FA-93401 / Solar tracker geometry / Open access

Fixed panel angle of incidence: relative azimuth · case 01

South-facing panels look best lit by a northern sun.

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

ROOT CAUSE

The azimuth difference adds the panel azimuth instead of subtracting it.

THE FAILURE

The azimuth difference adds the panel azimuth instead of subtracting it.

Unsuccessful approach: Subtracting a further 180 degrees applies a south-referenced panel azimuth.

Case contract

Panel tilted by tilt degrees from horizontal, facing pan_az (clockwise from north). zenith = 90 - sun_el. cos(aoi) = cos(zen)cos(tilt) + sin(zen)sin(tilt)cos(sun_az - pan_az), clamped to [-1, 1]. Return [aoi degrees rounded 3, max(cos aoi, 0) rounded 4, 'front' or 'back'], or [None, 0.0, 'night'] when sun_el <= 0.

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(tilt, pan_az, sun_az, sun_el):
    if sun_el <= 0:
        return [None, 0.0, 'night']
    zen = math.radians(90 - sun_el)
    t = math.radians(tilt)
    c = math.cos(zen) * math.cos(t) + math.sin(zen) * math.sin(t) * math.cos(math.radians(sun_az + pan_az))
    c = max(-1.0, min(1.0, c))
    aoi = math.degrees(math.acos(c))
    side = 'front' if c >= 0 else 'back'
    return [round(aoi, 3), round(max(c, 0.0), 4), side]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [10, 225, 60, 89], [10.969, 0.9817, 'front']],
  ['regression: relative azimuth (partial repair)', [30, 135, 0, 10], [101.408, 0.0, 'back']],
  ['control 1', [0, 180, 225, -5], [None, 0.0, 'night']],
  ['control 2', [0, 135, 150, 45], [45.0, 0.7071, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['regression: relative azimuth (partial repair)', [90, 180, 250, 45], [76.005, 0.2418, 'front']],
  ['control 1', [25, 180, 60, 10], [92.907, 0.0, 'back']],
  ['control 2', [60, 225, 270, 20], [41.716, 0.7465, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [10, 135, 30, 45], [48.35, 0.6646, 'front']],
  ['regression: relative azimuth (partial repair)', [30, 270, 225, 10], [60.095, 0.4986, 'front']],
  ['control 1', [60, 90, 135, 30], [38.709, 0.7803, 'front']],
  ['control 2', [45, 270, 60, 89], [45.868, 0.6963, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [30, 135, 100, 10], [56.376, 0.5537, 'front']],
  ['regression: relative azimuth (partial repair)', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['control 1', [45, 180, 315, 0], [None, 0.0, 'night']],
  ['control 2', [30, 90, 225, 45], [68.754, 0.3624, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [30, 225, 270, 60], [22.062, 0.9268, 'front']],
  ['regression: relative azimuth (partial repair)', [10, 180, 100, 30], [58.767, 0.5185, 'front']],
  ['control 1', [45, 180, 0, 75], [60.0, 0.5, 'front']],
  ['control 2', [45, 225, 270, -5], [None, 0.0, 'night']]]]
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 fixture	Actual	Expected	Outcome
boundary: sun on horizon	`[None, 0.0, 'night']`	`[None, 0.0, 'night']`	Passed
normal: sun normal to panel	`[0.0, 1.0, 'front']`	`[0.0, 1.0, 'front']`	Passed
boundary: sun behind vertical panel	`[160.0, 0.0, 'back']`	`[160.0, 0.0, 'back']`	Passed
regression: relative azimuth	`[9.788, 0.9854, 'front']`	`[10.969, 0.9817, 'front']`	Failed
regression: relative azimuth (partial repair)	`[101.408, 0.0, 'back']`	`[101.408, 0.0, 'back']`	Passed
control 1	`[None, 0.0, 'night']`	`[None, 0.0, 'night']`	Passed
control 2	`[45.0, 0.7071, 'front']`	`[45.0, 0.7071, 'front']`	Passed

