The Physics

The Physics — background theory

You never need the math to play — the Dashboard shows everything as speeds and percentages. But if you want to know exactly what the mod is doing to your ship, here it is. Everything below is special relativity only (no general relativity), applied as a force/rate layer.

The two quantities: β and γ

• β (beta) is your speed as a fraction of light speed: β = v / c. At half light speed β = 0.5.

• γ (gamma), the Lorentz factor, is how much relativity "bites" at that speed:

  γ = 1 / √(1 − β²)
  

  γ starts at 1 (no effect) and runs away to infinity as β → 1. This runaway is why c is an unreachable wall.

1. Thrust falls as 1/γ³ (the light wall)

For a force pushing along your direction of motion, special relativity gives the acceleration as

a = F / (γ³ · m)

so the thrust that actually accelerates you is F_eff = F_nominal / γ³ (this is the "longitudinal mass" γ³m). As β → 1, γ³ explodes and acceleration → 0 no matter how big the engine. No artificial speed cap is needed — the engine simply stops biting.

β	γ³	effective thrust
0.1	1.015	98.5%
0.5	1.54	65%
0.9	12.1	8%
0.99	356	0.3%

The curve is gentle below ~0.5c and steepens hard near c — the "pushing the light barrier" feel.

It is direction-blind. Braking is also an engine burn, so slowing down near c is exactly as feeble as speeding up. That is the single most important gameplay consequence: you must start arrival deceleration absurdly early. See Dashboard#brake-authority-cue.

Honesty note. This is a gameplay abstraction, not momentum-conserving SR. The mod burns propellant at the normal rate while delivering only F/γ³ of force, so fuel→Δv efficiency silently degrades near c — "the wall costs you fuel too". The dv/dt and the light-wall feel are correct; the momentum bookkeeping is not exact-SR.

2. Resource burn slows as 1/γ (proper time)

A moving crew's clock runs slow: proper time is dτ = dt / γ. Their onboard processes unfold in their time, so all onboard resource consumption scales by 1/γ — a fast crew ages and eats slower.

β	γ	effective thrust (×1/γ³)	resource burn (×1/γ)
0.5	1.15	65%	87%
0.9	2.29	8%	44%
0.99	7.09	0.3%	14%

The two effects have opposite sign — thrust is crushed, but a ship that already is fast keeps its crew alive far longer. That is the trade the whole mod is built around.

The gap is permanent. Slow back down and the burn rate returns to normal, but the time already saved while fast is kept for good — the twin-paradox outcome. Decelerating never "catches up".

What is not scaled (excluded from the 1/γ slowdown):

• Engine propellant + oxidizer — burned in coordinate time to make the force (scaling it too would double-reward).
• ElectricCharge — captured externally (solar) in coordinate time.
• Radiation dose — see below.

3. The twist: radiation stays on coordinate time

Radiation is an external flux, not an onboard process, so it is not dilated — dose keeps ticking at ×1.00 while life-support burn drops to ×0.39 at 0.9c. A fast crew ages less but soaks the same dose, so on a relativistic run radiation, not starvation, is the binding constraint. (An optional doseBeamingExponent can even raise forward dose at high β to model blueshifted/beamed cosmic rays — off by default. See Configuration.)

4. Attitude (turning) slows as 1/γ

Reorienting the ship — reaction wheels, RCS torque — is an internal proper-time process, so it slows by the time-dilation factor 1/γ (the same 1/γ as resource burn, not the 1/γ³ of translation). At γ = 7 (0.99c) a 180° flip takes ~7× longer. Combined with direction-blind braking, you need lead time just to point retrograde before a decel burn. Wheel/RCS resource use (EC, monopropellant) is not slowed — only the turn rate.

5. Reference frame — the Solar System barycenter

Speed relative to what? The mod measures β against the Solar System barycenter inertial frame, fixed at departure (for KSP that is the Sun-fixed inertial frame). Inside any planetary system your speed is a few km/s ≈ 10⁻⁵ c, so β ≈ 0 and the layer is effectively interstellar-cruise-only — it switches on by itself only when you are actually crossing between stars. Other stars' peculiar velocities (α Cen ≈ 22 km/s ≈ 7×10⁻⁵ c) are negligible, so "at rest at the destination" still reads β ≈ 0.

