FROM FORCES TO FLIGHT PATHS
Climb, Glide & Energy
Higher. Further. Longer. Different speeds for different goals.
ASTER JOne fixed teaching aircraft · still air
0.0 s
Altitude B—
Vertical speed B—
Flight-path angle B—
Distance B—
Quasi-steady projection: air density and thrust update with altitude; TAS stays fixed. Equal distance scales on both axes. Aircraft symbols are not to scale; they follow the flight path, not a solved pitch attitude. Editing a condition restarts the clock.
02 / CHOOSE WHAT YOU WANT TO ACHIEVE
Steepest climb ≠ fastest climb
Best climb rate
—03 / LIVE B AT THE PLAYHEAD
Forces along the flight path
L = W cos γ · T − D = W sin γ. Along-path forces and lift/weight use separate arrow scales. These are local steady balances.
04 / LIVE B AT THE PLAYHEAD
Where the energy goes
Height energy—
Speed energy—
Stored energy uses one shared scale, in MJ. With fixed mass and TAS, kinetic energy is constant. No transient exchange manoeuvre is modelled.
05 / COMPARE SPEEDS AT THE STARTING ALTITUDE
The initial performance picture
━ B · live┄ A · saved
Vertical speed
The highest point gives the greatest climb rate, or the smallest downward speed in glide.
Flight-path angle
Positive angles climb; negative angles descend. In still-air glide, the shallowest angle gives the greatest distance per unit height lost.
Velocity map Hodograph
Horizontal and vertical components of airspeed, on equal scales. The ray from the origin follows the numerical flight-path angle.
Curves and optima use each case’s starting altitude and setting. Click the first two graphs to change B’s TAS. Unsupported speeds are omitted. Playback does not silently replace these initial-condition curves.
06 / SAME CLOCK, TWO CASES
A / B comparison
| Quantity | A · saved | B · live |
|---|
READ THE DIFFERENCE
Angle measures height per distance.
A steeper path gains more height for a given horizontal distance. It does not necessarily reach a chosen height sooner.
FOLLOW THE POWER
Rate measures height per second.
Excess power changes height
Fixed mass and TAS; a sequence of local steady states.
Symbols & units
- Lift, weight, thrust and drag, N. Weight W = mg.
- True airspeed, m/s; aircraft mass, kg.
- Height, m; elapsed time, s. dh/dt is positive in climb.
For steady-speed climb, excess propulsive power becomes height energy. In glide, decreasing height supplies the energy dissipated by drag.
KNOW WHAT IS HELD FIXED
One speed for each playback.
The strategy buttons select an optimum at the starting altitude. That TAS is then held as the air gets thinner or denser. A continuously optimised speed schedule would be a different experiment.
Equations, assumptions & teaching sources
Steady at each local condition
Still air, fixed mass and clean drag polar. Thrust is parallel to velocity. We solve L = W cos γ and T − D = W sin γ together with D = qS CD0 + kL²/(qS). The engine law and atmosphere are shared with the Flight Envelope module.
The root continuous with shallow flight is used. Lift, Mach, dynamic-pressure and ±20° angle limits gate the solution. The angle limit is an illustrative modelling boundary, not a certified operating limit.
What the playback represents
A sequence of local steady states, integrated with changing altitude at constant TAS. It omits the normal acceleration needed as the path slowly curves; playback stops if its estimated magnitude exceeds 0.02g. This tolerance is a declared approximation criterion.
The sea-level stop is an altitude datum, not a landing or terrain prediction. The atmosphere ends at 15 km. No take-off, pitch trim, wind, fuel burn, post-stall or full flight dynamics are simulated.
Energy and glide
Input power TV − drag power DV = W dh/dt. Stored energy is mgh + ½mV². Here V and mass stay fixed, so all net power changes height energy. Glide sets thrust to exactly zero; it does not simulate an engine failure, windmilling drag or idle thrust.
Best angle / rate and best glide / minimum sink are local, constrained optima within this model. They are not instructions for operating a real aircraft.
Sources and verification
Week 10: Static Aircraft Performance Analysis, Part 2 — 27 Mar 2026, slides 25–41. Glide is a related teaching extension. Illustrations are original.
Force and energy closure, analytic glide landmarks, optimum speeds and playback step sensitivity are checked. Numerical verification does not establish experimental accuracy.