Reentry - A Theoretical Primer

[NathanKell]

First, let's define some terms. Ballistic Coefficient (BC) is the craft mass divided by the effective frontal area. It is basically a measure of how strongly drag slows you down--the higher your BC, the less influence drag will have on you, the lower your BC the faster you'll slow down. Think bullets (very high BC) vs rocks (medium BC--heavy, but lots of area) vs paper (very low BC flat-on, medium BC edge-on). Total heat load, Q, is the total amount of heat a given reentry will saddle you with. Peak heat flux, q", is the maximum heating rate you will suffer in a given reentry.

Your BC, combined with any lifting ability your craft has, will determine, for a entry angle and speed, what geometry the reentry will take. Your maximum q" will determine how low a periapsis (more or less interchangeable with entry angle) you can survive for a given entry speed. Your maximum Q will determine how long you can survive reentry (though remember that the lower you are, the more heat you'll get).

There's three ways to deal with heat: sink it, reradiate it, and use ablator. Everything radiates heat, proporitonal to its temperature^4, so some of the heat you take in will radiate back out. Everything has a thermal mass (your temperature doesn't immediately reach the temperature of the shockwave, it takes heat over time to raise temperature) so you can sink heat for a while. Heat shields have ablator.

For Kerbin reentries up to Munar-return velocity, reradiation and sinking is generally enough (there's a narrow corridor for a single-pass Munar reentry, although you can of course make multiple passes, there's no life-support-induced time limit). For faster reentries, you generally need a heat shield which (a) has a higher maximum temperature (i.e. you can suffer higher q" and the higher max temp means much higher reradiation potential) and (b) has ablator which is another way to shed heat.

Note that heat rate scales, roughly, with velocity³ * density^0.5, while drag is proportional to velocity² * density. This means that while a shallow reentry will have a low q", it may have a much higher Q than a steeper one. If you're better at reradiating heat (i.e. you can reach thermal equilibrium, where incoming heat == radiating-out heat), you want a shallow reentry. If you're not so good at it, or the reentry is too fast (too high a heat load) you'll need a steeper reentry, but not so steep that your q" goes above the maximum at which you can ablate/reradiate at max temperature (if you are at max temp and in flux > out flux, you blow up). BC is relevant here because, as should be intuitively obvious, the lower your BC, the faster you'll slow down, thus suffering less time at higher (hotter) velocity--and that compounds, due to the cube on velocity!

If you have lifting surfaces (or tilt your pod during descent to take advantage of body lift) you can fly a lifting reentry. This allows you to stay "artificially" high in the atmosphere. It also, depending on your roll angle, can let you steer your reentry, just like in an aeroplane. It's no different than gliding. If you're overshooting, roll inverted and increase your descent rate; if you're coming in to the left, roll right so lift pushes you right. Etc. However, lifting reentries--because they stay higher longer--do impose a higher heat load than ballistic ones, though a lower q". So make sure your craft can take the slow roast.

One other wrinkle: the blunter the bit that's facing the wind, the more likely you are to get a detached shockwave, rather than one attached to your forward-most part. That will greatly lower the shockwave temperature that you feel. For this reason, if you're flying a spaceplane, always come in bottom-first, not nose-first.

Practical examples:

Spaceplanes don't have ablator. That means you need to either sink the heat, or reach thermal equilibrium. Given the above regarding detached shockwaves, and the q" limit you have due to lack of ablator, you probably can't come in steep enough to survive just sinking the heat, so you need to fly a very shallow, lifting reentry that keeps q" low enough you can radiate the heat away.

Capsules from LKO don't have to worry much, as long as it's just a capsule. If you add on crew cabins or materials bays or whatever, then you do have to worry, because you've not changed your frontal area (it's still a circle of 1.25m or 2.5m diameter) but you've increased your mass, raising your ballistic coefficient.

Transmunar reentries are on the dividing line, at least for a reasonable-BC craft. You'll probably be OK without a heatshield if you are careful with periapsis, but shielding would help.

Interplanetary flight definitely needs heatshields. A simple chute + Mk1-2 pod + 2.5m heat shield can just barely survive an aerocapture/reentry to Eve at 5.5km/sec. If your BC is higher than that, or your velocity is, you won't be so lucky.

[hypervelocity]

this is great Nathan, it ties perfectly with my earlier queries, I am learning a lot here and who doesn't like learning?????

Many thanks!!! new information to introduce to my designs!!!!

[Norcalplanner]

Thanks for explaining what I had sorta figured out by trial and error in my current 3X scale game (where Kerbin orbital speed is around 4 km/sec).  I've found I use up less ablator with a 20 km periapsis reentry than a 40 km periapsis reentry with a typical capsule and heat shield combo.

