Side view of a reentering booster free to rotate about its own center of mass. The grid fins are mounted a fixed arm's length from that center of mass, so any lift force they produce creates a torque — exactly the mechanism that steers the real 3D booster, but here it is the vehicle's attitude, not just its position, that responds:
ρ(h) = ρ₀ · e^(−h/H) ρ₀ = 1.225 kg/m³, H = 8500 m
q = ½ ρ(h) v² dynamic pressure, from your altitude + airspeed sliders
α = θ + δ effective angle of attack: body attitude + fin deflection
F_fin = q · A_fin · C_L(α) genuine lift-coefficient curve, not a flat slope
τ = F_fin · L_arm − B·q·ω torque about the center of mass, with aero pitch damping
ω += (τ / I) dt, θ += ω dt angular-rate and attitude ODE, integrated every frame
The key difference between fin types is the shape of C_L(α). A conventional planar fin follows a straight line up to roughly 14° angle of attack, then stalls — flow separates and lift collapses toward zero, so a control surface that stalls loses its steering torque exactly when it is needed most. A grid fin's lattice of small cells keeps the local flow attached cell-by-cell even at very high incidence, so its C_L stays near its peak out to roughly 50°. Because the fins sit ahead of the center of mass here (as they do on the real booster), an undeflected fin at nonzero attitude actually adds torque in the same direction as the tilt — the vehicle is open-loop unstable and needs active deflection commands (or the autopilot) to hold attitude, just like real reentry guidance software.
- Fin deflection δ — your steering command, added to body attitude to get the fin's true angle of attack.
- Grid / Conventional toggle — swaps which C_L(α) curve drives the physics; try large deflections at high attitude with conventional fins to watch the torque collapse and control authority vanish.
- Gust kick — injects an angular-velocity disturbance (like a separation tumble or wind shear) so you can watch each fin type fight to recover.
- Autopilot — a proportional-derivative law, δ = −(K_p·θ + K_d·ω), that nulls attitude the way real flight software does; it stays in control with grid fins even after a hard kick, but a conventional fin's autopilot can stall out and lose the vehicle.
- The two live charts plot the exact functions driving the simulation: torque vs. deflection at your current q (grid solid, conventional dashed) and C_L vs. angle of attack for both fin families, each with a marker at the current operating point.
Real-world relevance: this is the same aerodynamic control-authority trade-off that made SpaceX's grid fins — rather than conventional planar fins — the enabling choice for Falcon 9 and Falcon Heavy booster reentry, where angles of attack routinely exceed what a planar fin could survive without stalling.