Flight dynamics - 2D side view

A light aircraft flies at a fixed angle of attack; throttle, mass and speed decide whether it cruises, climbs, glides or bobs through a phugoid.

Switch to 3D

Presets

Playback

Controls

Aircraft and start

Changing mass, altitude or start speed restarts the flight.

Model checks

The science

Equations of motion

In the vertical plane a point mass obeys m dV/dt = T cosα − D − m g sinγ and m V dγ/dt = L + T sinα − m g cosγ, with L = ½ ρ V² S CL, D = ½ ρ V² S CD and the parabolic polar CD = CD0 + k CL². Density falls as ρ = 1.225 e−h/8500.

Trim, glide and phugoid

Level flight needs V = √(2 m g / (ρ S CL)). Best glide is at CL = √(CD0/k) with path angle −atan(CD/CL). With the angle of attack held fixed, trading speed for height gives the slow phugoid oscillation of period ≈ π√2 V / g (Lanchester).

Honest simplifications: a point mass with no pitch dynamics (angle of attack is set directly), a linear lift curve with a simple stall roll-off, a propeller thrust model T = min(Tstatic, P/V), no ground effect, no weather or terrain model; the 3D page adds the alpine scenery. Educational physics only.

What to try
  • Press Level cruise: the plane bobs gently around its trim speed.
  • Press Power-off glide and compare the path angle with atan(CD/CL).
  • Press Edge of stall to see the lift curve saturate.
Drag polar CL against CD
Airspeed and altitude
Phase plane speed against path angle