FAILURE MAP
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FA-93546 / Solar tracker geometry / Open access

Tracker row-to-row shaded fraction: relative sun angle · case 01

Rows facing the morning sun report heavy shading while rows facing away report none.

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

ROOT CAUSE

The rotation and projected sun angle are added instead of differenced.

THE FAILURE

The rotation and projected sun angle are added instead of differenced.

Unsuccessful approach: Differencing magnitudes loses the sign when the sun is on the other side.

Case contract

rot is the row rotation and proj the sun zenith projected on the plane perpendicular to the axis, both signed degrees. |proj| >= 90 or cos(rot - proj) <= 0 means no direct light: [1.0, True]. Otherwise shaded fraction = clip(1 - cos(proj)/(gcr*cos(rot - proj)), 0, 1). Return [fraction rounded 4, fraction > 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(rot, proj, gcr):
    if abs(proj) >= 90:
        return [1.0, True]
    c = math.cos(math.radians(rot + proj))
    if c <= 0:
        return [1.0, True]
    fs = 1 - math.cos(math.radians(proj)) / (gcr * c)
    fs = min(1.0, max(0.0, fs))
    return [round(fs, 4), fs > 0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [-30, -80, 0.5], [0.4597, True]],
  ['regression: relative sun angle (partial repair)', [45, -70, 0.4], [1.0, True]],
  ['control 1', [45, -45, 0.5], [0.0, False]], ['control 2', [45, 80, 0.6], [0.6467, True]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [-60, -70, 0.6], [0.4212, True]],
  ['regression: relative sun angle (partial repair)', [20, -80, 0.5], [1.0, True]],
  ['control 1', [-10, -45, 0.6], [0.0, False]], ['control 2', [30, 45, 0.5], [0.0, False]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [-60, -80, 0.6], [0.692, True]],
  ['regression: relative sun angle (partial repair)', [60, -45, 0.4], [1.0, True]],
  ['control 1', [-30, 0, 0.5], [0.0, False]], ['control 2', [30, -80, 0.6], [1.0, True]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [60, -60, 0.6], [1.0, True]],
  ['regression: relative sun angle (partial repair)', [-45, 80, 0.4], [1.0, True]],
  ['control 1', [-45, -30, 0.6], [0.0, False]], ['control 2', [-20, 45, 0.6], [0.0, False]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [30, -80, 0.5], [1.0, True]],
  ['regression: relative sun angle (partial repair)', [-60, 70, 0.6], [1.0, True]],
  ['control 1', [0, -95, 0.5], [1.0, True]], ['control 2', [-10, -70, 0.4], [0.0, 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
normal: rows facing the sun at noon[0.0, False][0.0, False]Passed
boundary: steep morning sun[1.0, True][0.3054, True]Failed
boundary: sun below horizon[1.0, True][1.0, True]Passed
regression: relative sun angle[1.0, True][0.4597, True]Failed
regression: relative sun angle (partial repair)[0.0566, True][1.0, True]Failed
control 1[0.0, False][0.0, False]Passed
control 2[1.0, True][0.6467, True]Failed

SHA-256 / e70d45ebf05aed3c1cb447bff83e2971f2d306206dbe81f7dddb7316366080bb

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(rot, proj, gcr):
    if abs(proj) >= 90:
        return [1.0, True]
    c = math.cos(math.radians(abs(rot) - abs(proj)))
    if c <= 0:
        return [1.0, True]
    fs = 1 - math.cos(math.radians(proj)) / (gcr * c)
    fs = min(1.0, max(0.0, fs))
    return [round(fs, 4), fs > 0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [-30, -80, 0.5], [0.4597, True]],
  ['regression: relative sun angle (partial repair)', [45, -70, 0.4], [1.0, True]],
  ['control 1', [45, -45, 0.5], [0.0, False]], ['control 2', [45, 80, 0.6], [0.6467, True]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [-60, -70, 0.6], [0.4212, True]],
  ['regression: relative sun angle (partial repair)', [20, -80, 0.5], [1.0, True]],
  ['control 1', [-10, -45, 0.6], [0.0, False]], ['control 2', [30, 45, 0.5], [0.0, False]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [-60, -80, 0.6], [0.692, True]],
  ['regression: relative sun angle (partial repair)', [60, -45, 0.4], [1.0, True]],
  ['control 1', [-30, 0, 0.5], [0.0, False]], ['control 2', [30, -80, 0.6], [1.0, True]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [60, -60, 0.6], [1.0, True]],
  ['regression: relative sun angle (partial repair)', [-45, 80, 0.4], [1.0, True]],
  ['control 1', [-45, -30, 0.6], [0.0, False]], ['control 2', [-20, 45, 0.6], [0.0, False]]],
 [['normal: rows facing the sun at noon', [0, 0, 0.4], [0.0, False]],
  ['boundary: steep morning sun', [-60, -70, 0.5], [0.3054, True]],
  ['boundary: sun below horizon', [0, 95, 0.4], [1.0, True]],
  ['regression: relative sun angle', [30, -80, 0.5], [1.0, True]],
  ['regression: relative sun angle (partial repair)', [-60, 70, 0.6], [1.0, True]],
  ['control 1', [0, -95, 0.5], [1.0, True]], ['control 2', [-10, -70, 0.4], [0.0, 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
normal: rows facing the sun at noon[0.0, False][0.0, False]Passed
boundary: steep morning sun[0.3054, True][0.3054, True]Passed
boundary: sun below horizon[1.0, True][1.0, True]Passed
regression: relative sun angle[0.4597, True][0.4597, True]Passed
regression: relative sun angle (partial repair)[0.0566, True][1.0, True]Failed
control 1[0.0, False][0.0, False]Passed
control 2[0.6467, True][0.6467, True]Passed

SHA-256 / 73c3050dce7a2cfd7aab29cf851f966ac7803779d9c28adcbcc6004a1f6b53e0

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 2026-09-29T14:51:56.195384+00:00.

Case digest / 865dee98fb407f8a79d519292758c3c3f710cab6216989108d5ffe8ff0809c39