03 / LIVE FORCES
FROM RUNWAY TO FLIGHT
Take-off & Landing Performance
Airspeed lifts you. Groundspeed carries you along the runway.
ASTER JGeneric aircraft · normal operations
Preparing the runway…
AIRCRAFT ENLARGED ×4 / DISTANCES TO SCALE
Drag to orbit · scroll to zoom. The flight path is computed; airframe pitch and gear geometry are schematic.
True airspeed B
Groundspeed BAlong the runway
Distance required B
Runway remaining BAvailable − required
Change one thing. Watch the difference.
Preset comparisons replace A and B, then pause at the start.
02 / DISTANCE, IN SEGMENTS
Every metre has a story.
B ━ liveA ┄ saved
Segment bars share one distance scale. Drag the cyan runway-end handle or violet screen-height handle. Click the path to inspect B at that distance. A and B use the same elapsed time. Beyond-runway paths are hypothetical distance comparisons; terrain beyond the runway is not modelled.
04 / WATCH THE ENERGY
Speed becomes distance. Braking removes energy.
Ground-frame kinetic energy
Height energy above the runway
Work and ground-relative kinetic energy
The schematic “forces × distance” statement is the work integral when forces vary.
Symbols & units
- Kinetic energy in the Earth frame, J.
- Ground-relative velocity, m/s; includes both horizontal and vertical components.
- Net force including gravity, N; Earth-frame displacement, m. Bold symbols are vectors; the dot denotes the scalar product.
Kinetic energy uses the full ground-relative velocity. With wind, aerodynamic work in the ground frame includes the lift contribution.
05 / FOLLOW THE SAME PLAYHEAD
The numbers behind the motion.
B ━A ┄
Air & ground speed
Bright line: TAS. Muted line: horizontal groundspeed. A keeps its dashed lines. Initial tailwind can briefly reverse relative flow on the ground; TAS is its magnitude.
Ground distance
At equal elapsed time, the two cases can be in different phases.
Horizontal acceleration
Phase changes can produce jumps in this idealised model. No actuator or suspension dynamics are implied.
Mechanical energy
Reference height: runway. Lift and thrust are solved consistently for the prescribed airborne segments.
06 / HOLD A, EXPLORE B
A / B comparison
| Quantity | A · saved | B · live |
|---|
A is held for this page session. Changing operation clears A. Reloading clears the comparison.
Equations, assumptions & teaching sources
Ground motion
m du/dt = T − D − μN, with N = max(0, W − L). TAS along the runway is u + headwind. Rolling resistance and braking use wheel load, not total weight.
A 3 s prescribed lift-coefficient ramp begins at 1.05 times the take-off stall TAS. Lift-off occurs when the wheel load reaches zero. This is a lift schedule, not a solved pitch manoeuvre.
Airborne motion
Constant TAS, with L = W cos γ + mV dγ/dt and T = D + W sin γ. Circular transitions join straight paths. Every air segment must remain within CLmax and the available thrust limit.
Take-off uses a modest supported climb angle. Landing starts on a 3° approach, then flares to zero vertical speed. Impact, bounce and pilot reaction dynamics are excluded.
Explicit teaching assumptions
Flat runway; constant mass and longitudinal wind; uniform density across the short height change. Synthetic take-off and landing polars include gear/flap drag. Induced drag is reduced near the ground by a declared smooth approximation.
Landing thrust is solved in the air, then set to zero on the ground. Lift reduces after touchdown; a fixed 1 s brake delay is used. Reverse thrust, V₁, balanced field length and certified runway factors are outside this version.
Sources & scope
Week 12, Accelerated Aircraft Performance, updated 15 April 2026, slides 23–45. No lecture artwork is copied.
FAA · Pilot’s Handbook of Aeronautical Knowledge
Original generic geometry and teaching model. Numerical consistency checks do not establish real-aircraft performance. Three.js is reused locally under its existing MIT licence.