FA-66106 / Aviation weight and balance / Open access

CG divided from the reduced moment · case 01

The loaded CG is reported near zero inches.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The CG uses the reduced (divided by 1000) moment rather than the full moment.

VERIFIED REPAIR

Compute CG from the unreduced moment divided by total weight.

Unsuccessful approach: Scaling the rounded reduced moment back up reintroduces rounding error of up to 5 lb-in into the CG.

Case contract

Input [[quantity, 'kg'|'lb', arm, 'in'|'cm'|'mm']]. Convert to lb (1 kg = 2.20462 lb) and inches (2.54 cm, 25.4 mm per inch); other units -> 'ERR_UNIT'; total weight <= 0 -> 'ERR_WEIGHT'. Return [weight lb r1, reduced moment (lb-in/1000) r2, CG in r2 computed from the unreduced moment].

Why this case matters

Imported aircraft documentation mixes metric and imperial units; reduced moments (moment/1000) are a charting convenience and must not feed the CG division.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    wf = {'kg': 2.20462, 'lb': 1.0}
    af = {'in': 1.0, 'cm': 1 / 2.54, 'mm': 1 / 25.4}
    w = 0.0
    m = 0.0
    for q, wu, arm, au in x:
        if wu not in wf or au not in af: return 'ERR_UNIT'
        lb = q * wf[wu]
        w += lb
        m += lb * arm * af[au]
    if w <= 0: return 'ERR_WEIGHT'
    return [round(w, 1), round(m / 1000, 2), round(round(m / 1000, 2) / w, 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mixed kg and cm', [[81.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [348.6, 12.97, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3510.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 498.38, 150.71]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [120.0, 'lb', 48.0, 'in']], [2110.0, 83.02, 39.35]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[10.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 251.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 560.51, 97.91]], ['sampled case 1', [[1412.5, 'kg', 3138.2, 'cm'], [645.7, 'lb', 3313.7, 'cm'], [780.8, 'lb', 1136.3, 'cm'], [548.1, 'kg', 3196.1, 'cm'], [708.5, 'kg', 4627.1, 'in']], [7310.9, 13786.98, 1885.82]], ['sampled case 2', [[446.5, 'lb', 1614.2, 'cm'], [1166.3, 'lb', 934.4, 'mm'], [1321.5, 'lb', 2983.7, 'in'], [1133.4, 'lb', 4571.3, 'mm']], [4067.7, 4473.6, 1099.79]], ['sampled case 3', [[880.0, 'kg', 2334.3, 'mm']], [1940.1, 178.3, 91.9]], ['regression: CG from reduced moment', [[394.5, 'lb', 719.5, 'in']], [394.5, 283.84, 719.5]]], [['mixed kg and cm', [[82.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [350.8, 13.05, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3520.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 499.42, 151.02]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [240.0, 'lb', 48.0, 'in']], [2230.0, 88.78, 39.81]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[20.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 252.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 562.68, 98.28]], ['sampled case 1', [[451.1, 'lb', 2563.5, 'mm'], [525.2, 'kg', 1580.7, 'in'], [1447.9, 'kg', 4822.5, 'cm'], [324.3, 'kg', 4534.3, 'in']], [5516.0, 11178.14, 2026.5]], ['sampled case 2', [[741.8, 'lb', 489.9, 'mm']], [741.8, 14.31, 19.29]], ['sampled case 3', [[65.8, 'lb', 769.9, 'cm'], [1474.8, 'kg', 2706.1, 'mm'], [1498.3, 'kg', 2769.1, 'cm']], [6620.4, 3967.46, 599.28]]], [['mixed kg and cm', [[83.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [353.0, 13.13, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3530.