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FA-93616 / Solar tracker geometry / Open access

Torque-tube inclinometer rotation: half-turn canonical value · case 01

An upside-down tube reads -180 instead of 180.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The -180 representation is not canonicalised.

THE FAILURE

The -180 representation is not canonicalised.

Unsuccessful approach: Remapping everything below -179 corrupts valid angles near the flip.

Case contract

ax (across-axis) and az (normal) are gravity components in g. The magnitude must be within [0.8, 1.2] g, else [None, 'fault']. Rotation = atan2(ax, az) in degrees, negated for a sensor mounted on the west side, then minus the calibration offset, normalised to (-180, 180]. Return [angle rounded 2, 'ok'].

Why this case matters

Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
    mag = math.hypot(ax, az)
    if not 0.8 <= mag <= 1.2:
        return [None, 'fault']
    ang = math.degrees(math.atan2(ax, az))
    if mount == 'west':
        ang = -ang
    ang -= offset
    ang = (ang + 180) % 360 - 180
    return [round(ang, 2), 'ok']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -1.1, 'east', 0], [180.0, 'ok']],
  ['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
  ['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -0.8, 'west', 0], [180.0, 'ok']],
  ['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
  ['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -0.8, 'west', 0], [180.0, 'ok']],
  ['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
  ['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -1.0, 'west', 0], [180.0, 'ok']],
  ['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
  ['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -1.1, 'east', 0], [180.0, 'ok']],
  ['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
  ['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
boundary: magnitude at lower bound[0.0, 'ok'][0.0, 'ok']Passed
boundary: magnitude at upper bound[90.0, 'ok'][90.0, 'ok']Passed
boundary: upside-down reading[-180.0, 'ok'][180.0, 'ok']Failed
regression: angle just inside the flip[-179.5, 'ok'][-179.5, 'ok']Passed
regression: half-turn canonical value[-180.0, 'ok'][180.0, 'ok']Failed
control 1[90.0, 'ok'][90.0, 'ok']Passed
control 2[None, 'fault'][None, 'fault']Passed

SHA-256 / 9fa3efbded14319d8d3141a7e83943f0a4053fc0d8b34bdcc3e06bdaaa0ea0c4

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
    mag = math.hypot(ax, az)
    if not 0.8 <= mag <= 1.2:
        return [None, 'fault']
    ang = math.degrees(math.atan2(ax, az))
    if mount == 'west':
        ang = -ang
    ang -= offset
    ang = (ang + 180) % 360 - 180
    if ang < -179:
        ang = 180.0
    return [round(ang, 2), 'ok']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -1.1, 'east', 0], [180.0, 'ok']],
  ['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
  ['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -0.8, 'west', 0], [180.0, 'ok']],
  ['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
  ['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -0.8, 'west', 0], [180.0, 'ok']],
  ['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
  ['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -1.0, 'west', 0], [180.0, 'ok']],
  ['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
  ['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: angle just inside the flip', [-0.0175, -0.9998, 'east', 0.5], [-179.5, 'ok']],
  ['regression: half-turn canonical value', [0.0, -1.1, 'east', 0], [180.0, 'ok']],
  ['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
  ['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
boundary: magnitude at lower bound[0.0, 'ok'][0.0, 'ok']Passed
boundary: magnitude at upper bound[90.0, 'ok'][90.0, 'ok']Passed
boundary: upside-down reading[180.0, 'ok'][180.0, 'ok']Passed
regression: angle just inside the flip[180.0, 'ok'][-179.5, 'ok']Failed
regression: half-turn canonical value[180.0, 'ok'][180.0, 'ok']Passed
control 1[90.0, 'ok'][90.0, 'ok']Passed
control 2[None, 'fault'][None, 'fault']Passed

SHA-256 / b6838cc36d292bf4393403677ab4f974e9908004ac206130d88df3e017c659a8

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:56.829362+00:00.

Case digest / b16cc67bc7380072ee07989e91d5e9600e8239ead82bd25eaabfb3622e5680c1