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The Mach Angle refers to the angle from the center axis to the shock front generated by supersonic object. It is roughly 90 degrees (actually it is parabolic but perpendicular to the shock origin) at Mach 1, and roughly 30 degrees at Mach 2. The Mach angle can be quite accurately estimated with the equation -- θ = asin (1/M) where M is the speed on the object in Mach.

There are generally two very major shock fronts coming off an aircraft that is relevant to the wing and fuselage plan form. The first is the nose shock and the second is the root shock of the wing itself. The speed at which the aircraft runs into its wing root shock and when it ultimately runs into its nose shock as well can be a little telling with regard to the speed for which its plan form is optimized for. Of course, the aerodynamics of an aircraft is not solely about the Mach angles associated with its plan form, but for wave drag efficiency most fast aircrafts have small Mach angles and slow ones have large ones. In most cases, the nose shock to wing tip angle is such that it is at or around the maximum speed of the aircraft. It doesn't mean that an aircraft cannot go faster than that, it does however mean that it may be rather inefficient above the speed at which its wing is running through the primary nose shock.

The following shows the difference between the F-35 and the F-22's plan form. Surprisingly, there is practically no difference in the nose to wing tip Mach angle. The differences in root shock angle is more pronounced, but is still nonetheless a Mach 0.135 difference.

Based on the above observations, the F-22 will run into its own nose shock at Mach 2.184 whereas the F-35 will run into it at Mach 2.148. The F-22's wing will be completely within its own root shock up to Mach 1.356, whereas the F-35's will only be so up to Mach 1.221.

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Elite 1K Joined: Jul 20, 2005 Posts: 1033 Status: Offline

Whats the point of this here?

It shows their drag efficiency at speed; effecting supersonic manouveurability. Hence why they say a delta is best at supersonic speeds, as the angles that are achieved mean alot less drag therefore can manouveur better at supersonic speeds.

Andy

Elite 1K Joined: Jul 20, 2005 Posts: 1033 Status: Offline

Ahhh...gotchya.

checksixx wrote:

Whats the point of this here?

The point is that there does not appear to be a hell of a lot of difference in high speed flight drag between the F-35 and F-22 attributable to their plan forms. Of course, plan form is not everything and many extremely fast aircraft -- the X-15 for instance -- does not have a sharply swept delta. The X-15 does however have very short span wings to tuck them within a very sharp nose shock cone.

Quote:

It shows their drag efficiency at speed; effecting supersonic manouveurability. Hence why they say a delta is best at supersonic speeds, as the angles that are achieved mean alot less drag therefore can manouveur better at supersonic speeds.

Yes. And the delta is also notoriously bad at landing speeds requiring very high AoAs and have generally bad yaw characteristics at landing speeds. Also, in subsonic or and low supersonic cruise they are somewhat less efficient because the of the short span and wide chord of the air foil. In general, a long and narrow wing is more efficient that a short and wide one until wave drag becomes an issue.

so how do these figures compare with modern fast (2.0+ Mach) fighters like F-15, Su-27, MiG-29, or F-14?

sprstdlyscottsmn wrote:

so how do these figures compare with modern fast (2.0+ Mach) fighters like F-15, Su-27, MiG-29, or F-14?

Its easy to find out! Go draw a line from the nose to the wingtip, and another along the leading edge of the wing. Measure the angles. The Mach speed at which the angles will touch the shock fronts will be 1/sinθ, with θ being the angle you measured.

Elite 1K Joined: Aug 19, 2004 Posts: 1090

Dwight,

Very nice work from an introductory aerodynamic standpoint, but you're applying 2D theory to complex 3D shapes. There IS theory covering basic 3D shapes (cones and other "well-defined" bodies of revolution), but I remember it being quite a bit more complex than 2D analysis. I'm thankful the professor of the graduate-level aerodynamics course I took as an undergrad didn't stress the topic much during the course of the semester. I had a hard enough time understanding the more advanced 2D concepts. However, if you wanted to do a "simple" supersonic analysis on the F-22 and F-35, you'd have to use 3D theory and approximate the nose sections of both aircraft with similar geometric shapes. The one thing I remember (at least I think I do) about 3D shock theory is that a 2D projection of a 3D shock wave front can be significantly different than what 2D shock theory predicts. You're looking at things from the top down too. Keep in mind that the shock wave coming off the nose of the F-22 or F-35 may intersect the canopy at a lower Mach number than the wingtips. In other words, sometimes the canopy is more of a limiting factor in terms of supersonic performance than the main wing.

