Chassis Lateral Load

What an accelerometer measures

An accelerometer measures specific force $f = a - g$: its own acceleration minus gravity. At rest it reads $+g_0$ along the up direction ($g_0 = 9.80665$ m/s²); in free fall it reads zero. GoPro's GRAV stream is the up unit vector in camera coordinates (verified on stationary data: RMS error 0.016–0.036 g after a fixed axis permutation). Raw accelerometer magnitude on a dirt car is dominated by vibration (99th percentile 46–59 m/s², occasional ±8 g sensor clipping) and is never shown as a G number.

Frames and rotation convention

frame	axes
C — camera	$+Z_C$ = up at rest; $X_C, Y_C$ complete a right-handed frame (lens direction not assumed)
V — vehicle (ISO 8855)	$+X_V$ forward, $+Y_V$ left, $+Z_V$ up; yaw positive turning left
E — earth	east, north, up
P — path	along the horizontal velocity, left of travel, up

$R_{V\leftarrow C}$ maps vector components from the camera frame to the vehicle frame; its rows are the vehicle axes expressed in camera coordinates. Quaternions use the Hamilton convention. Five closed-form test cases (stationary level, parked on a slope, steady banked turn, straight-line acceleration with pitch, free fall) are unit tests with tolerance 1e-9.

The channel

$$f_V = s_a\,R_{V\leftarrow C}\,f_{C,filt}, \qquad \text{Chassis Lateral Load} = f_{body,y}$$

• $f_{C,filt}$: camera-frame specific force after (1) replacing samples at the ±8 g rail by an 11-sample rolling median, (2) a zero-phase Butterworth low-pass, order 4 in second-order sections, cutoff 5 Hz, per contiguous run, and (3) decimation to 50 Hz. The statistical Hampel filter is disabled: during development, on real recordings, it replaced 1–9 % of racing samples and injected up to 0.12 g RMS of low-band error.
• $s_a$: the accelerometer sign, +1 on every reference recording (GoPro reports $f$, not $-f$; the handedness test would flip it and warn otherwise).
• Positive $f_{body,y}$ = load toward the left of the car.

In a steady turn with horizontal centripetal acceleration $a_c$ (= Cornering G) and lean $\lambda$ (bank + body roll, positive leaning into a left turn):

$$f_{body,y} = a_c\cos\lambda - g_0\sin\lambda, \qquad f_{body,z} = a_c\sin\lambda + g_0\cos\lambda$$

Banking reduces felt lateral load. Chassis Load ≠ Cornering G on a banked track is physics, not an error, and the difference is reported as a lean diagnostic:

$$\lambda_{est} = \operatorname{atan2}(f_{body,z}, f_{body,y}) - \operatorname{atan2}(g_0, a_{lat,path})$$

(undefined below 8 m/s; low-passed at 0.5 Hz when used elsewhere). On the Hamilton County reference recording the chassis leans out by ~7° relative to its parked attitude in the corners, and Chassis Load reads 0.08–0.14 g more than Cornering G — both instruments agree, so it is reported, not corrected.

Mount calibration $R_{V\leftarrow C}$

Automatic, per session:

1. $\hat z_V$ = mean up vector over stationary periods (speed < 0.5 m/s, ≥ 30 s of stationary data; else the low-passed $f/|f|$ over the session with confidence 0.6). When stationary runs disagree by more than 3° the pre-race run is used and a note is recorded.
2. Lateral axis first (ovals have almost no straight-line braking windows): the horizontal specific force is fitted by least squares onto the GPS path accelerations $(a_{long}, a_{lat})$ on racing samples; $\hat y_V$ is the lateral direction, $\hat x_V = \hat y_V \times \hat z_V$. The lateral correlation (corr_lat in the Mount panel, 0.90–0.96 on the reference recordings) is the primary quality, the longitudinal correlation (corr_long, 0.53–0.77) a diagnostic.
3. GPS lag: the GPS-derived channels are shifted by the measured GPS lag (cross-correlation of the low-passed $f_{body,x}$ with $a_{long,path}$, ±2.5 s) before any comparison.
4. Handedness: in left turns ($a_{lat,path} >$ 2 m/s²) the lateral sign agreement must be ≥ 95 %, the net rotation $\int r_V\,dt$ over the racing samples must be positive with the GPS sign and exceed half a turn, and the yaw sign must agree in ≥ 60 % of corner samples.
5. Confidence = min(stationary 1.0/0.6, correlation 1.0/0.7/0.4 at a lateral correlation of ≥ 0.8 / ≥ 0.6 / below, handedness 1.0/0.3/0.7); method auto at ≥ 0.8, else auto_low_confidence.

Manual override (engineer): lens facing forward/rearward/left/right, upside-down, roll, pitch → a deterministic $R_{V\leftarrow C}$ with method manual, confidence 0.75, full provenance.

Priority (never silent): 1 automatic ≥ 0.8 → 2 automatic 0.5–0.8 (shown with a warning) → 3 manual → 4 hidden. Vehicle-frame channels (Chassis Load, body-yaw lateral, lean) are shown only at priority ≤ 3; Cornering G needs no IMU and is always available. The same rule gates the chassis columns of the segment table.

Mount drift: per lap, the angle between the gyro-propagated up vector (complementary filter, time constant 15 s) and the calibrated $Z_V$ is reported; laps above 10° are flagged "Mount moved" and their vehicle-frame values are marked unreliable. This caught a camera whose mount rotated 38° during a heat.

Sustained value (per segment)

Same definition as Cornering G: maximum 1 s sliding mean of $|f_{body,y}|$.

Limitations

• Requires a rigid mount. A flexing pole mount (I-35 "facing out" HERO9) gives 0.21 g RMS disagreement with the driver camera and is classified auto_low_confidence (0.3) → hidden.
• Only bank + roll relative to the parked attitude is observable; parking on a slope shifts $\lambda$ by the slope (the I-35 camera showed 4.9° between two stationary runs for that reason).
• The longitudinal axis $f_{body,x}$ carries $g_0\sin\theta$ from pitch and braking-in-corner content: it is an engineer diagnostic, never the driver's longitudinal number.

Verified

During development, on the real recordings: stationary $f_V = (0,0,g_0) \pm 0.05\,g_0$ and $|f| = 1.00 \pm 0.02\,g_0$; handedness pass on the three rigid cameras; GoPro GRAV confirmed to track true vertical mid-corner to 1–3°; two same-car cameras agree on the gyro lateral to 0.08–0.10 g RMS. Tests: closed-form cases for the frame conventions, a synthetic banked turn at 0/8/15° lean (Chassis Load within 0.02 g, lean within 0.5°), vibration + 5 g spike, mounted rearward/left/right/upside-down recovered within 2°.