Simulate a space capsule re-entering Earth's atmosphere from Low Earth Orbit at 7800 m/s. Entry angle determines outcome: too shallow and the capsule skips off the atmosphere; too steep and aerodynamic heating and g-forces become lethal. Lift-to-drag ratio allows lifting re-entry for softer deceleration. Track peak heating rate and g-load versus altitude.
This simulation models a blunt-body capsule descending from the 120 km entry interface into Earth's atmosphere. It integrates the equations of motion step by step using an exponential atmosphere, where density follows ρ = 1.225 × e−h/8500 kg/m³. Drag deceleration is computed as ½ρv²/β, gravity varies with altitude via the inverse-square law, and the trajectory, g-load and heating are tracked at each timestep.
Four sliders shape the outcome: Entry Angle (1–15° below horizontal), Lift-to-Drag ratio (0–4) for lifting versus purely ballistic descent, Initial Velocity (7400–11000 m/s) spanning orbital to lunar-return speeds, and the Ballistic Coefficient β (100–1000 kg/m²). Too shallow and the capsule skips back out of the atmosphere; too steep and the g-load or peak heating destroys it. This is exactly the corridor problem every returning spacecraft must thread.
What does this simulation show?
It shows a space capsule re-entering Earth's atmosphere from the 120 km entry interface. You watch its trajectory, velocity, g-load and aerodynamic heating evolve in real time as it decelerates, and you see whether it lands safely, skips back out, or is destroyed by excessive heat or deceleration.
How does the model calculate the descent?
It numerically integrates the equations of motion with a fixed small timestep. At each step it computes air density from an exponential atmosphere, drag from ½ρv²/β, lift as a multiple of drag set by the L/D ratio, and altitude-dependent gravity. Velocity and position are then updated and the new state is plotted.
Why is the entry angle so critical?
The re-entry corridor is narrow. A shallow angle (near 1–2°) spreads deceleration over a long path but risks skipping off the atmosphere back into space. A steep angle (above about 8°) plunges the capsule into dense air quickly, spiking g-load and heating to lethal levels. The safe band lies in between.
Entry Angle sets how steeply the capsule crosses the 120 km interface. L/D ratio (0–4) adds aerodynamic lift for a softer lifting descent versus a pure ballistic fall. Initial Velocity (7400–11000 m/s) sets entry speed, from orbital to lunar-return. Ballistic β controls how much the capsule decelerates for a given density.
The ballistic coefficient β (in kg/m²) is mass divided by the product of drag coefficient and frontal area. A low β means a light, draggy capsule that slows high in thin air; a high β means a dense, streamlined body that penetrates deeper before decelerating, raising both peak heating and lower-altitude g-loads.
Heating uses a Sutton-Graves-style relation, where the stagnation-point heat rate scales with the square root of density times velocity cubed (√ρ × v³). The result is displayed in kW/cm² and drives the colour of the glowing trail. Heating peaks not at the highest altitude but where density and speed combine most aggressively, typically around 50–70 km.
Adding lift (a non-zero L/D) lets the capsule "fly" partway through the atmosphere rather than simply falling. Upward lift slows the rate of descent into dense air, stretching the deceleration over more time and distance. This lowers peak g-load and heating and is why crewed vehicles such as Apollo and the Space Shuttle used lifting re-entry.
The core relationships are physically faithful: exponential atmosphere, inverse-square gravity, the drag equation and a recognised heating scaling. It is a 2D point-mass model, so it omits 3D rotation, real gas chemistry, ablation and detailed aerodynamics. The figures are representative and educational rather than mission-grade engineering values.
If the entry angle is too shallow, the capsule's lift and the curve of its path carry it back above the 120 km interface while still climbing, so it leaves the sensible atmosphere and is flagged as a skip-out. Real missions sometimes use a controlled skip deliberately to extend range, but an unplanned skip can leave a crew stranded.
In the model the capsule is destroyed above roughly 80 g or 100 kW/cm². Real human crews tolerate far less: Apollo peaked near 6–7 g, and a steep ballistic abort can reach 8–10 g briefly. Heat shields are sized for the expected peak heat flux, so exceeding it implies burn-through.
Lunar-return capsules cross the interface near 11 km/s rather than the 7.8 km/s of low orbit. Because heating scales with velocity cubed, that higher speed raises peak heat flux dramatically. Apollo addressed this with a thick ablative heat shield and a precise shallow corridor, often using a skip or lift to manage the energy.