FAILURE MAP
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FA-66236 / Aviation weight and balance / Open access

Ground CG taken as the plain average of item arms · case 01

A light item far aft moves the computed CG as much as the airframe itself.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The CG ignores item weights and averages arms.

VERIFIED REPAIR

Compute CG as total moment divided by total weight.

Unsuccessful approach: Rounding the CG to a whole inch before splitting gear loads changes reactions and the tip decision.

Case contract

Input {'items':[[lb,arm]],'main_arm','nose_arm'}. CG at or aft of the main gear -> ['TIP', CG r2]. Otherwise nose reaction = W*(main-CG)/(main-nose), main = W - nose; status 'LIGHT_NOSE' if nose < 5% of total weight else 'OK'. Return [status, nose r1, main r1].

Why this case matters

Ground stability depends on the split of weight between nose and main gear; a CG over or behind the mains tips the aircraft onto its tail.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    w = sum(a for a, _ in x['items'])
    m = sum(a * b for a, b in x['items'])
    cg = sum(b for _, b in x['items']) / len(x['items'])
    mg, ng = x['main_arm'], x['nose_arm']
    if cg >= mg: return ['TIP', round(cg, 2)]
    nose = w * (mg - cg) / (mg - ng)
    main = w - nose
    status = 'LIGHT_NOSE' if nose < 0.05 * w else 'OK'
    return [status, round(nose, 1), round(main, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal ground load', {'items': [[9000.0, 250.0], [1510.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1762.2, 8747.8]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 321.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 54.3, 11445.7]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 331.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 296.5]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 119.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2160.0, 7640.0]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[8891.0, 243.3], [4548.0, 151.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 4549.9, 8889.1]], ['sampled case 2', {'items': [[836.0, 112.7], [2149.0, 136.1], [3914.0, 149.9]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 4891.9, 2007.1]], ['sampled case 3', {'items': [[2341.0, 136.2], [1333.0, 147.9], [1880.0, 155.7]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 3207.8, 2346.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1520.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1763.5, 8756.5]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 322.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 43.5, 11456.5]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 332.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 296.75]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 118.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2163.5, 7636.5]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[966.0, 212.0], [6090.0, 178.6], [4538.0, 174.9], [1442.0, 103.6]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 7356.6, 5679.4]], ['sampled case 2', {'items': [[4506.0, 204.0], [8513.0, 219.6]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 3947.3, 9071.7]], ['sampled case 3', {'items': [[8984.0, 243.5], [6602.0, 268.8]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 2655.8, 12930.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1530.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1764.8, 8765.2]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 323.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 32.6, 11467.4]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 333.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.0]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 117.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2167.0, 7633.0]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[8812.0, 250.9]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 1640.7, 7171.3]], ['sampled case 2', {'items': [[4325.0, 295.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 295.0]], ['sampled case 3', {'items': [[7004.0, 198.3], [410.0, 239.6], [2416.0, 150.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 4350.8, 5479.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1540.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1766.1, 8773.9]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 324.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 21.7, 11478.3]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 334.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.25]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 116.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2170.4, 7629.6]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[1599.0, 205.2]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 645.7, 953.3]], ['sampled case 2', {'items': [[283.0, 287.5], [2116.0, 231.6], [600.0, 209.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 751.1, 2247.9]], ['sampled case 3', {'items': [[2210.0, 260.8]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 258.1, 1951.9]]], [['normal ground load', {'items': [[9000.0, 250.0], [1550.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1767.4, 8782.6]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 325.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 10.9, 11489.1]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 335.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.5]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 115.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2173.9, 7626.1]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[649.0, 272.6]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 49.1, 599.9]], ['sampled case 2', {'items': [[6458.0, 136.9], [8392.0, 168.7]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 8026.7, 6823.3]], ['sampled case 3', {'items': [[8932.0, 311.4]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['TIP', 311.4]]]]
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 fixtureActualExpectedOutcome
normal ground load['OK', 1599.3, 8910.7]['OK', 1762.2, 8747.8]Failed
aft cargo light nose['TIP', 300.5]['LIGHT_NOSE', 54.3, 11445.7]Failed
CG exactly over mains['TIP', 290.0]['TIP', 290.0]Passed
tail tipping['TIP', 308.0]['TIP', 296.5]Failed
nose exactly five percent['OK', 500.0, 9500.0]['OK', 500.0, 9500.0]Passed
forward loading['OK', 4495.2, 5304.8]['OK', 2160.0, 7640.0]Failed
CG a hair forward of mains['LIGHT_NOSE', 0.2, 9999.8]['LIGHT_NOSE', 0.2, 9999.8]Passed
sampled case 1['OK', 5419.4, 8019.6]['OK', 4549.9, 8889.1]Failed
sampled case 2['OK', 5161.1, 1737.9]['OK', 4891.9, 2007.1]Failed
sampled case 3['OK', 3185.8, 2368.2]['OK', 3207.8, 2346.2]Failed