[Rune]

I just found this out, and I approve of the informativeness. Just one thing to add: given enough control authority, spaceplanes have a variable BC. Go full prograde, and the plane will knife through the atmosphere, barely stopping at all and generating a completely unsurvivable q". But go in pointing normal, and the huge drag of the wings will make you stop so high up, the max temperature will be a joke and you'll be able to use parts with low temperature resistance. At intermediate angles, lift changes things completely, since as say you can fly a lifting reentry and dump the heat at your leisure, but the extreme case of ballistic reentry with wings acting as huge airbrakes is interesting enough to warrant a mention, the aerodynamics and thermodynamics being completely different. You "fly" like a capsule... only so high that you don't see anything heat up appreciably.

The comment about bow shock, though, is very interesting. Would you care to go through it in more detail? Because I find it a bit puzzling how KSP handles the foremost part presented to the airflow. Reentering rockets engine-bell first, for example, the engines get incredibly high heat fluxes, especially if they are clustered, but once they blow up the tanks immediately behind them see a much lower heat rate (I'm talking empty tanks, so no big thermal mass to dump stuff in). And if I flip around and go nose-first, I usually get much better results... that seems like it should be the other way around, for sure.

 

Rune. A "hidden" bow shock mechanic would explain so many things...

Edited February 17, 2016 by Rune
typos!

[NathanKell]

@Rune excellent points. The thing with engines is actually a bug in the aero model. The aero model can't tell whether a part is tapered like a cone or like a funnel, all it knows is the taper angle. So engines are very streamlined. >.> That means that they don't create a detached shock (the aero model says "not blunt") when they are the frontmost part and so they get higher shock temps.

[Gojira1000]

5 minutes ago, NathanKell said:

@Rune excellent points. The thing with engines is actually a bug in the aero model. The aero model can't tell whether a part is tapered like a cone or like a funnel, all it knows is the taper angle. So engines are very streamlined. >.> That means that they don't create a detached shock (the aero model says "not blunt") when they are the frontmost part and so they get higher shock temps.

Oho, that solves a long-time mystery for me, thanks to both @Rune and @NathanKell

[Skalou]

Nices explanations, amazing that you modeled it!

On 11/2/2016 at 7:06 PM, NathanKell said:

[...] if you're flying a spaceplane, always come in bottom-first, not nose-first.
 

I want an example of this kind of reentry!

But a fews questions remains (after reading the wikipedia: Bow shock ):

-can we have an idea of the shape of the shock cone, how can we detect it in game? it takes care of the shape of the parts, mach number or other things? ( i understand yes by reading your post but i'm not so sure to well understand)

maybe a drawing to better understand the differents situations?

 

[NathanKell]

For that kind of reentry, just imagine a space shuttle reentry like this:

Except tilted up even more so your angle of attack is about 90 degrees.

For attached/detached: sure, here's a pic:

 

In game it's like that; the shock angle is broadly similar for all detached shocks, but for attached ones varies heavily by mach number and part taper.

[Rune]

42 minutes ago, NathanKell said:

@Rune excellent points. The thing with engines is actually a bug in the aero model. The aero model can't tell whether a part is tapered like a cone or like a funnel, all it knows is the taper angle. So engines are very streamlined. >.> That means that they don't create a detached shock (the aero model says "not blunt") when they are the frontmost part and so they get higher shock temps.

That makes a lot of sense, thanks! More than that, it tells me how I have to design my tailsitters: so that the engines aren't the lowest part, and make sure the lowest part is as blunt as possible. At least until you get around to squashing this one...

 

Rune. Thanks for the clarification!

[Skalou]

oh thank's i missunderstood : i've read "engine first"

Direct Reentry from Duna with a MK1 cockpit (low max temperature), i needed to keep 90° +/-5° to don't explode it.

So is there a visual effect in game pr a mod that show when a part generate a detached shock cone instead of an attached one? or a way to know it (by looking the heat flux maybe)?

[HafCoJoe]

Very well written. For me this is the best explanation to why reentry works the way it does in KSP yet. Also the best explanation to why my orbiter has to reenter as shallow as it does. This is the kind of useful information that would be nice to have in stock reentry tutorials. An explanation as to why, as oppose to how. Thanks!

Edited February 18, 2016 by Avera9eJoe

[drewscriver]

Definitely great to know.  I've been struggling with overheating issues on Eve ascent, and that extra insight into the heating system is invaluable.  It's explained why the shielded docking port is so strong as a nosecone, so now I'm balancing tradeoffs.

Shielded docking port : less heating -> more efficient ascent path, but more drag

Pointier nosecones : less drag, but requires a less efficient ascent.