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Supersonic A/C Airfoil  
User currently offlineAlexEU From Serbia, joined Oct 2007, 1817 posts, RR: 2
Posted (6 years 9 months 1 week 2 days 20 hours ago) and read 9291 times:

I read somewhere that supersonic A/C have symmetrical airfoil. This didn't make any sense and my
aerodynamics professor told me that i was right (they use asymmetrical). So my question is which airfoils do supersonic A/C have (i assume asymmetrical, but which type of asymmetrical are most widely used, e.g. Concorde)? I am talking about wing airfoil, not tail unit airfoil (which is symmetrical for both subsonic and supersonic).


12 replies: All unread, jump to last
User currently offlineMneo From Bulgaria, joined Mar 2004, 776 posts, RR: 1
Reply 1, posted (6 years 9 months 1 week 2 days 18 hours ago) and read 9266 times:

From what i have in my aerodynamics textbook, a true supersonic airfoil is indeed symmetrical. But that is not practical because a symmetrical airfoil does not create any lift at AOA of 0 degrees. From what i remember from lecture there was one production military fighter that was with a fully symmetrical wings, (maybe someone could remember what it was F-104??)

And as for what airfoil different planes use, that is a very complicated answer. I know that my Piper Arrow uses an NACA airfoil, but im sure that every plane has a custom airfoil. All i remember about the concorde is that when that plane slowed down, the induced drag went off the chart.

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User currently offlineAlexEU From Serbia, joined Oct 2007, 1817 posts, RR: 2
Reply 2, posted (6 years 9 months 1 week 2 days 16 hours ago) and read 9236 times:

Thanks for reply.

I heard that there is also triangular assymetrical airfoil for supersonic A/C.
Are there any pics of symmetrical airfoil (on wing)?

If we are using Bernoulli's principe then symmetrical airfoil would not produce any lift...

Cheers, Alex

User currently offlineJoness0154 From United States of America, joined Nov 2005, 667 posts, RR: 0
Reply 3, posted (6 years 9 months 1 week 2 days 13 hours ago) and read 9215 times:

Quoting AlexEU (Reply 2):

If we are using Bernoulli's principe then symmetrical airfoil would not produce any lift...

I don't have much experience with airfoils, etc.

But wouldn't a symmetrical airfoil produce lift at any AOA other than 0? The air going over the wing would have a longer distance to travel than the air under it, which produces a relative low pressure, etc...

Thats what I would think anyways....

I don't have an attitude problem. You have a perception problem
User currently offlineJetMech From Australia, joined Mar 2006, 2684 posts, RR: 53
Reply 4, posted (6 years 9 months 1 week 2 days 13 hours ago) and read 9205 times:

Quoting AlexEU (Reply 2):
If we are using Bernoulli's principe then symmetrical airfoil would not produce any lift...

IIRC, many supersonic airfoils are a very thin symmetrical diamond shape in cross sectional. These air foils produce lift at angles of attack other than zero by a combination of shock waves over the top and bottom surfaces.

Quoting Mneo (Reply 1):
All i remember about the concorde is that when that plane slowed down, the induced drag went off the chart.

The Concorde has a delta wing, and lift was produced at low speeds by having a very high AOA. This produced massive vortex structures from the leading edge over the top surface of the wing. Because the vortex structures spun so fast the pressure inside them was reduced, which gave a net lift force. Unfortunately, this method of producing lift is not really too efficient, so you also get lots of drag.

Regards, JetMech

JetMech split the back of his pants. He can feel the wind in his hair.
User currently offlineLehpron From United States of America, joined Jul 2001, 7028 posts, RR: 21
Reply 5, posted (6 years 9 months 1 week 2 days 12 hours ago) and read 9197 times:

A diamond shaped triangular wedge foil produces the lowest wave drag superonically, but subsonic flow doesn't like sharp corners and adds turbulence drag subsonically. So most supersonic airfoils, whether fins or wings, are bi-convexal with a small angle of attack to generate lift for wings. They are symetical with an angle, don't need much maybe 1-2 dgerees is more than enough above Mach 1.5.

There is no standard for supersonic foils, every wing is tailored for a specific flight category. Generally, thinner foils are best to reduce drag (and thus thrust and fuel consumption) but lift drops so a larger surface is needed. But thinner foils aren't subsonic freindly, and foils have to be changed in some way so that the plane can land and takeoff.