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 500.47, 151.34]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [360.0, 'lb', 48.0, 'in']], [2350.0, 94.54, 40.23]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[30.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 253.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 564.85, 98.66]], ['sampled case 1', [[587.7, 'lb', 751.0, 'in'], [1481.3, 'kg', 2071.3, 'mm'], [1260.8, 'lb', 3264.1, 'in']], [5114.2, 4823.05, 943.07]], ['sampled case 2', [[1420.4, 'lb', 62.7, 'in'], [744.7, 'lb', 3096.0, 'cm'], [1460.6, 'lb', 2357.4, 'in'], [784.7, 'kg', 1562.0, 'mm']], [5355.7, 4546.38, 848.89]], ['sampled case 3', [[927.8, 'lb', 3339.6, 'mm'], [96.5, 'lb', 2857.2, 'in']], [1024.3, 397.71, 388.27]]], [['mixed kg and cm', [[84.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [355.2, 13.22, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3540.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 501.51, 151.65]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [480.0, 'lb', 48.0, 'in']], [2470.0, 100.3, 40.61]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[40.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 254.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 567.02, 99.04]], ['sampled case 1', [[845.6, 'lb', 549.1, 'mm'], [706.7, 'lb', 4259.5, 'cm'], [418.1, 'lb', 941.4, 'in'], [300.5, 'lb', 701.4, 'in']], [2270.9, 1807.76, 796.06]], ['sampled case 2', [[672.3, 'lb', 4546.6, 'cm'], [811.4, 'kg', 2178.7, 'mm'], [1336.5, 'kg', 2678.4, 'cm'], [437.9, 'lb', 3587.0, 'in']], [5845.5, 6034.62, 1032.35]], ['sampled case 3', [[932.7, 'lb', 1924.2, 'in'], [707.5, 'lb', 1732.9, 'cm']], [1640.2, 2277.39, 1388.48]]], [['mixed kg and cm', [[85.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [357.4, 13.3, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3550.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 502.55, 151.97]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [600.0, 'lb', 48.0, 'in']], [2590.0, 106.06, 40.95]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[50.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 255.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 569.19, 99.42]], ['sampled case 1', [[443.4, 'lb', 3757.6, 'mm'], [1247.8, 'lb', 3883.6, 'cm'], [863.0, 'kg', 1577.0, 'in']], [3593.8, 4973.83, 1384.01]], ['sampled case 2', [[1022.3, 'kg', 4134.6, 'cm'], [1227.6, 'kg', 1189.8, 'mm']], [4960.2, 3795.47, 765.19]], ['sampled case 3', [[516.4, 'kg', 3268.8, 'in'], [1320.8, 'kg', 2685.1, 'cm'], [1128.7, 'kg', 3910.9, 'cm'], [295.8, 'kg', 1659.2, 'cm'], [1025.6, 'lb', 579.9, 'cm']], [8216.4, 11291.14, 1374.22]], ['regression: CG from reduced moment', [[1026.8, 'lb', 537.4, 'in'], [882.1, 'lb', 1438.3, 'in'], [108.9, 'kg', 2100.3, 'cm'], [1314.8, 'lb', 3568.5, 'cm'], [1474.3, 'lb', 3755.8, 'in']], [4938.1, 9403.42, 1904.26]]]]
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
mixed kg and cm	`[348.6, 12.97, 0.04]`	`[348.6, 12.97, 37.21]`	Failed
millimetre arms	`[3306.9, 498.38, 0.15]`	`[3306.9, 498.38, 150.71]`	Failed
all imperial	`[2110.0, 83.02, 0.04]`	`[2110.0, 83.02, 39.35]`	Failed
unknown weight unit	`ERR_UNIT`	`ERR_UNIT`	Passed
unknown arm unit	`ERR_UNIT`	`ERR_UNIT`	Passed
removal leaves nothing	`ERR_WEIGHT`	`ERR_WEIGHT`	Passed
heavy kg load	`[5725.0, 560.51, 0.1]`	`[5725.0, 560.51, 97.91]`	Failed
sampled case 1	`[7310.9, 13786.98, 1.89]`	`[7310.9, 13786.98, 1885.82]`	Failed
sampled case 2	`[4067.7, 4473.6, 1.1]`	`[4067.7, 4473.6, 1099.79]`	Failed
sampled case 3	`[1940.1, 178.3, 0.09]`	`[1940.1, 178.3, 91.9]`	Failed
regression: CG from reduced moment	`[394.5, 283.84, 0.72]`	`[394.5, 283.84, 719.5]`	Failed

