FA-93556 / Solar tracker geometry / Open access
Tracker row-to-row shaded fraction: shaded fraction lower clip · case 01
Unshaded rows report negative shading and the shaded flag is wrong.
ROOT CAUSE
The fraction is not clipped at zero.
VERIFIED REPAIR
Clip the fraction to [0, 1].
Unsuccessful approach: Taking the absolute value turns large clearances into shading.
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, 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: shaded fraction lower clip', [-10, 45, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [0, -45, 0.3], [0.0, False]],
['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: shaded fraction lower clip', [0, -80, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-45, 45, 0.5], [0.0, False]],
['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: shaded fraction lower clip', [0, -30, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, -30, 0.3], [0.0, False]],
['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: shaded fraction lower clip', [0, 70, 0.6], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, -70, 0.4], [0.0, False]],
['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: shaded fraction lower clip', [-30, 60, 0.4], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, 45, 0.5], [0.0, False]],
['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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| normal: rows facing the sun at noon | [-1.5, False] | [0.0, False] | Failed |
| boundary: steep morning sun | [0.3054, True] | [0.3054, True] | Passed |
| boundary: sun below horizon | [1.0, True] | [1.0, True] | Passed |
| regression: shaded fraction lower clip | [-1.4656, False] | [0.0, False] | Failed |
| regression: shaded fraction lower clip (partial repair) | [-2.3333, False] | [0.0, False] | Failed |
| control 1 | [-2.3095860183650104e+16, False] | [0.0, False] | Failed |
| control 2 | [0.6467, True] | [0.6467, True] | Passed |
SHA-256 / 6e035a23d4d0b09025cb655145b64bf98cb5d1e24e6e49b44626250b020b86fe
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(rot - proj))
if c <= 0:
return [1.0, True]
fs = 1 - math.cos(math.radians(proj)) / (gcr * c)
fs = min(1.0, abs(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: shaded fraction lower clip', [-10, 45, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [0, -45, 0.3], [0.0, False]],
['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: shaded fraction lower clip', [0, -80, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-45, 45, 0.5], [0.0, False]],
['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: shaded fraction lower clip', [0, -30, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, -30, 0.3], [0.0, False]],
['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: shaded fraction lower clip', [0, 70, 0.6], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, -70, 0.4], [0.0, False]],
['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: shaded fraction lower clip', [-30, 60, 0.4], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, 45, 0.5], [0.0, False]],
['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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| normal: rows facing the sun at noon | [1.0, True] | [0.0, False] | Failed |
| boundary: steep morning sun | [0.3054, True] | [0.3054, True] | Passed |
| boundary: sun below horizon | [1.0, True] | [1.0, True] | Passed |
| regression: shaded fraction lower clip | [1.0, True] | [0.0, False] | Failed |
| regression: shaded fraction lower clip (partial repair) | [1.0, True] | [0.0, False] | Failed |
| control 1 | [1.0, True] | [0.0, False] | Failed |
| control 2 | [0.6467, True] | [0.6467, True] | Passed |
SHA-256 / 16e768a5aa6f0c58ea444fa7c84c67703778c3041f21ebdb20d0864fe90eb7ab
3 / The verified repair
Exit 0"""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: shaded fraction lower clip', [-10, 45, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [0, -45, 0.3], [0.0, False]],
['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: shaded fraction lower clip', [0, -80, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-45, 45, 0.5], [0.0, False]],
['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: shaded fraction lower clip', [0, -30, 0.5], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, -30, 0.3], [0.0, False]],
['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: shaded fraction lower clip', [0, 70, 0.6], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, -70, 0.4], [0.0, False]],
['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: shaded fraction lower clip', [-30, 60, 0.4], [0.0, False]],
['regression: shaded fraction lower clip (partial repair)', [-10, 45, 0.5], [0.0, False]],
['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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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: shaded fraction lower clip | [0.0, False] | [0.0, False] | Passed |
| regression: shaded fraction lower clip (partial repair) | [0.0, False] | [0.0, False] | Passed |
| control 1 | [0.0, False] | [0.0, False] | Passed |
| control 2 | [0.6467, True] | [0.6467, True] | Passed |
SHA-256 / ea7fa99692baaa155c196426fbbf2fd6d79da0bf722ba9af5fecbe02bdf7d4ab
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 2026-09-29T14:51:56.205182+00:00.
Case digest / f0557331a4e9358557faef8a6a35642b671d035f2d61bef4943367638fd9b6fc