Betaflight Rates Math

Reference for simulating a Betaflight rateprofile (stick → deg/s, throttle shaping) in a mod flight model. Implemented in FPV/src/FPVRates.cs; edited live on the FPV Options dialog's Rates tab (FPVOptionsDialog.DrawRatesTab).

Rates curve (Betaflight rates type, from fc/rc.c applyBetaflightRates)

Inputs per axis, configurator conventions: RC Rate (~1.0, CLI stores ×100), Rate / super rate (0..0.99), RC Expo (0..1). Stick s in -1..1, a = |s| before expo (the superfactor uses the pre-expo magnitude — easy to get wrong).

if expo > 0:   s = s·a³·expo + s·(1 − expo)          # bends the centre soft
rcRate = RC Rate;  if rcRate > 2: rcRate += 14.54·(rcRate − 2)   # the >2.0 kink
rate  = 200 · rcRate · s
if super > 0:  rate /= clamp(1 − a·super, 0.01, 1)   # steepens toward full stick

• Expo does not change the full-stick value (at a=1 the blend is identity), so max velocity = 200 · rcRate / (1 − super) — the configurator's "Max Vel" column. Sanity checks: 1.0/0.7 → 667°/s, 1.2/0.7 → 800°/s, 1.5/0.65 → 857°/s.

Throttle curve (MID/EXPO, from the firmware throttle lookup, normalized)

Mid m, expo e, stick t in 0..1:

tmp = t − m
half = tmp ≥ 0 ? 1 − m : m           # width of the half being traversed
out = m + tmp · (1 − e + e·tmp²/half²)

Exact at the ends (0→0, 1→1), pivots at m; e flattens response around the pivot. Throttle limit is applied after the curve (it lives in the mixer): SCALE multiplies by limit%, CLIP is min(out, limit%).

TPA (throttle PID attenuation)

Breakpoint is in RC µs (1000..2000). Normalized: bp = (breakpoint − 1000)/1000, factor = 1 − tpa · clamp01((thr − bp)/(1 − bp)), computed from the post-curve throttle. On real firmware TPA trims PID gains; a sim without a PID loop applies the factor to the commanded rates instead — same knob, same direction (more TPA = softer response at high throttle).

UI notes (IMGUI)

• Curve previews: rasterize into a cached Texture2D and rebuild only when a plotted value changes (hash the inputs); per-frame redraws with hundreds of GUI.DrawTexture calls are needlessly hot. Texture2D y=0 is the bottom row and GUI.DrawTexture keeps it there, so plot y-up directly.
• Slider drags: write the config object live (flight picks it up next frame) but defer the JSON Save() to mouse-up, or a drag writes the file at 60 Hz.

Building FPV outside deploy.ps1

FPV/src/FPV.csproj defaults GameDir to C:\Program Files (x86)\Steam\..., which is wrong on this machine — the game is at D:\SteamLibrary\steamapps\common\7 Days To Die. deploy.ps1 discovers the real path from the Steam registry/libraryfolders and passes it; a direct compile check needs dotnet build src/FPV.csproj -p:GameDir="D:\SteamLibrary\steamapps\common\7 Days To Die".