I don't mean to rain on your parade here, but it's beyond the ability of 2D theory or even 3D theory to accurately predict the aerodynamic drag on an F-22, F-35, and pretty much any other complex aerodynamic shape. You have to use numerical methods to come up with a decent prediction of an aircraft or complex shape's aerodynamic properties at various Mach numbers. The transonic regime is the most difficult area of them all too. It wasn't until two researchers by the names of Murman and Cole came up with a numerical algorithm to effectively capture shock waves via use of the transonic small perturbation theory. Before then, it was pretty much impossible to simulate transonic flow over an airfoil. One had to calculate the subsonic aerodynamic properties of an airfoil (or whatever) up to some the drag divergence Mach number (I think that's the right term) and then skip ahead to the supersonic regime. The big blank in the middle was approximated with empirical relationships resulting from wind tunnel testing of various shapes at transonic speeds. Now one can run a full 3D Navier-Stokes simulation on a complex 3D shape like an F-22 and, with any luck, predict its aerodynamic properties reasonably well. Computational fluid dynamics hasn't advanced to the point where wind tunnels are no longer needed, however. It would be interesting to see what the real Mach cone coming off the F-22 or F-35 looks like over a range of supersonic Mach numbers. You can expect it to look something like what you've posted above when viewed from the top down, but the devil is in the details on this one. 2D theory in this case only tells you what you can expect to see. The Mach numbers you've calculated up to the third decimal are certainly not significant. At most, your calculation shows that these are probably both Mach 2-capable fighters.

Another interesting note is that the YF-22 had a larger wing sweep angle relative to the F-22's. The F-22's wing is thinner than the YF-22's which makes up for the losses incurred by decreasing the sweep angle. If anything, this tells you that you can't make aerodynamic assumptions about a 3D aircraft based solely on 2D planform geometry. This makes perfect sens when you think about how much effort goes into the design and analysis of airfoil sections. The above analysis doesn't even take into account the effect of the wing's sectional properties which DO matter at supersonic speeds since an oblique shock off the nose of the aircraft won't decelerate air to subsonic conditions behind the shock. You need a normal shock to do that and you won't find any of those if the plane is well supersonic. Only in the transonic regime are there areas of subsonic flow around the aircraft. Thus, at supersonic speeds you need an efficient airfoil (or combination of airfoils) making up the finite wing or you'll be screwed no matter how swept back the thing is.

Interesting nonetheless... again, I'm not trying to rain on your parade here. I'd be interested to see the same sort of analysis as above using 3D theory. Much respect if you can teach yourself that topic. Smile

Enthusiast Joined: Oct 19, 2006 Posts: 88 Status: Offline

dwightlooi wrote:

The point is that there does not appear to be a hell of a lot of difference in high speed flight drag between the F-35 and F-22 attributable to their plan forms.

I have to concur with the fundamental conclusion of Dwight's simplified analysis. Yes, a more detailed evaluation would require that 3D effects be included, but the end conclusion - that both the F-22 and F-35 are intended to spend the majority of their lives below Mach 2, should be accurate.

This should not be a surprise to anyone. Experience from the past thirty years has confirmed that just because an airplane CAN go above Mach 2 (such as the F-15), that it will actually spend any meaningful time at these conditions. Neither the F-22 nor the F-35 are exceptions to this.

Elite 1K Joined: Aug 19, 2004 Posts: 1090

Huh? Cruising at or above Mach 2 is a propulsion issue and aerodynamic issue. If you need afterburner to sustain Mach 2+, a relatively small fighter will burn its fuel off in a real hurry. If you're talking about supercruising at Mach 2+ like the Concord did (without AB), then you have to optimize the entire design for that operating condition. A Mach angle analysis doesn't tell you that the F-22 and/or F-35 will "spend the majority of their lives below Mach 2". Seeing as how no fighter aircraft spends the majority of its time above Mach 2, it's a good bet the F-22 and F-35 won't either. A 2D Mach angle analysis tells you next to nothing about sustained cruise performance of a real world fighter. I think you've got the wrong idea about 2D compressible/supersonic flow theory. It's not some magic answer box that tells you how fast a complex fighter aircraft design will go or for how long it will sustain a certain speed. I've done supersonic wind tunnel testing in an academic environment using schliren photography. The object tested was a simple wedge and the shock system it created at supersonic speeds (which could be seen via the schliren system) closely matched what 2D shock theory would predict. That was a wedge, however. If you tested a cone or the nose shape of an F-22 or F-35, you'd DEFINITELY get different results. A cone-like 3D object will behave differently than a wedge. The latter can approximate 2D phenomenon under the right conditions, the former cannot.

