Dynamic
Flight path and airspeed evolve with pitch and power. The γ control is disabled. Watch the flight path respond to a change in attitude.
OPERATING GUIDE / 01
See the angle.
Understand flight.
An interactive laboratory for exploring the relationship between attitude, flight path, airspeed, and relative wind. Start with the controls, then watch what changes around the wing.
THE CORE RELATIONSHIP
α=θ−γ
01 / FIRST LOOK
Start in steady flight
Open the cockpit. The initial condition is 140 kt IAS, +4° pitch, 0° flight path angle, and 50% throttle, at sea level in the standard atmosphere. Angle of attack is +4°. Dynamic mode is active. Use Reset flight to return to this condition at any time.
The three windows belong to the cockpit. The wing window is an instrument overlaid on the scene. The sky has no clouds in this version.
02 / FLIGHT GEOMETRY
Three angles, different references
- Pitch · θ
- Aircraft attitude relative to the horizon. Positive means the nose is above the horizon.
- Flight path · γ
- Direction of motion relative to the air mass. Positive indicates an ascending path through the air.
- Angle of attack · α
- The difference between the wing chord direction and the air-relative flight path. In this app, wing incidence is zero: α = θ − γ.
A nose above the horizon does not necessarily mean a positive angle of attack.
03 / ATTITUDE
Control pitch
Drag the PITCH CONTROL slider, use its −/+ buttons, or drag a cockpit window up or down. The value beside the control is the command; the PITCH instrument shows the current attitude. The response is gradual while flight is running.
The wing follows pitch. The horizon reference moves across the windshield while the aircraft symbol stays fixed. The flight path marker indicates the direction of motion through the air. The separation between these references helps visualize angle of attack.
04 / FLIGHT PATH
Compare the two modes
Manual
The γ control is enabled. Set the flight path to study geometry separately. Pitch and throttle remain available.
05 / ENERGY
The throttle commands power
Drag the throttle upward to increase power and downward to reduce it. It does not select an airspeed directly: IAS responds gradually to thrust, drag, and the flight path angle.
- IAS: indicated airspeed, in knots. It represents the dynamic pressure of the air on the aircraft.
- GS: groundspeed, the horizontal speed over the ground, in knots.
- Vertical speed indicator: analog dial next to the IAS box. Zero is on the left; the needle moves up in a climb and down in a descent, up to 4,000 ft/min.
TAS, the true speed at which the air meets the wing, is still calculated. It drives the flight path, GS, vertical speed, and the airflow animation. Above sea level, TAS is higher than IAS.
06 / THE AIR REFERENCE
Relative wind over the airfoil
Relative wind is opposite to the aircraft's velocity through the air. Its magnitude follows TAS, and its direction follows the air-relative flight path. This is the freestream reference used by FoilShape. The wing window reports this speed as TAS; the panel shows IAS.
The air mass is stationary relative to the ground. GS shows the horizontal component of aircraft velocity; in level flight, it equals TAS. Angle of attack remains α = θ − γ. Gusts and vertical wind are not modeled.
07 / AIRFLOW
Read the motion around the wing
The right wing shows the detailed airfoil. Attached lines and particles come from the potential field. Animation speed follows TAS, and relative wind direction follows the air-relative flight path. Time is slowed for readability.
Above |α| = 13°, suction-side lines progressively leave the surface, with a recirculation region and animated wake. Negative angles show this on the lower side. Detachment, its location, local speeds, and colors in this regime are illustrative, not CFD or a prediction of real stall. The 13° threshold is an educational display parameter, not an operational limit.
Readouts beside the wing track pitch, flight path, and angle of attack. Metallic texture, reflections, and cockpit lighting are predefined. The two throttle levers move together and command a single educational power setting.
- Flow: shows or hides bands, lines, particles, and recirculation.
- Vectors: shows or hides pitch, flight path, and angle of attack references; it also affects the flight path marker in the cockpit.
