FA-93756 / Solar tracker geometry / Open access
Module edge ground clearance limit: edge drop magnitude · case 01
Negative rotations report more clearance than the hub height.
ROOT CAUSE
The edge drop uses the signed sine.
VERIFIED REPAIR
Use |sin(cmd)| for the low edge.
Unsuccessful approach: Taking the sine of the angle in degrees gives meaningless drops.
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 * 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.cos(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: edge drop magnitude', [-45, 1200, 2384, 300, 0], [-45, 357.1]],
['regression: edge drop magnitude (partial repair)', [-60, 1500, 1133, 500, 0], [-60, 1009.4]],
['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: edge drop magnitude', [-30, 1500, 1133, 1300, 0], [-20.674, 1300.0]],
['regression: edge drop magnitude (partial repair)', [60, 2000, 1133, 500, 0], [60, 1509.4]],
['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: edge drop magnitude', [-30, 1500, 2256, 300, 0], [-30, 936.0]],
['regression: edge drop magnitude (partial repair)', [45, 1200, 2256, 300, 0], [45, 402.4]],
['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: edge drop magnitude', [-30, 1500, 2384, 500, -5], [-30, 813.7]],
['regression: edge drop magnitude (partial repair)', [45, 2000, 4000, 500, 0], [45, 585.8]],
['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: edge drop magnitude', [-60, 2500, 2256, 300, -10], [-60, 1423.7]],
['regression: edge drop magnitude (partial repair)', [20, 2500, 2384, 300, -10], [20, 2289.8]],
['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: edge drop magnitude | [-45, 2042.9] | [-45, 357.1] | Failed |
| regression: edge drop magnitude (partial repair) | [-60, 1990.6] | [-60, 1009.4] | Failed |
| control 1 | [-45, 1894.3] | [-45, 208.5] | Failed |
| control 2 | [-0.0, 1400.1] | [-0.0, 1400.1] | Passed |
SHA-256 / 4bc29f8b86903184ea1a89da85ace5eca58d29181d84213b58c122b706be686b
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(abs(cmd)))
if cmd != 0:
side = 1 if cmd > 0 else -1
else:
side = 1 if slope >= 0 else -1
ground = side * half * math.cos(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: edge drop magnitude', [-45, 1200, 2384, 300, 0], [-45, 357.1]],
['regression: edge drop magnitude (partial repair)', [-60, 1500, 1133, 500, 0], [-60, 1009.4]],
['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: edge drop magnitude', [-30, 1500, 1133, 1300, 0], [-20.674, 1300.0]],
['regression: edge drop magnitude (partial repair)', [60, 2000, 1133, 500, 0], [60, 1509.4]],
['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: edge drop magnitude', [-30, 1500, 2256, 300, 0], [-30, 936.0]],
['regression: edge drop magnitude (partial repair)', [45, 1200, 2256, 300, 0], [45, 402.4]],
['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: edge drop magnitude', [-30, 1500, 2384, 500, -5], [-30, 813.7]],
['regression: edge drop magnitude (partial repair)', [45, 2000, 4000, 500, 0], [45, 585.8]],
['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: edge drop magnitude', [-60, 2500, 2256, 300, -10], [-60, 1423.7]],
['regression: edge drop magnitude (partial repair)', [20, 2500, 2384, 300, -10], [20, 2289.8]],
['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, 1156.2] | [60, 523.1] | Failed |
| 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: edge drop magnitude | [-45, 185.7] | [-45, 357.1] | Failed |
| regression: edge drop magnitude (partial repair) | [-60, 1327.3] | [-60, 1009.4] | Failed |
| control 1 | [-45, 37.1] | [-45, 208.5] | Failed |
| control 2 | [-0.0, 1400.1] | [-0.0, 1400.1] | Passed |
SHA-256 / 7ae72bd0476f55e48513d6966af71ebe1e7bee551f86db79afc90d88201947db
3 / The verified repair
Exit 0"""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.cos(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: edge drop magnitude', [-45, 1200, 2384, 300, 0], [-45, 357.1]],
['regression: edge drop magnitude (partial repair)', [-60, 1500, 1133, 500, 0], [-60, 1009.4]],
['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: edge drop magnitude', [-30, 1500, 1133, 1300, 0], [-20.674, 1300.0]],
['regression: edge drop magnitude (partial repair)', [60, 2000, 1133, 500, 0], [60, 1509.4]],
['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: edge drop magnitude', [-30, 1500, 2256, 300, 0], [-30, 936.0]],
['regression: edge drop magnitude (partial repair)', [45, 1200, 2256, 300, 0], [45, 402.4]],
['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: edge drop magnitude', [-30, 1500, 2384, 500, -5], [-30, 813.7]],
['regression: edge drop magnitude (partial repair)', [45, 2000, 4000, 500, 0], [45, 585.8]],
['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: edge drop magnitude', [-60, 2500, 2256, 300, -10], [-60, 1423.7]],
['regression: edge drop magnitude (partial repair)', [20, 2500, 2384, 300, -10], [20, 2289.8]],
['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: edge drop magnitude | [-45, 357.1] | [-45, 357.1] | Passed |
| regression: edge drop magnitude (partial repair) | [-60, 1009.4] | [-60, 1009.4] | Passed |
| control 1 | [-45, 208.5] | [-45, 208.5] | Passed |
| control 2 | [-0.0, 1400.1] | [-0.0, 1400.1] | Passed |
SHA-256 / dea91d675c8d7cba3907b447c6bcd8b736de61830f80e5b390aaea5318376349
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 2026-09-29T14:51:58.099237+00:00.
Case digest / 7c65dc31ca4b882f505893fc315db9651b2c9c5fe958b995a1ebee613f1ce145