SHA-256 / 462742d305a15835b22f9a8a4b77c1e865fd79eb070296659c79cc80266a665e

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    wf = {'kg': 2.20462, 'lb': 1.0}
    af = {'in': 1.0, 'cm': 1 / 2.54, 'mm': 1 / 25.4}
    w = 0.0
    m = 0.0
    for q, wu, arm, au in x:
        if wu not in wf or au not in af: return 'ERR_UNIT'
        lb = q * wf[wu]
        w += lb
        m += lb * arm * af[au]
    if w <= 0: return 'ERR_WEIGHT'
    return [round(w, 1), round(m / 1000, 2), round(round(m / 1000, 2) * 1000 / w, 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mixed kg and cm', [[81.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [348.6, 12.97, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3510.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 498.38, 150.71]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [120.0, 'lb', 48.0, 'in']], [2110.0, 83.02, 39.35]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[10.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 251.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 560.51, 97.91]], ['sampled case 1', [[1412.5, 'kg', 3138.2, 'cm'], [645.7, 'lb', 3313.7, 'cm'], [780.8, 'lb', 1136.3, 'cm'], [548.1, 'kg', 3196.1, 'cm'], [708.5, 'kg', 4627.1, 'in']], [7310.9, 13786.98, 1885.82]], ['sampled case 2', [[446.5, 'lb', 1614.2, 'cm'], [1166.3, 'lb', 934.4, 'mm'], [1321.5, 'lb', 2983.7, 'in'], [1133.4, 'lb', 4571.3, 'mm']], [4067.7, 4473.6, 1099.79]], ['sampled case 3', [[880.0, 'kg', 2334.3, 'mm']], [1940.1, 178.3, 91.9]], ['regression: CG from reduced moment', [[394.5, 'lb', 719.5, 'in']], [394.5, 283.84, 719.5]]], [['mixed kg and cm', [[82.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [350.8, 13.05, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3520.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 499.42, 151.02]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [240.0, 'lb', 48.0, 'in']], [2230.0, 88.78, 39.81]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[20.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 252.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 562.68, 98.28]], ['sampled case 1', [[451.1, 'lb', 2563.5, 'mm'], [525.2, 'kg', 1580.7, 'in'], [1447.9, 'kg', 4822.5, 'cm'], [324.3, 'kg', 4534.3, 'in']], [5516.0, 11178.14, 2026.5]], ['sampled case 2', [[741.8, 'lb', 489.9, 'mm']], [741.8, 14.31, 19.29]], ['sampled case 3', [[65.8, 'lb', 769.9, 'cm'], [1474.8, 'kg', 2706.1, 'mm'], [1498.3, 'kg', 2769.1, 'cm']], [6620.4, 3967.46, 599.28]]], [['mixed kg and cm', [[83.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [353.0, 13.13, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3530.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 500.47, 151.34]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [360.0, 'lb', 48.0, 'in']], [2350.0, 94.54, 40.23]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[30.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 253.