FA-65901 / Aviation weight and balance / Open access

Index converted to CG without removing the K constant · case 01

The %MAC is several percent aft for every load and does not match the balance chart.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The conversion back to an arm treats the whole index as moment, including the constant K offset.

VERIFIED REPAIR

Subtract K before scaling the index by C over total weight.

Unsuccessful approach: Inverting the C and weight scaling removes K but produces an arm that grows with weight.

Case contract

Input {'dow','doi','ref','c','k','lemac','mac','items':[[kg,arm m]]}. Item index = kg*(arm-ref)/c; the dry operating index already contains K. Total index = doi + item indices; CG arm = ref + (index-K)*c/total weight; %MAC = (CG-LEMAC)/MAC*100. Return [index r2, %MAC r1].

Why this case matters

Airline loadsheets carry balance as a dimensionless index offset by K; converting back to %MAC requires removing K and scaling by C over total weight.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    ref, c, k = x['ref'], x['c'], x['k']
    w = x['dow']
    ti = x['doi']
    for iw, arm in x['items']:
        w += iw
        ti += iw * (arm - ref) / c
    cg = ref + ti * c / w
    pmac = (cg - x['lemac']) / x['mac'] * 100
    return [round(ti, 2), round(pmac, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3100.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [50.3, 37.6]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.1]]}, [80.4, 54.0]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.2]]}, [17.2, 19.5]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[2500.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36050.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33485.0, 'doi': 37.0, 'ref': 20.4, 'c': 500.0, 'k': 44.4, 'lemac': 18.68, 'mac': 3.58, 'items': [[4603.0, 5.73], [2919.0, 25.41], [5509.0, 29.73], [5663.0, 28.02]]}, [120.3, 68.4]], ['sampled case 2', {'dow': 45884.0, 'doi': 51.2, 'ref': 20.0, 'c': 200.0, 'k': 57.4, 'lemac': 14.39, 'mac': 4.79, 'items': [[4694.0, 15.31], [4327.0, 9.7], [185.0, 15.41], [4752.0, 22.51], [992.0, 14.27]]}, [-254.74, 95.7]], ['sampled case 3', {'dow': 36007.0, 'doi': 45.2, 'ref': 20.5, 'c': 2000.0, 'k': 46.9, 'lemac': 17.4, 'mac': 3.61, 'items': []}, [45.2, 83.3]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3200.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.9, 37.5]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.2]]}, [80.8, 54.2]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.4]]}, [17.9, 19.9]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[5000.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36100.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 41485.0, 'doi': 53.7, 'ref': 17.2, 'c': 500.0, 'k': 53.6, 'lemac': 14.91, 'mac': 4.7, 'items': [[323.0, 8.3], [3020.0, 17.98], [2440.0, 14.22]]}, [38.12, 45.2]], ['sampled case 2', {'dow': 36221.0, 'doi': 55.1, 'ref': 19.8, 'c': 2000.0, 'k': 56.4, 'lemac': 18.06, 'mac': 3.42, 'items': [[1053.0, 22.91]]}, [56.74, 51.4]], ['sampled case 3', {'dow': 36359.0, 'doi': 27.6, 'ref': 16.4, 'c': 200.0, 'k': 30.8, 'lemac': 14.16, 'mac': 3.79, 'items': [[2072.0, 5.02]]}, [-90.3, 42.5]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3300.