FA-66041 / Aviation weight and balance / Open access

Burned fuel moment added instead of removed · case 01

Landing CG moves the wrong way as fuel is used and ends far aft.

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

ROOT CAUSE

The fuel burn is removed from weight but its moment is added to the takeoff moment.

VERIFIED REPAIR

Subtract burned fuel weight times the fuel arm from the takeoff moment.

Unsuccessful approach: Removing the burn at the takeoff CG keeps the CG constant and hides the tank-location shift.

Case contract

Input {'tow','tocg','burn_gal','fuel_arm','density','mlw','env':[fwd,aft]}. Burned fuel weight = gallons*density removed at the fuel arm. Status 'MLW' if landing weight exceeds MLW (checked first), 'CG' if landing CG outside the inclusive envelope, else 'OK'. Return [LW r1, LCG r2, status].

Why this case matters

Landing CG differs from takeoff CG because fuel is removed at the tank arm; landing weight has its own structural limit.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    dens = x['density']
    bw = x['burn_gal'] * dens
    lw = x['tow'] - bw
    lm = x['tow'] * x['tocg'] + bw * x['fuel_arm']
    lcg = lm / lw
    fwd, aft = x['env']
    if lw > x['mlw']: status = 'MLW'
    elif lcg < fwd or lcg > aft: status = 'CG'
    else: status = 'OK'
    return [round(lw, 1), round(lcg, 2), status]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 26.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2344.0, 41.6, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.2, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2518.8, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.65, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.21, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.9]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 61.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4591.3, 141.29, 'OK']], ['sampled case 1', {'tow': 3210.0, 'tocg': 43.86, 'burn_gal': 48.2, 'fuel_arm': 50.2, 'density': 6.7, 'mlw': 3144.0, 'env': [37.4, 44.6]}, [2887.1, 43.15, 'OK']], ['sampled case 2', {'tow': 2319.0, 'tocg': 45.94, 'burn_gal': 37.7, 'fuel_arm': 46.1, 'density': 6.7, 'mlw': 2223.0, 'env': [35.6, 44.7]}, [2066.4, 45.92, 'CG']], ['sampled case 3', {'tow': 2538.0, 'tocg': 42.69, 'burn_gal': 42.3, 'fuel_arm': 39.8, 'density': 6.7, 'mlw': 2436.0, 'env': [38.5, 45.3]}, [2254.6, 43.05, 'OK']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 27.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2338.0, 41.58, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.4, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2517.6, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.7, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.27, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.8]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 62.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4584.6, 141.28, 'OK']], ['sampled case 1', {'tow': 2616.0, 'tocg': 44.14, 'burn_gal': 50.6, 'fuel_arm': 35.7, 'density': 6.0, 'mlw': 2515.0, 'env': [35.7, 46.3]}, [2312.4, 45.25, 'OK']], ['sampled case 2', {'tow': 3505.0, 'tocg': 45.73, 'burn_gal': 51.8, 'fuel_arm': 36.9, 'density': 6.7, 'mlw': 3402.0, 'env': [38.6, 44.7]}, [3157.9, 46.7, 'CG']], ['sampled case 3', {'tow': 4317.0, 'tocg': 45.35, 'burn_gal': 46.0, 'fuel_arm': 30.4, 'density': 6.7, 'mlw': 3966.0, 'env': [37.2, 44.7]}, [4008.8, 46.5, 'MLW']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 28.