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 564.85, 98.66]], ['sampled case 1', [[587.7, 'lb', 751.0, 'in'], [1481.3, 'kg', 2071.3, 'mm'], [1260.8, 'lb', 3264.1, 'in']], [5114.2, 4823.05, 943.07]], ['sampled case 2', [[1420.4, 'lb', 62.7, 'in'], [744.7, 'lb', 3096.0, 'cm'], [1460.6, 'lb', 2357.4, 'in'], [784.7, 'kg', 1562.0, 'mm']], [5355.7, 4546.38, 848.89]], ['sampled case 3', [[927.8, 'lb', 3339.6, 'mm'], [96.5, 'lb', 2857.2, 'in']], [1024.3, 397.71, 388.27]]], [['mixed kg and cm', [[84.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [355.2, 13.22, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3540.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 501.51, 151.65]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [480.0, 'lb', 48.0, 'in']], [2470.0, 100.3, 40.61]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[40.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 254.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 567.02, 99.04]], ['sampled case 1', [[845.6, 'lb', 549.1, 'mm'], [706.7, 'lb', 4259.5, 'cm'], [418.1, 'lb', 941.4, 'in'], [300.5, 'lb', 701.4, 'in']], [2270.9, 1807.76, 796.06]], ['sampled case 2', [[672.3, 'lb', 4546.6, 'cm'], [811.4, 'kg', 2178.7, 'mm'], [1336.5, 'kg', 2678.4, 'cm'], [437.9, 'lb', 3587.0, 'in']], [5845.5, 6034.62, 1032.35]], ['sampled case 3', [[932.7, 'lb', 1924.2, 'in'], [707.5, 'lb', 1732.9, 'cm']], [1640.2, 2277.39, 1388.48]]], [['mixed kg and cm', [[85.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [357.4, 13.3, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3550.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 502.55, 151.97]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [600.0, 'lb', 48.0, 'in']], [2590.0, 106.06, 40.95]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[50.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 255.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 569.19, 99.42]], ['sampled case 1', [[443.4, 'lb', 3757.6, 'mm'], [1247.8, 'lb', 3883.6, 'cm'], [863.0, 'kg', 1577.0, 'in']], [3593.8, 4973.83, 1384.01]], ['sampled case 2', [[1022.3, 'kg', 4134.6, 'cm'], [1227.6, 'kg', 1189.8, 'mm']], [4960.2, 3795.47, 765.19]], ['sampled case 3', [[516.4, 'kg', 3268.8, 'in'], [1320.8, 'kg', 2685.1, 'cm'], [1128.7, 'kg', 3910.9, 'cm'], [295.8, 'kg', 1659.2, 'cm'], [1025.6, 'lb', 579.9, 'cm']], [8216.4, 11291.14, 1374.22]], ['regression: CG from reduced moment', [[1026.8, 'lb', 537.4, 'in'], [882.1, 'lb', 1438.3, 'in'], [108.9, 'kg', 2100.3, 'cm'], [1314.8, 'lb', 3568.5, 'cm'], [1474.3, 'lb', 3755.8, 'in']], [4938.1, 9403.42, 1904.26]]]]
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
mixed kg and cm	`[348.6, 12.97, 37.21]`	`[348.6, 12.97, 37.21]`	Passed
millimetre arms	`[3306.9, 498.38, 150.71]`	`[3306.9, 498.38, 150.71]`	Passed
all imperial	`[2110.0, 83.02, 39.35]`	`[2110.0, 83.02, 39.35]`	Passed
unknown weight unit	`ERR_UNIT`	`ERR_UNIT`	Passed
unknown arm unit	`ERR_UNIT`	`ERR_UNIT`	Passed
removal leaves nothing	`ERR_WEIGHT`	`ERR_WEIGHT`	Passed
heavy kg load	`[5725.0, 560.51, 97.91]`	`[5725.0, 560.51, 97.91]`	Passed
sampled case 1	`[7310.9, 13786.98, 1885.82]`	`[7310.9, 13786.98, 1885.82]`	Passed
sampled case 2	`[4067.7, 4473.6, 1099.79]`	`[4067.7, 4473.6, 1099.79]`	Passed
sampled case 3	`[1940.1, 178.3, 91.9]`	`[1940.1, 178.3, 91.9]`	Passed
regression: CG from reduced moment	`[394.5, 283.84, 719.49]`	`[394.5, 283.84, 719.5]`	Failed

