FA-71251 / Weather index computation / Open access

Vector-mean wind and steadiness: degree to radian conversion · case 01

Directions from different sensors average to meaningless values.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Bearings in degrees are passed to sin and cos as radians.

THE FAILURE

Bearings in degrees are passed to sin and cos as radians.

Unsuccessful approach: Using pi/360 halves every angle.

Case contract

obs are [speed, direction_from_deg]. Components u=-s*sin(d), v=-s*cos(d); average them. Return [vector speed rounded 0.01, direction the wind blows FROM in [0,360) rounded 0.1 or None if the vector speed is below 1e-9, steadiness = vector speed / scalar mean speed rounded 0.001 (0.0 if calm)]; empty input returns None.

Why this case matters

Wind roses, dispersion inputs and runway selection need vector-mean wind direction.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(obs):
    if not obs:
        return None
    u = v = s = 0.0
    for spd, d in obs:
        r = d
        u += -spd * math.sin(r)
        v += -spd * math.cos(r)
        s += spd
    n = len(obs)
    u /= n
    v /= n
    vs = math.hypot(u, v)
    if vs < 1e-9:
        direction = None
    else:
        direction = round(math.degrees(math.atan2(-u, -v)) % 360, 1)
    steadiness = round(vs / (s / n), 3) if s > 0 else 0.0
    return [round(vs, 2), direction, steadiness]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mast 0', [[[2, 180], [2, 170], [5, 180]]], [2.99, 177.8, 0.997]], ['mast 1', [[[2, 170], [8, 210], [5, 210], [5, 190], [12, 140]]], [5.47, 178.5, 0.855]], ['mast 2', [[[0, 50], [5, 340], [2, 340]]], [2.33, 340.0, 1.0]], ['mast 3', [[[2, 10], [5, 60], [0, 10], [12, 10], [12, 320]]], [5.1, 357.9, 0.823]], ['mast 4', [[[2, 190], [2, 180], [0, 170]]], [1.33, 185.0, 0.996]], ['mast 5', [[[8, 90], [0, 90], [5, 50], [0, 100], [0, 50], [5, 50]]], [2.82, 67.7, 0.94]], ['mast 6', [[[0, 30], [12, 350], [12, 350], [12, 30], [0, 320], [0, 0]]], [5.68, 3.1, 0.947]], ['mast 7', [[[8, 120], [8, 120], [5, 90]]], [6.83, 113.0, 0.975]]], [['mast 3', [[[2, 10], [5, 60], [0, 10], [12, 10], [12, 320]]], [5.1, 357.9, 0.823]], ['mast 6', [[[0, 30], [12, 350], [12, 350], [12, 30], [0, 320], [0, 0]]], [5.68, 3.1, 0.947]], ['mast 7', [[[8, 120], [8, 120], [5, 90]]], [6.83, 113.0, 0.975]], ['mast 8', [[[2, 300], [12, 270], [12, 260], [8, 260], [2, 330]]], [6.89, 268.8, 0.957]], ['mast 9', [[[8, 320], [5, 30], [12, 320], [0, 60], [5, 350]]], [5.4, 335.5, 0.901]], ['mast 10', [[[5, 240], [2, 