THE DISTANCE IN YOUR FUEL

Range, Endurance & Fuel Planning

The same fuel. A different speed. A different journey.

ASTER JGeneric jet · cruise only

THE AIRCRAFT GETS LIGHTER AS IT FLIESCruise projection

FUEL REMAINING800 kg

TOTAL MASS4,200 kg

Ground range BTo retained-fuel threshold

Cruise endurance BTo the same threshold

Fuel at destination B

Current fuel per distance Bkg per ground kilometre

ANo reference saved

One fuel budget. Three useful comparisons.

Each preset replaces A and B and pauses at the start.

02 / HOW FAR DOES THE FUEL TAKE YOU?

Put the destination within reach.

A · savedB · live

Drag the destination diamond or use its arrow keys. Both aircraft share one elapsed-time clock; the earlier endpoint is held. The projection continues past the destination to the retained-fuel threshold. Distance is measured from the start of cruise. On narrow screens, scroll this view sideways.

03 / TWO DIFFERENT OBJECTIVES

More time, or more distance?

Best ground range now

Best endurance now

Time per unit fuel consumed

\frac{d t}{d f_{used}} = \frac{1}{{\dot{m}}_{fuel}}

Symbols & units

$f_{used}$: Fuel mass consumed, kg, increasing positively; not fuel remaining.
${\dot{m}}_{fuel}$: Positive fuel mass-flow rate, kg/s. Here ṁfuel = cₜD, with mass TSFC cₜ.
$\frac{d t}{d f_{used}}$: Specific endurance, s/kg.

Ground distance per unit fuel consumed

\frac{d x_{ground}}{d f_{used}} = \frac{V - w}{{\dot{m}}_{fuel}}

Symbols & units

$V, w$: True airspeed and headwind, m/s; negative w is a tailwind. V − w is groundspeed.
$\frac{d x_{ground}}{d f_{used}}$: Specific ground range, m/kg. The same positive fuel-consumed convention applies.

The markers below use the current B mass and altitude. Optima are constrained by lift margin, available thrust and speed limits.

04 / WEIGHT CHANGES THE BALANCE

Less fuel. Less lift required.

This is a sequence of level-flight equilibria: lift equals weight and thrust equals drag. Fuel flow = constant TSFC × required thrust.

05 / CHANGE THE SPEED, SEE THE COST

Two curves. Two different minima.

Feasible cruise speeds only. Click to try a fixed TAS.
Arrow keys change fixed TAS by 1 m/s.

Fuel per hour · current B mass

The lowest fuel flow maximises time per kilogram. Amber dashed marker: best endurance. Cyan marker: best ground range.

Fuel per ground kilometre · current B mass

Groundspeed changes with wind. The lowest fuel cost per kilometre maximises specific ground range.

06 / FOLLOW THE SAME CLOCK

Watch the cruise unfold.

A ┄B ━

Fuel remaining

Each line ends at its own retained-fuel threshold.

Ground distance

An arrival marker is recorded only if the destination is reached before the threshold.

True airspeed

Following an optimum adjusts speed gradually as mass decreases. Fixed TAS keeps the selected speed throughout.

Required thrust

Required thrust is matched to drag at each steady state. An infeasible cruise is not presented as achievable.

07 / KEEP THE COMPARISON

A / B results

Quantity	A · saved	B · live

A remains fixed until replaced or cleared. Reloading clears the comparison. No student data is collected by this module.

Equations, assumptions & teaching sources

Mass and fuel

m = dry base mass + payload + fuel; dm/dt = −cₜD. The illustrative constant mass TSFC is 2.0 × 10⁻⁵ kg/(N·s). Groundspeed = TAS − headwind. Distance and time are integrated against fuel consumed.

The Aster J clean polar and thrust capability are shared unchanged with Drag & Flight Envelope. The 2,800 kg dry base mass and fuel allocation are new illustrative teaching assumptions.

Level-cruise closure

L = mg, Cᴸ = mg/(½ρV²S), Cᴰ = Cᴰ₀ + kCᴸ², T = D. Best endurance minimises fuel flow. Best ground range maximises (V − headwind)/fuel flow over feasible speeds.

A 1.2 × stall-speed margin, maximum available thrust, Mach 0.60 and 140 m/s equivalent airspeed bound the calculation. These are model limits, not certified operating limits.

What this projection excludes

Constant altitude and ISA atmosphere; uniform longitudinal wind; clean configuration; constant TSFC. Speed schedules are quasi-steady: acceleration energy is neglected and its force scale is reported below. No instant manoeuvre is being simulated.

All fuel is measured at the start of cruise. Taxi, take-off, climb, descent, landing, diversions and regulatory fuel reserves are excluded. Comparing cruise altitudes does not include the fuel needed to reach them.

Teaching sources and verification

Week 10, Static Aircraft Performance Analysis, Part 2, 27 March 2026, slides 10–24. Original diagrams; no lecture artwork copied.

FAA-hosted · Aerodynamics for Naval Aviators

Analytic constant-CL range/endurance checks, integration refinement and bounded-domain tests verify the implementation. They do not validate a real aircraft.