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First post to this site, and I've got at most a high school background in physics - I really appreciate any answer, but I may not be able to follow you if you're too advanced.

I suppose this goes for regular planes too, but I'm especially interested in supersonic planes.

I read some reports in the news about various people working on commercial supersonic travel, but there were a lot of comments attached to these news posts listing essentially what were physics constraints that would make such travel severely cost ineffective:

  1. "skin friction," causing high heat and stress, leading to different metaled (thus more expensively researched/manufactured) and heavier (thus less efficient) airplanes.
  2. increased drag, requiring more fuel to overcome.
  3. sonic booms.

I'll leave alone sonic booms - I understand as well as I can why this could be hard to engineer around, and why various countries have made generating them over land illegal.

The other two I don't get. After spending some time on wikipedia this evening, if I've got this right, it seems that, holding the shape of the airplane constant, skin friction, lift, and drag are each equal to a scalar times density times velocity squared.

Density drops as the altitude raises, which seems to mean to me that you could keep drag, lift, and skin friction constant when increasing speed by merely increasing altitude.

I assume this is right, so I guessed that the "gas mileage" issue had to do with needing to burn too much more gas to achieve thrust required for the higher velocity. And yet, the wikipedia article on jet engines states that the concorde was actually more fuel efficient than some conventional subsonic turbofan engines used in 747's.

Given all this, what did I get wrong? Why can't supersonic planes just fly higher to be as cost effective, or more, than conventional subsonic commercial jetliners, using the same construction materials? Relatedly, why do current jets have service ceilings and max speeds (assuming it's not just about the high stress of breaking through the sound barrier)?

Thanks!

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If there's no density at all, then a jet engine doesn't work. That's why spaceships, for example, have to carry all the mass they need for propulsion. –  Lagerbaer May 14 '13 at 6:38
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To echo Lagerbaer, it's all about oxygen density. To burn the fuel the jet engine needs oxygen but too much oxygen means drag and "skin friction". There is some optimal trade-off height that is dependent of the oxygen needs and drag coefficient of each plane. –  Brandon Enright May 14 '13 at 7:24
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The heat is not just skin friction. Where the air hits a forward-facing surface it has to stop, which compresses it, which makes it very hot (stagnation temperature). Even if it's very low density, it still gets very hot. That's what spacecraft re-entry is all about. –  Mike Dunlavey May 14 '13 at 12:36
    
Conventional subsonic aircraft have to contend with the coffin corner. –  Mike Dunlavey May 14 '13 at 12:38
    
remember that the "formula" for lift is also only an approximation. As speed increases you do increase lift for a short time, but at a high enough speed, the wings become unable to produce lift because of decreased laminar flow and increased turbulent flow; the plane essentially stalls due to overspeed. If you design the wings to compensate for that, you can still stall from overspeed because at low pressure and high speed, the pressure differential between the top and bottom of the wings is too low to sustain any lift. –  Jim May 14 '13 at 14:05
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2 Answers

up vote 13 down vote accepted

There are lots of questions here that I will try to answer, hopefully I'll get to them all...

Creature Comforts

It's hard to "just fly higher" when you consider passenger planes. Supersonic military aircraft like the SR-71 do fly ridiculously high. It's service ceiling is 85,000 feet! But, it has the advantage that it doesn't need to keep anybody but the pilot comfortable. The issue deals with pressurization. As you increase altitude, the aircraft must also be able to withstand a larger pressure differential if the cabin will be kept at a comfortable pressure. Most very high altitude military aircraft do not pressurize the cabin; rather, the pilot wears a pressure suit. Imagine if you had to suit up for a flight to visit relatives!

It's not that we can't build a plane that can withstand the pressure difference, but doing so would require very heavy or very expensive materials. The former makes it much harder to fly while the latter makes it not very commercially viable.

Increased Drag

There's a reason going past the speed of sound was called "breaking the sound barrier." There is a magic number called the Drag Divergence Mach Number (Mach number is the fraction of the speed of sound at which you are traveling). Beyond this number, the drag increases tremendously until you are supersonic, at which point it decreases quite rapidly (but is still higher than subsonic).