240], [8, 180], [0, 210], [5, 170]]], [3.45, 197.5, 0.861]], ['mast 11', [[[2, 35], [12, 45], [8, 75], [8, 105]]], [6.76, 68.0, 0.902]], ['mast 12', [[[12, 100], [5, 100], [0, 80]]], [5.67, 100.0, 1.0]]], [['mast 6', [[[0, 30], [12, 350], [12, 350], [12, 30], [0, 320], [0, 0]]], [5.68, 3.1, 0.947]], ['mast 11', [[[2, 35], [12, 45], [8, 75], [8, 105]]], [6.76, 68.0, 0.902]], ['mast 14', [[[12, 45], [8, 55], [8, 35], [8, 45], [12, 105], [8, 35]]], [8.41, 55.3, 0.901]], ['mast 15', [[[2, 60], [5, 320], [2, 0], [0, 0]]], [1.75, 347.8, 0.777]], ['mast 16', [[[8, 330], [12, 270], [12, 280]]], [9.75, 288.0, 0.914]], ['mast 17', [[[12, 30], [0, 350], [12, 0], [8, 0], [8, 60]]], [7.35, 20.6, 0.919]], ['mast 18', [[[2, 330], [2, 230], [2, 280], [8, 270]]], [3.13, 273.6, 0.895]], ['mast 19', [[[8, 5], [2, 45], [0, 105]]], [3.21, 12.7, 0.962]]], [['mast 9', [[[8, 320], [5, 30], [12, 320], [0, 60], [5, 350]]], [5.4, 335.5, 0.901]], ['mast 16', [[[8, 330], [12, 270], [12, 280]]], [9.75, 288.0, 0.914]], ['mast 21', [[[12, 170], [5, 180], [5, 240], [0, 190]]], [4.86, 186.6, 0.884]], ['mast 22', [[[0, 260], [8, 270], [5, 260], [12, 260]]], [6.23, 263.2, 0.997]], ['mast 23', [[[5, 180], [8, 240], [0, 190], [0, 140], [2, 180], [0, 240]]], [2.17, 212.2, 0.867]], ['mast 24', [[[12, 190], [12, 240], [0, 170]]], [7.25, 215.0, 0.906]], ['mast 25', [[[5, 210], [2, 190], [8, 210], [8, 210], [5, 240]]], [5.45, 213.8, 0.974]], ['mast 26', [[[8, 350], [8, 0], [5, 30], [0, 60], [8, 350]]], [5.62, 359.4, 0.969]]], [['mast 12', [[[12, 100], [5, 100], [0, 80]]], [5.67, 100.0, 1.0]], ['mast 21', [[[12, 170], [5, 180], [5, 240], [0, 190]]], [4.86, 186.6, 0.884]], ['mast 28', [[[12, 310], [12, 20], [2, 0], [8, 350], [5, 0], [12, 350]]], [7.75, 349.4, 0.911]], ['mast 29', [[[0, 340], [0, 20], [5, 350]]], [1.67, 350.0, 1.0]], ['north wrap', [[[5, 350], [5, 10]]], [4.92, 360.0, 0.985]], ['opposed winds', [[[5, 90], [5, 270]]], [0.0, None, 0.0]], ['calm', [[[0, 0], [0, 180]]], [0.0, None, 0.0]], ['empty', [[]], None]]]
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
mast 0	`[1.81, 244.8, 0.604]`	`[2.99, 177.8, 0.997]`	Failed
mast 1	`[5.25, 116.4, 0.82]`	`[5.47, 178.5, 0.855]`	Failed
mast 2	`[2.33, 40.6, 1.0]`	`[2.33, 340.0, 1.0]`	Failed
mast 3	`[3.07, 248.4, 0.496]`	`[5.1, 357.9, 0.823]`	Failed
mast 4	`[0.38, 159.7, 0.284]`	`[1.33, 185.0, 0.996]`	Failed
mast 5	`[1.26, 36.7, 0.421]`	`[2.82, 67.7, 0.94]`	Failed
mast 6	`[5.87, 261.9, 0.978]`	`[5.68, 3.1, 0.947]`	Failed
mast 7	`[5.83, 51.9, 0.833]`	`[6.83, 113.0, 0.975]`	Failed

