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What are the highest aerodynamic pressures encountered in any aircraft? And does this limit the maximum speed of any aircraft at certain altitudes? Broadly, 'how fast can you go [at a given altitude]?'

Where dynamic pressure $q$ is: $$q = \frac{1}{2} \rho v^2$$

$\rho$ is local air density, and $v$ is true airspeed.

I'm mostly concerned with high performance fighters/bombers. Here's some data I've culled (Mk-12A and 787 added for reference):

#   | Airframe      | Mach       | Speed     | Altitude    | q (kgf/m^2)
----|---------------|------------|-----------|-------------|------------
1.  | Mk-12A        | Mach  6.15 | 2,100 m/s |       0 ft  | 273,000
2.  | Mk-12A        | Mach 22.6  | 6,900 m/s | 100,000 ft  |  39,300
3.  | X-51A         | Mach  5.1  | 1,500 m/s |  64,000 ft  |  11,100
4.  | HTV-2         | Mach 20.   | 5,812 m/s | 125,000 ft? |  10,700
5.  | F-111         | Mach  1.2  |   410 m/s |       0 ft  |  10,400
6.  | B-1A          | Mach  1.2  |   410 m/s |       0 ft  |  10,400
7.  | B-1B          | Mach  0.9  |   310 m/s |       0 ft  |   6,100
8.  | X-43A         | Mach  9.6  | 3,000 m/s | 109,000 ft  |   4,800
9.  | Skylon        | Mach  5.5  | 1,630 m/s |  85,300 ft  |   4,600
10. | SR-72         | Mach  6    | 1,800 m/s |  90,000 ft? |   4,400
11. | Space Shuttle | Mach  1.3? |   400 m/s |  35,000 ft  |   3,200?
12. | XB-70         | Mach  3.0  |   880 m/s |  73,000 ft  |   2,500
13. | SR-71         | Mach  3.2  |   930 m/s |  78,740 ft  |   2,300
14. | Concorde      | Mach  2.0  |   600 m/s |  60,000 ft  |   2,100
15. | Boeing 787    | Mach   .85 |   250 m/s |  35,000 ft  |   1,200

Airframes #3, #4, and #5/6 are quite different from each other, so I'm surprised they share roughly the same max $Q$. Is 11,000 kgf/m^2 a common limit?

Note: All figures are for level flight except for the Mk-12A (reentry), Space Shuttle (ascent), and HTV-2 (glide).

  • [Mk-12A]: Current reentry vehicle for the Minuteman III ICBM, houses the W78 warhead (350 kT). Figures are for reentry.
  • [HTV-2]: Rocket glider.
  • [B-1B]: "[top speed] is limited by the need to avoid damage to its structure and air intakes," according to Wikipedia. The B-1B used less structural Titanium and a simpler fixed geometry inlet when the speed requirement was lowered from the B-1A.
  • [Skylon]: Obviously doesn't exist yet. Reaction Engines' "user manual" for the Skylon discusses the flight profile.
  • [SR-72]: Obviously doesn't exist yet. Lockheed Martin discussed Mach 6 cruise. 90,000 ft cruising altitude is just my placeholder value.
  • [Space Shuttle]: Figures for ascent.

Some background and purpose: For fun, I'm trying to design a hypersonic long-range heavy bomber. I was curious what would limit the maximum low/mid-altitude speed: drag (available engine thrust), max $Q$ (structural strength), or skin temperature (thermal protection system)... but I'll get to that in another question.

I've read through nearly all the aerodynamic, military, aircraft design, aircraft performance, and jet engine tags, looking for answers. (Really, this is a marvelous community.) Finally realized I could ask my own question.

I've tried to follow the etiquette as best as I can, but I'm pretty new to Stack Exchange, so let me know if I should change anything :) Thanks!