SHA-256 / 40ab0c03fa49dd1c6fa034a23a9854d02ef692e6897f2d50b18e1c87e2c40944

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(tilt, pan_az, sun_az, sun_el):
    if sun_el <= 0:
        return [None, 0.0, 'night']
    zen = math.radians(90 - sun_el)
    t = math.radians(tilt)
    c = math.cos(zen) * math.cos(t) + math.sin(zen) * math.sin(t) * math.cos(math.radians(sun_az - pan_az - 180))
    c = max(-1.0, min(1.0, c))
    aoi = math.degrees(math.acos(c))
    side = 'front' if c >= 0 else 'back'
    return [round(aoi, 3), round(max(c, 0.0), 4), side]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [10, 225, 60, 89], [10.969, 0.9817, 'front']],
  ['regression: relative azimuth (partial repair)', [30, 135, 0, 10], [101.408, 0.0, 'back']],
  ['control 1', [0, 180, 225, -5], [None, 0.0, 'night']],
  ['control 2', [0, 135, 150, 45], [45.0, 0.7071, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['regression: relative azimuth (partial repair)', [90, 180, 250, 45], [76.005, 0.2418, 'front']],
  ['control 1', [25, 180, 60, 10], [92.907, 0.0, 'back']],
  ['control 2', [60, 225, 270, 20], [41.716, 0.7465, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [10, 135, 30, 45], [48.35, 0.6646, 'front']],
  ['regression: relative azimuth (partial repair)', [30, 270, 225, 10], [60.095, 0.4986, 'front']],
  ['control 1', [60, 90, 135, 30], [38.709, 0.7803, 'front']],
  ['control 2', [45, 270, 60, 89], [45.868, 0.6963, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [30, 135, 100, 10], [56.376, 0.5537, 'front']],
  ['regression: relative azimuth (partial repair)', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['control 1', [45, 180, 315, 0], [None, 0.0, 'night']],
  ['control 2', [30, 90, 225, 45], [68.754, 0.3624, 'front']]],
 [['boundary: sun on horizon', [30, 180, 180, 0], [None, 0.0, 'night']],
  ['normal: sun normal to panel', [30, 180, 180, 60], [0.0, 1.0, 'front']],
  ['boundary: sun behind vertical panel', [90, 180, 0, 20], [160.0, 0.0, 'back']],
  ['regression: relative azimuth', [30, 225, 270, 60], [22.062, 0.9268, 'front']],
  ['regression: relative azimuth (partial repair)', [10, 180, 100, 30], [58.767, 0.5185, 'front']],
  ['control 1', [45, 180, 0, 75], [60.0, 0.5, 'front']],
  ['control 2', [45, 225, 270, -5], [None, 0.0, 'night']]]]
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 fixture	Actual	Expected	Outcome
boundary: sun on horizon	`[None, 0.0, 'night']`	`[None, 0.0, 'night']`	Passed
normal: sun normal to panel	`[60.0, 0.5, 'front']`	`[0.0, 1.0, 'front']`	Failed
boundary: sun behind vertical panel	`[20.0, 0.9397, 'front']`	`[160.0, 0.0, 'back']`	Failed
regression: relative azimuth	`[9.038, 0.9876, 'front']`	`[10.969, 0.9817, 'front']`	Failed
regression: relative azimuth (partial repair)	`[60.095, 0.4986, 'front']`	`[101.408, 0.0, 'back']`	Failed
control 1	`[None, 0.0, 'night']`	`[None, 0.0, 'night']`	Passed
control 2	`[45.0, 0.7071, 'front']`	`[45.0, 0.7071, 'front']`	Passed

SHA-256 / 32bd88282ada19254a10bab8f9fca8e9f0c5427ae09e121d4628e8d998581ba1

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 2026-09-29T14:51:54.865221+00:00.

Case digest / 72290d85ff36de0ea232f0cde2746ddb00bf397b69de03852e9ac48ca02d1226