FA-93571 / Solar tracker geometry / Open access

Fixed-tilt row pitch for a design sun: footprint and height terms · case 01

Flat rows get a large shadow allowance and steep rows get almost none.

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

ROOT CAUSE

Horizontal depth and vertical height use swapped trigonometric functions.

VERIFIED REPAIR

depth = length*cos(tilt), height = length*sin(tilt).

Unsuccessful approach: Using the full slant length as depth overstates the footprint of tilted rows.

Case contract

Rows of slant length length (mm) tilted by tilt degrees face row_az. The shadow reaches forward height*max(cos(sun_az - row_az), 0)/tan(sun_el). Minimum unshaded pitch = length*cos(tilt) + shadow. Return [pitch rounded 3, length/pitch rounded 4]; None when sun_el <= 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(length, tilt, sun_el, sun_az, row_az):
    if sun_el <= 0:
        return None
    t = math.radians(tilt)
    rel = math.cos(math.radians(sun_az - row_az))
    depth = length * math.sin(t)
    height = length * math.cos(t)
    shadow = height * max(rel, 0.0) / math.tan(math.radians(sun_el))
    pitch = depth + shadow
    return [round(pitch, 3), round(length / pitch, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [1700, 10, 15, 340, 200], [1674.173, 1.0154]],
  ['regression: footprint and height terms (partial repair)', [2300, 30, 30, 0, 180],
   [1991.858, 1.1547]],
  ['control 1', [1700, 30, 30, 90, 200], [1472.243, 1.1547]],
  ['control 2', [1700, 30, 0, 90, 180], None]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [1000, 0, 10, 300, 0], [1000.0, 1.0]],
  ['regression: footprint and height terms (partial repair)', [1700, 20, 10, 300, 180],
   [1597.477, 1.0642]],
  ['control 1', [1700, 30, 0, 225, 170], None],
  ['control 2', [2000, 30, 30, 135, 180], [2956.796, 0.6764]]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2300, 35, 20, 200, 200], [5508.593, 0.4175]],
  ['regression: footprint and height terms (partial repair)', [1000, 30, 20, 60, 0],
   [1552.895, 0.644]],
  ['control 1', [2000, 0, -2, 315, 0], None], ['control 2', [2000, 30, 0, 30, 0], None]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2000, 10, 15, 200, 180], [3187.577, 0.6274]],
  ['regression: footprint and height terms (partial repair)', [1000, 25, 10, 135, 200],
   [1919.234, 0.521]],
  ['control 1', [2300, 35, 30, 60, 0], [3026.533, 0.7599]],
  ['control 2', [1000, 30, 20, 250, 180], [1335.872, 0.7486]]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2300, 30, 30, 60, 200], [1991.858, 1.1547]],
  ['regression: footprint and height terms (partial repair)', [1700, 10, 20, 100, 180],
   [1815.012, 0.9366]],
  ['control 1', [2000, 35, -2, 225, 170], None],
  ['control 2', [1700, 20, 20, 90, 170], [1874.877, 0.9067]]]]
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: winter noon design sun	`[7464.102, 0.2679]`	`[5464.102, 0.366]`	Failed
boundary: flat rows	`[7464.102, 0.2679]`	`[2000.0, 1.0]`	Failed
boundary: sun behind the rows	`[1000.0, 2.0]`	`[1732.051, 1.1547]`	Failed
regression: footprint and height terms	`[295.202, 5.7588]`	`[1674.173, 1.0154]`	Failed
regression: footprint and height terms (partial repair)	`[1150.0, 2.0]`	`[1991.858, 1.1547]`	Failed
control 1	`[850.0, 2.0]`	`[1472.243, 1.1547]`	Failed
control 2	`None`	`None`	Passed

