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Let's assume a reentry craft designed to not use heat protection like Soyuz or the Space Shuttle, and budget is not an issue. The Concorde max surface temperature was 400 K, so let's use this as a max temperature for our craft as well.

Let's also assume that size and shape of the orbiting craft is no problem, though mass still is. It can have inflatable or unfolding aerogel wings like an atmospheric satellite, or some other technique, in order to have a wingspan as wide as necessary without adding too much mass.

The craft is designed to spend as much time as possible in the extreme high atmosphere, in order to slow down at a rate low enough that heat load can be dealt with simply by radiating it away (I doubt ambient air would be much good to carry heat away at those altitudes and speeds). As such, as it is slowing down, it must use lift for staying high enough, and use control surfaces for attitude control if possible.

Ideally, it would slow down to low supersonic or even subsonic speed before reaching a part of the atmosphere where heating is a problem, then fly like a plane or a glider. If possible, let's ignore what exactly happens after that point.

What characteristics would such a craft need? What lift-to-drag ratio, radiative surface area and general shape would it have? What would be its flight path?

I hesitated between here and Aviation SE, but there are already related questions here:

Gliding into the atmosphere is more about attempting it with a Cessna instead of a purpose-built craft.

Challenging Karman line from above is leaving aside the question of heat, with a hypothetically heat-resistant glider

Can a reentry be done slowly? is a more general question about shallower reentry

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    $\begingroup$ "Ideally, it would slow down to low supersonic or even subsonic speed before reaching a part of the atmosphere where heating is a problem" -- unfortunately, moving at low speeds outside of the atmosphere means falling. You can't get enough lift to stay up unless you've got enough atmosphere for heating to be a problem. $\endgroup$ – Russell Borogove Oct 23 '18 at 19:03
  • $\begingroup$ I second @RussellBorogove 's objection. That sentence he quoted is the crux of the problem. I think all the facts in Phil H's answer to the Cessna question explain why this isn't going to work. In fact, I think this question is basically a duplicate of that one. You must get rid of your orbital energy. $\endgroup$ – Organic Marble Oct 23 '18 at 21:12
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    $\begingroup$ @Hobbes ...which leads us back to the Kármán line, loath as I am to mention it here right now. $\endgroup$ – Russell Borogove Oct 23 '18 at 21:29
  • $\begingroup$ This question is also similar but not a duplicate Could you take a Cessna from the ISS to Earth? $\endgroup$ – uhoh Oct 23 '18 at 23:56
  • $\begingroup$ Are you talking about no heat shields or an internal cooling is allowed and can be a Thermal protection used for the aircraft. Because that would work and we'd be using a cooling system internally to combat the high heating associated with re entry and a shallow enough re entry should allow for a moderate heat loss rate and may need a few skips in order to lose energy sufficiently to land, but hypothetically possible, $\endgroup$ – Rajath Pai Oct 24 '18 at 2:59
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If you want to minimize heating, you need to spend time at high altitudes (>100 km) gradually losing speed. This means you need wings to provide lift. So for now I'm going to ignore the heating issue and just look at what kind of wing you'd need.

This question arrives at a wing loading of 20 kg/m2 for an aircraft that can fly at 100 km altitude at ~8 km/s.

You're also slowing down from 8 km/s to an aluminium-survivable 600 m/s. Since lift depends on v2, your lift drops by a factor of 177 slowing down that much. So we go from 20 kg/m2 to 0.11 kg/m2 of wing loading.

  • a sheet of aluminium 1 mm thick and 1 m2 area weighs 2.7 kg, and you need two to make the wing surfaces. We're already over the limit for our low-speed-capable wing.
  • the only wings in the 0.11 kg/m2 bracket are superlight wings for model airplanes: a thin balsa wood frame with rice paper surfaces. These models barely withstand slow flight at ground level, I see no way to scale this for orbital flight.

  • let's say the wing structure adds another 5 kg in structure. This is enough for the ribs, but the main spar is probably a lot heavier than that. I don't know how to estimate spar weight, so let's ignore it for now.

We're already at 10 kg/m2 and we only have the bare wing structure.

  • if our aircraft fuselage weighs 7 tons (the weight of a Soyuz capsule), at 20 kg/m2 that's 700 m2 of wing, or 70x10 m of wing area. So even a small capsule gets a wing the size of a Boeing 747.

I suspect a wing that large will be a lot heavier than 20 kg/m2 in order not to collapse.

Sailplanes have the lowest wing loadings in use today (except microlights, but their structure is definitely unsuitable) at 60 kg/m2, that gives a lower limit to what's physically possible.

A Boeing 747-8 has an empty weight of 220 tons and 554 m2 wing area. If the wing constitutes 40% of total empty weight, that's 88 tons, or 158 kg/m2 of structural weight.

From this I conclude it's impossible to build a wing large enough to support flight at 8 km/s an altitude of 100 km. Slowing down to 600 m/s (Mach 2) to get below the safe limits for aluminium is even more impossible.

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  • $\begingroup$ These wing should work for an extremly wide range of velocities from hypersonic to subsonic and for a very wide range of pressure from nearly vacuum at 100 km height to full atmospheric pressure at ground. $\endgroup$ – Uwe Oct 24 '18 at 8:58
  • $\begingroup$ This is half of a great answer, but the question is precisely about what happens when trying to keep heat low enough. For the sake of the question, we can leave aside the problems of excessively light wingload: using a smaller craft, a smaller payload fraction or even ultralight materials... there are at least theoretical ways to keep it low enough. Sure, a manned glider is cooler, but a cubesat with wings will do. The problem is, what would its descent profile be? What would such a craft look like? $\endgroup$ – Eth Oct 24 '18 at 10:55
  • $\begingroup$ @Uwe Worst case, once slow enough the payload is dropped and uses some other means, like for example a parachute. It would be nice for the wings to work at all speed and pressure ranges, but not required by the question. $\endgroup$ – Eth Oct 24 '18 at 10:58
  • $\begingroup$ I've added some more detail on 'what happens when trying to keep heat low enough'. $\endgroup$ – Hobbes Oct 24 '18 at 12:13
  • $\begingroup$ I'm not actually convinced we need a stiff, metal-based wing at all. As long as the wing load is low, we could use any material. (Not saying this is viable, but it should be included in the discussion) $\endgroup$ – asdfex Oct 24 '18 at 12:23
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It can be done like they did it for some of the Mars lander. It requires a highly eccentric orbit. According to this Wiki article about aerobraking.

You dip into the upper atmosphere at each periapsis (low point in orbit). This will slow the craft fractionally (and allow the craft to radiate the small amount of heat built up), lowering the apoapsis (high point of the orbit).

This can slow you down enough to reach non-destructive air speeds.

However, you better not be in a hurry. It took about six months to brake the Mars lander.

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    $\begingroup$ This doesn't help the Earth reentry situation much. It can get you from lunar or interplanetary orbit speed (~10-11km/s) down to circular low orbit speed (~8km/s) (at the cost of spending a lot of time) but then you're still faced with the usual reentry scenario from LEO. $\endgroup$ – Russell Borogove Oct 23 '18 at 19:00

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