Pick a scenario; the sliders stay editable.
Passengers that fit under the take-off weight and tank limits (100 kg each with bags); the dot is the selected route.
Passengers per flight (tourism + business) as the economy fare multiplier changes; revenue per flight is the second curve.
The science
Great circles. The shortest path between two points on a sphere (haversine, R = 6371 km); aircraft follow it with the heading changing along the way. An independent Vincenty solution on the WGS-84 ellipsoid agrees within about 0.3 % for the checked pairs. LHR-JFK is about 5,540 km.
Atmosphere and speed. International Standard Atmosphere: above 11 km the temperature is constant at 216.65 K, so the speed of sound is a = √(γRT) = 295.07 m/s; Mach 0.85 at 37,000 ft is 903 km/h, the figure shown on the flight card. Ground speed adds a westerly jet-stream tailwind (u = 32 · season · exp(-((|lat|-45)/14)²) m/s, a simple illustrative climatology), so eastbound flights are faster than westbound.
Fuel: the Breguet range equation. R = (V/(c g)) (L/D) ln(W0/W1), with c the thrust-specific fuel consumption (1.62e-5 kg/(N s), typical), L/D 16-20. The trip fuel is W1(ex - 1), x = R c g/(V L/D), plus 4.5 % for taxi and climb, 3 % route extension and a reserve. Because W0 may not exceed the maximum take-off mass, long routes are payload-limited (see the payload-range chart). Aircraft numbers are generic class values (typical, rounded), not data of any manufacturer.
Flight profile. Taxi 12 min, climb at about 11.5 m/s average to the cruise altitude, cruise at constant Mach, descent at about 10.5 m/s with a final approach, taxi 7 min. Climb and descent speeds ramp linearly, so the distance covered is closed-form and is checked by numerical integration.
Demand and fares. A gravity model, D = K (IA IB) f(d) with business and tourism indices and a distance decay f(d), gives the weekly one-way market per segment, modulated by season (tourism peaks in summer, business dips in August and at Christmas) and weekday. Your share against the rival frequency is a logit: U = a ln(1 + F) - β (p - 1) + 2 (sat - 0.85) + brand; business travellers weigh frequency more and price less than tourists (a = 1.3 vs 1.0, β = 1.6 vs 4.5, illustrative). Lower fares also stimulate the market (price elasticity -0.4). All market constants, fares, costs and rewards are illustrative game numbers, not airline data.
Costs and satisfaction. Per flight: fuel (Breguet burn x price), crew and maintenance per block hour, landing fee per tonne of take-off mass, en-route charge 70 (d/100) √(MTOW/50), passenger charge and catering; monthly: leases, overhead, gates and loan interest (7 %/year). Satisfaction blends value for money, punctuality, comfort (aircraft condition and age) and service level, and feeds back into your market share.
Sun and light. The sky and the globe terminator follow a solar-position model (declination, equation of time, hour angle). The clock is London time, and at 18:25 on spring day 12 the sun is on the London horizon, which is the sunset in the picture; the check compares two independent formulas.
Checks. (1) haversine vs Vincenty; (2) ISA speed of sound and Mach 0.85; (3) Breguet closed form vs RK4 integration of dW/dt = -c g W/(L/D); (4) integral of the speed profile vs route length; (5) cash ledger = sum of every transaction = monthly rows; (6) determinism and reset; (7) solar elevation at 18:25; (8) loan annuity vs month-by-month amortisation. Simplifications: one airline, no rival simulation (rivals are a frequency pool), no air-traffic limits, no cargo, single fare class per segment, constant TSFC and L/D, coarse hand-drawn continent outlines. Not a flight-planning tool.
The airliner, terminal, tower, ground vehicles, apron and the planet maps were modelled and baked in Blender; the page runs the model in Three.js.