swept wings

[clear_right]

Hi

Could someone explain to me how a swept wing will increase the critical mach number.

Cheers

[Empty Cruise]

When increasing sweep angle for same wing profile, the effective chord of the wing increases in length. Increased chord for same thickness = decreased camber (not sure this is correct technical term here:confused: ), decreased camber = increased mach no.

Hope this is close enough for government work.

Brgds,
Empty.

[Genghis the Engineer]

Not how I was taught it, although the argument about thin aerofoils is true - it doesn't explain why high speed aircraft don't simply have deep chord, thin stubby wings (apart from the horrendous tip losses).

The critical Mach number is not the absolute Mach number, it is the local Mach No, perpendicular to the leading edge of the wing. So, if you resolve the triangle of velocities, for the "ambient" Mach number to be that parallel with the wing centreline, then we get a lower apparent Mach number perpendicular to the wing leading edge. (It's a bit like calculating crosswind component). So, the greater the sweep, the lower the perpendicular Mach number for the same flightpath Mach number.

G

[BEagle]

Yes, Ghengis - I too was given that load of hor$e****!

Empty cruise's explanation is far more plausible - and remember the effect on apparent Reynold's No as the effective chord length increases at high sweep angles.

[Genghis the Engineer]

Ah, but I was given that load of horse dung by a professor of aerodynamics, who got it from a book by another professor of aerodynamics.

Another such prof (mine is long retired) gives a good explanation at http://142.26.194.131/aerodynamics1/High-Speed/Page2e.html which covers both reasons.

G

[BEagle]

"When the wings are swept back the airflow is accelerated less as it flows over the wing. Only the component of the airflow perpendicular to the wing is actually accelerated at all. Therefore, a swept wing will have a proportionally higher critical mach number."

BOLLEAUX!

[Genghis the Engineer]

That is a rather poor piece of wording I'll grant you, but the general sense of the piece is relatively sound, as well as being rather more accessible than the traditional textbooks like Houghton.

G

[Empty Cruise]

Genghis,

You are absolutely right - it is a more grapically correct representation to use the airflow vector resolution. I tried to give a "laymans" explaination of the problem :oh: - should know that it would cause notin' but trouble :}

High-speed aircraft have used short/stubby, deep chord wings, X3 and X15 being some of the more extreme examples, the F104 one of the more conventional. These aircraft used it instead of large sweep angles to achieve a high Mcrit. But of course, the low aspect ratio made for lousy low-speed handling, so not an option on transports.

Btw, your explaination also demonstrates how big an increse in sweep angle it takes to bring by a small increase in Mcrit.


Brgds,
Empty

[Keith.Williams.]

The explanations above are essentially the same thing, but with slightly different emphasis.

Mcrit is the lowest mach number at which the airflow at any point on an aircraft becomes sonic (mach1). The speed of airflow at any point on an aircraft is the freestream speed plus whatever acceleration the aircraft has given to it. So Mcrit is mach 1 minus the greatest acceleration found at any point on the aircraft. If for example the greatest acceleration is mach 0.2 then Mcrit is 1 - 0.2 = 0.8. So if we can reduce this acceleration we will increase Mcrit.

If we restrict our discussions to only the wings of the aircraft, we can examine the effects of increasing wing sweep. As air flows over the wings it must move apart, so that some passes over the wing and some passes under it. The acceleration given to the air depends upon the distance that the air must move apart (the thickness of the wing) and the time available for this movement to take place. The time available depends upon the freestream speed and the chord length.

If the wing is very thick with a short chord length, a large acceleration will be required. If however the wing is thin with a long chord length, the acceleration will be much less. So thin wings with large chord lengths will give high values of Mcrit.

Now if we consider a straight wing of moderate thickness and chord length, say 20% thickness to chord ratio. For any given angle of attack and freestream speed, this will give a certain acceleration of the aiflow passing over it. If we subtract this aceleration from 1 we will get its Mcrit.

If we now sweep this wing backwards, the aiflow will take a longer path over it. In effect we have increased the chord length without changing the thickness. This gives more time for the air to separate to allow the wing to pass through it. Subtracting this reduced acceleration from 1 will give an increased value of Mcrit.

A second way of looking at this situation is to consider the airflow over the wing as two components. One is at right angles to the wing leading edge, while the other is parallel to the leading edge. The flow at right angles to the leading edge experiences the same thickness to chord ratio as that produced when the wing was straight. But the flow parallel to the leading edge experiences no aerofoil section and hence no acceleration. So part of the velocity gets accelerated and the other part does not. Because only part of the flow is accelerated, the overall acceleration is less. Subtracting this reduced acceleration from 1 gives an increased Mcrit.

So whether we use the vector argument or the thickness to chord ratio argument, the effect is the same. Increasing sweep back angle decreases acceleration and so increases Mcrit. If we want to carry out accurate calulations we must use the mathematical method. But for most people the thickness to chord ratio argument is easier to understand.

[Specnut727]

K.W.

I haven't done any reading on this, but here's a question which sprang to mind.

Taking your 'increasing chord' idea a bit further, it would appear that a delta wing would achieve this better than a swept wing. I assume there are some other factors which make swept wings a better option for high subsonic speeds. Can you explain please.

Thanks in advance,
Spec.

[FE Hoppy]

K.W
Wasn't this called the fineness ratio or the thickness ratio?
The other way to reduce Mcrit is to use a supercritical section. This has a larger radius leeding edge and quite flat top surface the underside being under cambered towards the trailing edge. This allows quite a thick section to be used.

[Prof2MDA]

Any object moving through a fluid sends a wave in front of it that effects the flow of the air as the object approaches. Those waves move out radially, so the portion of wing that is upwind essentially transmits a wave that influences the air that is in front of the portions that are more downwind of it. So, essentially, sweeping a wing transmits a signal to the air that the wing is approaching, where otherwise it is taken more by "surprise".

[Keith.Williams.]

Specnut,

Delta wings are indeed very good for high speed flight, and make the creation of very strong structures easy. But like most things in life they have their drawbacks.

They tend to have very low aspect ratios, so the induced drag is high, particularly at low speeds. They also require very high angles of attack at take-off and landing, which makes forward visibilty problematic. Look at what they had to do with the nose of Concorde to overcome this problem. Other problems include the difficulty in using trailing edge flaps without also using a tailplane or canard. It is of course possible to solve such problems, but they do exist.

For the mach numbers at which commercial aircraft currently cruise, high aspect ratio, supercritical swept wings provide a much better compromise.


FE Hoppy,

As you have said, supercritical wings also increase Mcrit. They may be considered to be a form of Area Rule, in that reducing the camber reduces the rate of change of cross-sectional area. This reduces airflow accelerations, which in turn increases Mcrit and reduces the intensity of the shock waves when they finally occur.

In most cases, some of the potential increase in Mcrit is traded off to enable thicker cross-sections to be used, thereby making the wings stiffer and increasing fuel storage space. In effect the supercritical section increases Mcrit, then the thicker section reduces it a bit, but still leaving it higher than for a conventional wing of equal thickness.

[Specnut727]

Thanks K.W.

That's a great explanation. Despite it's drawbacks, there still aren't many aircraft around as pretty as Concorde. Too bad they're all destined to be static in museums.

Spec.