Sizing Mission Profile

Design Mission Profile and Block Fuel/Time (vehicle-design/conceptual/sizing-mission-profile)

Use when the task is defining the design mission profile and estimating block fuel and block time for conceptual aircraft sizing: building the ordered segment list, computing per-segment fuel burns, applying reserve fuel rules, and sizing the required fuel weight that feeds the sizing weight fraction and the payload-range trade.

Domain quick reference

• Mission profile: an ordered list of segments (taxi, takeoff, climb, cruise, descent, loiter, reserve). Every segment carries a distinct fuel model; each segment burns from the weight remaining after all earlier segments, so the weight chains through the mission.
• Units: weight W in lb, range R in nautical miles, speed V in knots (nm/hr), time in hours, TSFC in lb fuel per lbf thrust per hour (treated as 1/hr, lbf and lb weight numerically equal on Earth), lift-to-drag ratio L/D unitless. This matches the transport-category sizing practice the equations come from.
• Cruise fuel, Breguet range equation: W_fuel = W_start * (1 - exp(-R / (V * TSFC * (L/D)))). The fuel fraction is the weight ratio the range equation leaves after the cruise leg.
• Loiter and hold fuel, Breguet endurance: W_fuel = W_start * (1 - exp(-E * TSFC / (L/D))), with E the endurance in hours. Used for the loiter segment and for reserve holds such as 45 minutes at 1500 ft.
• Taxi, takeoff, descent: fuel flow (lb/hr) times segment time (hr). Climb: fuel flow times time, or a fraction of the segment start weight when only a climb fuel fraction is known.
• Block fuel: sum of the segment fuels. Block time: sum of the segment times (cruise time derives from R/V, loiter and reserve time from the endurance E).
• Reserve rules: hold45_5pct = 45 minute hold at 1500 ft plus 5 percent contingency on trip fuel; far121 = alternate airport fuel plus a 30 minute hold at 1500 ft (FAR 121.645 style). FAR-25 sets the certification context for transport-category reserves and payload rules; the fuel models are common conceptual sizing methodology.
• Mission fuel fraction: block fuel divided by takeoff weight, the quantity the sizing weight fraction method chains segment by segment.
• Payload-range trade point: the knee of the payload-range curve, the range at the design payload when the fuel on board equals the minimum of tank capacity and the fuel the takeoff weight allows with payload and operating empty weight on board.

Workflow

1. Define the design mission as an ordered segment list, one dict per segment with type and params. Choose the segment types and their fuel models: taxi, takeoff, and descent burn fuel flow times time; climb burns fuel flow times time or a fraction of start weight; cruise burns by the Breguet range equation; loiter and the reserve hold burn by Breguet endurance.
2. Set the aircraft inputs: takeoff weight, cruise speed, TSFC, and L/D per segment (the hold L/D and TSFC are usually worse than the cruise values).
3. Compute cruise fuel with breguet_cruise_fuel, or let segment_fuel dispatch by segment type. The cruise and hold equations are exact analytic results, not tables.
4. Sum the mission with block_fuel_and_time: it chains the segment weights (each segment burns from the weight after earlier segments) and returns block fuel, block time, and the landing weight.
5. Apply the reserve rule with reserve_fuel: hold45_5pct for the common 45 minute hold at 1500 ft plus 5 percent contingency, far121 for an alternate plus 30 minute hold. The reserve burns from the landing weight.
6. Size the required fuel with required_fuel (block plus reserves), derive the mission fuel fraction with mission_fuel_fraction, and locate the payload-range trade point with payload_range_trade_point.
7. Feed the mission fuel fraction and required fuel into the sizing weight fraction (see related skills) and iterate until takeoff weight converges.

Worked example

Turbofan transport, W0 = 150000 lb, cruise at V = 450 kt, TSFC = 0.6 lb/lbf/hr, L/D = 18, design range 3000 nm.

