Fuel System Weight Estimation

Fuel System Weight Estimation (vehicle-design/sizing/fuel-system-weight-estimation)

Use when you must predict the fuel system group weight at the class-II level for the weight statement: converting the total fuel weight and the tank arrangement into the fuel system group mass, the hardware mass of the tanks, sealing, pumps, collector tanks, plumbing, distribution and filling equipment, through a published statistical power-law regression. This leaf implements the class-II fuel system weight prediction of the fuel system weight estimation treatment of Roskam, Airplane Design Part V: Component Weight Estimation (the Torenbeek method for commercial transport airplanes with integral fuel tanks), paraphrased in this leaf's own notation (the books are proprietary-sold; summary-only), in pure Python, stdlib only. It pairs with vehicle-design/sizing/fuel-tank-sizing, which converts the fuel mass to the tank volume this leaf's tank arrangement builds on, and with vehicle-design/mass-properties/mass-budget, which collects the fuel system group mass this leaf produces alongside the other subsystem mass estimates for the rollup.

Domain quick reference

• Fixed count allowance term (lb): W_a = 80 * (N_t + N_e - 1), with N_t the number of separate fuel tanks and N_e the number of engines. Fuel independent; linear in the tank and engine count sum.
• Volume-scaled tankage term (lb): W_v = 15 * (N_t)^0.5 * V^(1/3), with V = W_F / 6.55 the fuel quantity in US gallons at the published fuel specific weight and W_F the total fuel weight in lb. Sublinear in both the tank count (exponent 0.5) and the fuel quantity (exponent 1/3).
• Fuel system group: W_fs = W_a + W_v, the sum of the two published terms of the source equation.
• Fuel specific weight: 6.55 lb per US gallon, the published JP-4 jet-fuel value of the source; modern Jet A sits within about 2 percent of it, and the fixed constant keeps every published coefficient visible.
• Unit boundary: inputs and outputs are SI (kg, dimensionless counts); the regression runs in the published lb / US gallon closed form and converts at the boundary with fixed constants (1 kg = 1/0.45359237 lb).
• The group total scales strictly sublinearly in the fuel weight: the allowance is fuel independent and the tankage term carries the one-third exponent, so the fuel system group fraction of the fuel weight falls as the fuel weight grows.
• The public NASA comparison of conceptual design weight methods (Horvath and Wells) reports the FLOPS and actual Boeing 737-200 fuel system (tanks and plumbing) weights near 553 lb and 575 lb, about 0.02 of that airplane's fuel weight and about 0.005 of its gross weight, the class-II magnitude cross-check band.

Workflow

1. Fix the design point: the total fuel weight in kg (the design total fuel weight, mission fuel including reserves), the number of separate fuel tanks, and the number of engines.
2. Evaluate fuel_system_count_allowance_kg on the tank and engine counts, the fixed count allowance term.
3. Evaluate fuel_system_volume_term_kg on the total fuel weight and the tank count, the volume-scaled tankage term.
4. Sum the two terms with fuel_system_group_weight, and take fuel_system_group_fraction of that total against the total fuel weight and against MTOW for the weight statement fraction check.
5. Sanity-check the class-II band and the exact-power identities: the volume term scales by 2^(1/3) when the fuel weight doubles and by 2^0.5 when the tank count doubles, all else fixed, and the fuel system group fraction of the fuel weight falls as the fuel weight grows.
6. Reject non-physical inputs with ValueError, and confirm the deterministic checks with the contract test scripts/test_fuel_system_weight_estimation.py.

Worked example

180-seat narrowbody transport: total fuel weight 22000.0 kg (design total fuel weight, mission fuel including reserves), 3 separate integral fuel tanks (left wing, right wing and center wing), 2 engines, MTOW 79000.0 kg for the weight-statement fractions. The fuel quantity at the published specific weight is 7404.839341 US gallons.

• fuel_system_count_allowance_kg(3, 2) gives 145.149558400 kg (the 320 lb allowance at 4 count units), fuel_system_volume_term_kg(22000.0,
  3. gives 229.697449925 kg, and fuel_system_group_weight(22000.0, 3,
  4. gives 374.847008325 kg, the exact sum of the two terms.
• Fractions: 0.017038500 of the 22000.0 kg total fuel weight, 0.004744899 of the 79000.0 kg MTOW. The group mass sits inside the class-II band (the NASA weight-methods comparison FLOPS and actual Boeing 737-200 tanks-and-plumbing weights sit near 0.02 of the fuel weight and near 0.005 of gross weight), and the MTOW fraction sits far below the class-I transport empty-weight band lower bound 0.42 that the weight-estimation sibling checks.
• Fuel volume power law: recomputing fuel_system_volume_term_kg at 44000.0 kg gives 289.400652267 kg, a ratio of 1.259921049895 against its value at 22000.0 kg, matching 2^(1/3).
• Tank count power law: recomputing fuel_system_volume_term_kg with 6 tanks at the same fuel gives 324.841248926 kg, a ratio of 1.414213562373 against the 3 tank value, matching 2^0.5.
• Count allowance additivity: one extra tank at 2 engines adds 36.287389600 kg and one extra engine at 3 tanks adds 36.287389600 kg, each exactly the 80.0 lb allowance unit, and the allowance is fuel independent.
• Sublinear fuel scaling: fuel_system_group_weight at 44000.0 kg gives 434.550210667 kg, a ratio of 1.159273519641 against the 22000.0 kg value, below 2^(1/3) = 1.259921049895, and the fuel system fraction of the fuel weight falls from 0.017038500 at 22000.0 kg to 0.009876141 at 44000.0 kg.
• Monotonicity: the group at 1.01 times the fuel (22220.0 kg) gives 375.610128382 kg and the group at 4 tanks gives 446.668717092 kg, both strictly above the worked 374.847008325 kg.

