Compare Apollo, Shuttle, and Starship reentry profiles. Tune entry velocity, angle, ballistic coefficient, and nose radius to explore peak g-load, heat flux, and wall temperature.
$\rho(h) = \rho_0 e^{-h/H}$ (H=7 km)
$\dot{q}\approx C_h \rho^{0.5}V^3 R_n^{-0.5}$
Equilibrium wall temp: $\varepsilon\sigma T_w^4 = \dot{q}$
The simulator uses a simplified exponential atmosphere model. Air density drops off exponentially with altitude, which is a good approximation for calculating the peak heating during the critical phase of reentry.
$$\rho(h) = \rho_0 e^{-h/H}$$Here, $\rho$ is the air density at altitude $h$, $\rho_0$ is the sea-level density (approx. 1.225 kg/m³), and $H$ is the scale height (about 7 km for Earth). This model lets us estimate how quickly a vehicle encounters thick air.
The core equation for convective heat flux at the stagnation point (the hottest spot on the nose) is derived from hypersonic theory. It shows the dramatic influence of velocity and the benefit of a blunt shape.
$$\dot{q}\approx C_h \rho^{0.5}V^3 R_n^{-0.5}$$$\dot{q}$ is the heat flux (W/m²), $C_h$ is a heating coefficient, $\rho$ is local air density, $V$ is velocity, and $R_n$ is the nose radius. Note the $V^3$ term—doubling speed increases heating eightfold! The $R_n^{-0.5}$ term confirms that a larger, blunter radius reduces peak heating.
Apollo Command Module Design: The capsule's blunt, bowl-like shape was chosen specifically to manage the extreme heat of lunar return at about 11 km/s. Its high ballistic coefficient (β) meant a short, intense deceleration and heating pulse, which the ablative heat shield could handle by charring and eroding away.
Space Shuttle Thermal Protection System: The Shuttle's low ballistic coefficient allowed a slower, gentler descent, but its sharp leading edges needed incredibly robust materials. The reinforced carbon-carbon (RCC) on the nose and wing leading edges had high emissivity to radiate the sustained heat load during its long glide through the upper atmosphere.
Modern Starship Reentry: SpaceX's Starship faces a unique challenge: returning from Mars or the Moon at high velocity while being large and reusable. Its stainless steel construction relies on high emissivity and possibly transpiration cooling. Engineers use tools like this simulator to trade off entry angle, velocity, and material properties to find a survivable flight path.
Hypersonic Vehicle Testing: Before any flight, CAE (Computer-Aided Engineering) tools run thousands of simulations using these fundamental equations to predict heating environments. This guides the placement of thermal protection tiles and the design of test articles for wind tunnels, saving immense cost and risk.
There are a few key points you should be especially mindful of when starting to use this tool. First, a location with high heat flux does not necessarily mean it's the hottest spot on the vehicle. It's true that an intense heat flux acts on the nose tip. However, while the "intensity" of heat flowing in is the heat flux, the actual temperature a part reaches is determined by its material's heat capacity and how easily it can dissipate heat (thermal conductivity). For example, a structure that experiences high heat flux but can quickly conduct heat internally or shed it to the rear can keep the surface temperature surprisingly low. Conversely, with highly insulating materials, heat can build up, causing temperatures to rise steadily and potentially damaging internal equipment. Remember, the simulator's "equilibrium wall temperature" is merely a theoretical value for "a state where, after sufficient time has passed, the incoming heat and the heat radiated away are balanced."
Next, a pitfall in parameter settings: "Velocity" and "Altitude" are not independent variables. In an actual re-entry, velocity drops sharply due to atmospheric drag as altitude decreases. For simplicity, this tool calculates based on the "conditions" at a single instant you input, but in practice, "trajectory calculation," which tracks changes over time throughout the entire "flight path," is essential. For instance, the atmospheric density differs by over 100 times between a state at 70 km altitude at 7 km/s and one at 40 km altitude at 7 km/s, resulting in completely different heat flux values. When experimenting with the tool, get into the habit of considering realistic combinations of altitude and velocity. For example, starting with the initial values of the "Apollo" preset (120 km altitude, 11 km/s velocity) is recommended.
Finally, note that this calculation is a "local" evaluation. The temperature distribution across the entire vehicle or how heat propagates through the internal structure (thermal conduction analysis) is the domain of more complex CAE software (Conjugate Heat Transfer: CHT). Think of this tool as a "screening" tool for the first step in TPS (Thermal Protection System) design, used to identify "which parts of the vehicle are thermally most severe."
Apollo Command Module reentry: velocity 11 km/s, flight path angle −6.5°, nose radius 1.2 m, ballistic coefficient 60 kg/m². Simulation yields peak g-load 6.8 g, peak heat flux 8.4 MW/m² at 68 km altitude, stagnation wall temperature 3180 K, total heat load 2.1 MJ/m². Space Shuttle peak heating occurred at Mach 15–18 (8.2 km/s), generating 12.2 MW/m² with wall temperatures near 1645 K on leading edges and 1260 K on fuselage.