The meaning of life is curiosity; we were put on this planet to explore opportunities.
User currently offlineBoeingfixer From Canada, joined exactly 9 years ago today! , 529 posts, RR: 0
Reply 6, posted (6 years 9 months 1 week 2 days 11 hours ago) and read 9177 times:

Quoting AlexEU (Thread starter):
I am talking about wing airfoil, not tail unit airfoil (which is symmetrical for both subsonic and supersonic).

You may want to refresh your understanding of horizontal stabilizers and what they do before you make a statement like that. On fixed wing aircraft, the centre of lift is behind the centre of gravity which requires a down force from the H-Stab. That down force requires that the H-Stab is either at a negative angle of incidence or an inverted airfoil in the case of larger aircraft.



Cheers, John YYC
User currently offlineAeroWeanie From United States of America, joined Dec 2004, 1607 posts, RR: 52
Reply 7, posted (6 years 9 months 1 week 2 days 10 hours ago) and read 9175 times:
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Some supersonic aircraft do have symmetrical biconvex airfoils (F-104 for example), others don't. Judge for yourself from this list: http://www.ae.uiuc.edu/m-selig/ads/aircraft.html

User currently offlineBlackbird From , joined Dec 1969, posts, RR:
Reply 8, posted (6 years 9 months 1 week 2 days 10 hours ago) and read 9166 times:


That's not entirely true!

If you had a straight-wing for supersonic use, or possibly if the shockwave swept back beyond the sweep-angle of the wing you'd use a symmetrical foil.

The reason is that the some of the principles behind a regular airfoil -- the curved portion of the top section of the foil producing a low-pressure zone on the top seems to go largely in reverse at supersonic speeds. Convex curvature increases pressure and slows the airflow down which reduces lift. AoA will have to be increased to negate this, and more to produce positive lift.

While inverse-camber would be better for supersonic flight as pressure would be increased on the bottom, it often isn't exactly the best choice as the design would produce negative lift at subsonic speed requiring higher AoA's to get positive lift while subsonic. Since supersonic foils are kind of thin, this could make takeoff speeds very high, and critical AoA's quite low. So instead symmetrical are typically used since it's the next best thing. Sure at 0-degrees AoA it produces no lift, but once you get the AoA up you start producing lift. It produces better performance at supersonic speed than a standard subsonic airfoil, without substantial losses at subsonic speed (although there are some losses). I should note that even with this said, you will still require a higher AoA at supersonic speed as the L/D ratio falls off due to the thicker boundary layer, increased turbulence, and a lower pressure differential (the low-pressure zone up top isn't as low as at subsonic speed), but it would be substantially better than a subsonic airfoil.

These particular airfoils only have some limited applications. Straight wings experience a massive shift in the center of pressure (on a straight wing once the upwash up front goes away, the center of pressure shifts back to the 50% mark). This produces a strong nose-down tendency in supersonic flight requiring considerable longitudinal trim deflections which produce excessive amounts of drag if you're looking for endurance. Not to mention, the thickest point on the wing is often half way down the wing (due to the center of pressure being at 50% instead of 25% at subsonic flight) which does degrade low-speed performance (Still better than an inverse camber supersonic-foil). The airfoil-thinness can pose a problem as fuel might not be able to be carried in the design (the F-104 could not carry any fuel in it's wing and needed the fuselage to do the whole job). The serious advantage they do have is that they have very low drag when flow over them is fully supersonic compared to other airfoil types. They call this supersonic-drag. In fact even if shockwaves produced on the other parts of the plane sweep beyond the wing's leading edge, it's not that big a deal. Tapered, or trapezoidal wings (low-sweep) a'la the F-104 type will feature a shockwave that will form on the root and sweep back... even if they sweep back well beyond the wing's leading edge, it's not a significant problem. In fact, the F-104 aircraft's geometry (if airframe and temperature restrictions weren't an issue -- and they are) could easily allow for speeds in excess of Mach 3 maybe 4 (I've been told it's shape could allow for twice the speed if engine temps and structual limitations didn't matter)

There are other types of airfoils though used for supersonic flight though and a large number of them do not have fully-supersonic flow over them.

