Entry Descent Landing

Entry Descent and Landing (space-systems/mission-design/entry-descent-landing)

Use when the task is the atmospheric entry, descent, and landing (EDL) phase of a spacecraft mission: checking the entry corridor against the flight path angle, computing the ballistic coefficient, estimating the peak deceleration g-load and the stagnation point convective heating of a ballistic entry, and sizing the parachute descent. This leaf is the entry-side counterpart of the mission delta-v budget leaf (which sizes the propulsion to reach the entry interface) and sits next to the radiation-debris leaf (environment hazards on the same trajectory); the hohmann-transfer leaf covers the interplanetary transfer that sets the entry speed.

Domain quick reference

• Entry corridor: the band of flight path angles between the undershoot limit (too shallow: skip-out or excessive altitude float) and the overshoot limit (too steep: excessive g-load and heating). Corridor angles are negative for descent; a shallower angle is numerically greater (for example -6 degrees) and a steeper angle numerically smaller (for example -11.5 degrees).
• Ballistic coefficient: beta = m / (Cd * A), the entry mass divided by the product of the drag coefficient and the reference area, in kg/m^2. A high beta (heavy, small drag area) penetrates deep and peaks the deceleration and heating low and hard; a low beta (light, large drag area) decelerates high and soft.
• Peak deceleration of a steep ballistic entry: a_peak = V^2 * sin(|gamma|) / (2 * e * H), with V the entry speed (m/s), gamma the flight path angle (deg, negative for descent), e the base of natural logarithms, and H the atmospheric scale height (m). The g-load is a_peak / g0; it scales as V^2 and with the sine of the flight path angle, so doubling the entry speed quadruples the load.
• Convective heating (Sutton-Graves): stagnation point heat rate q_dot = k * sqrt(rho / r_n) * V^3 (W/m^2), with rho the freestream density (kg/m^3), r_n the nose radius (m), V the flight speed (m/s), and k a correlation constant near 1.83e-4 for Earth and Mars stagnation flows. The cubic speed dependence makes heating the entry-speed driver: an 8 km/s Earth return heats about 4.6 times a 5.5 km/s Mars-class entry at equal density and nose radius.
• Heat load: the integral of q_dot over the heating pulse, in J/m^2. For a discrete heat rate history sampled at a constant time step it is the rectangle-rule sum dt * sum(q_dot); the heat load drives the thermal protection system thickness.
• Ballistic vs lifting entry: a purely ballistic entry flies at zero lift and takes whatever g-load and heating the corridor gives; a lifting entry modulates the flight path angle with L/D to flatten the deceleration and heating peak (Apollo's lifting entry kept the crew g-load near 6 g where a steep ballistic return at the same speed would exceed 30 g). The formulas in this leaf are the ballistic baseline; lifting entries stay below them.
• Parachute descent terminal velocity: v = sqrt(2 * W / (rho * Cd * S)), with W the payload weight (m * g_local), rho the descent density, Cd the canopy drag coefficient (about 0.75 for a disk-gap-band canopy), and S the canopy reference area. Terminal velocity scales as the square root of the weight-to-drag ratio, so a 4x canopy area halves the touchdown speed.
• Landing site constraints: the touchdown speed (v at the surface density) must stay under the landing system limit, the descent duration sets the landing ellipse dispersion from winds, and the deceleration at chute deployment must stay under the payload and parachute load limits.
• Mars vs Earth atmospheres: Mars surface density is about 0.02 kg/m^3 versus Earth's 1.225 kg/m^3, and Mars gravity is 3.711 m/s^2 versus 9.80665 m/s^2, so a Mars parachute descent is much faster at equal canopy loading; Mars entry speeds from low orbit are near 5.5 km/s versus Earth orbital return near 7.8 km/s and direct lunar return near 11 km/s. Use the local gravity and the deployment altitude density for each planet.
• ECSS-E-ST-10C (systems engineering general requirements) frames the mission analysis and entry sequence within the ECSS lifecycle; ECSS standards are free to download from https://ecss.nl/standards/ (name
  • paraphrase + link only). The entry mechanics above are common hypersonic methodology, summary-only.

Workflow

1. Record the entry interface state: entry speed (m/s), flight path angle (deg, negative), atmospheric scale height (m), and the local gravity for the target planet.
2. Check the flight path angle against the corridor with entry_corridor_check; a shallow angle risks skip-out and a steep angle risks excessive g-load and heating.
3. Compute the ballistic coefficient with ballistic_coefficient from the entry mass, drag coefficient, and reference area; a high beta pushes the peak deceleration and heating lower into the atmosphere.
4. Estimate the peak deceleration g-load with entry_deceleration from the entry speed, flight path angle, and scale height; compare it with the payload and crew structural limits.
5. Estimate the stagnation point convective heat rate with sutton_graves_heat_rate at the peak heating density and speed, and integrate the heat rate history with heat_load to get the thermal protection sizing driver.
6. Size the parachute descent with parachute_terminal_velocity from the payload weight, canopy drag coefficient, reference area, and deployment altitude density; check the touchdown speed against the landing system limit.
7. Confirm the deterministic checks with the contract test scripts/test_entry_descent_landing.py.

