FA-93366 / Solar tracker geometry / Open access
Horizontal single-axis true tracking: axis azimuth units · case 01
Rotation angles look random for any axis orientation.
ROOT CAUSE
The axis azimuth in degrees is used as radians.
VERIFIED REPAIR
Convert axis_az + 90 to radians.
Unsuccessful approach: Adding 90 after converting mixes radians with degrees.
Case contract
Sun azimuth clockwise from north and elevation in degrees. The horizontal axis points to axis_az; rotation is positive toward azimuth axis_az+90. Sun vector east=cos(el)sin(az), north=cos(el)cos(az), up=sin(el). Rotation = atan2(component along axis_az+90, up). Clamp to +-max_angle (status 'limited', else 'tracking'); sun_el <= 0 returns [0.0, 'night']. Round to 3 decimals.
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(sun_az, sun_el, axis_az, max_angle):
if sun_el <= 0:
return [0.0, 'night']
az = math.radians(sun_az)
el = math.radians(sun_el)
e = math.cos(el) * math.sin(az)
n = math.cos(el) * math.cos(az)
u = math.sin(el)
pa = axis_az + 90
perp = e * math.sin(pa) + n * math.cos(pa)
rot = math.degrees(math.atan2(perp, u))
status = 'tracking'
if abs(rot) > max_angle:
rot = math.copysign(max_angle, rot)
status = 'limited'
return [round(rot, 3), status]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [30, 10, 180, 55], [-55.0, 'limited']],
['regression: axis azimuth units (partial repair)', [315, 75, 20, 45], [-13.65, 'tracking']],
['control 1', [150, 10, 190, 45], [-45.0, 'limited']],
['control 2', [180, 89, 0, 55], [0.0, 'tracking']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [90, 60, 0, 60], [30.0, 'tracking']],
['regression: axis azimuth units (partial repair)', [200, 10, 190, 55], [44.561, 'tracking']],
['control 1', [60, 0, 20, 45], [0.0, 'night']],
['control 2', [340, 60, 170, 45], [5.725, 'tracking']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [0, 10, 190, 60], [44.561, 'tracking']],
['regression: axis azimuth units (partial repair)', [300, 45, 20, 45], [-44.561, 'tracking']],
['control 1', [135, 0, 0, 60], [0.0, 'night']],
['control 2', [60, 20, 170, 55], [-55.0, 'limited']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [45, 10, 20, 45], [45.0, 'limited']],
['regression: axis azimuth units (partial repair)', [270, 75, 0, 60], [-15.0, 'tracking']],
['control 1', [90, 20, 0, 60], [60.0, 'limited']],
['control 2', [30, 3, 190, 45], [-45.0, 'limited']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [30, 20, 170, 45], [-45.0, 'limited']],
['regression: axis azimuth units (partial repair)', [150, 89, 180, 60], [-0.5, 'tracking']],
['control 1', [100, 3, 190, 60], [-60.0, 'limited']],
['control 2', [90, 75, 170, 55], [-14.782, 'tracking']]]]
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 the horizon | [0.0, 'night'] | [0.0, 'night'] | Passed |
| normal: solar noon on N-S axis | [-29.611, 'tracking'] | [0.0, 'tracking'] | Failed |
| boundary: low morning sun hits east limit | [-44.954, 'tracking'] | [-60.0, 'limited'] | Failed |
| regression: axis azimuth units | [55.0, 'limited'] | [-55.0, 'limited'] | Failed |
| regression: axis azimuth units (partial repair) | [-10.254, 'tracking'] | [-13.65, 'tracking'] | Failed |
| control 1 | [45.0, 'limited'] | [-45.0, 'limited'] | Failed |
| control 2 | [0.448, 'tracking'] | [0.0, 'tracking'] | Failed |
SHA-256 / 2c34214a89f7b364ef10cffec5607a8170722880679a3615858183905d039cab
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(sun_az, sun_el, axis_az, max_angle):
if sun_el <= 0:
return [0.0, 'night']
az = math.radians(sun_az)
el = math.radians(sun_el)
e = math.cos(el) * math.sin(az)
n = math.cos(el) * math.cos(az)
u = math.sin(el)
pa = math.radians(axis_az) + 90
perp = e * math.sin(pa) + n * math.cos(pa)
rot = math.degrees(math.atan2(perp, u))
status = 'tracking'
if abs(rot) > max_angle:
rot = math.copysign(max_angle, rot)
status = 'limited'
return [round(rot, 3), status]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [30, 10, 180, 55], [-55.0, 'limited']],
['regression: axis azimuth units (partial repair)', [315, 75, 20, 45], [-13.65, 'tracking']],
['control 1', [150, 10, 190, 45], [-45.0, 'limited']],
['control 2', [180, 89, 0, 55], [0.0, 'tracking']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [90, 60, 0, 60], [30.0, 'tracking']],
['regression: axis azimuth units (partial repair)', [200, 10, 190, 55], [44.561, 'tracking']],
['control 1', [60, 0, 20, 45], [0.0, 'night']],
['control 2', [340, 60, 170, 45], [5.725, 'tracking']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [0, 10, 190, 60], [44.561, 'tracking']],