Verification

• Confirm fuel_system_count_allowance_kg(3, 2) returns 145.149558400 kg, fuel_system_volume_term_kg(22000.0, 3) returns 229.697449925 kg, and fuel_system_group_weight(22000.0, 3, 2) returns 374.847008325 kg, all within 1e-6 relative.
• Confirm the group fractions are 0.017038500 of the total fuel weight and 0.004744899 of MTOW, inside the class-II expectation band.
• Confirm every exact-power identity in the Worked example holds within 1e-9 relative when its regressor doubles, and the count allowance additivity holds within 1e-9 relative.
• Confirm the group mass equals the count allowance plus the volume term within 1e-12 relative.
• Confirm every non-positive or non-number total fuel weight, every tank or engine count below 1 or fractional, and a tank count below the engine count, raises ValueError with the documented message.
• Run the contract test offline: python3 scripts/test_fuel_system_weight_estimation.py (32 tests, deterministic, no randomness).

Related leaves

• vehicle-design/sizing/fuel-tank-sizing: converts the fuel mass to the fuel volume and the required tank volume; this leaf takes the resulting tank arrangement as an input and produces the tank hardware group mass instead of a volume.
• vehicle-design/sizing/fuel-feed-system-sizing: feed line hydraulics, Reynolds number, pressure loss, NPSH and boost pump power between the tank and the engine; a separate hydraulic sizing output, never a group mass.
• vehicle-design/sizing/component-weight-estimation: the wave-47 sibling that predicts the four airframe structural group masses (wing, horizontal tail, vertical tail, fuselage); the fuel system group is deliberately outside that four-group claim, and this leaf produces the fuel system line of the weight statement instead.
• vehicle-design/mass-properties/mass-budget: collects the fuel system group mass this leaf produces alongside the other subsystem mass estimates for the rollup.
• vehicle-design/sizing/weight-estimation: takes component weights (including the fuel system group total this leaf produces) as given inputs for the class-I/class-II weight and balance moments and CG.

Pitfalls

• Using the mission fuel weight instead of the design total fuel weight: the regressor W_F is the design total fuel weight including reserves per the source convention; a partial or block fuel value understates both the volume term and the group total.
• Sizing the volume term on the wrong specific weight: the published form fixes 6.55 lb per US gallon (JP-4); the aviation gasoline value 5.87 is outside the claim and would inflate the fuel quantity and the volume term.
• Feeding a tank count below the engine count: the integral-tank transport arrangement of the source feeds every engine from its own tank group, so a tank count below the engine count is outside the arrangement and raises ValueError rather than a silently wrong answer.
• Reading the fuel system group mass as a fuel volume, a tank capacity, a feed flow, a jettison rate, an installed engine weight or any four-airframe-group weight: this leaf produces the class-II hardware MASS estimate only, never the outputs the fuel-chain and component-weight-estimation siblings own.
• Assuming linear scaling with fuel weight: the tankage term carries the one-third exponent, so doubling the fuel weight scales the group by only 1.159273519641, not 2.0, and the fuel system fraction of the fuel weight falls as the design fuel weight grows.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_fuel_system_weight_estimation.py

The test covers the worked example (count allowance, volume term and group weight within 1e-6 relative, and the group fractions of the total fuel weight and MTOW), the class-II physical-sanity bands (positive mass, group below the total fuel weight and MTOW, fraction bands, and the MTOW fraction far below the class-I empty-weight band), the exact-power identities for the fuel weight and tank count regressors, the count allowance additivity and fuel independence, the group additivity identity, the sublinear fuel scaling and fraction fall, monotonicity in the fuel weight and the tank count, ValueError rejection of every non-physical input with the documented message, and determinism across repeated calls (32 tests, deterministic, no randomness).

Compliance

Standards referenced, not reproduced: 14 CFR Part 25 and CS-25 are reference-only per standards-map.yaml; the class-II statistical fuel system weight method above is paraphrased engineering methodology, summary-only, no verbatim text from the source treatments. compliance: STANDARDS-REF, gated: false.