I was looking online for a profile depicting the Dragon re-entry similar to those showing the launch and first stage re-entry (e.g. https://www.elonx.net/wp-content/uploads/profile_Inspiration4_Infographic_EN.png) but could not find anything.
Ideally that chart would contain time, velocity and altitude information for the different phases of the re-entry.
Is something like that online? (If this has been asked and answered already feel free to flag as dup, but I didn't see anything.)
In lieu of authoritative data there is always homebrew simulation.
The necessary details about Crew Dragon & its entry, short of aerodynamics, are relatively easy to find:
| Parameter | Value | Justification |
|---|---|---|
| Final Orbit | 418 km x 22 km | curve fit of altitude callouts from Demo-2 splashdown livestream |
| Cross-Sectional Area | 12.6 $m^2$ | 4 m diameter circular cross-section via SpaceX |
| Entry Mass | 9,615 kg | item 4 of Top 10 Things to Know for NASA’s SpaceX Demo-2 Return |
| Orbital Inclination | 51.6° | inclination of ISS |
Critical aerodynamic parameters are the drag coefficient, $C_d$, and the lift to drag ratio, $L/D$. While in general a function of Mach number, these values are (pretty much) invariant in the hypersonic regime (Mach >= 5) and are therefore treated as constant in this simulation.
I was able to infer a drag coefficient from the abstract of A. A. Gonzales et al., "Mars Sample Return using commercial capabilities: Mission architecture overview" and its associated presentation focusing on EDL.
From abstract:
Total entry masses between 7 and 10 mt were considered
Plot from presentation:
Where $\beta$ is the ballistic coefficient $\beta=\frac{m}{C_D S}$:
| Area, S ($m^2$) | Mass (kg) | $\beta$ ($kg/m^2$) | $C_D$ |
|---|---|---|---|
| 12.6 | 7,000 | 450 | 1.24 |
| 12.6 | 10,000 | 650 | 1.22 |
Thus $C_D=1.23$ (and $\beta=622$ $kg/m^2$).
The $L/D$ is dependent on the axial displacement of the center of mass of the vehicle (which determines the trim angle of attack) and is configurable prior to entry/flight (I believe Apollo experimented with this in test flights; see $L/D$ differences in flight data from AS-202 & Apollo 4).
The value used in the plot, 0.27, is definitely plausible; however, it is higher than other low-Earth orbit crewed entry capsules (Soyuz: 0.26, Dragon 1: 0.18, Gemini: ~0.15, Mercury: 0, ballistic). I used $L/D$ as a fudge factor to make the maximum inertial loading (g-force) about 4.2 g's as described by Demo-2 astronaut Bob Behnken. Here is a plot of the (significant) variation of some entry stats based on differing $L/D$ values, with 0.13 being the selected value:
With all of that out of the way, here is a selection of figures from the simulation (please comment what others you wish to see):
Entry Setup:
Note I have defined entry interface at 120 km (extremes of my atmospheric model), in reality this is sometimes a dynamically sensed condition (g-detect) so the duration may seem a little long (click to enlarge):
References:
notto be rocket science to find that out if you are able to start an icbm with a nuke but yeah. All the pesky differentiation and integration, angles and stuff, it's really not everybody's cup of tea. – Peter - Reinstate Monica Sep 20 '21 at 14:04