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2332.0, 41.57, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.6, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2516.4, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.75, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.32, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.7]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 63.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4577.9, 141.26, 'OK']], ['sampled case 1', {'tow': 3241.0, 'tocg': 42.19, 'burn_gal': 26.4, 'fuel_arm': 41.7, 'density': 6.7, 'mlw': 2992.0, 'env': [38.5, 45.7]}, [3064.1, 42.22, 'MLW']], ['sampled case 2', {'tow': 2273.0, 'tocg': 38.95, 'burn_gal': 26.8, 'fuel_arm': 59.5, 'density': 6.7, 'mlw': 2176.0, 'env': [38.3, 44.8]}, [2093.4, 37.19, 'CG']], ['sampled case 3', {'tow': 4321.0, 'tocg': 45.0, 'burn_gal': 28.2, 'fuel_arm': 37.5, 'density': 6.7, 'mlw': 4074.0, 'env': [38.0, 44.9]}, [4132.1, 45.34, 'MLW']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 29.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2326.0, 41.55, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.8, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2515.2, 40.9, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.800000000000004, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.38, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.6]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 64.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4571.2, 141.25, 'OK']], ['sampled case 1', {'tow': 2016.0, 'tocg': 40.79, 'burn_gal': 78.4, 'fuel_arm': 52.8, 'density': 6.0, 'mlw': 1662.0, 'env': [35.1, 46.3]}, [1545.6, 37.13, 'OK']], ['sampled case 2', {'tow': 5687.0, 'tocg': 39.23, 'burn_gal': 51.9, 'fuel_arm': 54.5, 'density': 6.7, 'mlw': 5345.0, 'env': [37.9, 46.1]}, [5339.3, 38.24, 'OK']], ['sampled case 3', {'tow': 5347.0, 'tocg': 40.15, 'burn_gal': 5.1, 'fuel_arm': 42.2, 'density': 6.7, 'mlw': 5370.0, 'env': [35.1, 43.8]}, [5312.8, 40.14, 'OK']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 30.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2320.0, 41.53, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 6.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2514.0, 40.9, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.85, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.43, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.5]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 65.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4564.5, 141.24, 'OK']], ['sampled case 1', {'tow': 4773.0, 'tocg': 38.16, 'burn_gal': 54.7, 'fuel_arm': 51.7, 'density': 6.0, 'mlw': 4762.0, 'env': [38.1, 45.8]}, [4444.8, 37.16, 'CG']], ['sampled case 2', {'tow': 5036.0, 'tocg': 43.65, 'burn_gal': 50.5, 'fuel_arm': 57.4, 'density': 6.7, 'mlw': 4986.0, 'env': [39.0, 46.7]}, [4697.6, 42.66, 'OK']], ['sampled case 3', {'tow': 4947.0, 'tocg': 43.42, 'burn_gal': 41.6, 'fuel_arm': 57.9, 'density': 6.7, 'mlw': 4824.0, 'env': [39.6, 44.2]}, [4668.3, 42.56, 'OK']]]]
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
normal trip	`[2344.0, 47.99, 'CG']`	`[2344.0, 41.6, 'OK']`	Failed
landing overweight	`[2518.8, 42.1, 'MLW']`	`[2518.8, 40.91, 'MLW']`	Failed
exactly max landing	`[2450.0, 43.18, 'OK']`	`[2450.0, 40.83, 'OK']`	Failed
burn moves CG forward out	`[2060.0, 45.4, 'OK']`	`[2060.0, 34.21, 'CG']`	Failed
forward tank burn moves CG aft	`[4597.0, 182.02, 'CG']`	`[4597.0, 150.54, 'CG']`	Failed
jet fuel density	`[4591.3, 167.99, 'CG']`	`[4591.3, 141.29, 'OK']`	Failed
sampled case 1	`[2887.1, 54.38, 'CG']`	`[2887.1, 43.15, 'OK']`	Failed
sampled case 2	`[2066.4, 57.19, 'CG']`	`[2066.4, 45.92, 'CG']`	Failed
sampled case 3	`[2254.6, 53.06, 'CG']`	`[2254.6, 43.05, 'OK']`	Failed