SHA-256 / 45e83c455d8e7bab436cd176ce24e04782275dc2470e8d3c8df0a0039bd20fee

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    wf = {'kg': 2.20462, 'lb': 1.0}
    af = {'in': 1.0, 'cm': 1 / 2.54, 'mm': 1 / 25.4}
    w = 0.0
    m = 0.0
    for q, wu, arm, au in x:
        if wu not in wf or au not in af: return 'ERR_UNIT'
        lb = q * wf[wu]
        w += lb
        m += lb * arm * af[au]
    if w <= 0: return 'ERR_WEIGHT'
    return [round(w, 1), round(m / 1000, 2), round(m / w, 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mixed kg and cm', [[81.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [348.6, 12.97, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3510.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 498.38, 150.71]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [120.0, 'lb', 48.0, 'in']], [2110.0, 83.02, 39.35]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[10.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 251.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 560.51, 97.91]], ['sampled case 1', [[1412.5, 'kg', 3138.2, 'cm'], [645.7, 'lb', 3313.7, 'cm'], [780.8, 'lb', 1136.3, 'cm'], [548.1, 'kg', 3196.1, 'cm'], [708.5, 'kg', 4627.1, 'in']], [7310.9, 13786.98, 1885.82]], ['sampled case 2', [[446.5, 'lb', 1614.2, 'cm'], [1166.3, 'lb', 934.4, 'mm'], [1321.5, 'lb', 2983.7, 'in'], [1133.4, 'lb', 4571.3, 'mm']], [4067.7, 4473.6, 1099.79]], ['sampled case 3', [[880.0, 'kg', 2334.3, 'mm']], [1940.1, 178.3, 91.9]], ['regression: CG from reduced moment', [[394.5, 'lb', 719.5, 'in']], [394.5, 283.84, 719.5]]], [['mixed kg and cm', [[82.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [350.8, 13.05, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3520.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 499.42, 151.02]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [240.0, 'lb', 48.0, 'in']], [2230.0, 88.78, 39.81]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[20.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 252.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 562.68, 98.28]], ['sampled case 1', [[451.1, 'lb', 2563.5, 'mm'], [525.2, 'kg', 1580.7, 'in'], [1447.9, 'kg', 4822.5, 'cm'], [324.3, 'kg', 4534.3, 'in']], [5516.0, 11178.14, 2026.5]], ['sampled case 2', [[741.8, 'lb', 489.9, 'mm']], [741.8, 14.31, 19.29]], ['sampled case 3', [[65.8, 'lb', 769.9, 'cm'], [1474.8, 'kg', 2706.1, 'mm'], [1498.3, 'kg', 2769.1, 'cm']], [6620.4, 3967.46, 599.28]]], [['mixed kg and cm', [[83.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [353.0, 13.13, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3530.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 500.47, 151.34]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [360.0, 'lb', 48.0, 'in']], [2350.0, 94.54, 40.23]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[30.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 253.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 564.85, 98.66]], ['sampled case 1', [[587.7, 'lb', 751.0, 'in'], [1481.3, 'kg', 2071.3, 'mm'], [1260.8, 'lb', 3264.1, 'in']], [5114.2, 4823.05, 943.07]], ['sampled case 2', [[1420.4, 'lb', 62.7, 'in'], [744.7, 'lb', 3096.0, 'cm'], [1460.6, 'lb', 2357.4, 'in'], [784.7, 'kg', 1562.0, 'mm']], [5355.7, 4546.38, 848.89]], ['sampled case 3', [[927.8, 'lb', 3339.6, 'mm'], [96.5, 'lb', 2857.2, 'in']], [1024.3, 397.71, 388.27]]], [['mixed kg and cm', [[84.