SHA-256 / 837d8f178b72785c39704fca419c228da4a55a0083028a40b814294b7e524ec2

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(length, tilt, sun_el, sun_az, row_az):
    if sun_el <= 0:
        return None
    t = math.radians(tilt)
    rel = math.cos(math.radians(sun_az - row_az))
    depth = length
    height = length * math.sin(t)
    shadow = height * max(rel, 0.0) / math.tan(math.radians(sun_el))
    pitch = depth + shadow
    return [round(pitch, 3), round(length / pitch, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [1700, 10, 15, 340, 200], [1674.173, 1.0154]],
  ['regression: footprint and height terms (partial repair)', [2300, 30, 30, 0, 180],
   [1991.858, 1.1547]],
  ['control 1', [1700, 30, 30, 90, 200], [1472.243, 1.1547]],
  ['control 2', [1700, 30, 0, 90, 180], None]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [1000, 0, 10, 300, 0], [1000.0, 1.0]],
  ['regression: footprint and height terms (partial repair)', [1700, 20, 10, 300, 180],
   [1597.477, 1.0642]],
  ['control 1', [1700, 30, 0, 225, 170], None],
  ['control 2', [2000, 30, 30, 135, 180], [2956.796, 0.6764]]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2300, 35, 20, 200, 200], [5508.593, 0.4175]],
  ['regression: footprint and height terms (partial repair)', [1000, 30, 20, 60, 0],
   [1552.895, 0.644]],
  ['control 1', [2000, 0, -2, 315, 0], None], ['control 2', [2000, 30, 0, 30, 0], None]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2000, 10, 15, 200, 180], [3187.577, 0.6274]],
  ['regression: footprint and height terms (partial repair)', [1000, 25, 10, 135, 200],
   [1919.234, 0.521]],
  ['control 1', [2300, 35, 30, 60, 0], [3026.533, 0.7599]],
  ['control 2', [1000, 30, 20, 250, 180], [1335.872, 0.7486]]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2300, 30, 30, 60, 200], [1991.858, 1.1547]],
  ['regression: footprint and height terms (partial repair)', [1700, 10, 20, 100, 180],
   [1815.012, 0.9366]],
  ['control 1', [2000, 35, -2, 225, 170], None],
  ['control 2', [1700, 20, 20, 90, 170], [1874.877, 0.9067]]]]
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: winter noon design sun	`[5732.051, 0.3489]`	`[5464.102, 0.366]`	Failed
boundary: flat rows	`[2000.0, 1.0]`	`[2000.0, 1.0]`	Passed
boundary: sun behind the rows	`[2000.0, 1.0]`	`[1732.051, 1.1547]`	Failed
regression: footprint and height terms	`[1700.0, 1.0]`	`[1674.173, 1.0154]`	Failed
regression: footprint and height terms (partial repair)	`[2300.0, 1.0]`	`[1991.858, 1.1547]`	Failed
control 1	`[1700.0, 1.0]`	`[1472.243, 1.1547]`	Failed
control 2	`None`	`None`	Passed

SHA-256 / 59189821b29506c8b455133ddb3d13e7cd70fbf4cf240c16730dc35ed3732db4

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(length, tilt, sun_el, sun_az, row_az):
    if sun_el <= 0:
        return None
    t = math.radians(tilt)
    rel = math.cos(math.radians(sun_az - row_az))
    depth = length * math.cos(t)
    height = length * math.sin(t)
    shadow = height * max(rel, 0.0) / math.tan(math.radians(sun_el))
    pitch = depth + shadow
    return [round(pitch, 3), round(length / pitch, 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [1700, 10, 15, 340, 200], [1674.173, 1.0154]],
  ['regression: footprint and height terms (partial repair)', [2300, 30, 30, 0, 180],
   [1991.858, 1.1547]],
  ['control 1', [1700, 30, 30, 90, 200], [1472.243, 1.1547]],
  ['control 2', [1700, 30, 0, 90, 180], None]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [1000, 0, 10, 300, 0], [1000.0, 1.0]],
  ['regression: footprint and height terms (partial repair)', [1700, 20, 10, 300, 180],
   [1597.477, 1.0642]],
  ['control 1', [1700, 30, 0, 225, 170], None],
  ['control 2', [2000, 30, 30, 135, 180], [2956.796, 0.6764]]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2300, 35, 20, 200, 200], [5508.593, 0.4175]],
  ['regression: footprint and height terms (partial repair)', [1000, 30, 20, 60, 0],
   [1552.895, 0.644]],
  ['control 1', [2000, 0, -2, 315, 0], None], ['control 2', [2000, 30, 0, 30, 0], None]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2000, 10, 15, 200, 180], [3187.577, 0.6274]],
  ['regression: footprint and height terms (partial repair)', [1000, 25, 10, 135, 200],
   [1919.234, 0.521]],
  ['control 1', [2300, 35, 30, 60, 0], [3026.533, 0.7599]],
  ['control 2', [1000, 30, 20, 250, 180], [1335.872, 0.7486]]],
 [['normal: winter noon design sun', [2000, 30, 15, 180, 180], [5464.102, 0.366]],
  ['boundary: flat rows', [2000, 0, 15, 180, 180], [2000.0, 1.0]],
  ['boundary: sun behind the rows', [2000, 30, 15, 0, 180], [1732.051, 1.1547]],
  ['regression: footprint and height terms', [2300, 30, 30, 60, 200], [1991.858, 1.1547]],
  ['regression: footprint and height terms (partial repair)', [1700, 10, 20, 100, 180],
   [1815.012, 0.9366]],
  ['control 1', [2000, 35, -2, 225, 170], None],
  ['control 2', [1700, 20, 20, 90, 170], [1874.877, 0.9067]]]]
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: winter noon design sun	`[5464.102, 0.366]`	`[5464.102, 0.366]`	Passed
boundary: flat rows	`[2000.0, 1.0]`	`[2000.0, 1.0]`	Passed
boundary: sun behind the rows	`[1732.051, 1.1547]`	`[1732.051, 1.1547]`	Passed
regression: footprint and height terms	`[1674.173, 1.0154]`	`[1674.173, 1.0154]`	Passed
regression: footprint and height terms (partial repair)	`[1991.858, 1.1547]`	`[1991.858, 1.1547]`	Passed
control 1	`[1472.243, 1.1547]`	`[1472.243, 1.1547]`	Passed
control 2	`None`	`None`	Passed

SHA-256 / 7c9cbd062cb37d3a50ea1bd9cde100c0ae0f4125d93e676228350dbb89de526b

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 2026-09-29T14:51:56.322211+00:00.

Case digest / 8ede73213c96df8a8c298a97264deefb1a3b2f7eb657d18a99e1dff38b0cc823