# What is the AeroVironment Helios' Kármán line?

If it's true that the NASA/AeroVironment Helios maintained level flight 96,000 ft above sea level at a maximum airspeed of 23.5 kts (43.5 km/h) I assume it must have a very high Kármán altitude, the altitude at which it would have to fly at orbital velocity (15,100 kts) in order not to stall. By contrast the SR-71 Blackbird e.g. couldn't even fly at 23.5 kts near sea level. Is there a way to figure out the Helios' Kármán line, or any plane's for that matter? Known is only that of the X-2 which is 57 mi (91.7 km) according to Von Kármán's calculations himself. The X-2 flew at 2,000 mph (3,200 km/h or 1,740 kts).

• Related Feb 28 at 16:46
• This really looks like a better fit for Space.SE, to my mind. Feb 28 at 20:36
• This shouldn't move to Space.SE because it's about aerodynamics: how thin must air be for Helios to need 15,100 knots to get enough lift to support itself; then, how high that is. This may be for a fictional Helios, though, because its solar panels might not give enough power, and its propellers might fall apart at that many RPM. Feb 28 at 20:50
• I’ve always felt that the principle of the Kármán line is somewhat flawed; at orbital velocity an object can maintain altitude without any aerodynamic life at all, so a little below this speed it would need to generate only a small amount of lift. My understanding of the Kármán line principle is that this is the altitude at which an aircraft couldn’t generate enough lift to support its stationary weight, which of course it wouldn’t need to when moving at best-orbital speed. In the case of Helios the situation is rather clearer cut, since the aircraft travels at a speed far below orbital.
– Frog
Mar 1 at 6:22
• Mach Limited Airframe. Mar 3 at 17:00

There are no different Karman lines between the two aircraft. The Karman line starts at ~62 miles (327,362 ft) above MSL, an altitude neither aircraft can attain. In addition the Aerovironment Helios had a wing loading of 0.69 lbf/ft^2 whereas the Blackbird’s wing loading is 84 lbf/ft^2. As such, I’m not surprised at all that a Blackbird cannot maintain level flight at 23 KIAS but a Helios can.

• The 62 miles are actually a rounding of the FAI's 100 km (62.14 mi / 328,100 ft) line which they established as "the" Kármán line. In fact, the line is different for each aircraft and varies by other factors as well. Von Kármán himself determined 91.7 km (57 mi) for the X-2 as stated. These are theoretical values because it's clear no plane can fly horizontally at those altitudes, only the Space Shuttle and the Buran could during reentry. Mar 2 at 6:29
• @Betternottell No, the line is not different for each aircraft. Check the wiki: "The Kármán line (or von Karman line) is an attempt to define a boundary between Earth's atmosphere and outer space". Further along in the article one can read that he used the X-2 to illustrate an example of division of lift & Kepler force. He did not state that the calculation was specific to the X-2 only, it is indeed a singular line for all aircraft. Mar 3 at 1:58
• @Betternottell Eh - no. As can be clearly distilled from any article on this topic. Mar 3 at 8:01
• @Betternottell, your last two comments appear to be diametrically opposed… Mar 4 at 16:15
• Do you have a reference for your claim that it depends on stall speed? Because I’m new to the term, but that doesn’t mesh with common sense in context with the definition I have read. And there are people here whose answers I respect who disagree with you… Mar 5 at 5:40

The limitations of winged aircraft are far below the Karman line due to far lower air density and wastefulness of carrying the weight of a wing to those altitudes, in addition to practical sustained propulsion issues.

Lift = Density × Area × Lift coefficient × Velocity$$^2$$

Holding Area and Lift coefficient constant (to best Angle of Attack), a rough comparison of density to velocity$$^2$$ to generate Lift = Weight for various altitudes becomes possible.

Velocity$$^2$$ = k/Density

Since the IAS of Helios is known, let's plug in some density and velocity numbers, starting with sea level density.

Sea level: 23 knots$$^2$$ (TAS) = 12574/23.77 (IAS = TAS)

10000 feet: 27 knots$$^2$$ = 12574/17.56

50000 feet: 59 knots$$^2$$ = 12574/3.64

150000 feet: 583 knots$$^2$$ = 12574/0.037

250000 feet: 4398 knots$$^2$$ = 12574/0.00065

Although it might be tempting to think at a very high altitude one might need only a little lift, the thought goes by the wayside when one realizes most of thrust in very high speed flight is involved with overcoming drag. At 4000+ knots, as the X-15 did, while still in the atmosphere, a great amount of heat is produced, much like a meteor. Better to get above this and follow a suborbital ballistic path.