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [355.2, 13.22, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3540.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 501.51, 151.65]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [480.0, 'lb', 48.0, 'in']], [2470.0, 100.3, 40.61]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[40.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 254.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 567.02, 99.04]], ['sampled case 1', [[845.6, 'lb', 549.1, 'mm'], [706.7, 'lb', 4259.5, 'cm'], [418.1, 'lb', 941.4, 'in'], [300.5, 'lb', 701.4, 'in']], [2270.9, 1807.76, 796.06]], ['sampled case 2', [[672.3, 'lb', 4546.6, 'cm'], [811.4, 'kg', 2178.7, 'mm'], [1336.5, 'kg', 2678.4, 'cm'], [437.9, 'lb', 3587.0, 'in']], [5845.5, 6034.62, 1032.35]], ['sampled case 3', [[932.7, 'lb', 1924.2, 'in'], [707.5, 'lb', 1732.9, 'cm']], [1640.2, 2277.39, 1388.48]]], [['mixed kg and cm', [[85.0, 'kg', 95.0, 'cm'], [170.0, 'lb', 37.0, 'in']], [357.4, 13.3, 37.21]], ['millimetre arms', [[1200.0, 'kg', 3550.0, 'mm'], [300.0, 'kg', 5100.0, 'mm']], [3306.9, 502.55, 151.97]], ['all imperial', [[1650.0, 'lb', 39.2, 'in'], [340.0, 'lb', 37.0, 'in'], [600.0, 'lb', 48.0, 'in']], [2590.0, 106.06, 40.95]], ['unknown weight unit', [[10.0, 'st', 50.0, 'in']], 'ERR_UNIT'], ['unknown arm unit', [[50.0, 'kg', 2.0, 'm']], 'ERR_UNIT'], ['removal leaves nothing', [[20.0, 'kg', 100.0, 'cm'], [-50.0, 'lb', 39.37, 'in']], 'ERR_WEIGHT'], ['heavy kg load', [[2500.0, 'kg', 255.0, 'cm'], [90.0, 'kg', 180.0, 'cm'], [15.0, 'lb', 120.0, 'in']], [5725.0, 569.19, 99.42]], ['sampled case 1', [[443.4, 'lb', 3757.6, 'mm'], [1247.8, 'lb', 3883.6, 'cm'], [863.0, 'kg', 1577.0, 'in']], [3593.8, 4973.83, 1384.01]], ['sampled case 2', [[1022.3, 'kg', 4134.6, 'cm'], [1227.6, 'kg', 1189.8, 'mm']], [4960.2, 3795.47, 765.19]], ['sampled case 3', [[516.4, 'kg', 3268.8, 'in'], [1320.8, 'kg', 2685.1, 'cm'], [1128.7, 'kg', 3910.9, 'cm'], [295.8, 'kg', 1659.2, 'cm'], [1025.6, 'lb', 579.9, 'cm']], [8216.4, 11291.14, 1374.22]], ['regression: CG from reduced moment', [[1026.8, 'lb', 537.4, 'in'], [882.1, 'lb', 1438.3, 'in'], [108.9, 'kg', 2100.3, 'cm'], [1314.8, 'lb', 3568.5, 'cm'], [1474.3, 'lb', 3755.8, 'in']], [4938.1, 9403.42, 1904.26]]]]
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
mixed kg and cm	`[348.6, 12.97, 37.21]`	`[348.6, 12.97, 37.21]`	Passed
millimetre arms	`[3306.9, 498.38, 150.71]`	`[3306.9, 498.38, 150.71]`	Passed
all imperial	`[2110.0, 83.02, 39.35]`	`[2110.0, 83.02, 39.35]`	Passed
unknown weight unit	`ERR_UNIT`	`ERR_UNIT`	Passed
unknown arm unit	`ERR_UNIT`	`ERR_UNIT`	Passed
removal leaves nothing	`ERR_WEIGHT`	`ERR_WEIGHT`	Passed
heavy kg load	`[5725.0, 560.51, 97.91]`	`[5725.0, 560.51, 97.91]`	Passed
sampled case 1	`[7310.9, 13786.98, 1885.82]`	`[7310.9, 13786.98, 1885.82]`	Passed
sampled case 2	`[4067.7, 4473.6, 1099.79]`	`[4067.7, 4473.6, 1099.79]`	Passed
sampled case 3	`[1940.1, 178.3, 91.9]`	`[1940.1, 178.3, 91.9]`	Passed
regression: CG from reduced moment	`[394.5, 283.84, 719.5]`	`[394.5, 283.84, 719.5]`	Passed

SHA-256 / 909e03c07a136f9d6b02e47672f51b0f5f0c41465d1da7e08a95ca024dc38521

Verification & scope

A deterministic toy loading model with stipulated constants; it is not an approved aircraft flight manual procedure and makes no claim of regulatory conformance. 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 2026-09-29T14:47:40.196931+00:00.

Case digest / 51252ba24fbf2e4eb82d488905b624b716055331637bde16710a1f05320b2e05