SHA-256 / be3968b76f30aa7e0a514ddbcf82d2cf3c8e0888faff052be1d62b648e7189ac

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    dens = x['density']
    bw = x['burn_gal'] * dens
    lw = x['tow'] - bw
    lm = x['tow'] * x['tocg'] - bw * x['tocg']
    lcg = lm / lw
    fwd, aft = x['env']
    if lw > x['mlw']: status = 'MLW'
    elif lcg < fwd or lcg > aft: status = 'CG'
    else: status = 'OK'
    return [round(lw, 1), round(lcg, 2), status]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 26.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2344.0, 41.6, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.2, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2518.8, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.65, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.21, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.9]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 61.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4591.3, 141.29, 'OK']], ['sampled case 1', {'tow': 3210.0, 'tocg': 43.86, 'burn_gal': 48.2, 'fuel_arm': 50.2, 'density': 6.7, 'mlw': 3144.0, 'env': [37.4, 44.6]}, [2887.1, 43.15, 'OK']], ['sampled case 2', {'tow': 2319.0, 'tocg': 45.94, 'burn_gal': 37.7, 'fuel_arm': 46.1, 'density': 6.7, 'mlw': 2223.0, 'env': [35.6, 44.7]}, [2066.4, 45.92, 'CG']], ['sampled case 3', {'tow': 2538.0, 'tocg': 42.69, 'burn_gal': 42.3, 'fuel_arm': 39.8, 'density': 6.7, 'mlw': 2436.0, 'env': [38.5, 45.3]}, [2254.6, 43.05, 'OK']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 27.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2338.0, 41.58, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.4, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2517.6, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.7, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.27, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.8]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 62.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4584.6, 141.28, 'OK']], ['sampled case 1', {'tow': 2616.0, 'tocg': 44.14, 'burn_gal': 50.6, 'fuel_arm': 35.7, 'density': 6.0, 'mlw': 2515.0, 'env': [35.7, 46.3]}, [2312.4, 45.25, 'OK']], ['sampled case 2', {'tow': 3505.0, 'tocg': 45.73, 'burn_gal': 51.8, 'fuel_arm': 36.9, 'density': 6.7, 'mlw': 3402.0, 'env': [38.6, 44.7]}, [3157.9, 46.7, 'CG']], ['sampled case 3', {'tow': 4317.0, 'tocg': 45.35, 'burn_gal': 46.0, 'fuel_arm': 30.4, 'density': 6.7, 'mlw': 3966.0, 'env': [37.2, 44.7]}, [4008.8, 46.5, 'MLW']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 28.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2332.0, 41.57, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.6, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2516.4, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.75, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.32, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.7]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 63.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4577.9, 141.26, 'OK']], ['sampled case 1', {'tow': 3241.0, 'tocg': 42.19, 'burn_gal': 26.4, 'fuel_arm': 41.7, 'density': 6.7, 'mlw': 2992.0, 'env': [38.5, 45.7]}, [3064.1, 42.22, 'MLW']], ['sampled case 2', {'tow': 2273.0, 'tocg': 38.95, 'burn_gal': 26.8, 'fuel_arm': 59.5, 'density': 6.7, 'mlw': 2176.0, 'env': [38.3, 44.8]}, [2093.4, 37.19, 'CG']], ['sampled case 3', {'tow': 4321.0, 'tocg': 45.0, 'burn_gal': 28.2, 'fuel_arm': 37.5, 'density': 6.7, 'mlw': 4074.0, 'env': [38.0, 44.9]}, [4132.1, 45.34, 'MLW']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 29.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2326.0, 41.55, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.8, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2515.2, 40.9, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.800000000000004, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.38, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.6]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 64.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4571.2, 141.25, 'OK']], ['sampled case 1', {'tow': 2016.0, 'tocg': 40.79, 'burn_gal': 78.4, 'fuel_arm': 52.8, 'density': 6.0, 'mlw': 1662.0, 'env': [35.1, 46.3]}, [1545.6, 37.13, 'OK']], ['sampled case 2', {'tow': 5687.0, 'tocg': 39.23, 'burn_gal': 51.9, 'fuel_arm': 54.5, 'density': 6.7, 'mlw': 5345.0, 'env': [37.9, 46.1]}, [5339.3, 38.24, 'OK']], ['sampled case 3', {'tow': 5347.0, 'tocg': 40.15, 'burn_gal': 5.1, 'fuel_arm': 42.2, 'density': 6.7, 'mlw': 5370.0, 'env': [35.1, 43.8]}, [5312.8, 40.14, 'OK']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 30.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2320.0, 41.53, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 6.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2514.0, 40.9, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.85, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.43, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.5]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 65.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4564.5, 141.24, 'OK']], ['sampled case 1', {'tow': 4773.0, 'tocg': 38.16, 'burn_gal': 54.7, 'fuel_arm': 51.7, 'density': 6.0, 'mlw': 4762.0, 'env': [38.1, 45.8]}, [4444.8, 37.16, 'CG']], ['sampled case 2', {'tow': 5036.0, 'tocg': 43.65, 'burn_gal': 50.5, 'fuel_arm': 57.4, 'density': 6.7, 'mlw': 4986.0, 'env': [39.0, 46.7]}, [4697.6, 42.66, 'OK']], ['sampled case 3', {'tow': 4947.0, 'tocg': 43.42, 'burn_gal': 41.6, 'fuel_arm': 57.9, 'density': 6.7, 'mlw': 4824.0, 'env': [39.6, 44.2]}, [4668.3, 42.56, 'OK']]]]
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
normal trip	`[2344.0, 42.0, 'OK']`	`[2344.0, 41.6, 'OK']`	Failed
landing overweight	`[2518.8, 41.0, 'MLW']`	`[2518.8, 40.91, 'MLW']`	Failed
exactly max landing	`[2450.0, 41.0, 'OK']`	`[2450.0, 40.83, 'OK']`	Failed
burn moves CG forward out	`[2060.0, 35.65, 'OK']`	`[2060.0, 34.21, 'CG']`	Failed
forward tank burn moves CG aft	`[4597.0, 147.0, 'OK']`	`[4597.0, 150.54, 'CG']`	Failed
jet fuel density	`[4591.3, 142.0, 'OK']`	`[4591.3, 141.29, 'OK']`	Failed
sampled case 1	`[2887.1, 43.86, 'OK']`	`[2887.1, 43.15, 'OK']`	Failed
sampled case 2	`[2066.4, 45.94, 'CG']`	`[2066.4, 45.92, 'CG']`	Failed
sampled case 3	`[2254.6, 42.69, 'OK']`	`[2254.6, 43.05, 'OK']`	Failed