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    $\begingroup$ "For fun, I'm trying to design a hypersonic long-range heavy bomber" O_o $\endgroup$ – bjb568 Mar 2 '15 at 15:26
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    $\begingroup$ @bjb568 It's just a fun project to challenge myself and see how much I can get away with (I have about two weeks' worth of aerodynamics background). It's more of a design exercise than anything else. I assure you I'm not taking it that seriously! Did I mention it's powered by an aneutronic fusion reactor? :P $\endgroup$ – Hephaestus Aetnaean Mar 2 '15 at 17:04
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    $\begingroup$ You seem to be assuming that max Q is at cruise altitude and speed, but I'm not convinced of this. $\endgroup$ – raptortech97 Mar 2 '15 at 21:45
  • $\begingroup$ @raptortech97 Oh, not at all. But my design thrust is capable of pushing much higher speeds [than the airframe can handle]. Cruise speed is ~Mach 10 at 100,000ft =D. For q=11000kgf/m^2, I think max speed is Mach 1.2 at sea_level, Mach 2.5 at 40,000ft, and finally Mach 7.5 at 85,000ft, at which point [maybe] heating dominates and skin temperature becomes the limiting factor. Certainly $q$ dominates at low altitude, I just don't know how much... But really I'd love to be disabused of my ignorance, that's why I'm here. Speaking of which, how do I vote up a comment? $\endgroup$ – Hephaestus Aetnaean Mar 2 '15 at 22:11
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    $\begingroup$ Ehm...dynamic pressure is only $ \frac{1}{2} \rho V^2$ at speeds where compressibility issues can be neglected, about M 0.6. Above that, dynamic pressure becomes $ \frac{1}{2} \cdot \gamma \cdot p \cdot M^2 $ $\endgroup$ – Koyovis Jun 24 '17 at 2:20
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First, your example list doesn't distinguish between stationary and instationary trajectories. A reentry vehicle will see the highest dynamic pressure only momentarily at the end of its trip, and aerodynamic heating can be tolerated either by ablative cooling or a decently sized heat sink. All it has to sustain is the dynamic pressure at the tip.

The first samples on your list which need to continuously sustain the given dynamic pressure are the low-altitude attack aircraft B-1B and F-111. Here the dynamic pressure is given by wing loading, aerodynamics and raw thrust to keep the aircraft moving at its maximum speed. Aerodynamic heating comes on top at high altitude, because the stagnation point heat is independent of air density.

Reasons to limit the maximum dynamic pressure are:

  • gust loads at low altitude. Hitting the same updraft at higher speed will proportionally increase the load factor.
  • Aeroelastic deformation: Higher dynamic pressure means also higher torsional and bending loads, and the deformed structure might become unstable when the deformation increases the loads which lead to this deformation. Flying at higher dynamic pressure requires a stiffer and heavier structure.

If you look at the flight envelope of the SR-71 (below), it should be obvious that at each altitude only a narrow band of speed was available due to the high wing loading (= high minimum dynamic pressure) and the maximum dynamic pressure (at low altitude) rsp. the aerodynamic heating (at high altitude).

SR-71 flight envelope

SR-71 flight envelope (picture source)

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  • $\begingroup$ Thanks! I'll edit to clarify. I actually used that same chart to pick a top speed. I guess what I'm trying to ask is, "Roughly how fast can you go [at a given altitude] considering aerodynamic loads alone?" (I'll get to heating in a separate question.) I know that's a broad question (different designs, mass budget, what have you), which is why I didn't ask it. I'm trying to get a sense for a common upper bound on a fighter or high performance bomber. $\endgroup$ – Hephaestus Aetnaean Mar 2 '15 at 17:25
  • $\begingroup$ @HephaestusAetnaean: There is no real limit. Use low-aspect ratio wings of solid steel, and you can increase the maximum dynamic pressure a lot. If that is still not stiff enough, make the wings from diamond, or use a thicker airfoil. Practical limits are close to what you give in your list, which is about 100,000 N/m² or 1 bar. $\endgroup$ – Peter Kämpf Mar 4 '15 at 13:04
  • $\begingroup$ That's exactly what I was looking for. Thanks! I've actually read/skimmed through most of your answers, and they've been incredibly helpful. What do you do, if you don't mind me asking? And what do you use for your sources on aerodynamics? $\endgroup$ – Hephaestus Aetnaean Mar 6 '15 at 15:14
  • $\begingroup$ Oops. Forgot to accept and vote! Thanks again, Peter! $\endgroup$ – Hephaestus Aetnaean Mar 7 '15 at 20:06
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    $\begingroup$ @HephaestusAetnaean: What I do? Currently working on an IoT thingy. Have worked in aerospace for two decades and was too disgusted to continue. Corruption, vanity and idiocy were too much for me, even though I worked with many good people. $\endgroup$ – Peter Kämpf Mar 7 '15 at 21:11
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Used to be a fighter pilot in the F-111 and the F-105. They have the highest Q limit I have encountered or read about. (To us high speed on the deck) That limit is 810 knots/Mach 1.2 down low. Both aircraft could sustain that airspeed, I have personally done it in the F105 below sea level in Death Valley. Attached are the Technical order airspeed limits:

F105 Airspeed Limit

F111F Airspeed Limit

I do not believe the B-1B is capable of these speeds, there were all sorts of additional limits placed on it. Modern fighters are no longer designed for this regime.

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