FAILURE MAP
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FA-93486 / Solar tracker geometry / Open access

Heliostat mirror normal aiming: target vector direction · case 01

Heliostats reflect sunlight away from the tower.

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

ROOT CAUSE

The target vector points from the receiver to the mirror.

THE FAILURE

The target vector points from the receiver to the mirror.

Unsuccessful approach: Absolute differences lose the direction of west and south receivers.

Case contract

mirror and receiver are [east, north, up] positions in metres. The mirror normal bisects the unit sun vector (east=cos(el)sin(az), north=cos(el)cos(az), up=sin(el)) and the unit vector from the mirror to the receiver. Return [normal azimuth 0..360 clockwise from north, normal elevation], rounded to 3; None when sun_el <= 0; 'invalid' when receiver equals mirror.

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, mirror, receiver):
    if sun_el <= 0:
        return None
    dx = [mirror[i] - receiver[i] for i in range(3)]
    d = math.sqrt(sum(v * v for v in dx))
    if d == 0:
        return 'invalid'
    t = [v / d for v in dx]
    az = math.radians(sun_az)
    el = math.radians(sun_el)
    s = [math.cos(el) * math.sin(az), math.cos(el) * math.cos(az), math.sin(el)]
    h = [s[i] + t[i] for i in range(3)]
    m = math.sqrt(sum(v * v for v in h))
    h = [v / m for v in h]
    n_az = math.degrees(math.atan2(h[0], h[1])) % 360
    n_el = math.degrees(math.asin(h[2]))
    return [round(n_az, 3), round(n_el, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [270, 60, [6, -1, 1], [0, 5, 0]], [300.29, 28.278]],
  ['regression: target vector direction (partial repair)', [270, 80, [-16, -19, 1], [0, 0, 0]],
   [31.588, 46.473]],
  ['control 1', [90, -3, [-12, 43, 1], [0, 0, 0]], None],
  ['control 2', [200, 60, [-10, 12, 0], [0, 0, 60]], [180.839, 70.11]]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [315, 25, [47, -28, 0], [0, 0, 60]], [308.943, 36.527]],
  ['regression: target vector direction (partial repair)', [90, 25, [-19, 40, 2], [-10, 5, 60]],
   [116.262, 47.684]],
  ['control 1', [135, 60, [31, 24, 2], [10, 0, 60]], [177.1, 67.63]],
  ['control 2', [225, -3, [-22, -29, 0], [0, 5, 30]], None]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [60, 40, [7, -5, 0], [0, 0, 60]], [49.649, 66.233]],
  ['regression: target vector direction (partial repair)', [315, 10, [-37, 26, 0], [0, -5, 60]],
   [323.691, 69.061]],
  ['control 1', [90, 10, [-6, -40, 0], [-10, 0, 30]], [48.617, 32.61]],
  ['control 2', [30, 10, [-44, 5, 1], [-10, 0, 0]], [64.473, 5.033]]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [315, 60, [-28, -33, 2], [-10, 5, 60]],
   [353.399, 62.028]],
  ['regression: target vector direction (partial repair)', [200, 80, [9, 42, 3], [-10, 0, 30]],
   [203.614, 55.19]],
  ['control 1', [150, 40, [16, -12, 0], [0, 0, 0]], [261.353, 56.729]],
  ['control 2', [90, 0, [46, -4, 0], [0, -5, 0]], None]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [225, 40, [-5, 13, 2], [-10, -5, 30]], [212.668, 49.07]],
  ['regression: target vector direction (partial repair)', [200, 10, [41, -47, 2], [0, 0, 30]],
   [255.744, 31.113]],
  ['control 1', [250, -3, [-49, 36, 3], [-10, 5, 60]], None],
  ['control 2', [300, 80, [-27, -17, 1], [-10, 0, 60]], [18.225, 78.974]]]]
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: receiver at mirrorinvalidinvalidPassed
normal: receiver due north on tower[180.0, -2.5][180.0, 87.5]Failed
boundary: nightNoneNonePassed
regression: target vector direction[163.934, 53.374][300.29, 28.278]Failed
regression: target vector direction (partial repair)[226.918, 42.492][31.588, 46.473]Failed
control 1NoneNonePassed
control 2[230.257, -13.244][180.839, 70.11]Failed

