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FA-93381 / Solar tracker geometry / Open access

Ground-coverage-ratio backtracking: cosine argument units · case 01

Backtracking switches on and off erratically through the day.

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

ROOT CAUSE

The ideal angle in degrees is passed to cos as radians.

THE FAILURE

The ideal angle in degrees is passed to cos as radians.

Unsuccessful approach: Shifting by 90 degrees uses the sine, treating the rotation as an elevation.

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(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: cosine argument units', [45, 1.0], [0.0, True]],
  ['regression: cosine argument units (partial repair)', [-10, 0.4], [-10, False]],
  ['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: cosine argument units', [-29.5, 0.5], [-29.5, False]],
  ['regression: cosine argument units (partial repair)', [-10, 0.5], [-10, False]],
  ['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: cosine argument units', [-70, 0.4], [-38.765, True]],
  ['regression: cosine argument units (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: cosine argument units', [-60, 1.0], [-0.0, True]],
  ['regression: cosine argument units (partial repair)', [10, 0.35], [10, False]],
  ['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: cosine argument units', [-69.5, 1.0], [0.0, True]],
  ['regression: cosine argument units (partial repair)', [-9.5, 0.35], [-9.5, False]],
  ['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 fixtureActualExpectedOutcome
boundary: noon never backtracks[0, False][0, False]Passed
normal: steep morning angle backtracks[-75, False][-25.319, True]Failed
boundary: continuous rows[42.253, True][0.0, True]Failed
regression: cosine argument units[-13.31, True][0.0, True]Failed
regression: cosine argument units (partial repair)[-10, False][-10, False]Passed
control 1[-21.902, True][30, False]Failed
control 2[17.918, True][-29.5, False]Failed

SHA-256 / d30a51a9a0825d891a6fd7920e9a70163543a18c51901e5155eaabe0e98f6525

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(abs(ideal) - 90))) / 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: cosine argument units', [45, 1.0], [0.0, True]],
  ['regression: cosine argument units (partial repair)', [-10, 0.4], [-10, False]],
  ['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: cosine argument units', [-29.5, 0.5], [-29.5, False]],
  ['regression: cosine argument units (partial repair)', [-10, 0.5], [-10, False]],
  ['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: cosine argument units', [-70, 0.4], [-38.765, True]],
  ['regression: cosine argument units (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: cosine argument units', [-60, 1.0], [-0.0, True]],
  ['regression: cosine argument units (partial repair)', [10, 0.35], [10, False]],
  ['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: cosine argument units', [-69.5, 1.0], [0.0, True]],
  ['regression: cosine argument units (partial repair)', [-9.5, 0.35], [-9.5, False]],
  ['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 fixtureActualExpectedOutcome
boundary: noon never backtracks[-90.0, True][0, False]Failed
normal: steep morning angle backtracks[-75, False][-25.319, True]Failed
boundary: continuous rows[30.0, True][0.0, True]Failed
regression: cosine argument units[0.0, True][0.0, True]Passed
regression: cosine argument units (partial repair)[54.271, True][-10, False]Failed
control 1[30, False][30, False]Passed
control 2[-19.513, True][-29.5, False]Failed

SHA-256 / 482dfaf21008f7ef5ee4c62adf8c04881bf3f2925171fea4e45fb30011d9d42e

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 2026-09-29T14:51:54.607569+00:00.

Case digest / f9e4a7fbdf939accb5b56b66a24d12edb4948bef93040e790eb5c02234568e57