Presets
Playback
Vehicle and world
Engine, propellant load and the planet it lands on.
Approach and control
Starting state, wind and how aggressively the autopilot steers.
Layers
Model checks
The science
Rocket equation and fuel
Thrust T burns propellant at mdot = T / (Isp g0), so the stage gets lighter while it burns and the acceleration a = T/m rises. Over a burn the velocity change is the Tsiolkovsky result dv = Isp g0 ln(m0/m1), ignoring gravity and drag. A landing must spend roughly v + g t worth of dv, so fuel left at touchdown is the margin of the landing.
Suicide burn
The most fuel-efficient landing waits and burns once, as late as possible. With maximum net deceleration a_net = T_max/m - g, the stopping distance from speed v is v^2 / (2 a_net); ignition happens when the altitude equals that distance (plus a margin). The autopilot then follows the speed profile v_des(h) = -sqrt(2 a_d h) by throttling between the engine minimum and maximum. If the engine cannot throttle low enough, the stage may hover or climb: set a higher minimum throttle to see it.
Steering
Sideways position is controlled by tilting the thrust vector (gimbal): a horizontal acceleration command a_x = kp (x_pad - x) - kd v_x is turned into a tilt angle limited to the gimbal range; the steering gain slider scales kp and kd. Wind acts as an extra horizontal acceleration.
Simplifications
Point mass with instantaneous attitude (no rotation dynamics), constant gravity, no atmosphere drag except the wind term, perfect sensors, constant Isp. A teaching model of the physics, not a flight-software replica; the pad and stage are generic.
What to try
- Lower the engine thrust-to-weight ratio toward 1.3: ignition must start much higher and fuel use rises.
- Switch to the Moon preset: gravity is one sixth, the burn is short and cheap.
- Raise the wind and lower the steering gain: the stage lands off the pad centre.
- Reduce the fuel load until the tank runs dry before touchdown.