SHA-256 / 6654575dd44746a87d4ce0d43aa803ef4398361b264eeab5fb6a627dde56ebe0

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    w = sum(a for a, _ in x['items'])
    m = sum(a * b for a, b in x['items'])
    cg = round(m / w)
    mg, ng = x['main_arm'], x['nose_arm']
    if cg >= mg: return ['TIP', round(cg, 2)]
    nose = w * (mg - cg) / (mg - ng)
    main = w - nose
    status = 'LIGHT_NOSE' if nose < 0.05 * w else 'OK'
    return [status, round(nose, 1), round(main, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal ground load', {'items': [[9000.0, 250.0], [1510.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1762.2, 8747.8]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 321.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 54.3, 11445.7]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 331.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 296.5]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 119.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2160.0, 7640.0]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[8891.0, 243.3], [4548.0, 151.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 4549.9, 8889.1]], ['sampled case 2', {'items': [[836.0, 112.7], [2149.0, 136.1], [3914.0, 149.9]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 4891.9, 2007.1]], ['sampled case 3', {'items': [[2341.0, 136.2], [1333.0, 147.9], [1880.0, 155.7]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 3207.8, 2346.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1520.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1763.5, 8756.5]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 322.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 43.5, 11456.5]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 332.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 296.75]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 118.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2163.5, 7636.5]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[966.0, 212.0], [6090.0, 178.6], [4538.0, 174.9], [1442.0, 103.6]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 7356.6, 5679.4]], ['sampled case 2', {'items': [[4506.0, 204.0], [8513.0, 219.6]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 3947.3, 9071.7]], ['sampled case 3', {'items': [[8984.0, 243.5], [6602.0, 268.8]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 2655.8, 12930.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1530.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1764.8, 8765.2]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 323.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 32.6, 11467.4]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 333.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.0]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 117.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2167.0, 7633.0]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[8812.0, 250.9]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 1640.7, 7171.3]], ['sampled case 2', {'items': [[4325.0, 295.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 295.0]], ['sampled case 3', {'items': [[7004.0, 198.3], [410.0, 239.6], [2416.0, 150.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 4350.8, 5479.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1540.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1766.1, 8773.9]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 324.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 21.7, 11478.3]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 334.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.25]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 116.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2170.4, 7629.6]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[1599.0, 205.2]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 645.7, 953.3]], ['sampled case 2', {'items': [[283.0, 287.5], [2116.0, 231.6], [600.0, 209.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 751.1, 2247.9]], ['sampled case 3', {'items': [[2210.0, 260.8]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 258.1, 1951.9]]], [['normal ground load', {'items': [[9000.0, 250.0], [1550.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1767.4, 8782.6]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 325.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 10.9, 11489.1]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 335.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.5]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 115.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2173.9, 7626.1]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[649.0, 272.6]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 49.1, 599.9]], ['sampled case 2', {'items': [[6458.0, 136.9], [8392.0, 168.7]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 8026.7, 6823.3]], ['sampled case 3', {'items': [[8932.0, 311.4]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['TIP', 311.4]]]]
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 fixtureActualExpectedOutcome
normal ground load['OK', 1782.1, 8727.9]['OK', 1762.2, 8747.8]Failed
aft cargo light nose['LIGHT_NOSE', 50.0, 11450.0]['LIGHT_NOSE', 54.3, 11445.7]Failed
CG exactly over mains['TIP', 290]['TIP', 290.0]Passed
tail tipping['TIP', 296]['TIP', 296.5]Failed
nose exactly five percent['OK', 521.7, 9478.3]['OK', 500.0, 9500.0]Failed
forward loading['OK', 2173.0, 7627.0]['OK', 2160.0, 7640.0]Failed
CG a hair forward of mains['TIP', 290]['LIGHT_NOSE', 0.2, 9999.8]Failed
sampled case 1['OK', 4557.6, 8881.4]['OK', 4549.9, 8889.1]Failed
sampled case 2['OK', 4895.0, 2004.0]['OK', 4891.9, 2007.1]Failed
sampled case 3['OK', 3199.1, 2354.9]['OK', 3207.8, 2346.2]Failed