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.5, 37.3]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.3]]}, [81.2, 54.5]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.6]]}, [18.6, 20.2]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[7500.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36150.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33923.0, 'doi': 39.1, 'ref': 19.3, 'c': 200.0, 'k': 45.3, 'lemac': 16.18, 'mac': 4.5, 'items': [[3739.0, 10.15]]}, [-131.96, 48.4]], ['sampled case 2', {'dow': 40403.0, 'doi': 39.1, 'ref': 21.4, 'c': 1000.0, 'k': 44.8, 'lemac': 14.64, 'mac': 4.94, 'items': [[4674.0, 28.04]]}, [70.14, 148.2]], ['sampled case 3', {'dow': 30111.0, 'doi': 38.1, 'ref': 15.0, 'c': 200.0, 'k': 36.0, 'lemac': 15.26, 'mac': 4.8, 'items': [[5589.0, 17.22]]}, [100.14, 2.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3400.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.1, 37.1]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.4]]}, [81.6, 54.7]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.8]]}, [19.3, 20.6]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[10000.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36200.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 40381.0, 'doi': 38.2, 'ref': 17.2, 'c': 200.0, 'k': 35.3, 'lemac': 17.91, 'mac': 3.25, 'items': [[1141.0, 14.25], [3763.0, 12.45]]}, [-68.0, -35.9]], ['sampled case 2', {'dow': 40833.0, 'doi': 53.7, 'ref': 21.5, 'c': 2000.0, 'k': 48.5, 'lemac': 17.83, 'mac': 3.22, 'items': [[4174.0, 19.61], [2120.0, 18.46], [4779.0, 27.55], [1973.0, 12.04]]}, [51.66, 117.6]], ['sampled case 3', {'dow': 33856.0, 'doi': 31.0, 'ref': 19.9, 'c': 200.0, 'k': 36.6, 'lemac': 18.08, 'mac': 4.82, 'items': []}, [31.0, 37.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [48.7, 36.9]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.5]]}, [82.0, 54.9]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 10.0]]}, [20.0, 21.0]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[12500.0, 18.0]]}, [48.0, 36.6]], ['different constants', {'dow': 36250.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 34075.0, 'doi': 33.7, 'ref': 19.6, 'c': 2000.0, 'k': 36.1, 'lemac': 15.76, 'mac': 3.12, 'items': [[4801.0, 23.6], [3956.0, 16.47], [1810.0, 18.75], [1491.0, 15.01], [3514.0, 6.44]]}, [9.8, 89.1]], ['sampled case 2', {'dow': 33834.0, 'doi': 57.4, 'ref': 20.6, 'c': 500.0, 'k': 55.3, 'lemac': 15.75, 'mac': 3.95, 'items': [[3292.0, 11.8], [4846.0, 14.0], [3222.0, 25.52], [2090.0, 7.1], [168.0, 27.97]]}, [-86.76, 84.9]], ['sampled case 3', {'dow': 46921.0, 'doi': 51.0, 'ref': 17.8, 'c': 500.0, 'k': 52.3, 'lemac': 14.61, 'mac': 3.01, 'items': [[2487.0, 11.85], [4542.0, 19.68]]}, [38.48, 101.7]]]]
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
typical cabin and hold	`[50.3, 62.0]`	`[50.3, 37.6]`	Failed
empty operating aircraft	`[48.0, 66.1]`	`[48.0, 36.3]`	Failed
aft hold heavy	`[80.4, 81.2]`	`[80.4, 54.0]`	Failed
forward hold heavy	`[17.2, 47.0]`	`[17.2, 19.5]`	Failed
item at reference arm	`[48.0, 64.5]`	`[48.0, 36.4]`	Failed
different constants	`[34.0, 75.8]`	`[34.0, 58.2]`	Failed
sampled case 1	`[120.3, 80.2]`	`[120.3, 68.4]`	Failed
sampled case 2	`[-254.74, 99.6]`	`[-254.74, 95.7]`	Failed
sampled case 3	`[45.2, 155.4]`	`[45.2, 83.3]`	Failed