Worked example

A Mars mission ballistic entry check, Curiosity-style (approximately 1000 kg entry mass, 4.5 m diameter capsule at Cd = 1.3, entry at 5500 m/s and -12 degrees, Mars scale height 11.1 km):

• Entry corridor: entry_corridor_check(-12.0, -6.0, -11.5) reports the -12 degree angle below the -11.5 degree steep limit, so the entry is outside the corridor and must be lifted shallower or flown with lift modulation. A -8 degree angle sits inside the corridor.
• Ballistic coefficient: beta = 1000 / (1.3 * 15.9) about 48 kg/m^2, a low-ballistic coefficient Mars entry (light capsule, large drag area) that decelerates high in the thin atmosphere.
• Peak deceleration: entry_deceleration(5500.0, -12.0, 11100.0) returns about 104 m/s^2, about 10.6 g, within the entry system design load of a Mars lander; a steeper -20 degree angle at the same speed would push past 17 g.
• Peak heat rate: sutton_graves_heat_rate(2e-4, 4800.0) with a 1 m nose radius returns about 0.29 MW/m^2 at the peak heating point; doubling the speed to 9600 m/s would raise it 8x to about 2.3 MW/m^2, the difference between a Mars-class and an Earth-return thermal protection system.
• Heat load: over a 60 s heating pulse sampled every 10 s at [1e5, 2.5e5, 3.0e5, 2.5e5, 1.5e5, 5e4] W/m^2, heat_load returns 1.1e7 J/m^2, the ablator sizing driver.
• Parachute descent: parachute_terminal_velocity(600.0, 0.75, 110.0, 0.02, g=3.711) returns about 52 m/s at 0.02 kg/m^3; deploying the same canopy at a 2x larger area (220 m^2) cuts the descent speed by the square root of 2 to about 37 m/s.

Pitfalls

• Reading corridor angles with the wrong sign sense: corridor angles are negative for descent and a shallower angle is numerically greater (-6 deg) than a steeper one (-11.5 deg); the worked example -12 deg entry sits below the steep limit and is outside the corridor.
• Using the planet surface density for the parachute terminal velocity: v = sqrt(2 W / (rho Cd S)) must be evaluated at the deployment altitude density (0.02 kg/m^3 on Mars, not 1.225); the touchdown speed check then uses the surface density.
• Scaling heating linearly with speed: the Sutton-Graves rate is cubic in V (doubling 4800 to 9600 m/s raises q_dot 8x), so an entry-speed change of a few percent is a double-digit percent change in the heat rate.
• Forgetting the entry speed - g-load square law: peak deceleration scales as V^2 and with sin(|gamma|); a steeper angle at the same speed (the -20 deg case at about 17 g) or a faster entry at the same angle can exceed the payload load limit even when the nominal corridor point is fine.
• Applying Earth gravity to a Mars descent: the ballistic and terminal-velocity formulas take the local gravity (3.711 m/s^2 on Mars), so pass g explicitly instead of assuming g0.
• Treating the ballistic formulas as lifting-entry loads: these are the zero-lift baseline, and a lifting entry (Apollo-style L/D) stays below them; sizing the TPS or structure off the ballistic peak for a lifting vehicle over-penalizes the design.

Related leaves

• mission-design/mission-delta-v-budget: sizes the propulsion and the entry interface state (speed and angle) that feed the EDL sizing.
• mission-design/radiation-debris: the environment hazards on the same trajectory, with their own gating treatment.
• orbit-mechanics/hohmann-transfer: the interplanetary transfer that sets the entry speed at the target planet.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_entry_descent_landing.py

The test covers the ballistic coefficient, the peak deceleration g-load (V^2 scaling, angle and speed monotonicity, very high speed finiteness), the entry corridor check, the Sutton-Graves heat rate (V^3 and sqrt(rho) scaling, nose radius effect, zero density, very high velocity), the heat load integration, the parachute terminal velocity (canopy area and density monotonicity, massless payload), and invalid-input edge cases.

Compliance

• Standards referenced, not reproduced: ECSS-E-ST-10C (systems engineering general requirements) frames the mission analysis and entry sequence within the ECSS lifecycle, name + paraphrase + link only per standards-map.yaml; the entry mechanics above are common hypersonic methodology, summary-only.
• compliance: STANDARDS-REF, gated: false.