Mars Entry Landing - 2D Descent Profile: Aeroshell, Parachute and Powered Landing

Presets

Live readouts

Graphs

Altitude against speed, with the ballistic (Allen-Eggers) curve dashed

Deceleration in Earth g against time

Convective heat flux on the heat shield against time

Experiments

Deploy parachute now and Ignite engines now let you override the automatic sequence; Restart descent replays with the current sliders. Try the presets "Too steep" (burns and crashes), "Too shallow" (skips out) and "Chute opened too fast" (canopy torn above 1400 Pa).

Numerical checks

running...

How to use

Choose a preset, then change entry speed and angle, vehicle mass and size, parachute and engine settings. The main picture is a side profile (altitude against downrange) with a close-up of the vehicle in the corner: the glow is the shock layer, the canopy opens over 2 s, the flame shows thrust. The trail is coloured by heat flux. Use the time-scale selector to speed things up; Space pauses and R restarts.

The science

Entry is a drag problem. A point-mass vehicle at position r with velocity v feels gravity, drag, lift and thrust: dv/dt = -mu r / |r|^3 - (rho v^2 Cd A / 2m) v^ + (L/D)(drag) n^ - (T/m) v^ with the Martian gravitational parameter mu = 4.2828e13 m3/s2, radius 3389.5 km and a simple exponential atmosphere rho = 0.020 exp(-h / 11.1 km) kg/m3. Everything is integrated with fourth-order Runge-Kutta.

Ballistic coefficient and the Allen-Eggers solution. For a straight path at angle gamma and no gravity, with beta = m / (Cd A): v(h) = v0 exp( -rho(h) H / (2 beta sin gamma) ), a_max = v0^2 sin(gamma) / (2 e H) The peak deceleration depends only on speed and angle, not on mass; mass only decides where it happens (at rho = beta sin(gamma)/H). Mars air is about 1% as dense as Earth's, so even a 4.5 m shield reaches the parachute altitude at roughly Mach 2: the vehicle is still going too fast for a simple chute and needs rockets.

Heating. Stagnation-point convective heating uses the Sutton-Graves relation for CO2 atmospheres: q = 1.9027e-4 sqrt(rho / Rn) v^3 [W/m2], T_wall = (q / eps sigma)^(1/4) with nose radius Rn = d/4 and emissivity 0.85. Heat flux scales with v cubed, so the time of peak heating comes earlier and higher than peak deceleration. The integrated heat load decides how thick the shield must be.

Parachute. Canopy drag adds Cd,c * pi D^2/4 to the drag area, ramping up over 2 s (inflation). Terminal speed under the canopy is sqrt(2 m g / (rho CdA)). If the dynamic pressure q = rho v^2 / 2 at deployment exceeds 1400 Pa the canopy is torn, as in the "opened too fast" preset.

Powered descent. The engines follow a guidance law that asks for the deceleration needed to reach the touchdown speed at the ground: a_req = (v_down^2 - v_t^2) / (2 h) + 0.9 g, thrust limited to the maximum; propellant burns at mdot = T / (Isp g0). If thrust or propellant are too small, the vehicle hits the ground.

Honest simplifications. Planar motion, zero angle of attack (no trim dynamics), constant Cd, a single exponential atmosphere with no winds or dust, a heat shield that is never jettisoned (the parachute adds drag only), instant throttle response and vertical-only guidance. Numbers are in the right range for Viking- and MSL-class vehicles but are not mission data. Peak g is lower than the real flight because of the simple lift model.

Checks run in the page. Peak deceleration and the speed at which it occurs against the Allen-Eggers formulas (vertical entry, gravity off); orbital energy conservation of the integrator over 3000 s in vacuum; parachute terminal speed against sqrt(2mg/(rho CdA)).