SHA-256 / bbd81478766e2e2201bbb6c45630257c1b89e37d887df8432ed45e137f1f7ccf

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    dens = x['density']
    bw = x['burn_gal'] * dens
    lw = x['tow'] - bw
    lm = x['tow'] * x['tocg'] - bw * x['fuel_arm']
    lcg = lm / lw
    fwd, aft = x['env']
    if lw > x['mlw']: status = 'MLW'
    elif lcg < fwd or lcg > aft: status = 'CG'
    else: status = 'OK'
    return [round(lw, 1), round(lcg, 2), status]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 26.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2344.0, 41.6, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.2, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2518.8, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.65, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.21, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.9]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 61.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4591.3, 141.29, 'OK']], ['sampled case 1', {'tow': 3210.0, 'tocg': 43.86, 'burn_gal': 48.2, 'fuel_arm': 50.2, 'density': 6.7, 'mlw': 3144.0, 'env': [37.4, 44.6]}, [2887.1, 43.15, 'OK']], ['sampled case 2', {'tow': 2319.0, 'tocg': 45.94, 'burn_gal': 37.7, 'fuel_arm': 46.1, 'density': 6.7, 'mlw': 2223.0, 'env': [35.6, 44.7]}, [2066.4, 45.92, 'CG']], ['sampled case 3', {'tow': 2538.0, 'tocg': 42.69, 'burn_gal': 42.3, 'fuel_arm': 39.8, 'density': 6.7, 'mlw': 2436.0, 'env': [38.5, 45.3]}, [2254.6, 43.05, 'OK']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 27.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2338.0, 41.58, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.4, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2517.6, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.7, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.27, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.8]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 62.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4584.6, 141.28, 'OK']], ['sampled case 1', {'tow': 2616.0, 'tocg': 44.14, 'burn_gal': 50.6, 'fuel_arm': 35.7, 'density': 6.0, 'mlw': 2515.0, 'env': [35.7, 46.3]}, [2312.4, 45.25, 'OK']], ['sampled case 2', {'tow': 3505.0, 'tocg': 45.73, 'burn_gal': 51.8, 'fuel_arm': 36.9, 'density': 6.7, 'mlw': 3402.0, 'env': [38.6, 44.7]}, [3157.9, 46.7, 'CG']], ['sampled case 3', {'tow': 4317.0, 'tocg': 45.35, 'burn_gal': 46.0, 'fuel_arm': 30.4, 'density': 6.7, 'mlw': 3966.0, 'env': [37.2, 44.7]}, [4008.8, 46.5, 'MLW']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 28.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2332.0, 41.57, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.6, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2516.4, 40.91, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.75, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.32, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.7]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 63.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4577.9, 141.26, 'OK']], ['sampled case 1', {'tow': 3241.0, 'tocg': 42.19, 'burn_gal': 26.4, 'fuel_arm': 41.7, 'density': 6.7, 'mlw': 2992.0, 'env': [38.5, 45.7]}, [3064.1, 42.22, 'MLW']], ['sampled case 2', {'tow': 2273.0, 'tocg': 38.95, 'burn_gal': 26.8, 'fuel_arm': 59.5, 'density': 6.7, 'mlw': 2176.0, 'env': [38.3, 44.8]}, [2093.4, 37.19, 'CG']], ['sampled case 3', {'tow': 4321.0, 'tocg': 45.0, 'burn_gal': 28.2, 'fuel_arm': 37.5, 'density': 6.7, 'mlw': 4074.0, 'env': [38.0, 44.9]}, [4132.1, 45.34, 'MLW']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 29.