SHA-256 / a19e4e47a605ce7ed351d190f8598abfd0f9cce85dc3bf6fafceb9cd476ef9ed

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    w = sum(a for a, _ in x['items'])
    m = sum(a * b for a, b in x['items'])
    cg = m / w
    mg, ng = x['main_arm'], x['nose_arm']
    if cg >= mg: return ['TIP', round(cg, 2)]
    nose = w * (mg - cg) / (mg - ng)
    main = w - nose
    status = 'LIGHT_NOSE' if nose < 0.05 * w else 'OK'
    return [status, round(nose, 1), round(main, 1)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal ground load', {'items': [[9000.0, 250.0], [1510.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1762.2, 8747.8]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 321.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 54.3, 11445.7]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 331.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 296.5]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 119.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2160.0, 7640.0]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[8891.0, 243.3], [4548.0, 151.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 4549.9, 8889.1]], ['sampled case 2', {'items': [[836.0, 112.7], [2149.0, 136.1], [3914.0, 149.9]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 4891.9, 2007.1]], ['sampled case 3', {'items': [[2341.0, 136.2], [1333.0, 147.9], [1880.0, 155.7]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 3207.8, 2346.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1520.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1763.5, 8756.5]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 322.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 43.5, 11456.5]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 332.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 296.75]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 118.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2163.5, 7636.5]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[966.0, 212.0], [6090.0, 178.6], [4538.0, 174.9], [1442.0, 103.6]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 7356.6, 5679.4]], ['sampled case 2', {'items': [[4506.0, 204.0], [8513.0, 219.6]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 3947.3, 9071.7]], ['sampled case 3', {'items': [[8984.0, 243.5], [6602.0, 268.8]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 2655.8, 12930.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1530.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1764.8, 8765.2]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 323.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 32.6, 11467.4]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 333.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.0]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 117.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2167.0, 7633.0]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[8812.0, 250.9]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 1640.7, 7171.3]], ['sampled case 2', {'items': [[4325.0, 295.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 295.0]], ['sampled case 3', {'items': [[7004.0, 198.3], [410.0, 239.6], [2416.0, 150.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 4350.8, 5479.2]]], [['normal ground load', {'items': [[9000.0, 250.0], [1540.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1766.1, 8773.9]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 324.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 21.7, 11478.3]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 334.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.25]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 116.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2170.4, 7629.6]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[1599.0, 205.2]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['OK', 645.7, 953.3]], ['sampled case 2', {'items': [[283.0, 287.5], [2116.0, 231.6], [600.0, 209.2]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 751.1, 2247.9]], ['sampled case 3', {'items': [[2210.0, 260.8]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 258.1, 1951.9]]], [['normal ground load', {'items': [[9000.0, 250.0], [1550.0, 260.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 1767.4, 8782.6]], ['aft cargo light nose', {'items': [[9000.0, 280.0], [2500.0, 325.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 10.9, 11489.1]], ['CG exactly over mains', {'items': [[9000.0, 290.0], [1000.0, 290.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 290.0]], ['tail tipping', {'items': [[9000.0, 285.0], [3000.0, 335.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['TIP', 297.5]], ['nose exactly five percent', {'items': [[10000.0, 278.5]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 500.0, 9500.0]], ['forward loading', {'items': [[9000.0, 250.0], [800.0, 115.0]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 2173.9, 7626.1]], ['CG a hair forward of mains', {'items': [[10000.0, 289.995]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['LIGHT_NOSE', 0.2, 9999.8]], ['sampled case 1', {'items': [[649.0, 272.6]], 'main_arm': 290.0, 'nose_arm': 60.0}, ['OK', 49.1, 599.9]], ['sampled case 2', {'items': [[6458.0, 136.9], [8392.0, 168.7]], 'main_arm': 290.0, 'nose_arm': 40.0}, ['OK', 8026.7, 6823.3]], ['sampled case 3', {'items': [[8932.0, 311.4]], 'main_arm': 290.0, 'nose_arm': 80.0}, ['TIP', 311.4]]]]
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 fixtureActualExpectedOutcome
normal ground load['OK', 1762.2, 8747.8]['OK', 1762.2, 8747.8]Passed
aft cargo light nose['LIGHT_NOSE', 54.3, 11445.7]['LIGHT_NOSE', 54.3, 11445.7]Passed
CG exactly over mains['TIP', 290.0]['TIP', 290.0]Passed
tail tipping['TIP', 296.5]['TIP', 296.5]Passed
nose exactly five percent['OK', 500.0, 9500.0]['OK', 500.0, 9500.0]Passed
forward loading['OK', 2160.0, 7640.0]['OK', 2160.0, 7640.0]Passed
CG a hair forward of mains['LIGHT_NOSE', 0.2, 9999.8]['LIGHT_NOSE', 0.2, 9999.8]Passed
sampled case 1['OK', 4549.9, 8889.1]['OK', 4549.9, 8889.1]Passed
sampled case 2['OK', 4891.9, 2007.1]['OK', 4891.9, 2007.1]Passed
sampled case 3['OK', 3207.8, 2346.2]['OK', 3207.8, 2346.2]Passed

SHA-256 / b806b1a487a374606ede77cb6427dfcfc0369016f31034f9fbc1c0a546e779a8

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 2026-09-29T14:47:41.238384+00:00.

Case digest / 54749a31d4e34714fed1e0e987eede1749bde81cb9ca205f5f9eecc70e4439d5