• Cruise fuel, hand Breguet: W_fuel = 150000 * (1 - exp(-3000 / (450 * 0.6 * 18))) = 69088.9 lb. breguet_cruise_fuel(3000, 450, 0.6, 18,
  150000. returns the same value.
• Full mission (taxi 0.25 hr at 1200 lb/hr, takeoff 0.05 hr at 18000 lb/hr, climb 0.25 hr at 24000 lb/hr, cruise 3000 nm, descent 0.30 hr at 2500 lb/hr, loiter 0.5 hr at L/D 15): block fuel 75233.0 lb, block time 8.017 hr, landing weight 74767.0 lb, mission fuel fraction 0.5016.
• Reserve hold45_5pct at the landing weight: hold 1846.0 lb plus 5 percent of trip fuel 3761.7 lb = 5607.7 lb reserve.
• Required fuel including reserves: 75233.0 + 5607.7 = 80840.7 lb.

Pitfalls

• Burning every segment from the takeoff weight: each segment burns from the weight remaining after all earlier segments (the weight chains through the mission), so recomputing cruise from W0 after a climb segment overstates the block fuel.
• Sizing loiter and hold fuel with the cruise equation: the loiter and reserve hold burn by Breguet ENDURANCE (E * TSFC / (L/D)), not by the range equation, and the hold L/D and TSFC are usually worse than cruise values.
• Forgetting the reserve is more than the hold: hold45_5pct adds the 45 minute hold AND 5 percent of the trip fuel; far121 adds the alternate leg plus a 30 minute hold - a reserve that is only the hold under-sizes the required fuel.
• Mixing the unit convention: weight in lb, range in nm, speed in knots, time in hours and TSFC in lb/lbf/hr; feeding SI or metric values into the Breguet chain breaks the range equation silently.
• Letting an unknown segment type burn nothing: unknown segment types and missing params must raise ValueError, never silently burn zero fuel.
• Stopping at block fuel: the sizing loop needs the mission fuel fraction and the required fuel (block plus reserves), and the weight fraction iteration continues until the takeoff weight converges.

Verification checklist

• Cruise fuel matches the hand Breguet value within 1 percent for the contract case (3000 nm, L/D 18, TSFC 0.6, V 450 kt, W0 150000 lb).
• Loiter and reserve hold fuel come from Breguet endurance, not from a fuel flow estimate.
• Block fuel chains segment weights: every segment burns from the weight after earlier segments.
• Block time sums explicit and derived times (cruise R/V, hold E).
• Reserve fuel includes the contingency or alternate leg, not just the hold.
• Required fuel equals block fuel plus reserve fuel.
• Unknown segment types and missing params raise ValueError, never silently burn zero.
• Contract test passes: python3 scripts/test_mission_profile.py.

Scripts

• scripts/mission_profile_logic.py: segment_fuel, breguet_cruise_fuel, breguet_loiter_fuel, block_fuel_and_time, reserve_fuel, mission_fuel_fraction, payload_range_trade_point, required_fuel.
• scripts/test_mission_profile.py: gate 3 contract test (stdlib unittest, offline, deterministic). Run: python3 scripts/test_mission_profile.py

Related skills

• skills/vehicle-design/conceptual/tow-estimation/: closes the sizing loop with the takeoff weight estimate the fuel fraction feeds.
• skills/vehicle-design/conceptual/payload-range-diagram/: builds the payload-range curve whose knee is the trade point computed here.
• skills/vehicle-design/conceptual/constraint-analysis/: fixes the thrust to weight and wing loading that set the cruise L/D and fuel burn assumptions.
• skills/vehicle-design/sizing/fuel-tank-sizing/: checks the required fuel against the tank volume available.
• skills/vehicle-design/sizing/weight-estimation/: the weight breakdown that supplies operating empty weight to the trade point.
• skills/vehicle-design/sizing/ws-tw-trade/: the sizing trade that consumes the mission fuel fraction.

Behavior contract (gate 3)

The mission segment fuel models, block fuel and time chaining, reserve rules, fuel fraction and payload-range trade point are exercised by the gate 3 contract test scripts/test_mission_profile.py against scripts/mission_profile_logic.py (stdlib unittest, offline, deterministic). Run:

python3 scripts/test_mission_profile.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain); the Breguet equations and reserve rules are common conceptual design methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.