FA-93376 / Solar tracker geometry / Open access
Ground-coverage-ratio backtracking: correction direction · case 01
Backtracking steepens the rows instead of flattening them.
ROOT CAUSE
The correction has the same sign as the ideal angle.
VERIFIED REPAIR
Correct toward flat with -sign(ideal).
Unsuccessful approach: A fixed negative correction is right in the afternoon only.
Case contract
Horizontal single-axis rows with ground coverage ratio gcr in (0, 1]. temp = |cos(ideal)|/gcr. When temp < 1 the rows would shade each other and the angle is corrected by -sign(ideal)*acos(temp) degrees (backtracking, flag True). gcr <= 0 disables backtracking. Return [angle rounded to 3, backtracking flag].
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(ideal, gcr):
if gcr <= 0:
return [round(ideal, 3), False]
temp = abs(math.cos(math.radians(ideal))) / gcr
if temp < 1:
corr = math.copysign(1, ideal) * math.degrees(math.acos(temp))
return [round(ideal + corr, 3), True]
return [round(ideal, 3), False]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [45, 1.0], [0.0, True]],
['regression: correction direction (partial repair)', [-70, 0.4], [-38.765, True]],
['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-70, 0.5], [-23.16, True]],
['regression: correction direction (partial repair)', [-79.5, 0.4], [-16.603, True]],
['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [85.5, 1.0], [0.0, True]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-70, 0.4], [-38.765, True]],
['regression: correction direction (partial repair)', [-79.5, 0.3], [-26.905, True]],
['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-60, 1.0], [-0.0, True]],
['regression: correction direction (partial repair)', [-80, 0.3], [-25.368, True]],
['control 1', [-59.5, 1.0], [0.0, True]], ['control 2', [-45, 0.5], [-45, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-69.5, 1.0], [0.0, True]],
['regression: correction direction (partial repair)', [-60, 1.0], [-0.0, True]],
['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]]]]
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: noon never backtracks | [0, False] | [0, False] | Passed |
| normal: steep morning angle backtracks | [-124.681, True] | [-25.319, True] | Failed |
| boundary: continuous rows | [120.0, True] | [0.0, True] | Failed |
| regression: correction direction | [90.0, True] | [0.0, True] | Failed |
| regression: correction direction (partial repair) | [-101.235, True] | [-38.765, True] | Failed |
| control 1 | [30, False] | [30, False] | Passed |
| control 2 | [-29.5, False] | [-29.5, False] | Passed |
SHA-256 / d7309b56ffce110083df9efe348160e289e3a92571f16f113d30db3ad937e1ac
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ideal, gcr):
if gcr <= 0:
return [round(ideal, 3), False]
temp = abs(math.cos(math.radians(ideal))) / gcr
if temp < 1:
corr = -math.degrees(math.acos(temp))
return [round(ideal + corr, 3), True]
return [round(ideal, 3), False]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [45, 1.0], [0.0, True]],
['regression: correction direction (partial repair)', [-70, 0.4], [-38.765, True]],
['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-70, 0.5], [-23.16, True]],
['regression: correction direction (partial repair)', [-79.5, 0.4], [-16.603, True]],
['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [85.5, 1.0], [0.0, True]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-70, 0.4], [-38.765, True]],
['regression: correction direction (partial repair)', [-79.5, 0.3], [-26.905, True]],
['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-60, 1.0], [-0.0, True]],
['regression: correction direction (partial repair)', [-80, 0.3], [-25.368, True]],
['control 1', [-59.5, 1.0], [0.0, True]], ['control 2', [-45, 0.5], [-45, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-69.5, 1.0], [0.0, True]],
['regression: correction direction (partial repair)', [-60, 1.0], [-0.0, True]],
['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]]]]
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: noon never backtracks | [0, False] | [0, False] | Passed |
| normal: steep morning angle backtracks | [-124.681, True] | [-25.319, True] | Failed |
| boundary: continuous rows | [0.0, True] | [0.0, True] | Passed |
| regression: correction direction | [0.0, True] | [0.0, True] | Passed |
| regression: correction direction (partial repair) | [-101.235, True] | [-38.765, True] | Failed |
| control 1 | [30, False] | [30, False] | Passed |
| control 2 | [-29.5, False] | [-29.5, False] | Passed |
SHA-256 / 81fdad1306c9e0006db9fb94e13186d30b577122cddd6e8898ffe67dc8da0f58
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ideal, gcr):
if gcr <= 0:
return [round(ideal, 3), False]
temp = abs(math.cos(math.radians(ideal))) / gcr
if temp < 1:
corr = -math.copysign(1, ideal) * math.degrees(math.acos(temp))
return [round(ideal + corr, 3), True]
return [round(ideal, 3), False]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [45, 1.0], [0.0, True]],
['regression: correction direction (partial repair)', [-70, 0.4], [-38.765, True]],
['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-70, 0.5], [-23.16, True]],
['regression: correction direction (partial repair)', [-79.5, 0.4], [-16.603, True]],
['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [85.5, 1.0], [0.0, True]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-70, 0.4], [-38.765, True]],
['regression: correction direction (partial repair)', [-79.5, 0.3], [-26.905, True]],
['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-60, 1.0], [-0.0, True]],
['regression: correction direction (partial repair)', [-80, 0.3], [-25.368, True]],
['control 1', [-59.5, 1.0], [0.0, True]], ['control 2', [-45, 0.5], [-45, False]]],
[['boundary: noon never backtracks', [0, 0.4], [0, False]],
['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],
['boundary: continuous rows', [60, 1.0], [0.0, True]],
['regression: correction direction', [-69.5, 1.0], [0.0, True]],
['regression: correction direction (partial repair)', [-60, 1.0], [-0.0, True]],
['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]]]]
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: noon never backtracks | [0, False] | [0, False] | Passed |
| normal: steep morning angle backtracks | [-25.319, True] | [-25.319, True] | Passed |
| boundary: continuous rows | [0.0, True] | [0.0, True] | Passed |
| regression: correction direction | [0.0, True] | [0.0, True] | Passed |
| regression: correction direction (partial repair) | [-38.765, True] | [-38.765, True] | Passed |
| control 1 | [30, False] | [30, False] | Passed |
| control 2 | [-29.5, False] | [-29.5, False] | Passed |
SHA-256 / dddc2580226e6577d17c83fd0e4cfcb06b1d0056cd83bf6efa8dffd3024f3c5e
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 2026-09-29T14:51:54.518760+00:00.
Case digest / e3e5a0b2f49c16385398c9f5ebc38aaf7b1d322be94f8ad2759b9dc9d8a85e17