Under Principia this is free — it already integrates in a barycentric inertial frame and hands over the velocity directly.

6. Safety guards

Three cheap, fail-safe guards keep the layer honest (see Configuration for the thresholds):

• Activation gate — below betaMin everything is identity (no correction, no scaling). This is what makes it interstellar-only for free.
• Warp exemption — warp/jump motion is a metric bubble, not real speed-through-space, so a vessel under warp has β ≈ 0 and is treated as identity. Warp mods raise a generic WarpFlag the layer reads.
• Kraken fail-safe — KSP physics bugs can fling parts to absurd/superluminal velocity (β ≥ 1 → NaN). Above betaSane the layer disables for that vessel and logs a one-liner rather than trying to "fix" the glitch. The thrust correction is inherently bounded (it can never exceed full thrust cancellation), so the mod cannot amplify a kraken.

7. What the mod models — and what it doesn't

KSP is a Newtonian, single-frame, floating-point simulator. This mod is a force/rate layer on top: it reproduces the feel and the bookkeeping of special relativity, not its kinematics. That is a deliberate line, and it is worth knowing exactly where it falls — so here is the honest ledger.

Modeled (what you actually get)

Effect	How	Section
Thrust collapses 1/γ³ (the light wall)	corrective force on the vessel	§1
Crew/resource consumption slows 1/γ (proper time)	rate scaling	§2
Radiation dose stays on coordinate time	excluded from the 1/γ scaling	§3
Turn rate slows 1/γ	torque scaling	§4
Two clocks + a permanent twin-paradox gap	per-vessel proper-time integral τ = ∫dt/γ, persisted, ticks even while unloaded	§2
β measured against a fixed barycentric frame; auto-gated to interstellar cruise	speed sampling + betaMin/betaSane/warp guards	§5, §6

Every one of these is a scalar applied to force, a rate, or a torque. That is the whole toolbox.

Not modeled (and why)

These are real SR effects the mod does not reproduce. None of them is a bug — each is either outside KSP's engine or deliberately out of scope.

1. The c wall is not hard-enforced. In reality c is unreachable, full stop. Here it is enforced only softly, by the 1/γ³ thrust collapse — push by some means that isn't a force (cheat menu, a kraken, an orbit-editing warp/PT mod) and KSP's Newtonian integrator will happily let the number cross c. Above betaSane the mod simply stops modelling rather than pretending. So the wall is a very strong disincentive, not a law of the sim.

2. No length contraction. Ships and objects keep their rest length at any β. KSP has no mechanism for it and it would not affect gameplay.

3. No relativistic optics — aberration, Doppler, the "starbow". A real near-c view is beamed and blueshifted forward, the star field aberrated into a tunnel ahead. The mod renders the ordinary KSP sky. A visual layer is explicitly out of scope (this is a mechanics mod, not a shader).

4. Velocity addition is Galilean (linear). KSP adds velocities the Newtonian way. Real SR uses the relativistic sum so nothing ever crosses c. This shows up any time you add a small Δv at high β — an EVA jump, a decouple, a docking-port shove near c all add linearly in-game.

5. One privileged frame — no relativity of simultaneity, no mutual dilation. The mod dilates you against a single barycentric frame fixed at departure (§5), as a scalar 1/γ. Real SR has no privileged frame: each observer sees the other's clock run slow, and "at the same time" is frame-dependent. So two relativistic ships here do not see each other dilate — both are just scored against the barycenter. It is time-dilation bookkeeping, not a 4-D Lorentz transform.