SHA-256 / 86aaa53e6e4e4339d8c97453f5ea991d45accb88b19ff7ee9a7ebff69b9809f0

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    ref, c, k = x['ref'], x['c'], x['k']
    w = x['dow']
    ti = x['doi']
    for iw, arm in x['items']:
        w += iw
        ti += iw * (arm - ref) / c
    cg = ref + (ti - k) / c * w
    pmac = (cg - x['lemac']) / x['mac'] * 100
    return [round(ti, 2), round(pmac, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3100.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [50.3, 37.6]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.1]]}, [80.4, 54.0]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.2]]}, [17.2, 19.5]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[2500.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36050.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33485.0, 'doi': 37.0, 'ref': 20.4, 'c': 500.0, 'k': 44.4, 'lemac': 18.68, 'mac': 3.58, 'items': [[4603.0, 5.73], [2919.0, 25.41], [5509.0, 29.73], [5663.0, 28.02]]}, [120.3, 68.4]], ['sampled case 2', {'dow': 45884.0, 'doi': 51.2, 'ref': 20.0, 'c': 200.0, 'k': 57.4, 'lemac': 14.39, 'mac': 4.79, 'items': [[4694.0, 15.31], [4327.0, 9.7], [185.0, 15.41], [4752.0, 22.51], [992.0, 14.27]]}, [-254.74, 95.7]], ['sampled case 3', {'dow': 36007.0, 'doi': 45.2, 'ref': 20.5, 'c': 2000.0, 'k': 46.9, 'lemac': 17.4, 'mac': 3.61, 'items': []}, [45.2, 83.3]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3200.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.9, 37.5]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.2]]}, [80.8, 54.2]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.4]]}, [17.9, 19.9]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[5000.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36100.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 41485.0, 'doi': 53.7, 'ref': 17.2, 'c': 500.0, 'k': 53.6, 'lemac': 14.91, 'mac': 4.7, 'items': [[323.0, 8.3], [3020.0, 17.98], [2440.0, 14.22]]}, [38.12, 45.2]], ['sampled case 2', {'dow': 36221.0, 'doi': 55.1, 'ref': 19.8, 'c': 2000.0, 'k': 56.4, 'lemac': 18.06, 'mac': 3.42, 'items': [[1053.0, 22.91]]}, [56.74, 51.4]], ['sampled case 3', {'dow': 36359.0, 'doi': 27.6, 'ref': 16.4, 'c': 200.0, 'k': 30.8, 'lemac': 14.16, 'mac': 3.79, 'items': [[2072.0, 5.02]]}, [-90.3, 42.5]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3300.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.5, 37.3]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.3]]}, [81.2, 54.5]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.6]]}, [18.6, 20.2]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[7500.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36150.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33923.0, 'doi': 39.1, 'ref': 19.3, 'c': 200.0, 'k': 45.3, 'lemac': 16.18, 'mac': 4.5, 'items': [[3739.0, 10.15]]}, [-131.96, 48.4]], ['sampled case 2', {'dow': 40403.0, 'doi': 39.1, 'ref': 21.4, 'c': 1000.0, 'k': 44.8, 'lemac': 14.64, 'mac': 4.94, 'items': [[4674.0, 28.04]]}, [70.14, 148.2]], ['sampled case 3', {'dow': 30111.0, 'doi': 38.1, 'ref': 15.0, 'c': 200.0, 'k': 36.0, 'lemac': 15.26, 'mac': 4.8, 'items': [[5589.0, 17.22]]}, [100.14, 2.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3400.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.1, 37.1]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.4]]}, [81.6, 54.7]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.8]]}, [19.3, 20.6]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[10000.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36200.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 40381.0, 'doi': 38.2, 'ref': 17.2, 'c': 200.0, 'k': 35.3, 'lemac': 17.91, 'mac': 3.25, 'items': [[1141.0, 14.25], [3763.0, 12.45]]}, [-68.0, -35.9]], ['sampled case 2', {'dow': 40833.0, 'doi': 53.7, 'ref': 21.5, 'c': 2000.0, 'k': 48.5, 'lemac': 17.83, 'mac': 3.22, 'items': [[4174.0, 19.61], [2120.0, 18.46], [4779.0, 27.55], [1973.0, 12.04]]}, [51.66, 117.6]], ['sampled case 3', {'dow': 33856.0, 'doi': 31.0, 'ref': 19.9, 'c': 200.0, 'k': 36.6, 'lemac': 18.08, 'mac': 4.82, 'items': []}, [31.0, 37.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [48.7, 36.9]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.5]]}, [82.0, 54.9]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 10.0]]}, [20.0, 21.0]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[12500.0, 18.0]]}, [48.0, 36.6]], ['different constants', {'dow': 36250.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 34075.0, 'doi': 33.7, 'ref': 19.6, 'c': 2000.0, 'k': 36.1, 'lemac': 15.76, 'mac': 3.12, 'items': [[4801.0, 23.6], [3956.0, 16.47], [1810.0, 18.75], [1491.0, 15.01], [3514.0, 6.44]]}, [9.8, 89.1]], ['sampled case 2', {'dow': 33834.0, 'doi': 57.4, 'ref': 20.6, 'c': 500.0, 'k': 55.3, 'lemac': 15.75, 'mac': 3.95, 'items': [[3292.0, 11.8], [4846.0, 14.0], [3222.0, 25.52], [2090.0, 7.1], [168.0, 27.97]]}, [-86.76, 84.9]], ['sampled case 3', {'dow': 46921.0, 'doi': 51.0, 'ref': 17.8, 'c': 500.0, 'k': 52.3, 'lemac': 14.61, 'mac': 3.01, 'items': [[2487.0, 11.85], [4542.0, 19.68]]}, [38.48, 101.7]]]]
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
typical cabin and hold	`[50.3, 422.3]`	`[50.3, 37.6]`	Failed
empty operating aircraft	`[48.0, -2062.5]`	`[48.0, 36.3]`	Failed
aft hold heavy	`[80.4, 34997.5]`	`[80.4, 54.0]`	Failed
forward hold heavy	`[17.2, -37272.5]`	`[17.2, 19.5]`	Failed
item at reference arm	`[48.0, -2187.5]`	`[48.0, 36.4]`	Failed
different constants	`[34.0, -27471.9]`	`[34.0, 58.2]`	Failed
sampled case 1	`[120.3, 221294.1]`	`[120.3, 68.4]`	Failed
sampled case 2	`[-254.74, -1982028.3]`	`[-254.74, 95.7]`	Failed
sampled case 3	`[45.2, -761.9]`	`[45.2, 83.3]`	Failed

