Syplheed-Reborn/docs/re/flight-speed-law.md

# The throttle is a TARGET-SPEED selector — measured against the definition (2026-08-13)

**Status: ✅ for the shape of the law, 🟡 for the unit scale.**

The unit definition gives `MinimumVelocity 100`, `CruisingVelocity 350`,
`MaximumVelocity 1200`, `Acceleration 600` and `Deceleration 500` for
`UN_f001_TCAF_DeltaSaber_T_Player` ([values](captures/unit-runtime-fields.csv)),
but not **how** the game applies them. This measures it.

Method — [`tools/re-capture/speed_law.py`](../../tools/re-capture/speed_law.py):
lock onto the player entity once, then sample its own position triple in guest RAM
while holding each throttle input in turn (8 s per phase, 20 Hz). Speed is
differentiated over **1-second windows**, never per sample.

## Result

| phase | measured speed (1 s windows) | settles to | definition field |
|---|---|---|---|
| no throttle | 367 403 471 365 463 463 365 | **~420** | `CruisingVelocity` 350 |
| `RT` held | 1041 1376 1551 1379 1596 1510 1620 | **~1 530** | `MaximumVelocity` 1200 |
| release | 1314 672 432 452 432 450 408 | back to **~440** | — |
| `LT` held | 203 121 135 121 115 146 122 | **~125** | `MinimumVelocity` 100 |
| release | 369 451 427 425 445 390 465 | back to **~430** | — |

So the throttle **selects a target speed** — minimum / cruise / maximum — and the
craft converges to it; releasing either trigger returns it to cruise. It is not a
force model with the throttle adding thrust, which is what a reimplementation would
most likely have assumed from `Acceleration`/`Deceleration` alone. Those two fields
govern the **convergence rate**: the release phase falls ~1 314 → ~432 in about two
seconds (~440 units/s², against `Deceleration` 500) and the `RT` phase climbs ~420 →
~1 550 in two to three seconds (~470–560 units/s², against `Acceleration` 600).

## 🟡 The unit scale

Measured world-space speeds run **≈1.2–1.3× the definition numbers** in all three
regimes (cruise 1.21, maximum 1.28, minimum 1.32). The HUD, meanwhile, reads
**350** at cruise — the definition value exactly. So the definition's velocity unit
is the HUD's, and entity world coordinates are a constant multiple of it, close to
**1.25**. The spread across regimes is larger than the constant itself is precise,
because the craft is manoeuvring under fire while sampled (straight-line
displacement per window under-reads a curving path), so this is recorded as a
measured range rather than a pinned constant.

## Traps

* **`RT`/`LT` are analogue triggers**, so `vgamepad trig RT 1.0` holds the throttle;
  the button verb `hold RT` is a **silent no-op**. The first run of this probe
  measured the drift of a craft nobody was flying.
* **Do not differentiate per sample.** The guest updates the position slower than
  20 Hz, so per-sample differences alternate between 0 and a double step —
  `0, 1519, 1985, 0, 2681…` for a craft flying smoothly.
* **Bind late, measure fast.** The player entity is not in the typed-entity scan
  for the first ~15 s of a mission, and the craft dies within a few minutes if
  nobody is flying it — one earlier attempt ended at `GAME OVER` mid-probe.

Raw samples: [`captures/speed-law-throttle-phases.csv`](captures/speed-law-throttle-phases.csv).

---

# Turn rates: `AV_*` are rate caps, and `_Min`/`_Max` mean *at minimum/maximum speed*

`tools/re-capture/turn_law.py` pins the speed regime with a throttle, holds a stick
axis, and differentiates the craft's **own forward vector** over 1-second windows.

**Control mapping, measured** — `LX` is **roll** (the forward vector barely moves
under it: 3–5 °/s residual), `LY` is **pitch** (`vgamepad` documents `LY: -1 = up`,
so `+1` is nose down = the `PitchMinus` family), and the **right stick does not
steer at all** (0 °/s).

| phase | measured (1 s windows) | definition |
|---|---|---|
| slow + nose down | 85 · 96 · 82 → **~87** | `AV_PitchMinus_Min` **75** |
| fast + nose down | 55 · 45 · 63 → **~54** | `AV_PitchMinus_Max` **40** |
| slow + nose up | 181 · 164 · 181 → **~175** | `AV_PitchPlus_Min` **150** |
| fast + nose up | 103 · 130 · 175 → **~136** | `AV_PitchPlus_Max` **70** |

Two claims of the field names are confirmed:

* **Agility falls with speed** — every rate drops when the throttle goes from `LT`
  to `RT`, so `_Min`/`_Max` are *at minimum / maximum speed*, not floor/ceiling of
  the rate.
* **Pitching up is about twice as fast as pitching down**, exactly as the pair
  150/75 (slow) and 70/40 (fast) says.

## The ~1.2× factor is a TIME BASE, not a unit scale

The speed law measured 1.21 / 1.28 / 1.32 × its definition values; the pitch rates
measure 1.16 / 1.35 / 1.17 / 1.94 × theirs. A **unit scale** would have to differ
between metres-per-second and degrees-per-second — it cannot explain both. A **time
base** does: if the guest's simulated second is shorter than the wall-clock second
this probe measures against, every rate reads high by the same factor. So the
definition numbers are self-consistent and a reimplementation should take them at
face value; these measurements confirm the **shape** of the law (which field governs
what, and how the regimes switch), not a scale correction.

🟡 **No yaw input was found.** `AV_Yaw_{Min,Max}` (45 / 25 °/s) exists, but neither
stick yaws the craft. With `MaximumBank_Normal` (60) and roll on `LX`, a
**bank-to-turn** model is the obvious reading — sustained turns come from rolling and
pitching — but the yaw fields may equally belong to the AI or to an input this probe
has not driven.

Raw samples: [`captures/turn-law-pitch-phases.csv`](captures/turn-law-pitch-phases.csv).

---

# The afterburner is not on the obvious buttons — a bounded negative

The definition describes the burner without naming its input: `AB_ConsumeShield_Begin`
**50**, `AB_ConsumeShield` **10**, and a set of `AB_AV_*` turn caps far below the
normal ones (roll 40 vs 125–200 °/s, pitch-up 30 vs 70–150). Notably there is **no
`AB_*Velocity`**, so the burner may not raise the speed target at all.

Two independent probes, both negative for `A`, `B`, `X`, `LB` (and `LS`/`RS` on the
first):

* [`tools/re-capture/ab_probe.py`](../../tools/re-capture/ab_probe.py) — hold `RT`
  for a max-speed baseline, then hold each candidate: speed stayed inside the
  baseline's own noise band (1 200–1 580 units/s) for every one.
* [`tools/re-capture/ab_state_probe.py`](../../tools/re-capture/ab_state_probe.py) —
  sample a window of the player object while each candidate is held and report any
  float that falls during the hold: **nothing fell**.
* And the cheapest oracle of the three, needing no offsets at all: **count the green
  pixels of the HUD's SHIELD bar** before and after each hold, on a freshly spawned
  craft with a full shield. `AB_ConsumeShield_Begin 50` should take a visible bite;
  the bar read **156, 156, 156, 157, 157** across baseline and all four buttons.

So the burner is **not a simple hold on `A`/`B`/`X`/`LB`/`LS`/`RS`**. What remains:
a chord (something plus `RT`), an input this pad cannot reach, a craft variant that
has it, or fields that belong to the AI rather than the player. Worth knowing before
anyone re-probes the obvious buttons.

(`RB` is the nose gun, `Y` the missile mount and the d-pad the tactical map — see
[flight controls](flight-controls-runtime.md) — so those were not held here.)