sequence of flux-pump transfers; energy can likewise be moved between strands where they meet at a terminal. A strand is therefore at once the guideway, its own power bus, and a distributed energy reservoir, with terminals as the interface to the habitat grid.

This distributed store also softens the failure mode. Because the standoff and lift fields live in persistent loops, a power interruption does not drop them — the rings coast on their trapped current; what a strand loses on interruption is active control, not field. Local control electronics carry their own backup, so a strand rides through grid transients, and loss of control — not loss of current — is the design’s true hazard.

Free strands as reaction mass#

The reaction described above — the collar pushing on the rings — becomes a propulsion method in its own right when the strand is free-floating rather than anchored to a habitat. A spacecraft grips an untethered strand and drives along it; the rings are pushed the opposite way, and momentum is conserved between vehicle and lattice, so the vehicle gains velocity without expelling any propellant of its own. The strand is the reaction mass — but unlike propellant it is not consumed. It is recovered and used again, which is what makes the scheme attractive for repetitive intra-orbit transport among co-orbiting structures: ferries, tugs, and cargo pods that stay within the strand network carry no tanks, no thrusters, and never run dry.

Momentum budget. For a vehicle of mass m_v leaving a strand of reaction mass M_r,

m_v Δv_v = M_r Δv_r.

Take a 30 t vehicle (m_v = 3 × 10⁴ kg) accelerated to Δv_v = 100 m·s⁻¹, a useful transfer increment within an orbital cluster. The momentum exchanged is p = 3 × 10⁶ kg·m·s⁻¹. Holding the ring recoil to a recoverable Δv_r ≈ 10 m·s⁻¹ requires

M_r = p / Δv_r = 3 × 10⁵ kg ≈ 2000 rings ≈ a 500 m strand.

Energy and length. The kinetic energy delivered is

E = ½ m_v Δv_v² + ½ M_r Δv_r² ≈ 1.5 × 10⁸ + 1.5 × 10⁷ ≈ 165 MJ,

a small fraction of the few gigajoules a 2000-ring strand already stores, and so drawn from the strand itself through its flux pumps or topped up at a terminal — this is electric propulsion, with the grid supplying energy and the structure absorbing momentum. At a passenger-comfortable 0.15 g the push lasts Δv_v/a ≈ 67 s at ≈ 2.5 MW average, and the vehicle traverses d = Δv_v²/2a ≈ 3.4 km of strand; cargo accelerated harder needs proportionally less length (≈ 0.5 km at 1 g). Thrust, ≈ 4.5 × 10⁴ N, is two orders below the collar’s capacity.

Momentum recovery. Every push leaves its reaction mass drifting, so the momentum is not destroyed but relocated, and recovering it is as essential as spending it. A spent strand is decelerated against the habitat’s primary structure — a reservoir of order 10⁹–10¹² kg, which absorbs the 3 × 10⁶ kg·m·s⁻¹ of a launch as a velocity change of only millimetres per second — against an oppositely directed transfer, or reeled in by a terminal, after which its rings are redistributed into fresh strands. The cluster-scale coordination of this capture, momentum-banking, and redistribution — informally the ballet — is treated in Ring choreography.

Limits. This is not free delta-v: the energy is electrical and the recoil momentum must be banked in the structure, whose own orbit and spin are perturbed unless traffic is balanced. The method is scoped to relative transport within reach of the strand network — intra-orbit and intra-cluster — rather than orbit-raising or interplanetary flight, though a sufficiently long free strand is simply a mass driver and the same principle scales to launching cargo at high delta-v. The binding operational constraint is recollection reliability: a strand whose rings are not recovered is reaction mass lost to space, so the choreography that returns them is as essential as the push that spends them.

Ring-winding classes#

The internal conducting paths of a ring are what make flux steering possible, and several windings have been used. They are listed here with the trade-off that decides between them; the standard-gauge guideway uses the last.

• Monolithic loop with bulk flux-pinning. A single persistent loop levitated against a flux-pinned bulk superconductor. Lift is lossless and intrinsically stable, but lateral control is stiff and slow and the trapped flux creeps over time. Retained only for low-speed freight sidings.
• Azimuthal sector arcs. The ring is split into three or more independently driven arcs; redistributing current among them walks the magnetic centroid sideways. Control is direct, but every arc needs its own current path and the superconducting joints dissipate, so the winding cannot run fully persistent. Used where simplicity of control outweighs efficiency.
• Concentric nested loops. Current is transposed between an inner and an outer coplanar loop. This changes the dipole strength and field gradient — and so trims lift and stiffness — but moves the centre not at all, providing no lateral steering. Used as an auxiliary lift-trim winding, never alone.
• Continuous helix. The naïve reading of the slinky analogy: a single helical conductor. Its current is unidirectional, so neighbouring turns attract rather than repel and the standoff vanishes. It is not a viable guideway and survives only as a common misconception about the name.
• Persistent main loop with dual saddle trims (standard). A closed, persistent main loop provides lossless lift and standoff and, through modulation of its own current by an integrated flux pump, the bidirectional axial force used for station-keeping; two orthogonal transverse-dipole saddle windings, each likewise flux-pumped, add two-axis lateral steering without continuous leads. This combines the lossless persistence of the monolithic loop with the direct vectoring of the sector design while avoiding the joint losses of both the sector arcs and any leaded winding, and it is what lets a ring be charged, trimmed, ejected, and re-incorporated without a physical connection. It is the basis for all figures on this page.

Design assumptions and known limits#

The quantitative claims rest on the following assumptions; each is a place where a more detailed analysis or a change in materials would move the numbers.

• Conductor. Jₑ = 1000 A·mm⁻² at 40–60 K and multi-tesla field. Lower current density enlarges the windings and λ, shortening one-gravity spans.
• Per-ring force. Computed as magnetic pressure (B_gap ≈ 3 T) over the facing annulus. This is the least certain figure and a conservative one; a full mutual-inductance field solution would refine it, and a larger value raises station-keeping stiffness, reaction capacity, and span together.
• Span limit. The one-gravity span equates per-ring moment authority M_max ≈ F_ring·a to the gravity bending moment w_lin L²/8. It is a force-authority (strength) limit, with deflection actively nulled, and lengthens as √(F_ring/w_lin).
• Station-keeping power and failure mode. Spacing, guidance, and beam stiffness are all active and draw continuous control power (not quantified here). Persistent loops hold the fields through power loss, so the hazard is loss of control, not current; it is mitigated by per-ring energy storage, local control backup, and the optional safety tether.
• Energy transfer. Power moves along and between strands by flux-pump ratcheting between inductively coupled rings; the transfer rate (not quantified) sets how quickly a strand can source or absorb power as a bus.
• Collar geometry. A 2 m collar and 25 mm gap set the lift and guidance authority. Both are generous relative to demand, so neither is a binding constraint at standard gauge.
• Losses. Hysteresis and eddy losses in the collar, flux-pump switching losses, and cryogenic load are treated as small relative to propulsion power and are not quantified here; with station-keeping power they set the standby budget and are the next item for a full energy accounting.

The headline conclusions are robust to these assumptions: levitation capacity is in large surplus, propulsion is comfort-limited rather than force-limited, guidance and station-keeping have meganewton authority, and the self-supporting span is modest in spin gravity (a few tens of metres, hence closely spaced terminals) but effectively unlimited in microgravity, where the free-flying strand defines the technology’s role.