SHA-256 / 19e87d8991b80e680dee80e9cc9cdfcbdef7885904f085403d0b76c4762c83c0

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    ref, c, k = x['ref'], x['c'], x['k']
    w = x['dow']
    ti = x['doi']
    for iw, arm in x['items']:
        w += iw
        ti += iw * (arm - ref) / c
    cg = ref + (ti - k) * c / w
    pmac = (cg - x['lemac']) / x['mac'] * 100
    return [round(ti, 2), round(pmac, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3100.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [50.3, 37.6]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.1]]}, [80.4, 54.0]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.2]]}, [17.2, 19.5]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[2500.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36050.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33485.0, 'doi': 37.0, 'ref': 20.4, 'c': 500.0, 'k': 44.4, 'lemac': 18.68, 'mac': 3.58, 'items': [[4603.0, 5.73], [2919.0, 25.41], [5509.0, 29.73], [5663.0, 28.02]]}, [120.3, 68.4]], ['sampled case 2', {'dow': 45884.0, 'doi': 51.2, 'ref': 20.0, 'c': 200.0, 'k': 57.4, 'lemac': 14.39, 'mac': 4.79, 'items': [[4694.0, 15.31], [4327.0, 9.7], [185.0, 15.41], [4752.0, 22.51], [992.0, 14.27]]}, [-254.74, 95.7]], ['sampled case 3', {'dow': 36007.0, 'doi': 45.2, 'ref': 20.5, 'c': 2000.0, 'k': 46.9, 'lemac': 17.4, 'mac': 3.61, 'items': []}, [45.2, 83.3]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3200.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.9, 37.5]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.2]]}, [80.8, 54.2]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.4]]}, [17.9, 19.9]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[5000.0, 18.0]]}, [48.0, 36.4]], ['different constants', {'dow': 36100.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 41485.0, 'doi': 53.7, 'ref': 17.2, 'c': 500.0, 'k': 53.6, 'lemac': 14.91, 'mac': 4.7, 'items': [[323.0, 8.3], [3020.0, 17.98], [2440.0, 14.22]]}, [38.12, 45.2]], ['sampled case 2', {'dow': 36221.0, 'doi': 55.1, 'ref': 19.8, 'c': 2000.0, 'k': 56.4, 'lemac': 18.06, 'mac': 3.42, 'items': [[1053.0, 22.91]]}, [56.74, 51.4]], ['sampled case 3', {'dow': 36359.0, 'doi': 27.6, 'ref': 16.4, 'c': 200.0, 'k': 30.8, 'lemac': 14.16, 'mac': 3.79, 'items': [[2072.0, 5.02]]}, [-90.3, 42.5]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3300.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.5, 37.3]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.3]]}, [81.2, 54.5]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.6]]}, [18.6, 20.2]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[7500.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36150.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 33923.0, 'doi': 39.1, 'ref': 19.3, 'c': 200.0, 'k': 45.3, 'lemac': 16.18, 'mac': 4.5, 'items': [[3739.0, 10.15]]}, [-131.96, 48.4]], ['sampled case 2', {'dow': 40403.0, 'doi': 39.1, 'ref': 21.4, 'c': 1000.0, 'k': 44.8, 'lemac': 14.64, 'mac': 4.94, 'items': [[4674.0, 28.04]]}, [70.14, 148.2]], ['sampled case 3', {'dow': 30111.0, 'doi': 38.1, 'ref': 15.0, 'c': 200.0, 'k': 36.0, 'lemac': 15.26, 'mac': 4.8, 'items': [[5589.0, 17.22]]}, [100.14, 2.