› Sports Math & Physics Engine
Free · no account · saves in this browser · FOR LEARNING — simplified physics model
Four sports, four families of real math
Switch across 4 sports and 12 starter scenarios to see how trigonometry, quadratic kinematics, 3D cross products, and cubic power laws govern real athletic performance. Every slider updates the free-body vectors, trajectory curves, and substituted equations live in your browser.
Skiing: Descent & Carving
Decompose gravity into normal load N = mg cos(θ) and downhill pull mg sin(θ), solve terminal velocity against snow friction and quadratic air drag, then tilt the ski to edge angle φ so its sidecut bends into a tighter carved turn radius R_T = R cos(φ).
Basketball: Arc & Rim Aperture
Launch a parabolic shot toward a 3.05 m (10 ft) rim and compare how a high-arc release increases the entry angle α, expanding the effective target window d_eff = d_rim sin(α) − d_ball.
Baseball & Soccer: Magnus Spin Curve
Compare a spinning pitch or free kick against a dashed zero-spin baseline as the Magnus cross product ω × v lifts a backspin fastball, drops a topspin curveball, or bends a soccer ball around a wall.
Cycling: Cubic Drag & Drafting
Solve the cubic power balance where aerodynamic drag power scales with v³, and measure how drafting in a paceline or peloton cuts effective C_dA and boosts steady road speed.
Download a CSV telemetry table for spreadsheets, a 1-page printable vector PDF lab sheet for class or home study, a standalone SVG diagram, or a `.hbsport` project file. FOR LEARNING — simplified physics model. More engines →