- Colors: attached flow compares local speed with TAS. In schematic separation, ILLUSTRATIVE COLORS replaces the numerical scale. Colors do not represent pressure.
The RIGHT and LEFT tabs next to Flow, Vectors, and Colors switch the window between the right wing and the left wing at the same size. The LEFT tab uses a simplified drawing without vectors or colors, so Vectors and Colors are disabled there. Without roll, both wings have the same angle of attack.
3D view: drag the wing image to rotate it through 360°; double-click it to return to the side view, which is the default. Away from the side view, the image zooms out slightly and shows a wing segment, with the same flow repeated on a few planes along the span, close to the wing. The color field stays on the middle plane, and the pitch, flight path, and angle of attack references stay on the end face turned toward you. The header shows 3D while the view is rotated; Reset flight also returns to the side view.
08 / EXERCISES
Separate attitude from angle of attack
Select Manual. Set pitch and flight path, then wait for the instruments to reach the commanded values. You can also pause and adjust the angles to compare static conditions.
| Pitch θ | Flight path γ | AoA α |
|---|---|---|
| +4° | 0° | +4° |
| +4° | +10° | −6° |
| −2° | −8° | +6° |
Then reset flight and increase pitch in Dynamic mode. Compare the initial change in α with the flight path's later response. Change one variable at a time.
09 / OPERATION
Pause, window, and keyboard
Use the top buttons to pause, reset, and enter full screen. On a computer, drag the wing window's header to reposition it. Drag the wing image to rotate the 3D view; double-click returns to the side view. The × button closes the window; WINGS opens it again. On a phone, the window and instruments are arranged in a vertical sequence.
- ↑ / ↓
- Command pitch in 1° steps; hold Shift for 0.1° steps.
- + / −
- Change power by 5 percentage points.
- Space
- Pause or resume.
- R
- Reset to the initial condition.
General shortcuts depend on focus: when you select a control, the keyboard operates that control. On the throttle, ↑/↓ changes power; Home selects 0% and End selects 100%. Escape closes the explanation.
10 / MODEL AND REFERENCES
What this visualization represents
The airfoil and attached flow use the Joukowski transformation with circulation set by the Kutta condition. This is a two-dimensional, incompressible, inviscid, quasi-steady potential field. It does not use CFD or resolve the boundary layer.
Above |α| = 13°, the warning and wake are illustrative. The model does not predict real separation, turbulence, or stall; this angle is not an operational limit. Longitudinal dynamics use educational coefficients independent of the displayed field, with their own speed and flight path limits. MODEL LIMIT indicates that one of those limits has been reached.
IAS follows FoilShape: standard atmosphere and dynamic pressure q0 = ½ρV². The indicator converts that pressure using sea-level density: IAS = TAS × √(ρ/ρ0), with no instrument or position error. Flight starts at sea level. Lift and drag depend on dynamic pressure: for the same angle of attack and flight path, the equilibrium IAS does not change with altitude, while TAS increases in a climb. Thrust does not vary with altitude.
This version has no specific aircraft, clouds, or roll dynamics. Bank angle alone does not imply different angles of attack on the two wings.
The 3D view adds no physics to the model. FoilShape treats a two-dimensional airfoil, so the same field repeats along a short span segment, like a section of an infinite-span wing. Wingtip vortices and downwash, three-dimensional effects of a finite wing, are not represented.
Conceptual references: NASA — Joukowski and the Kutta condition; NASA — angle of attack; NASA — downwash and wingtip vortices.
FAA — Pilot’s Handbook of Aeronautical Knowledge · Chapters 4 (Principles of Flight) and 5 (Aerodynamics of Flight). NASA — forces in a climb.
NASA/BGA — FoilShape (Tom Benson) · Reference for Joukowski geometry, local velocity, the standard atmosphere, dynamic pressure, and simplified high-angle flow visualization. This app's JavaScript implementation and animations are independent.