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3400.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [49.1, 37.1]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.4]]}, [81.6, 54.7]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 9.8]]}, [19.3, 20.6]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[10000.0, 18.0]]}, [48.0, 36.5]], ['different constants', {'dow': 36200.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 40381.0, 'doi': 38.2, 'ref': 17.2, 'c': 200.0, 'k': 35.3, 'lemac': 17.91, 'mac': 3.25, 'items': [[1141.0, 14.25], [3763.0, 12.45]]}, [-68.0, -35.9]], ['sampled case 2', {'dow': 40833.0, 'doi': 53.7, 'ref': 21.5, 'c': 2000.0, 'k': 48.5, 'lemac': 17.83, 'mac': 3.22, 'items': [[4174.0, 19.61], [2120.0, 18.46], [4779.0, 27.55], [1973.0, 12.04]]}, [51.66, 117.6]], ['sampled case 3', {'dow': 33856.0, 'doi': 31.0, 'ref': 19.9, 'c': 200.0, 'k': 36.6, 'lemac': 18.08, 'mac': 4.82, 'items': []}, [31.0, 37.1]]], [['typical cabin and hold', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 14.0], [5000.0, 19.5], [1200.0, 24.0]]}, [48.7, 36.9]], ['empty operating aircraft', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': []}, [48.0, 36.3]], ['aft hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[4000.0, 26.5]]}, [82.0, 54.9]], ['forward hold heavy', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[3500.0, 10.0]]}, [20.0, 21.0]], ['item at reference arm', {'dow': 42000.0, 'doi': 48.0, 'ref': 18.0, 'c': 1000.0, 'k': 50.0, 'lemac': 16.5, 'mac': 4.0, 'items': [[12500.0, 18.0]]}, [48.0, 36.6]], ['different constants', {'dow': 36250.0, 'doi': 40.0, 'ref': 20.0, 'c': 500.0, 'k': 45.0, 'lemac': 18.0, 'mac': 3.2, 'items': [[1800.0, 22.0], [2200.0, 17.0]]}, [34.0, 58.2]], ['sampled case 1', {'dow': 34075.0, 'doi': 33.7, 'ref': 19.6, 'c': 2000.0, 'k': 36.1, 'lemac': 15.76, 'mac': 3.12, 'items': [[4801.0, 23.6], [3956.0, 16.47], [1810.0, 18.75], [1491.0, 15.01], [3514.0, 6.44]]}, [9.8, 89.1]], ['sampled case 2', {'dow': 33834.0, 'doi': 57.4, 'ref': 20.6, 'c': 500.0, 'k': 55.3, 'lemac': 15.75, 'mac': 3.95, 'items': [[3292.0, 11.8], [4846.0, 14.0], [3222.0, 25.52], [2090.0, 7.1], [168.0, 27.97]]}, [-86.76, 84.9]], ['sampled case 3', {'dow': 46921.0, 'doi': 51.0, 'ref': 17.8, 'c': 500.0, 'k': 52.3, 'lemac': 14.61, 'mac': 3.01, 'items': [[2487.0, 11.85], [4542.0, 19.68]]}, [38.48, 101.7]]]]
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
typical cabin and hold	`[50.3, 37.6]`	`[50.3, 37.6]`	Passed
empty operating aircraft	`[48.0, 36.3]`	`[48.0, 36.3]`	Passed
aft hold heavy	`[80.4, 54.0]`	`[80.4, 54.0]`	Passed
forward hold heavy	`[17.2, 19.5]`	`[17.2, 19.5]`	Passed
item at reference arm	`[48.0, 36.4]`	`[48.0, 36.4]`	Passed
different constants	`[34.0, 58.2]`	`[34.0, 58.2]`	Passed
sampled case 1	`[120.3, 68.4]`	`[120.3, 68.4]`	Passed
sampled case 2	`[-254.74, 95.7]`	`[-254.74, 95.7]`	Passed
sampled case 3	`[45.2, 83.3]`	`[45.2, 83.3]`	Passed

SHA-256 / 29e9cc4a8fe4ede3b8326c94a7b85ee7eaa307ffd8a5b9bb462fd3ae70532e71

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 2026-09-29T14:47:38.367890+00:00.

Case digest / eb0de061189deaac995ec387b590c7776890ee7304d420d63983052528bea9db