One example is a swept-wing. In addition to sacrificing span for a lower thickness/chord ratio (behaves better at high-subsonic and transonic speeds too), at Mach 1, the shockwave only forms off the wing-root, leaving the rest of the wing behind it, and as long as the shockwave is equal or less (or at least in *front* of) than the sweep-angle of the wing, some of the flow field will behave subsonically, at least the parts at angles to the wave (if you pointed an object dead ahead, you'll still get a shockwave). This subsonic effect enables one to design most of the wing (except maybe the root) with blunt leading-edges and such like you would on a subsonic plane, still achieve low pressure suction zones across the front, and retain some low-speed handling inherant in blunt-leading-edges. The subsonic effect only covers so much of the wing, the leading edges and a bit aft of that, but eventually it will go fully supersonic. Highly swept-wings generally have a lower shift in the center of pressure, and their stall onset is usually more gradual than a straight wing which is much more abrupt. They have some negative side-effects though including noticeable span-wise flow at subsonic speeds. The airflow despite the wingsweep at subsonic speed goes pretty much front to back over the wing (technically the inward spiraling vortices which are at the tips do cause the flow to slide inward a bit, but not factoring that...), on swept wings there's a tendency for the flow to slide sideways across the wing in such a way that could actually seriously reduce aerodynamic performance and even produce a stall. Stall fences, slats, and proper aerodynamic-contouring of the wing can deal with this problem. Another problem is flexibility. Swept-wings flex a lot which pose a number of problems, including aileron reversal in which the aileron deflections cause the wing's leading edges to twist in opposition nullifying and even reversing direction of roll. For supersonic flight there may even be a flutter-risk in some cases, although I'm not sure how big a problem that is. Swept wings designed for supersonic flight do often fly at higher indicated airspeeds as well which puts more stress on the wing during banks and turns, so they are often stiffened up -- this can result in a weight penalty. Tip-stall is the next problem, on a typical straight wing, it stalls at the root. Stalling occurs at the back of the wing where the flow has lost a lot of it's energy after flowing over the whole wing, so in this case it stalls at the inboard rear of the wing. This disrupts the downwash which is a downward flow off the back of the wing which increases the downward load on the tail (tails produce a negative lift since the center of pressure is behind the center of gravity which is necessary to produce stability), the reduction in downwash causes the tail to become less effective causing the wing's natural tendency to pitch down to take-over... once the wing's AoA lowers and recovers from the stall, the downwash is restored... On swept wings the tips tend to stall first, which along the span is much further aft... when it stalls, the inboard part of the wing which is further forward keeps lifting and the plane pitches up even further, AoA goes up with it and it makes stall recovery much more difficult than a root-stall. The solution involves twisting the wing such so that the inboard leading edge is at a higher angle of incidence than the outboard trailing-edge. Another problem that swept-wings have is known as dutch-roll, a type of lateral instability, believe it or not, not named after some kind of pastry, but actually the way that Dutch sailors used to stumble and roll all over the place while drunk on leave. Turbulence can cause yawing, which causes more airflow to go over one wing than the other, with swept wing, the effects of sideslip (which is like AoA on the sideways axis) cause one wing to dramatically produce more lift than the other -- the result is substantially increased roll rate over a straight-wing. Eventually the tail slows the yawing down and the plane starts yawing the other way, then causing another roll-rate in the new direction. It gets worse every cycle too. The greater the wing-sweep, typically the nastier the dutch roll... It's very difficult to correct because the amount of yaw input to cancel out the motion is often very little at high-speeds, and the pilot puts too much in aggravating the problem. There are a number of solutions which include increasing the tail area which would stop the yawing in its tracks typically, and the addition of a yaw-damper, a device which works through the autopilot and makes small movements to the rudder by detecting sideslip, cancelling out the motion before it is able to get too severe.

