FA-93406 / Solar tracker geometry / Open access
Fixed panel angle of incidence: back-side projection · case 01
Irradiance projection becomes negative when the sun is behind the panel.
ROOT CAUSE
The projection factor is not clipped at zero.
VERIFIED REPAIR
Report max(cos aoi, 0).
Unsuccessful approach: Taking the absolute value credits rear-side sun to the front face.
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(c, 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: back-side projection', [30, 135, 0, 10], [101.408, 0.0, 'back']],
['regression: back-side projection (partial repair)', [90, 180, 30, 20], [144.469, 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: back-side projection', [90, 180, 30, 75], [102.953, 0.0, 'back']],
['regression: back-side projection (partial repair)', [25, 180, 60, 10], [92.907, 0.0, 'back']],
['control 1', [60, 225, 270, 20], [41.716, 0.7465, 'front']],
['control 2', [20, 90, 0, 89], [20.024, 0.9395, '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: back-side projection', [90, 90, 200, 30], [107.229, 0.0, 'back']],
['regression: back-side projection (partial repair)', [20, 180, 30, 10], [97.384, 0.0, 'back']],
['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: back-side projection', [25, 270, 100, 3], [111.604, 0.0, 'back']],
['regression: back-side projection (partial repair)', [10, 180, 60, 3], [92.015, 0.0, 'back']],
['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: back-side projection', [90, 270, 150, 45], [110.705, 0.0, 'back']],
['regression: back-side projection (partial repair)', [30, 270, 90, 10], [110.0, 0.0, 'back']],
['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, -0.9397, 'back'] | [160.0, 0.0, 'back'] | Failed |
| regression: back-side projection | [101.408, -0.1978, 'back'] | [101.408, 0.0, 'back'] | Failed |
| regression: back-side projection (partial repair) | [144.469, -0.8138, 'back'] | [144.469, 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 / 1e32841279b0f0be1d2be54ecf4f9996fb77aa3846c5812a59414ccf14f37149
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))
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(abs(c), 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: back-side projection', [30, 135, 0, 10], [101.408, 0.0, 'back']],
['regression: back-side projection (partial repair)', [90, 180, 30, 20], [144.469, 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: back-side projection', [90, 180, 30, 75], [102.953, 0.0, 'back']],
['regression: back-side projection (partial repair)', [25, 180, 60, 10], [92.907, 0.0, 'back']],
['control 1', [60, 225, 270, 20], [41.716, 0.7465, 'front']],
['control 2', [20, 90, 0, 89], [20.024, 0.9395, '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: back-side projection', [90, 90, 200, 30], [107.229, 0.0, 'back']],
['regression: back-side projection (partial repair)', [20, 180, 30, 10], [97.384, 0.0, 'back']],
['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: back-side projection', [25, 270, 100, 3], [111.604, 0.0, 'back']],
['regression: back-side projection (partial repair)', [10, 180, 60, 3], [92.015, 0.0, 'back']],
['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: back-side projection', [90, 270, 150, 45], [110.705, 0.0, 'back']],
['regression: back-side projection (partial repair)', [30, 270, 90, 10], [110.0, 0.0, 'back']],
['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, 0.9397, 'back'] | [160.0, 0.0, 'back'] | Failed |
| regression: back-side projection | [101.408, 0.1978, 'back'] | [101.408, 0.0, 'back'] | Failed |
| regression: back-side projection (partial repair) | [144.469, 0.8138, 'back'] | [144.469, 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 / 7df7b772bdebde3ede30703a2b7721222c8712eca676eb5d0aa852f5932fb408
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: back-side projection', [30, 135, 0, 10], [101.408, 0.0, 'back']],
['regression: back-side projection (partial repair)', [90, 180, 30, 20], [144.469, 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: back-side projection', [90, 180, 30, 75], [102.953, 0.0, 'back']],
['regression: back-side projection (partial repair)', [25, 180, 60, 10], [92.907, 0.0, 'back']],
['control 1', [60, 225, 270, 20], [41.716, 0.7465, 'front']],
['control 2', [20, 90, 0, 89], [20.024, 0.9395, '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: back-side projection', [90, 90, 200, 30], [107.229, 0.0, 'back']],
['regression: back-side projection (partial repair)', [20, 180, 30, 10], [97.384, 0.0, 'back']],
['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: back-side projection', [25, 270, 100, 3], [111.604, 0.0, 'back']],
['regression: back-side projection (partial repair)', [10, 180, 60, 3], [92.015, 0.0, 'back']],
['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: back-side projection', [90, 270, 150, 45], [110.705, 0.0, 'back']],
['regression: back-side projection (partial repair)', [30, 270, 90, 10], [110.0, 0.0, 'back']],
['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: back-side projection | [101.408, 0.0, 'back'] | [101.408, 0.0, 'back'] | Passed |
| regression: back-side projection (partial repair) | [144.469, 0.0, 'back'] | [144.469, 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 / 678bd2132c193c6431036d1fc5a8fc27cd8e3fb115b4d1eb73a79b5b2b93d1ea
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 2026-09-29T14:51:54.903208+00:00.
Case digest / 6c9d66ea9389180b580885f1f5e681ee40d3e061833bc4ab086c6d302d3f887e