✈️ Paper Airplane
Fold, throw, glide. Real lift and drag in action — see how angle and speed change the flight path.
Fold, throw, glide. Real lift and drag in action — see how angle and speed change the flight path.
This simulation flies a paper aircraft as a point mass through air, integrating Newton's second law step by step. At each frame it computes the speed v, then aerodynamic forces scaled by the factor k = (0.5 · ρ · A) / m, where air density ρ is 1.2 kg/m³. Lift acts perpendicular to the velocity and drag opposes it, both proportional to v², while gravity g = 9.81 m/s² pulls constantly downward. The resulting glide path is drawn in real time.
You choose a paper type (Light A5, Standard A4, or Heavy card), which sets the mass, wing area, lift coefficient and drag coefficient. Two sliders control the launch angle (−5° to 40°) and throw speed (3 to 9 m/s). The panel reports distance, maximum height, flight time and your best throw. These same trade-offs between lift, drag and weight govern real gliders, wings and any unpowered flight.
What does this simulation actually model?
It treats the paper plane as a single point with mass, area, and lift and drag coefficients, then integrates its motion through the air. Each step adds the accelerations from lift, drag and gravity to the velocity, so you see a realistic gliding arc rather than a simple parabola.
How are lift and drag calculated?
Both scale with the factor k = 0.5 · ρ · A / m and with the speed v. Lift uses the lift coefficient and acts perpendicular to the direction of travel, while drag uses the drag coefficient and points directly against motion. Because force grows with v², a faster throw produces much stronger aerodynamic effects.
What do the three paper types change?
Each preset sets four values: mass, wing area, lift coefficient and drag coefficient. Light A5 (4 g) is nimble with high lift, Standard A4 (6 g) is a balanced glider, and Heavy card (10 g) carries more mass with higher drag, so it sinks faster and travels a shorter, steeper path.
The angle sets how the throw speed is split between horizontal and vertical velocity. A shallow throw covers ground quickly but loses height; a steep throw climbs but stalls and falls short. The on-screen tip suggests 10–20° as the sweet spot for the longest flight in this model.
It sets the initial launch velocity from 3 to 9 m/s. Higher speed gives more kinetic energy and stronger lift, which usually extends the glide. Beyond a point, however, extra drag grows with the square of speed and the gains taper off.
It is a simplified but physically grounded model. It correctly captures velocity-squared lift and drag, gravity, and the mass and area trade-offs. It ignores effects such as flutter, angle-of-attack changes, stall, turbulence and the plane's pitching, so it shows the right trends rather than exact real-world distances.
They are dimensionless numbers describing how efficiently the shape generates lift and how much it resists the air. In the presets they range from about 1.0 to 1.2 for lift and 0.14 to 0.20 for drag. A higher lift-to-drag ratio means a flatter, more efficient glide.
A projectile with no air would follow a parabola. Here lift pushes the plane sideways to its motion and drag slows it down, so the path flattens, sometimes dips and recovers, and finally settles into a gradual descent. That curved glide is exactly what distinguishes a wing from a thrown stone.
Distance is the horizontal range from the launch point to where the plane lands, maximum height is how far it rose above the release point, and flight time is its total time aloft. Best throw keeps the longest distance you have achieved until you clear it.
The same balance of lift, drag, weight and launch conditions governs full-size gliders and aeroplane wings. Engineers maximise the lift-to-drag ratio for efficient flight, just as you can here by picking a lighter paper and a moderate launch angle to stretch the distance.