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Once flying as (fast) glider in order to land, what was the angle of attack it would have stalled? I'm really interested in the angle of attack for such wings and not the speed.

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    $\begingroup$ Even if this question perfectly fits aviation SE, some people on space exploration SE surely have the data you need $\endgroup$ – qq jkztd Jan 26 at 12:44
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    $\begingroup$ @qqjkztd Although they may have good knowledge about all lots of things concerning the STS, especially all what makes it a rocket (SRB, tanks, engines, life support, reentry phase,...), I doubt they are concerned about AoA (which is a really specific aviation related thing). I may be wrong, I'll try asking there if I have no answer here within a reasonable time. $\endgroup$ – Manu H Jan 26 at 12:54
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    $\begingroup$ Related: aviation.stackexchange.com/a/23889/1379 $\endgroup$ – Řídící Jan 26 at 12:55
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    $\begingroup$ Just google "stalling AOA for Delta Wings" and you'll find what you need. They can operate to extreme AOAs without a break in the normal sense as the vortices made by the LE angle mitigate or prevent the flow separation it would normally suffer from. They just get draggier and draggier. $\endgroup$ – John K Jan 26 at 15:45
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    $\begingroup$ It depends on what you mean by "stall". In some definitions (eg. from the perspective of a pilot) delta wings may not have any stall angle. They just change glide angle vs AOA without ever losing control $\endgroup$ – slebetman Jan 27 at 1:56
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As far as I can tell, NASA has never given a straight-forward answer to this question. The theoretical stall AoA is likely in the 33-40° range (see reason for that guess below). However, at operational airspeeds, the orbiter becomes aerodynamically unstable at a lower angle of attack than the stall angle. Therefore, the stall angle never mattered for shuttle operations.

Just to be clear, this answer is only referring to the very late phases of shuttle flight (TAEM and approach and landing). The 40° of early entry might be beyond the wings' stall angle, but it doesn't really matter since dynamic pressure is low and the shuttle is on more of a ballistic trajectory.

What does NASA say?

From an old NASA answer to this question:

The question: "What is the Space Shuttle stall speed?" is a bit of a trick question because, as a delta wing aircraft, the Orbiter does not have a clearly defined stall point.

...

We have determined the minimum flyable speed based on the longitudinal stability characteristics. We start by evaluating the maximum angle of attack, alpha, for which the Orbiter is aerodynamically stable in the pitch axis. This is the angle of attack at which the pitching moment partial derivative with respect to alpha changes from negative (stable) to positive (unstable). This angle of attack is identified as the maximum usable angle of attack and it varies by Mach number.

From The Aerodynamic Challenges of the Design and Development of the Space Shuttle Orbiter document:

The low-speed longitudinal characteristics shown in figure 29 demonstrate stall-free characteristics over operating flight conditions.

Low-speed longitudinal characteristics

The diagram on the left shows that the lift coefficient continues to increase through at least ≈25° angle of attack (meaning the stall angle must be greater than 25°). δe = elevon deflection.

The only* reference to stalling in the Shuttle Crew Operations Manual is this diagram which depicts a stall speed (not angle). The NASA answer I referenced before gives more context to this graph.

Acceleration Limits
Shuttle Crew Operations Manual - Section 4.9-1

*There are a couple references to elevon stalls in the Operations Manual, but I'm not counting those.

Why does the stall angle not matter?

As we've already seen, the shuttle would exceed aerodynamic/structural limits before reaching the stall angle of attack at most airspeeds. Additionally, there are a couple other reasons for not worrying much about the stall angle.

Guidance always aimed to keep the orbiter on the "front side" of the L/D curve. This means that guidance would never command an angle of attack higher than required for "best glide". If it needed to dump energy, it would do so by deploying the speed brake and/or pitching nose down. It would never dump energy by pitching up (except during the flare). If the orbiter was low on energy, it would pitch for best glide. This means airspeed would always stay high and in the range where other factors are more limiting than the stall angle. Pitch-up maneuvers would be limited by dynamic pressure and Nz (normal acceleration — g's).

The only time the shuttle fell into the "back side" of the L/D curve was during the flare and landing. Incidentally, touchdown speed appears to be roughly the speed where the orbiter is finally slow enough that it might actually stall before becoming unstable for other reasons (see "VA" in the graph above - this is "maneuvering speed", just like in airplanes). However, at touchdown, the limiting angle is the tailscrape angle (15°), which is much lower than the stall angle.

Tailscrape diagram
Shuttle Crew Operations Manual - Section 7.4-17

What's the real answer?

Although not operationally significant, I think the specific question you're trying to ask is: what AoA produces the maximum lift coefficient? Generally speaking, that's considered the stall angle for most airfoils, since increasing AoA beyond that point results in decreased lift.

While I don't have a lift coefficient graph for the shuttle which goes beyond 25°, this paper discusses the results from studies on various delta and double-delta wing designs.

Lift coefficients of delta wings

None of the studied designs have the shuttle's exact 81/45 sweep angles. However, given that they all have a maximum lift coefficient somewhere in the 33-40° AoA range, I suspect the shuttle was similar. I can't prove that unless someone finds the appropriate data. I'm certainly not an expert on delta wings, so my interpretation could also be wrong.

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    $\begingroup$ Great, well sourced answer. $\endgroup$ – Organic Marble Jan 27 at 5:24
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    $\begingroup$ @OrganicMarble coming from you, that means a lot! :) $\endgroup$ – Bret Copeland Jan 27 at 7:26
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    $\begingroup$ The definition of stall given in how it flies is exactly the one you use in the last section. i'm tempted to consider it as a valid and consensual definition of stall. $\endgroup$ – Manu H Jan 27 at 15:59
  • $\begingroup$ I would expect that the shuttle would lose directional stability long before reaching its maximum AoA. $\endgroup$ – Peter Kämpf Jan 28 at 3:51

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