6. Felt (proper) acceleration is not held constant — in-game the crew feel the reduced push. This is the subtle one. In real SR an accelerometer reads a constant proper acceleration no matter how close to c you are; it is only the outside frame that sees your acceleration die as 1/γ³ (you could feel a steady 1 g forever and merely approach c). Because KSP is Newtonian, the mod delivers the reduced F/γ³ force to the ship, so the in-game G-meter and crew feel the 1/γ³-reduced acceleration. The mod is, in effect, applying the physical coordinate acceleration as though it were the felt one. (This is exactly why a future constant-acceleration governor compensates for mass only, not for γ — holding felt-g constant would fight the very mechanic in §1.)

7. No Rindler horizon / acceleration causal structure. A ship holding constant proper acceleration has an event horizon behind it (at distance c²/α — about a light-year at 1 g). Drop something and, if you keep accelerating, you permanently lose causal contact with it: it redshifts, freezes at the horizon, and light it emits past that point never reaches you again. In-game this is pure Newtonian separation — a dropped object just coasts and the ship pulls linearly ahead. No horizon, no lost contact. (See the worked example below.)

8. Momentum is not conserved. Already flagged in §1: propellant burns at the nominal rate while only F/γ³ is delivered, so fuel→Δv efficiency silently degrades. The dv/dt and the wall-feel are right; the momentum ledger is not exact-SR.

9. No general relativity — none. No gravitational time dilation, no frame-dragging. The crew clock responds only to speed, never to depth in a gravity well. (Principia adds high-fidelity Newtonian n-body gravity, but GR time dilation is not part of this mod.)

10. No relativistic kinetic energy / collisions. A near-c impact uses KSP's Newtonian KE, not the relativistic value. In practice KSP disassembles anything at these speeds regardless.

Worked example — dropping a crew member near c

A ship is cruising near c and still accelerating; a kerbal goes EVA. What happens?

Real special relativity. At release the kerbal keeps the ship's current velocity and becomes an inertial, free-coasting object — no engine, so constant velocity forever.

• A home-frame observer sees a near-c projectile: time-dilated (aging slowly), length-contracted, Doppler-shifted. The ship, still burning, creeps further toward c (coordinate accel α/γ³) and pulls ahead.
• The ship's own (accelerating) frame sees the kerbal fall toward the Rindler horizon behind it — slowing, reddening, freezing like matter at a black-hole horizon — and if the ship keeps accelerating it can never receive light the kerbal emits past that moment.
• The kerbal feels nothing at all — weightless, at rest in their own frame.

In-game (KSP + this mod). The kerbal EVAs, inherits the ship's velocity, and becomes a separate vessel coasting at that speed — that part matches reality. The mod's clock keeps ticking the kerbal's dilated proper time even after they drift out of range and unload, so their aging/life-support stay correctly slowed — that part matches too. Everything else does not: no length contraction, no visual distortion, Galilean relative motion, no Rindler horizon (the ship just pulls linearly ahead and never loses contact), and the c wall is soft. In one line: "inherits velocity, coasts, keeps dilating" is faithful; the deep kinematic and causal structure is not.

Reality vs in-game at a glance

	Real special relativity	This mod (KSP)
Thrust vs speed	coordinate accel ∝1/γ³; felt accel constant	net force ∝1/γ³ — felt too
Reach c?	never	soft wall; the number can cross if forced
Crew / resource clock	dτ = dt/γ	×1/γ ✓
Radiation dose	(external flux)	coordinate-time ✓
Length contraction	yes	no
Aberration / Doppler visuals	yes	no
Velocity addition	relativistic	Galilean (linear)
Simultaneity / mutual dilation	frame-dependent, mutual	single frame, scalar
Rindler horizon on accel	yes	no
Momentum conservation	yes	no (abstraction)
Gravitational (GR) time dilation	yes	no — SR only

The one-sentence version: this mod is a faithful scalar model of the three things that change how an interstellar trip plays — the thrust wall, the slowed crew clock, and the permanent twin-paradox gap — laid over a Newtonian engine that knows nothing of Lorentz transforms. It is relativity you can feel and budget, not a relativity simulator.

See also

• Dashboard — where all of this is displayed while you fly.
• Trip Planner — the same physics, run in the editor before launch.
• Configuration — the tunables (betaMin, betaSane, attitudeExponent, …).