SHA-256 / 8bc18683ba1e830a8a5070a2752f7a71decd5d59e768917d2ee95787e5699197

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(obs):
    if not obs:
        return None
    u = v = s = 0.0
    for spd, d in obs:
        r = d * math.pi / 360
        u += -spd * math.sin(r)
        v += -spd * math.cos(r)
        s += spd
    n = len(obs)
    u /= n
    v /= n
    vs = math.hypot(u, v)
    if vs < 1e-9:
        direction = None
    else:
        direction = round(math.degrees(math.atan2(-u, -v)) % 360, 1)
    steadiness = round(vs / (s / n), 3) if s > 0 else 0.0
    return [round(vs, 2), direction, steadiness]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mast 0', [[[2, 180], [2, 170], [5, 180]]], [2.99, 177.8, 0.997]], ['mast 1', [[[2, 170], [8, 210], [5, 210], [5, 190], [12, 140]]], [5.47, 178.5, 0.855]], ['mast 2', [[[0, 50], [5, 340], [2, 340]]], [2.33, 340.0, 1.0]], ['mast 3', [[[2, 10], [5, 60], [0, 10], [12, 10], [12, 320]]], [5.1, 357.9, 0.823]], ['mast 4', [[[2, 190], [2, 180], [0, 170]]], [1.33, 185.0, 0.996]], ['mast 5', [[[8, 90], [0, 90], [5, 50], [0, 100], [0, 50], [5, 50]]], [2.82, 67.7, 0.94]], ['mast 6', [[[0, 30], [12, 350], [12, 350], [12, 30], [0, 320], [0, 0]]], [5.68, 3.1, 0.947]], ['mast 7', [[[8, 120], [8, 120], [5, 90]]], [6.83, 113.0, 0.975]]], [['mast 3', [[[2, 10], [5, 60], [0, 10], [12, 10], [12, 320]]], [5.1, 357.9, 0.823]], ['mast 6', [[[0, 30], [12, 350], [12, 350], [12, 30], [0, 320], [0, 0]]], [5.68, 3.1, 0.947]], ['mast 7', [[[8, 120], [8, 120], [5, 90]]], [6.83, 113.0, 0.975]], ['mast 8', [[[2, 300], [12, 270], [12, 260], [8, 260], [2, 330]]], [6.89, 268.8, 0.957]], ['mast 9', [[[8, 320], [5, 30], [12, 320], [0, 60], [5, 350]]], [5.4, 335.5, 0.901]], ['mast 10', [[[5, 240], [2, 240], [8, 180], [0, 210], [5, 170]]], [3.45, 197.5, 0.861]], ['mast 11', [[[2, 35], [12, 45], [8, 75], [8, 105]]], [6.76, 68.0, 0.902]], ['mast 12', [[[12, 100], [5, 100], [0, 80]]], [5.67, 100.0, 1.0]]], [['mast 6', [[[0, 30], [12, 350], [12, 350], [12, 30], [0, 320], [0, 0]]], [5.68, 3.1, 0.947]], ['mast 11', [[[2, 35], [12, 45], [8, 75], [8, 105]]], [6.76, 68.0, 0.902]], ['mast 14', [[[12, 45], [8, 55], [8, 35], [8, 45], [12, 105], [8, 35]]], [8.41, 55.3, 0.901]], ['mast 15', [[[2, 60], [5, 320], [2, 0], [0, 0]]], [1.75, 347.8, 0.777]], ['mast 16', [[[8, 330], [12, 270], [12, 280]]], [9.75, 288.0, 0.914]], ['mast 17', [[[12, 30], [0, 350], [12, 0], [8, 0], [8, 60]]], [7.35, 20.6, 0.919]], ['mast 18', [[[2, 330], [2, 230], [2, 280], [8, 270]]], [3.13, 273.6, 0.895]], ['mast 19', [[[8, 5], [2, 45], [0, 105]]], [3.21, 12.7, 0.962]]], [['mast 9', [[[8, 320], [5, 30], [12, 320], [0, 60], [5, 350]]], [5.4, 335.5, 0.901]], ['mast 16', [[[8, 330], [12, 270], [12, 280]]], [9.75, 288.0, 0.914]], ['mast 21', [[[12, 170], [5, 180], [5, 240], [0, 190]]], [4.86, 186.6, 0.884]], ['mast 22', [[[0, 260], [8, 270], [5, 260], [12, 260]]], [6.23, 263.2, 0.997]], ['mast 23', [[[5, 180], [8, 240], [0, 190], [0, 140], [2, 180], [0, 240]]], [2.17, 212.2, 0.867]], ['mast 24', [[[12, 190], [12, 240], [0, 170]]], [7.25, 215.0, 0.906]], ['mast 25', [[[5, 210], [2, 190], [8, 210], [8, 210], [5, 240]]], [5.45, 213.8, 0.974]], ['mast 26', [[[8, 350], [8, 0], [5, 30], [0, 60], [8, 350]]], [5.62, 359.4, 0.969]]], [['mast 12', [[[12, 100], [5, 100], [0, 80]]], [5.67, 100.0, 1.0]], ['mast 21', [[[12, 170], [5, 180], [5, 240], [0, 190]]], [4.86, 186.6, 0.884]], ['mast 28', [[[12, 310], [12, 20], [2, 0], [8, 350], [5, 0], [12, 350]]], [7.75, 349.4, 0.911]], ['mast 29', [[[0, 340], [0, 20], [5, 350]]], [1.67, 350.0, 1.0]], ['north wrap', [[[5, 350], [5, 10]]], [4.92, 360.0, 0.985]], ['opposed winds', [[[5, 90], [5, 270]]], [0.0, None, 0.0]], ['calm', [[[0, 0], [0, 180]]], [0.0, None, 0.0]], ['empty', [[]], None]]]
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
mast 0	`[3.0, 88.9, 0.999]`	`[2.99, 177.8, 0.997]`	Failed
mast 1	`[6.16, 89.1, 0.963]`	`[5.47, 178.5, 0.855]`	Failed
mast 2	`[2.33, 170.0, 1.0]`	`[2.33, 340.0, 1.0]`	Failed
mast 3	`[2.1, 48.2, 0.339]`	`[5.1, 357.9, 0.823]`	Failed
mast 4	`[1.33, 92.5, 0.999]`	`[1.33, 185.0, 0.996]`	Failed
mast 5	`[2.95, 33.9, 0.985]`	`[2.82, 67.7, 0.94]`	Failed
mast 6	`[2.23, 157.1, 0.371]`	`[5.68, 3.1, 0.947]`	Failed
mast 7	`[6.96, 56.4, 0.994]`	`[6.83, 113.0, 0.975]`	Failed

SHA-256 / 526eb39e706882874fe1c5c2093d5f731bcc674c8a61820046cba9bc8a210f41

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 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

Stipulated deterministic teaching model of an operational weather index; coefficients and thresholds are fixed by the contract and no claim of standards conformance is made. 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 2026-09-29T14:48:28.001587+00:00.

Case digest / 55463b2c6cd1349d443e915c2613f177bb46d01b6fddb1b24ade52777e6fc99d