Cornering G

Definition

Cornering G is the kinematic lateral acceleration of the car's path: how hard the car is actually changing direction. It comes from GPS only.

$$a_{lat,path} = v_{analysis}\,\dot\psi, \qquad \psi = \operatorname{atan2}(\dot y, \dot x)$$

• $\dot x, \dot y$: Savitzky–Golay first derivatives of the local east/north position (window 1.0 s, order 2).
• $\psi$: path heading, unwrapped, then zero-phase low-passed at 1 Hz. Positive counter-clockwise: left turns increase $\psi$.
• $\dot\psi$: Savitzky–Golay derivative of $\psi$ (same window and order).
• Masked (undefined) where $v_{analysis} <$ 3 m/s.
• Equivalent form $v^2\kappa$ with path curvature $\kappa = \dot\psi / v$.

Sign: positive in a left turn. Displayed in g: $a / 9.80665$.

Because it is built from speed and heading of the path, it contains no gravity, no banking and no body roll. That is what makes it the driver-facing lateral number: it answers "how hard did the car corner", independent of how the camera is mounted.

Sustained value (per segment)

$$G_{sus} = \max_t \frac{1}{W}\int_t^{t+W} |a_{lat,path}|\,d\tau, \qquad W = 1.0\,\mathrm{s}$$

Inside a segment the channel is resampled onto a uniform 20 ms time axis and the maximum sliding-window mean of $|a|$ is taken. A spike of amplitude $S$ and duration $d$ can move it by at most $S\,d/W$; a spike test during development injected a 5 g sample into a real 1.5 g corner and measured a change below 0.01 g. The window was chosen from 0.5 / 0.75 / 1.0 / 1.5 s: lap-to-lap spread of the per-corner value is within noise for all candidates and 1.0 s is 8–16 % of a corner's duration, so it measures the loaded phase, not the whole corner. Mean and peak (filtered) values are also computed; the raw accelerometer peak is never called Cornering G.

Cross-validation

check	result on the reference recordings
Synthetic constant-speed circle, radius $R$	$a_{lat} = v^2/R$ within 2 %
Net rotation per lap: $\int r_V\,dt$ (gyro, vehicle frame) vs $\int \dot\psi\,dt$ (GPS)	0.957–1.033 vs 0.996–1.023 turns, i.e. ≤ 5 % on every stable lap
Bias between the gyro-derived lateral and Cornering G	within ±0.03 g on stable laps
Two cameras in the same car, gyro lateral	0.084–0.097 g RMS agreement

The instantaneous comparison with the gyro was expected to agree to 0.15 g RMS, and it does not on dirt (0.47–0.74 g RMS): the body yaw rate leads the path heading rate while the car is rotated into the corner (slip-angle rate RMS 0.17–0.31 rad/s, identical on two cameras). That is physics, not error; the gyro channel is therefore shown to engineers as body-yaw lateral and never labelled Cornering G.

Engineer channels on the same page

• Body-yaw lateral (gyro): $a_{lat,gyro} = v\,r_V/\cos\hat\lambda$ with $r_V$ the yaw rate in the vehicle frame (bias removed on stationary data) and $\hat\lambda$ the low-passed lean estimate (0.5 Hz low-pass).
• Slip-rate diagnostic: $r_V/\cos\hat\lambda - \dot\psi_{gps}$, reported as an RMS per lap.

Limitations

• Undefined below 3 m/s and in the first/last 0.5 s of a GPS run.
• Heading from positions at 10–18 Hz limits the bandwidth to ~1 Hz; very short transients are smoothed.
• Shares the GPS lag (0.15–0.40 s behind the IMU clock); the delta between two laps is unaffected.

Verified

Studied on the real recordings during development. Covered by synthetic cases, unit tests of the filters, and regression values for the sustained Cornering G of every corner (± 0.02 g).