FA-93761 / Solar tracker geometry / Open access

Module edge ground clearance limit: ground rise lever arm · case 01

Clearance on sloped ground is understated at steep rotations.

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

ROOT CAUSE

The horizontal reach of the low edge ignores the rotation.

THE FAILURE

The horizontal reach of the low edge ignores the rotation.

Unsuccessful approach: Using sin(cmd) gives zero ground rise when flat.

Case contract

Hub height h and module width w in mm. Maximum rotation keeps the low edge at least clear above flat ground: asin((h - clear)/(w/2)), 90 when that ratio >= 1, 0 when <= 0. The command is theta clamped to +-max. Reported clearance is h - (w/2)|sin cmd| minus the ground rise under the low edge, side*(w/2)cos(cmd)tan(slope), where side is the sign of cmd or, at 0, the sign of slope (>= 0 counts positive). Return [cmd rounded 3, clearance rounded 1].

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(theta, h, w, clear, slope):
    half = w / 2
    lim = (h - clear) / half
    if lim >= 1:
        amax = 90.0
    elif lim <= 0:
        amax = 0.0
    else:
        amax = math.degrees(math.asin(lim))
    cmd = max(-amax, min(amax, theta))
    r = math.radians(cmd)
    low = h - half * abs(math.sin(r))
    if cmd != 0:
        side = 1 if cmd > 0 else -1
    else:
        side = 1 if slope >= 0 else -1
    ground = side * half * math.tan(math.radians(slope))
    return [round(cmd, 3), round(low - ground, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [-30, 2000, 2384, 300, -5], [-30, 1313.7]],
  ['regression: ground rise lever arm (partial repair)', [20, 2500, 2000, 2600, -10],
   [-0.0, 2323.7]],
  ['control 1', [-45, 1200, 2384, 300, -10], [-45, 208.5]],
  ['control 2', [0, 1500, 1133, 2600, -10], [-0.0, 1400.1]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [-30, 2000, 2000, 300, -10], [-30, 1347.3]],
  ['regression: ground rise lever arm (partial repair)', [20, 1200, 4000, 500, 8], [20, 251.8]],
  ['control 1', [20, 2000, 2256, 500, -10], [20, 1801.1]],
  ['control 2', [0, 2500, 2000, 300, -5], [0, 2412.5]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [60, 1200, 2384, 500, 3], [35.962, 449.4]],
  ['regression: ground rise lever arm (partial repair)', [0, 2000, 2384, 2600, 3], [-0.0, 1937.5]],
  ['control 1', [60, 2500, 1133, 1300, 8], [60, 1969.6]],
  ['control 2', [20, 1200, 2000, 1300, 3], [-0.0, 1147.6]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [45, 1500, 2000, 300, 3], [45, 755.8]],
  ['regression: ground rise lever arm (partial repair)', [0, 1200, 2256, 1300, 8], [-0.0, 1041.5]],
  ['control 1', [60, 2000, 1133, 2600, -5], [-0.0, 1950.4]],
  ['control 2', [45, 1200, 1133, 300, 3], [45, 778.4]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [20, 2500, 2384, 300, -10], [20, 2289.8]],
  ['regression: ground rise lever arm (partial repair)', [-60, 2500, 2256, 300, -10],
   [-60, 1423.7]],
  ['control 1', [-30, 1500, 2384, 500, -5], [-30, 813.7]],
  ['control 2', [-30, 1200, 4000, 2600, 0], [-0.0, 1200.0]]]]
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: rotation limited by clearance	`[60, 523.1]`	`[60, 523.1]`	Passed
boundary: hub below required clearance	`[-0.0, 1200.0]`	`[-0.0, 1200.0]`	Passed
boundary: flat on sloped ground	`[0, 1412.5]`	`[0, 1412.5]`	Passed
regression: ground rise lever arm	`[-30, 1299.7]`	`[-30, 1313.7]`	Failed
regression: ground rise lever arm (partial repair)	`[-0.0, 2323.7]`	`[-0.0, 2323.7]`	Passed
control 1	`[-45, 146.9]`	`[-45, 208.5]`	Failed
control 2	`[-0.0, 1400.1]`	`[-0.0, 1400.1]`	Passed