Therein lies one of the biggest problems. You need very powerful engines to break the barrier, but then they don't need to be very powerful on the other side of it. So it's inefficient from a weight/cost standpoint because the engines are so over-engineered at cruise conditions (note: this does not imply the engines are inefficient on their own).

Increased Heat

There's no denying that it will get hot. It is storied that the SR-71 would get so hot and the metal would expand so much, that when it was fully fueled on the runway, the fuel would leak out of the gaps in the skin. The plane would have to take off, fly supersonic to heat the skin enough to close the gaps in the metal, then be refueled mid-air again because it used it all up. Then it would go about it's mission.

At the Mach numbers for a commercial aircraft, the heating would not be as extreme. But it would require some careful engineering, which makes it more expensive.

So why can't it just fly higher?

Ignoring international law for a moment, there's several reasons why flying higher just isn't as viable:

  1. Cabin pressure issues
  2. Emergency procedures: Let's assume for a moment we could pressurize the cabin. In the event it loses pressure, what do we do? The normal procedure would be to dive down to a safe altitude, that takes considerably longer from 60,000 feet than 30,000 feet.
  3. Drag is proportional to density, but so is lift. This means to fly higher, an aircraft needs bigger wings. But bigger wings mean more drag, so it gets into a vicious cycle. There is a sweet-spot that can be optimized for an ideal balance, but that means that "just go higher" may not be a good option.

Ceilings and Speeds

This one doesn't have to do entirely with legal issues, but that's part of it. A service ceiling is defined as the maximum altitude at which the aircraft can operate and maintain a specified rate of climb. This is entirely imposed by the aircraft design (laws may require a minimum ceiling, but not a maximum... although they may restrict a plane from flying at the maximum).

Likewise, an absolute ceiling is the altitude at which the aircraft can maintain level flight at maximum thrust. Naturally, as the plane burns fuel and becomes lighter, it needs less lift to stay at the same altitude. But the lift force is based solely on the geometry and speed, so actual lift will exceed what is needed and the plane will climb. As it climbs, the air density drops and so does lift. This means as the plane flies, it's absolute ceiling actually increases.

Now for the speeds... Commercial aircraft fly as close as they can to the Drag Divergence Mach Number because it's the most economic point to fly. The plane goes as fast as it can go without the drag coefficient increasing tremendously. This is usually around Mach 0.8. But they can, and often do, go faster than that.

It's not unusual for an airplane that is delayed taking off to land on time or even early. This happens because they can still go faster than they normally operate (not significantly of course, perhaps Mach 0.83-0.85). It may cost some more fuel because the drag coefficient is likely increasing as it approaches Mach 1, but a delayed plane is more expensive for the airline than the extra fuel used (maybe not in direct dollars, but in PR, reputation, etc.)

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Now there's an awesome, detailed answer! –  Chris White Jul 6 '13 at 5:15
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The Concorde heated and expanded so much in flight that everything on it was warm to the touch and a sizeable hole would open up between a control console and the cockpit bulkhead wall. It became a custom amongst the pilots of them in later years that, in the plane's last flight, the captain would put his / her hat into the hole so that it would be squashed there and become part of the plane when it landed. –  WetSavannaAnimal aka Rod Vance Jul 6 '13 at 12:17
    
^this. And Concorde could fly to FL 690 at a slow rate of climb. However, you must keep in mind that Concorde's airframe was cooled by using the fuel in the fuel tanks as a heatsink. I doubt the SR-71 had fuel tanks large enough to act as efficient heatsinks. It's also interesting to note that at the time of introduction, Concorde's cabin pressure was one of the highest among commercial airliners at a pressure equivalent to just 6000 feet ASML, compared to the industry standard of 8000 feet ASML. –  shortstheory Nov 1 '13 at 16:12
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As far as I remember, air flights at higher altitudes are also problematic as they are detrimental to the ozone layer: it's one thing when a limited number of military planes fly at high altitude, but thousands of commercial aircraft would have a much greater effect.

EDIT(07/06/2013): some assessments of climate effect of supersonic air traffic: http://www.atmos-chem-phys.net/7/5129/2007/acp-7-5129-2007.pdf . I prefer not to summarize the authors' longish conclusions here, as I don't want to oversimplify the complex issue.

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