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2326.0, 41.55, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 5.8, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2515.2, 40.9, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.800000000000004, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.38, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.6]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 64.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4571.2, 141.25, 'OK']], ['sampled case 1', {'tow': 2016.0, 'tocg': 40.79, 'burn_gal': 78.4, 'fuel_arm': 52.8, 'density': 6.0, 'mlw': 1662.0, 'env': [35.1, 46.3]}, [1545.6, 37.13, 'OK']], ['sampled case 2', {'tow': 5687.0, 'tocg': 39.23, 'burn_gal': 51.9, 'fuel_arm': 54.5, 'density': 6.7, 'mlw': 5345.0, 'env': [37.9, 46.1]}, [5339.3, 38.24, 'OK']], ['sampled case 3', {'tow': 5347.0, 'tocg': 40.15, 'burn_gal': 5.1, 'fuel_arm': 42.2, 'density': 6.7, 'mlw': 5370.0, 'env': [35.1, 43.8]}, [5312.8, 40.14, 'OK']]], [['normal trip', {'tow': 2500.0, 'tocg': 42.0, 'burn_gal': 30.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2320.0, 41.53, 'OK']], ['landing overweight', {'tow': 2550.0, 'tocg': 41.0, 'burn_gal': 6.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2514.0, 40.9, 'MLW']], ['exactly max landing', {'tow': 2510.0, 'tocg': 41.0, 'burn_gal': 10.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2450.0, 40.83, 'OK']], ['burn moves CG forward out', {'tow': 2300.0, 'tocg': 35.85, 'burn_gal': 40.0, 'fuel_arm': 48.0, 'density': 6.0, 'mlw': 2450.0, 'env': [35.0, 47.3]}, [2060.0, 34.43, 'CG']], ['forward tank burn moves CG aft', {'tow': 5200.0, 'tocg': 147.0, 'burn_gal': 90.0, 'fuel_arm': 120.0, 'density': 6.7, 'mlw': 5000.0, 'env': [138.0, 147.5]}, [4597.0, 150.54, 'CG']], ['jet fuel density', {'tow': 5000.0, 'tocg': 142.0, 'burn_gal': 65.0, 'fuel_arm': 150.0, 'density': 6.7, 'mlw': 4800.0, 'env': [138.0, 148.0]}, [4564.5, 141.24, 'OK']], ['sampled case 1', {'tow': 4773.0, 'tocg': 38.16, 'burn_gal': 54.7, 'fuel_arm': 51.7, 'density': 6.0, 'mlw': 4762.0, 'env': [38.1, 45.8]}, [4444.8, 37.16, 'CG']], ['sampled case 2', {'tow': 5036.0, 'tocg': 43.65, 'burn_gal': 50.5, 'fuel_arm': 57.4, 'density': 6.7, 'mlw': 4986.0, 'env': [39.0, 46.7]}, [4697.6, 42.66, 'OK']], ['sampled case 3', {'tow': 4947.0, 'tocg': 43.42, 'burn_gal': 41.6, 'fuel_arm': 57.9, 'density': 6.7, 'mlw': 4824.0, 'env': [39.6, 44.2]}, [4668.3, 42.56, 'OK']]]]
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
normal trip	`[2344.0, 41.6, 'OK']`	`[2344.0, 41.6, 'OK']`	Passed
landing overweight	`[2518.8, 40.91, 'MLW']`	`[2518.8, 40.91, 'MLW']`	Passed
exactly max landing	`[2450.0, 40.83, 'OK']`	`[2450.0, 40.83, 'OK']`	Passed
burn moves CG forward out	`[2060.0, 34.21, 'CG']`	`[2060.0, 34.21, 'CG']`	Passed
forward tank burn moves CG aft	`[4597.0, 150.54, 'CG']`	`[4597.0, 150.54, 'CG']`	Passed
jet fuel density	`[4591.3, 141.29, 'OK']`	`[4591.3, 141.29, 'OK']`	Passed
sampled case 1	`[2887.1, 43.15, 'OK']`	`[2887.1, 43.15, 'OK']`	Passed
sampled case 2	`[2066.4, 45.92, 'CG']`	`[2066.4, 45.92, 'CG']`	Passed
sampled case 3	`[2254.6, 43.05, 'OK']`	`[2254.6, 43.05, 'OK']`	Passed

SHA-256 / 4017be85c21926ac3b9d064659d5fcb8d28a9d7f3e3c67b5d6fc77a539386fdb

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 2026-09-29T14:47:39.632713+00:00.

Case digest / 7f34934dc307b365a3d3936904bfb92677ae7bc9c6663d6e46268803887827c2