Amazingly, above most of the atmosphere, all objects will have a very similar Karman line altitude, because at those altitudes aerodynamic forces are very small, and speeds required to produce them approach orbital velocity (in theory). However, the exact point where "space" begins is debatable, as satellites in higher orbit still experience significant atmospheric drag$$^1$$.

To get anywheres close to the Karman line, the aircraft must overcome the sonic and thermal "barriers" if it hopes to survive for long. Helios did neither, but did a fine job with a subsonic True airspeed.

$$^1$$ see Karman reference under Alternatives to the FAI definition

• What do you mean "above this"? If you're high enough / far enough from Earth air is too thin to cause heating. A suborbital ballistic path is any parabola whose perigee is within the Earth. Where do you have it from that the Helios' true airspeed is 400 kts; wouldn't Wikipedia mention that? You're above most of the atmosphere when you're above 18,000 ft (5.5 km) MSL btw but you actually mean mesosphere / lower thermosphere altitudes. Mar 2 at 6:23
• @Betternottell well, you're right, it need not be sub-orbital, it could be orbital, or going to Mars. But the notion aircraft had any business doing this does not match the physics of lifting flight. The Karman line is theoretical, extrapolated from a few (very dangerous) X-2 flights that didn't even come close in the 1950s. At the altitude it did fly, it was barely controllable. The X-15 did reach 100 km, but required rocket thrusters for control. Helios TAS is easily derived using TAS calculator on the net. Google it. Mar 2 at 11:27
• I know, but why do you think Wikipedia would mention IAS at record altitude only? If it mentions the maximum airspeed, then it would include sea level speeds probably, where IAS is the same as TAS. I mean the Helios ground-launched (near sea level), not mid-air. Mar 2 at 16:50
• @Betternottell it is somewhat dramatic to highlight its IAS, especially since NASA was into many wing mounted solar electric props (which greatly helped the sustained propulsion issue at those altitudes). Really an amazing aircraft (yet another lost flown on a windy day!). Mar 2 at 17:06

Pic from the wiki

The Helios is a slow moving aeroplane, while considerations regarding the Karman line are about very fast moving aeroplanes. From this link:

...the Karman line is determined by calculating at what elevation the Earth’s atmosphere becomes too weak to support flight. At the Karman line, the atmosphere is too thin to support flight, and the plane must go fast to stay aloft. The Karman line is situated above the Homopause, and above this point, the atmospheric gasses are not well-mixed.

So the Karman line is the line of orbital velocity where very little to no lift force is contributed by aerodynamics. Orbital velocities are very high, and high speed is not something that the Helios is capable of, it can remain aloft by aerodynamic lift only. Discussions about Helios and Kármán line are incompatible.

The orbital velocity at any altitude of any aeroplane or circulating object is purely a function of its maximum speed. Considering a simplistic situation (homogenous spherical earth etc.) in the above pic, the centrifugal force F$$_c$$ must be equal to gravitational force F$$_g$$:

$$F_c = \frac{m \cdot V^2}{r} = \frac{m \cdot V^2}{R + h}$$

$$F_g = m \cdot g_h = m \cdot g_0 \cdot \left( \frac{R}{R+h} \right)^2$$

With $$R$$ = earth radius, $$h$$ = altitude, $$g_h$$ = gravity at altitude

Equaling the two equations, and computing for several altitudes, results in:

There is no aeroplane that can fly that fast, not even the SR-71 or the X-2 which only reached about 1,000 m/s @ 24,000 m. They require aerodynamic lift!

So the Kármán line is not aeroplane dependent, it is the boundary where aerodynamic flight is not possible anymore by any aeroplane. From this site:

The Kármán line is based on physical reality in the sense that it roughly marks the altitude where traditional aircraft can no longer effectively fly. Anything traveling above the Kármán line needs a propulsion system that doesn’t rely on lift generated by Earth’s atmosphere — the air is simply too thin that high up. In other words, the Kármán line is where the physical laws governing a craft's ability to fly shift.

• Did you think I thought the Helios or the SR-71 can enter an orbit? I wrote "would have to", not "has to". I'm asking on the altitude at which it would have to reach orbital velocity, something the Helios isn't capable of. Mar 1 at 6:20
• @Betternottell Neither is the X-2. It was only used as an example to illustrate. Mar 3 at 2:02
• That's right, I'm doing the same here so don't claim I would think they can reach orbit. Mar 3 at 6:42
• @Koyovis it may be that Helios max altitude may have been limited by it Power available, as the wing may have been able to cruise a little higher while staying under Mach. Hope they build another one. Mar 3 at 16:34