FA-93411 / Solar tracker geometry / Open access

Fixed panel angle of incidence: tilt units · case 01

Incidence angles are nonsense for any tilted panel.

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

ROOT CAUSE

The tilt in degrees is used as radians.

VERIFIED REPAIR

Convert tilt to radians.

Unsuccessful approach: Measuring tilt from vertical swaps flat and vertical panels.

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 = 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: tilt units', [30, 135, 0, 10], [101.408, 0.0, 'back']],
  ['regression: tilt units (partial repair)', [10, 225, 60, 89], [10.969, 0.9817, 'front']],
  ['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: tilt units', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['regression: tilt units (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: tilt units', [10, 135, 30, 45], [48.35, 0.6646, 'front']],
  ['regression: tilt units (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: tilt units', [30, 135, 100, 10], [56.376, 0.5537, 'front']],
  ['regression: tilt units (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: tilt units', [10, 180, 100, 30], [58.767, 0.5185, 'front']],
  ['regression: tilt units (partial repair)', [30, 225, 270, 60], [22.062, 0.9268, '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	`[111.127, 0.0, 'back']`	`[0.0, 1.0, 'front']`	Failed
boundary: sun behind vertical panel	`[173.38, 0.0, 'back']`	`[160.0, 0.0, 'back']`	Failed
regression: tilt units	`[44.372, 0.7148, 'front']`	`[101.408, 0.0, 'back']`	Failed
regression: tilt units (partial repair)	`[146.075, 0.0, 'back']`	`[10.969, 0.9817, 'front']`	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 / 80d9672498211989aa4a32efd5bdaba91cfcd6c317b8e1cbc2b910a67698ad91

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(90 - 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: tilt units', [30, 135, 0, 10], [101.408, 0.0, 'back']],
  ['regression: tilt units (partial repair)', [10, 225, 60, 89], [10.969, 0.9817, 'front']],
  ['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: tilt units', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['regression: tilt units (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: tilt units', [10, 135, 30, 45], [48.35, 0.6646, 'front']],
  ['regression: tilt units (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: tilt units', [30, 135, 100, 10], [56.376, 0.5537, 'front']],
  ['regression: tilt units (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: tilt units', [10, 180, 100, 30], [58.767, 0.5185, 'front']],
  ['regression: tilt units (partial repair)', [30, 225, 270, 60], [22.062, 0.9268, '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	`[30.0, 0.866, 'front']`	`[0.0, 1.0, 'front']`	Failed
boundary: sun behind vertical panel	`[70.0, 0.342, 'front']`	`[160.0, 0.0, 'back']`	Failed
regression: tilt units	`[121.081, 0.0, 'back']`	`[101.408, 0.0, 'back']`	Failed
regression: tilt units (partial repair)	`[80.966, 0.157, 'front']`	`[10.969, 0.9817, 'front']`	Failed
control 1	`[None, 0.0, 'night']`	`[None, 0.0, 'night']`	Passed
control 2	`[46.92, 0.683, 'front']`	`[45.0, 0.7071, 'front']`	Failed

SHA-256 / 623957d97c4ddbcbbd92928050405f77e4edc2622fd49110b5afece65f10b502

3 / The verified repair

Exit 0

"""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: tilt units', [30, 135, 0, 10], [101.408, 0.0, 'back']],
  ['regression: tilt units (partial repair)', [10, 225, 60, 89], [10.969, 0.9817, 'front']],
  ['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: tilt units', [20, 225, 270, 3], [73.101, 0.2907, 'front']],
  ['regression: tilt units (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: tilt units', [10, 135, 30, 45], [48.35, 0.6646, 'front']],
  ['regression: tilt units (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: tilt units', [30, 135, 100, 10], [56.376, 0.5537, 'front']],
  ['regression: tilt units (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: tilt units', [10, 180, 100, 30], [58.767, 0.5185, 'front']],
  ['regression: tilt units (partial repair)', [30, 225, 270, 60], [22.062, 0.9268, '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: tilt units	`[101.408, 0.0, 'back']`	`[101.408, 0.0, 'back']`	Passed
regression: tilt units (partial repair)	`[10.969, 0.9817, 'front']`	`[10.969, 0.9817, 'front']`	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 / ab8c880b453743129257826c414296c919f0dbf5cdba863b6cd04b550fb02dec

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 2026-09-29T14:51:54.906766+00:00.

Case digest / 897806198c58f8fcc4978386387b0b20660e39ed4ddc6900a9e54f4fbd72a9ea