['regression: axis azimuth units (partial repair)', [300, 45, 20, 45], [-44.561, 'tracking']],
['control 1', [135, 0, 0, 60], [0.0, 'night']],
['control 2', [60, 20, 170, 55], [-55.0, 'limited']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [45, 10, 20, 45], [45.0, 'limited']],
['regression: axis azimuth units (partial repair)', [270, 75, 0, 60], [-15.0, 'tracking']],
['control 1', [90, 20, 0, 60], [60.0, 'limited']],
['control 2', [30, 3, 190, 45], [-45.0, 'limited']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [30, 20, 170, 45], [-45.0, 'limited']],
['regression: axis azimuth units (partial repair)', [150, 89, 180, 60], [-0.5, 'tracking']],
['control 1', [100, 3, 190, 60], [-60.0, 'limited']],
['control 2', [90, 75, 170, 55], [-14.782, 'tracking']]]]
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 the horizon | [0.0, 'night'] | [0.0, 'night'] | Passed |
| normal: solar noon on N-S axis | [-14.504, 'tracking'] | [0.0, 'tracking'] | Failed |
| boundary: low morning sun hits east limit | [-60.0, 'limited'] | [-60.0, 'limited'] | Passed |
| regression: axis azimuth units | [-18.487, 'tracking'] | [-55.0, 'limited'] | Failed |
| regression: axis azimuth units (partial repair) | [-14.994, 'tracking'] | [-13.65, 'tracking'] | Failed |
| control 1 | [-45.0, 'limited'] | [-45.0, 'limited'] | Passed |
| control 2 | [0.448, 'tracking'] | [0.0, 'tracking'] | Failed |
SHA-256 / 364f29ca008e9f25c156509a9b25722e73182c9951241fc41cfb0483feda3c34
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(sun_az, sun_el, axis_az, max_angle):
if sun_el <= 0:
return [0.0, 'night']
az = math.radians(sun_az)
el = math.radians(sun_el)
e = math.cos(el) * math.sin(az)
n = math.cos(el) * math.cos(az)
u = math.sin(el)
pa = math.radians(axis_az + 90)
perp = e * math.sin(pa) + n * math.cos(pa)
rot = math.degrees(math.atan2(perp, u))
status = 'tracking'
if abs(rot) > max_angle:
rot = math.copysign(max_angle, rot)
status = 'limited'
return [round(rot, 3), status]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [30, 10, 180, 55], [-55.0, 'limited']],
['regression: axis azimuth units (partial repair)', [315, 75, 20, 45], [-13.65, 'tracking']],
['control 1', [150, 10, 190, 45], [-45.0, 'limited']],
['control 2', [180, 89, 0, 55], [0.0, 'tracking']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [90, 60, 0, 60], [30.0, 'tracking']],
['regression: axis azimuth units (partial repair)', [200, 10, 190, 55], [44.561, 'tracking']],
['control 1', [60, 0, 20, 45], [0.0, 'night']],
['control 2', [340, 60, 170, 45], [5.725, 'tracking']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [0, 10, 190, 60], [44.561, 'tracking']],
['regression: axis azimuth units (partial repair)', [300, 45, 20, 45], [-44.561, 'tracking']],
['control 1', [135, 0, 0, 60], [0.0, 'night']],
['control 2', [60, 20, 170, 55], [-55.0, 'limited']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [45, 10, 20, 45], [45.0, 'limited']],
['regression: axis azimuth units (partial repair)', [270, 75, 0, 60], [-15.0, 'tracking']],
['control 1', [90, 20, 0, 60], [60.0, 'limited']],
['control 2', [30, 3, 190, 45], [-45.0, 'limited']]],
[['boundary: sun on the horizon', [90, 0, 180, 60], [0.0, 'night']],
['normal: solar noon on N-S axis', [180, 60, 180, 60], [0.0, 'tracking']],
['boundary: low morning sun hits east limit', [90, 10, 180, 60], [-60.0, 'limited']],
['regression: axis azimuth units', [30, 20, 170, 45], [-45.0, 'limited']],
['regression: axis azimuth units (partial repair)', [150, 89, 180, 60], [-0.5, 'tracking']],
['control 1', [100, 3, 190, 60], [-60.0, 'limited']],
['control 2', [90, 75, 170, 55], [-14.782, 'tracking']]]]
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 the horizon | [0.0, 'night'] | [0.0, 'night'] | Passed |
| normal: solar noon on N-S axis | [0.0, 'tracking'] | [0.0, 'tracking'] | Passed |
| boundary: low morning sun hits east limit | [-60.0, 'limited'] | [-60.0, 'limited'] | Passed |
| regression: axis azimuth units | [-55.0, 'limited'] | [-55.0, 'limited'] | Passed |
| regression: axis azimuth units (partial repair) | [-13.65, 'tracking'] | [-13.65, 'tracking'] | Passed |
| control 1 | [-45.0, 'limited'] | [-45.0, 'limited'] | Passed |
| control 2 | [0.0, 'tracking'] | [0.0, 'tracking'] | Passed |
SHA-256 / 5ec1a9a648bb3c9d05a77b4fe4c1bc75ae694d1f8d22ededdea16cf0b9ea01cb
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 2026-09-29T14:51:54.438434+00:00.
Case digest / ca850425076fab103bdcdf419a32358df8f830e2ebb6f9b0ba8b7f9ceb01d205