SHA-256 / 8dea8e05ee1b5e093305698c07305083820cacc516a40204f8dc720e7b6dc4dc

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(theta, h, w, clear, slope):
    half = w / 2
    lim = (h - clear) / half
    if lim >= 1:
        amax = 90.0
    elif lim <= 0:
        amax = 0.0
    else:
        amax = math.degrees(math.asin(lim))
    cmd = max(-amax, min(amax, theta))
    r = math.radians(cmd)
    low = h - half * abs(math.sin(r))
    if cmd != 0:
        side = 1 if cmd > 0 else -1
    else:
        side = 1 if slope >= 0 else -1
    ground = side * half * math.sin(r) * math.tan(math.radians(slope))
    return [round(cmd, 3), round(low - ground, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [-30, 2000, 2384, 300, -5], [-30, 1313.7]],
  ['regression: ground rise lever arm (partial repair)', [20, 2500, 2000, 2600, -10],
   [-0.0, 2323.7]],
  ['control 1', [-45, 1200, 2384, 300, -10], [-45, 208.5]],
  ['control 2', [0, 1500, 1133, 2600, -10], [-0.0, 1400.1]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [-30, 2000, 2000, 300, -10], [-30, 1347.3]],
  ['regression: ground rise lever arm (partial repair)', [20, 1200, 4000, 500, 8], [20, 251.8]],
  ['control 1', [20, 2000, 2256, 500, -10], [20, 1801.1]],
  ['control 2', [0, 2500, 2000, 300, -5], [0, 2412.5]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [60, 1200, 2384, 500, 3], [35.962, 449.4]],
  ['regression: ground rise lever arm (partial repair)', [0, 2000, 2384, 2600, 3], [-0.0, 1937.5]],
  ['control 1', [60, 2500, 1133, 1300, 8], [60, 1969.6]],
  ['control 2', [20, 1200, 2000, 1300, 3], [-0.0, 1147.6]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [45, 1500, 2000, 300, 3], [45, 755.8]],
  ['regression: ground rise lever arm (partial repair)', [0, 1200, 2256, 1300, 8], [-0.0, 1041.5]],
  ['control 1', [60, 2000, 1133, 2600, -5], [-0.0, 1950.4]],
  ['control 2', [45, 1200, 1133, 300, 3], [45, 778.4]]],
 [['normal: rotation limited by clearance', [60, 1500, 2256, 500, 0], [60, 523.1]],
  ['boundary: hub below required clearance', [30, 1200, 2000, 1300, 0], [-0.0, 1200.0]],
  ['boundary: flat on sloped ground', [0, 1500, 2000, 500, -5], [0, 1412.5]],
  ['regression: ground rise lever arm', [20, 2500, 2384, 300, -10], [20, 2289.8]],
  ['regression: ground rise lever arm (partial repair)', [-60, 2500, 2256, 300, -10],
   [-60, 1423.7]],
  ['control 1', [-30, 1500, 2384, 500, -5], [-30, 813.7]],
  ['control 2', [-30, 1200, 4000, 2600, 0], [-0.0, 1200.0]]]]
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: rotation limited by clearance	`[60, 523.1]`	`[60, 523.1]`	Passed
boundary: hub below required clearance	`[-0.0, 1200.0]`	`[-0.0, 1200.0]`	Passed
boundary: flat on sloped ground	`[0, 1500.0]`	`[0, 1412.5]`	Failed
regression: ground rise lever arm	`[-30, 1456.1]`	`[-30, 1313.7]`	Failed
regression: ground rise lever arm (partial repair)	`[-0.0, 2500.0]`	`[-0.0, 2323.7]`	Failed
control 1	`[-45, 505.7]`	`[-45, 208.5]`	Failed
control 2	`[-0.0, 1500.0]`	`[-0.0, 1400.1]`	Failed

SHA-256 / 5beadf3a9a5628acb80475b59b9bff8263007e1a13dc9b2350e8eb12f0d9eac6

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 2026-09-29T14:51:58.105791+00:00.

Case digest / b6076968e7f7db189016233e134710f7071027fe00aa40c6f479029b0952db93