02 / THE LIFT THAT TURNS YOU
LIFT IN A DIFFERENT DIRECTION
Coordinated Turns & Load Factor
Bank the wings. Bend the path. See the cost.
ASTER JSteady · level · still air
Preparing the 3D aircraft…
NORTH REFERENCE / STILL AIR
↗ Lift↓ Weight
Drag to orbit · scroll to zoom. Bank and heading are modelled; fuselage pitch and geometry are schematic. View recentres on the aircraft.
North ↑ · east → · equal distance scales. Both cases start at the origin, heading north. Markers are enlarged.
Required load factorn = L / W
Sustained turn radius
Sustained turn rate
Required engine settingTo hold TAS and altitude
Try a comparison Preset comparisons reset the starting conditions and replace A and B.
03 / WHAT THE TURN REQUIRES
More lift has a cost.
Lift-boundary TAS
Bank increases the lift demand
Required steady level-turn relationships do not by themselves establish a sustainable turn.
Symbols & units
- Required lift and weight, N.
- Bank angle. The code uses radians; controls display degrees.
- Induced drag, N; proportionality holds at fixed dynamic pressure and wing geometry.
At fixed mass, altitude and TAS, turning increases induced drag. The engine must replace that extra energy loss to keep the turn steady.
04 / FIND A SUSTAINABLE TURN
The speed–bank map
B ━A ┄
Click or drag: speed ↔, bank ↕. Arrow keys change speed/bank. The filled area meets lift, load-factor, thrust and upper-speed limits.
AT LIVE B'S SPEED
━ Sustainable boundary┄ Illustrative load ceiling● Selected condition
A keeps its own mass and altitude. Different cases can have different boundaries.
05 / ONE CONDITION, LINKED CURVES
Geometry meets performance.
B ━A ┄
Turn radius at each case's fixed bank
At a fixed non-zero bank, R ∝ V². Doubling TAS quadruples radius, where both turns are sustainable.
Turn rate magnitude, at fixed bank
At fixed bank, |ω| ∝ 1/V. Faster flight turns through fewer degrees each second.
Thrust required & available
Solid: required where the polar is supported. Dashed: maximum available within Mach/EAS scope. Only required ≤ available sustains a steady turn.
Load factor & lift boundary
n = 1/cos φ; VS,turn/VS,1g = √n. These are requested steady-turn relationships, even where the aircraft cannot sustain them.
06 / FIX A, EXPLORE B
A / B comparison
| Quantity | A · saved | B · live |
|---|
A is stored for this page session. Reloading clears it. CSV includes inputs, states, 120-second paths and performance curves.
Equations, assumptions & sources
A constant-altitude force balance
L cos φ = W; L sin φ = mVω; T = D. Thus n = sec φ, ω = g tan φ/V and R = V/|ω|. At zero bank, the path is straight and radius is infinite.
Drag follows the shared clean polar: D = qSCD0 + kL²/(qS). We solve the required engine setting; surplus maximum thrust is not applied as unmodelled acceleration.
What the animation represents
Established steady turns in still air, with constant mass, altitude, TAS and bank. No roll-in/out, pitch trim, sideslip, stall recovery or control-system dynamics. Editing starts a new case at time zero.
The 3D aircraft shows bank and heading. Fuselage pitch is schematic; a level trajectory does not imply zero aerodynamic angle of attack.
Respect the boundaries
CLmax, Mach and EAS limits are shared with the Flight Envelope lab. The additional n ≤ 2.5 ceiling is a declared illustrative assumption. This synthetic aircraft has no certified operating envelope.
Failed conditions retain requested-bank geometry for explanation, but no sustained trajectory is animated. A successful equation check does not establish real-aircraft accuracy.
Teaching sources
Week 12, Accelerated Aircraft Performance, updated 15 April 2026, slides 6–15. Original geometry and figures; no manufacturer artwork.
The force balance and model boundaries are stated above. Three.js is reused locally under its existing MIT licence.