FA-65911 / Aviation weight and balance / Open access

%MAC measured from the index reference instead of LEMAC · case 01

The reported %MAC is offset by the distance between the reference station and the leading edge.

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

ROOT CAUSE

The percentage is computed relative to the index reference arm instead of the leading edge of the MAC.

VERIFIED REPAIR

Measure the CG from LEMAC before dividing by the MAC length.

Unsuccessful approach: Reversing the subtraction uses LEMAC but flips the sign, so aft CGs become negative percentages.

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 - k) * c / w
    pmac = (cg - ref) / 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, 0.1]`	`[50.3, 37.6]`	Failed
empty operating aircraft	`[48.0, -1.2]`	`[48.0, 36.3]`	Failed
aft hold heavy	`[80.4, 16.5]`	`[80.4, 54.0]`	Failed
forward hold heavy	`[17.2, -18.0]`	`[17.2, 19.5]`	Failed
item at reference arm	`[48.0, -1.1]`	`[48.0, 36.4]`	Failed
different constants	`[34.0, -4.3]`	`[34.0, 58.2]`	Failed
sampled case 1	`[120.3, 20.3]`	`[120.3, 68.4]`	Failed
sampled case 2	`[-254.74, -21.4]`	`[-254.74, 95.7]`	Failed
sampled case 3	`[45.2, -2.6]`	`[45.2, 83.3]`	Failed

SHA-256 / 9d897df0bc82e560f0788bff85e3aaf754fb095dd9b342facac468c4a3bc9834

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 = (x['lemac'] - cg) / 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]`	Failed
empty operating aircraft	`[48.0, -36.3]`	`[48.0, 36.3]`	Failed
aft hold heavy	`[80.4, -54.0]`	`[80.4, 54.0]`	Failed
forward hold heavy	`[17.2, -19.5]`	`[17.2, 19.5]`	Failed
item at reference arm	`[48.0, -36.4]`	`[48.0, 36.4]`	Failed
different constants	`[34.0, -58.2]`	`[34.0, 58.2]`	Failed
sampled case 1	`[120.3, -68.4]`	`[120.3, 68.4]`	Failed
sampled case 2	`[-254.74, -95.7]`	`[-254.74, 95.7]`	Failed
sampled case 3	`[45.2, -83.3]`	`[45.2, 83.3]`	Failed

SHA-256 / fd8344157f5802e1d0fb0392f4fba01ae52c405ae8c469450af750d347db263d

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 2026-09-29T14:47:38.491955+00:00.

Case digest / acad1e3d3570664be0d945143cb912a834af3c94fdb1bb08b50ee1515b3b4f25