SHA-256 / 4cb00ccc75923cdeafed6b1a93b4af3abb5090283ce59c46a1e87f5c62d4e225

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, mirror, receiver):
    if sun_el <= 0:
        return None
    dx = [abs(receiver[i] - mirror[i]) for i in range(3)]
    d = math.sqrt(sum(v * v for v in dx))
    if d == 0:
        return 'invalid'
    t = [v / d for v in dx]
    az = math.radians(sun_az)
    el = math.radians(sun_el)
    s = [math.cos(el) * math.sin(az), math.cos(el) * math.cos(az), math.sin(el)]
    h = [s[i] + t[i] for i in range(3)]
    m = math.sqrt(sum(v * v for v in h))
    h = [v / m for v in h]
    n_az = math.degrees(math.atan2(h[0], h[1])) % 360
    n_el = math.degrees(math.asin(h[2]))
    return [round(n_az, 3), round(n_el, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [270, 60, [6, -1, 1], [0, 5, 0]], [300.29, 28.278]],
  ['regression: target vector direction (partial repair)', [270, 80, [-16, -19, 1], [0, 0, 0]],
   [31.588, 46.473]],
  ['control 1', [90, -3, [-12, 43, 1], [0, 0, 0]], None],
  ['control 2', [200, 60, [-10, 12, 0], [0, 0, 60]], [180.839, 70.11]]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [315, 25, [47, -28, 0], [0, 0, 60]], [308.943, 36.527]],
  ['regression: target vector direction (partial repair)', [90, 25, [-19, 40, 2], [-10, 5, 60]],
   [116.262, 47.684]],
  ['control 1', [135, 60, [31, 24, 2], [10, 0, 60]], [177.1, 67.63]],
  ['control 2', [225, -3, [-22, -29, 0], [0, 5, 30]], None]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [60, 40, [7, -5, 0], [0, 0, 60]], [49.649, 66.233]],
  ['regression: target vector direction (partial repair)', [315, 10, [-37, 26, 0], [0, -5, 60]],
   [323.691, 69.061]],
  ['control 1', [90, 10, [-6, -40, 0], [-10, 0, 30]], [48.617, 32.61]],
  ['control 2', [30, 10, [-44, 5, 1], [-10, 0, 0]], [64.473, 5.033]]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [315, 60, [-28, -33, 2], [-10, 5, 60]],
   [353.399, 62.028]],
  ['regression: target vector direction (partial repair)', [200, 80, [9, 42, 3], [-10, 0, 30]],
   [203.614, 55.19]],
  ['control 1', [150, 40, [16, -12, 0], [0, 0, 0]], [261.353, 56.729]],
  ['control 2', [90, 0, [46, -4, 0], [0, -5, 0]], None]],
 [['boundary: receiver at mirror', [180, 40, [0, 0, 0], [0, 0, 0]], 'invalid'],
  ['normal: receiver due north on tower', [180, 40, [0, -40, 0], [0, 0, 40]], [180.0, 87.5]],
  ['boundary: night', [90, 0, [10, 10, 0], [0, 0, 50]], None],
  ['regression: target vector direction', [225, 40, [-5, 13, 2], [-10, -5, 30]], [212.668, 49.07]],
  ['regression: target vector direction (partial repair)', [200, 10, [41, -47, 2], [0, 0, 30]],
   [255.744, 31.113]],
  ['control 1', [250, -3, [-49, 36, 3], [-10, 5, 60]], None],
  ['control 2', [300, 80, [-27, -17, 1], [-10, 0, 60]], [18.225, 78.974]]]]
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: receiver at mirrorinvalidinvalidPassed
normal: receiver due north on tower[180.0, 87.5][180.0, 87.5]Passed
boundary: nightNoneNonePassed
regression: target vector direction[16.066, 53.374][300.29, 28.278]Failed
regression: target vector direction (partial repair)[31.588, 48.804][31.588, 46.473]Failed
control 1NoneNonePassed
control 2[182.015, 81.426][180.839, 70.11]Failed

SHA-256 / ec56978f252404c4e615350df655306943bdd04aab822fa59d5f4759675028a3

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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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 2026-09-29T14:51:55.553256+00:00.

Case digest / 08dcee69ca9ee217b827864eb75d8236d62c4f6518149b42964c83f5f889eeb6