Another example is a delta-wing. The delta wing provides a number of aerodynamic advantages for a high-speed aircraft. It is naturally a rigid structure which does not require extensive structural beefening. It has a lot of external area which produces a lighter wing-loading than a swept wing could, and greater internal-area which allows for lots of fuel to be carried if needed. It's high leading-edge sweep angle causes a vortex to form at the root and flow spanwise ultimately merging with the wing-tip vortex, while the wing-tip vortex plays a role with downwash, it degrades lift and increases drag like any other... however the leading-edge vortex helps energize the flow over the leading edge causing the wing's critical AoA to be much higher than one would expect from that particular airfoil cross-section, even when stall occurs, the flow is still stable over the control surfaces mounted on the aft of the wing allowing easy recovery -- in stall, descent rate increases substatially though, however pushing the nose over will fix that problem. To my knowledge the same effect can occur with some highly swept (~60-degrees) wings too. Like highly-swept wings, the stall onset is more gradual than a straight wing, which occurs more abruptly. The delta-wing's leading-edge except the root rides behind the shockwave and as a result has a subsonic-flowfield over the leading-edges and over significant parts of the wing. This allows blunt leading edges as on the swept-wing and even a type of camber called conical-camber in which the leading edge kind of curves downward-- nonexistant at the root, and getting progressively more noticeable in terms of chordwise coverage and to an extent curvature as you get further and further down the span, with the curved wing often blended with a downward curved wing-tip which helps overall in the process, may even reduce vortex-drag. This conical-camber like blunt leading-edges will increase suction on the leading edge, increase the L/D ratio at supersonic speed and drastically improve low-speed handling. The problems with the delta-wing is while delta-wings may (due to large wing-area and vortex-lift) perform nicely at low-speeds, still take off and land at very high angles of attack which produces undesirable amount of drag. This reduces initial acceleration and climb-rate until the angle lowers a bit. Also, during approach it's very easy to end up losing too much speed with the AoA getting too high requiring large amounts of thrust to jack the speed up to get the AoA to a reasonable level for approach. Also, the difference in takeoff and landing speeds are further apart than you would see with most wings as well. Additionally since a delta is traditionally a tail-less design, the trailing edge of the wing needs to be deflected up which is contrary to what you'd ideally want on a wing, the problem is generally overcome once supersonic as the drag produced by having a tail would actually be more so than having elevons; at subsonic speed and transonic speed a tail produces an advantage. Delta wings because of their larger areas experience a greater shift in the center of pressure than highly swept wings. If the airplane is small like a fighter, the thrust to weight ratio should be able to overcome the trim-drag, larger designs would probably shift the fuel into rearward trim-tanks to put the CG and the Center of Pressure near eachother to provide low enough trim-drag. One of the biggest problems with Delta-wings, and it's not a huge one unless you plan to fly REALLY REALLY FAST, is that once the shockwave sweeps behind the wing drag increases to the point that a straight wing would be better.

Now there are other wing-designs that exists, but I'm rather tired right now and feel frankly like getting a good nap.

Andrea Kent

User currently offlineAlexEU From Serbia, joined Oct 2007, 1817 posts, RR: 2
Reply 9, posted (6 years 9 months 1 week 1 day 20 hours ago) and read 9097 times:

Thanks a lot for replies  bigthumbsup  you answered my questions.

User currently offlineJetlagged From United Kingdom, joined Jan 2005, 2543 posts, RR: 24
Reply 10, posted (6 years 9 months 1 week 1 day 11 hours ago) and read 9029 times:

Quoting AlexEU (Reply 2):
If we are using Bernoulli's principe then symmetrical airfoil would not produce any lift...

This is a mis-use of Bernoulli's equation, combined with the erroneous "equal time" theory of lift. You cannot predict the pressure distribution around an aerofoil merely by comparing the length of the upper surface to the lower surface. In this way, a flat plate would produce no lift. The heavily cambered thin aerofoils, as used in the early days of aviation, would not produce more lift than an uncambered aerofoil of the same thickness.

Symmetrical aerofoils produce lift at an AOA, and some subsonic aircraft used them too. Not producing lift at zero AOA is not a disadvantage. All wings have a zero lift AOA, whether symmetrical or asymmetrical section.

An aircraft designed only for supersonic flight would probably use rhomboid section symmetrical aerofoils. Many air launched missiles do have fins with such sections. However most supersonic aircraft spend most of their time flying subsonic. So a compromise has to be reached between subsonic efficiency and minimal wave drag when supersonic.

The glass isn't half empty, or half full, it's twice as big as it needs to be.
User currently offlineAlexEU From Serbia, joined Oct 2007, 1817 posts, RR: 2
Reply 11, posted (6 years 9 months 1 week 22 hours ago) and read 8993 times:

So, my aerodynamics proffesor was either confused or wrong... i will ask again. However she did mention rhomboid airfoil.

Quoting Boeingfixer (Reply 6):
That down force requires that the H-Stab is either at a negative angle of incidence or an inverted airfoil in the case of larger aircraft

AFAIK, supersonic a/c do not have elevators, they move the hole h-stab, but i understand what are you saying.
How about taildraggers?


User currently offlineBlackbird From , joined Dec 1969, posts, RR:
Reply 12, posted (6 years 9 months 1 week 16 hours ago) and read 8981 times:


Not all supersonic aircraft move the whole stab for pitch control. The HSCT concept, which to my knowledge was plenty stable featuerd a large elevator for pitch control and a horizontal stabilizer for trim.

Fighters often move the whole stabilizer for pitch control for the purpose of improved pitch control for pulling high-G forces...

Andrea Kent

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