the schliren system is so much fun to use, but SS wind tunnels are loud and the tests were short,(15-20 seconds for 30+ minutes of compression) Our tunnel could be run at up to mach 5 but that would last for only 5 seconds before pressure ran out. Great photos. I wanted to build a few bullet models to put into the test chamber for wave drag comparison but mounting became the issue.

This one is interestiing. Not because it is a Schliren photo showing shock fronts, but be because it actually shows that shock fronts can be of slightly different angles even when there is no doubt that the nose, body and tail of the bullet is traveling at exactly the same speed. The primary shock front is a little less acute than that coming off the discontinuity in the crimp amidships. Maybe it is because, despite the Spitzer ogive -- this .30 caliber bullet is not really all that pointed and a blunt nose tends to produce a pressure stack which reduces the shock front angle slightly.

Nonetheless, the simple ASIN(1/M) does predict it to be around 26 degrees which is spot on for the crimp shock, but ~5 degrees more acute than the prtimary nose shock coming from the rounded nose. (2559fps = 2808 km/h = ~M2.3 @ 65 degrees F)

wow, thanks for the pic. Looks like the nose fo the bullet tries to make a bow shock.

Senior member Joined: Apr 16, 2005 Posts: 455

Hi dwightlooi,

Regarding the wing root shock, does it slow down the aircraft? Does the aircraft need significantly more thrust to fly past the speed where the wing root shock starts to appear?

Regarding supercruise, would this mean for instance that it would'nt be too hard for the F-35 to get to M1.22 with MIL power only?

Thanks.

Viperalltheway wrote:

Hi dwightlooi,

Regarding the wing root shock, does it slow down the aircraft? Does the aircraft need significantly more thrust to fly past the speed where the wing root shock starts to appear?

Regarding supercruise, would this mean for instance that it would'nt be too hard for the F-35 to get to M1.22 with MIL power only?

Thanks.

There are a lot of other things that affects supersonic drag of an aircraft. The airfoil section, the area ruling, the flight control trim, etc. But based on the planform -- the planar layout of the wing, tail/canards and fuselage -- the F-35 is not very much different from the F-22. And based on the planform alone, there is no indication that its supersonic drag characteristics is a lot worse than that of the F-22. More precisely, the speed difference between the onset of the nose shock related drag is ~Mach 0.04 and the onset of root shock related drag is ~Mach 0.135. Again, this is based on a 2D analysis which (as Raptor_One has pointed out) has its inherent inaccuracies build into it.

Aircrafts usually fly faster than when their wings run into their root shock. It is just that -- from a plan form standpoint -- they become somewhat less efficient above that speed. There are also many techniques to mitigate the root shock issue. One of these is clearly used on BOTH the F-22 and the F-35...

Notice that the wing root has a similar extension fillet going all the way to the lips of the intakes? Apart from other things such as being stealthy and enhancing vortex lift, this kind of extension also tends to throw the primary root shock from from way ahead of the actual wing root by introducing a sharp discontinuity on the same plane as the root way ahead of the root. In doing so it may move the primary root shock forward and hence increase the speed at which the wing becomes inefficient due to wave drag. This is one of those things where I guess you can say "the devil is in the details".

This is an X-15 at ~Mach 6. Notice that there is practically no shock front coming off the wing root, but a big one emanates from the root of the conformal sidepods which met the fuselage way ahead of the wing?

I do not know if the F-35 will be able to easily fly faster than Mach 1.22, there are way more factors to consider than just the 2D planform analysis. But, it certainly has the potential to do so based on the installed thrust, weight and overall geometry. In terms of thrust to weight ratio the F-35 is roughly 68~70% the F-22's weight with roughly 57% the installed dry thrust. That in and of itself cannot account for a halving of the cruise speed (which will be the case if the F-35 does not supercruise at all). If you want a definitive answer you'll just have to wait until they either way it will or it won't officially.

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F-35 vs F-22 -- Mach Angle analysis of their planforms