Determining Cruise Speed by Mach Angle 4

[jamesv]

Is it safe to assume that at supersonic cruise speed, it is desirable for an aircraft to fit completely inside the "Mach Cone"? If so, can I then calculate the desired cruise speed of an aircraft (like the stealth bomber) by measuring the sweep angle of its wings and finding the corresponding mach number using the formula:
angle = sin^-1(1/M)

If not, what, if anything, can I infer about aircraft by the angle of sweep?

 

[IRstuff]

Is that ever true? The F-22 Raptor 13.56 m wingspan and overall length of 18.9 m, which is a 39 degree angle, but the F-22 has a top speed in excess of 2.2 M.

TTFN

 

[i278]

jamesv,

I'd say your assessment has merit; what I know of current design philosophy would agree with you. However, wing sweep isn't the prime motivator here, as the mach cone is being generated from the point of the nose. What you should be considering, then, is the smallest cone angle (vertex at the nose) that encompasses all the outward extremities of the plane.

Since IRStuff brought up the F-22, I thought I'd look at that (not that I have any great knowledge of the design). I found a fuzzy 3-view on the net and tossed it into CAD to measure angles. A line from the nose to the forward end of the wingtip (in plan view) is the minimum cone angle and comes out at about 29 degrees by my measure. That's mach 2.06--not quite IRStuff's value of top speed, but certainly including a posted supercruise of mach 1.85.

Note also, for interest's sake, that all of the plane in side view was also well within the 29 degree cone.

We're now getting into areas where my memory for this stuff gets all fuzzy, so bear with me... The cone angle doesn't remain a constant as it trails off into the farfield, it flares out to become a weak mach wave (cone angle 90 degrees). There's a cool mpeg floating around on the net of a low-level, high-speed fly-past of a naval fighter (F-14 I think) that really shows this effect off. Anyway, perhaps this flaring out of the mach cone allows the wingtips to remain inside the mach cone up to the quoted mach 2.2 (cone angle 27 degrees). Or, maybe the wingtips stick out in the supersonic breeze past mach 2.06 and the increased drag limits top speed to 2.2. I don't know, but I suspect the former.

Now, where wing sweep enters the picture is after the flow has already passed through the initial shockwave off the nose. As you probably know, with wave angles less than ninety, flow on the back side of the shock will likely remain supersonic, depending on the freestream mach number and wave angle. I don't have any mach tables in front of me, but I think it's a good bet that the post-shock flow in our example is still supersonic. Fortunately though, the flow over the wing isn't dictated by the freestream velocity, but by the velocity component perpendicular to the wing sweep (but I can't remember if it's quarter-chord sweep or leading-edge sweep). So, if the correct wing sweep is selected, the wing can experience sub-sonic flow conditions even in a supersonic freestream. Since the minimum wing sweep for this is based on the freestream mach number around the wing (behind the nose shock), the wing sweep angle can be checked to verify your first design cruise estimate based on the minimum cone angle above. This assumes, of course, that wing sweep isn't set by control, stability, CofG, or structural concerns; which is a pretty weak assumption. Whatever the case, checking wing sweep could give a one-way limit on design cruise speed.

This is all very rusty for me, perhaps someone could further explain/correct the above if I've erred.

The other option for estimating design cruise speed is to search the net and find: "Design Cruise= Mach 1.85". Whichever you prefer

Cheers

 

[jamesv]

Great reply, i278. I have little doubt that the F22's published speeds are untrue, for security purposes. As a more reliable check, cruise speed figures for a commercial aircraft such as the Concord are more likely to be truthful. I'll see if I can find a plan photo of it to see if the angle of it's minimum angle cone corresponds more closely to its published designed cruise speed.
Thanks again for a great response.
P.S. Any chance you could elaborate on what happens with respect to the cone as an aircraft accelerates increasingly above Mach 1? You alluded to the "initial shock wave off the nose". Does the craft penetrate the initial shock wave, then another one forms at the nose, etc.?

 

[i278]

Sorry, I guess I was a little unclear on that matter. By 'initial' I didn't mean it with respect to time, but with respect to distance along the aircraft. In other words, in the string of shock waves along the length of the aircraft (nose, front of canopy, intakes, wing and tail leading edges, etc. ad nauseum) the shock wave at the nose is the forwardmost, and most likely the strongest.

As far as changes with increasing speed, it works something like this: when an object accelerates to Mach 1 (we'll just consider the end of the nose cone), a mach wave forms right in front of the object; this shockwave is flat and perpendicular to the flow. As speed is increased, the shock wave strengthens and at the same time begins to bend aft, but its center remains attached to the tip of the object creating it. You could almost think of it as a membrane. The angle it assumes with respect to the freestream flow is the mach angle, and the resulting cone shaped shock wave is the mach cone. A good text or someone else in this forum could probably explain it better, but that's the gist of it. I hope that clears it up.

Cheers

 

[matt00000]

I think using a military aircraft as an example is a bit pointless as the job it is designed to do has no bearing on efficiency. Top speed is exactly that and also nothing to do with cruise. Concorde is a much better example and you will find that it does lie within the mach cone.
Areas that lie outside the nose shock will generate their own shock and the nose shock will join with this.

A good 'non technical' book describing aircraft is Mechanics of Flight by AC Kermode. It will describe to you what a shock is and how it is formed. The strongest shock is formed when there is the greatest change in pressure required for a given Mach No.

 

[IRstuff]

While older military supersonic planes were not as concerned about efficiency, the F-22 was designed with some significant concessions to overall efficiency.

The supercruise mode accomplishes supersonic performance without the use of the afterburners, which concurrently reduces the overall signature of the plane.

TTFN

 

[RITelectric]

IRstuff,

you piqued my curiosity and I was wondering if you could elaborate on your last post -

by "signature of the plane", were you talking about heat signature as a means to track the plane in supersonic flight? Is current IR detection technology capable of doing so at any significant range?

 

[poetix99]

Back to i278:

Yeah, I once saw the MPEG that you referred to. We see something looking rather like a drag chute appear out of nowhere.

It's a "lambda shock wave" that flares out behind the initial Mach cone. Has to do with the diffusive recovery of the high velocities, or some such thing. We can see it on the MPEG because water vapor appears at the shock interface when the humidity is in the "right" range.

I imagine that the pilot got a "scolding" for such a fly-by; it looked rather dangerous for the unprotected on deck...

 

[matt00000]

“the F-22 was designed with some significant concessions to overall efficiency. “

How do you know that? What ‘significant concessions’ are you referring to? I have just had a look online to see if I can find any information on the F-22. There is virtually nothing available to let one decide whether the airframe is efficient at any flight speed.

Sure the engine has a high dry thrust output and also it enables the aircraft to fly supersonic without using reheat. However there is no information available on the SFC at ‘supercruise’, or for any flight speed. The only thing you could say is the SFC is approximately half that for an engine in reheat so that makes it more efficient than an engine in reheat. The engine was designed to have such a high thrust so that reheat is used a lot less. I presume this is because of the thrust vectoring and the reduction of signature that you mention. Whilst you can still use the thrust vectoring in reheat I am sure that eventually the nozzle would melt! The spin off of that is the supercruise. It wasn’t designed to make it cheap to run.

The design of the aircraft is to do a job at any cost but to do it better than any other aircraft. Efficiency is dependant on what you use as a comparison. The speed of supercruise is probably the maximum speed of the aircraft without reheat. I doubt very much if this is the same speed at which the drag is a minimum. In fact for maximum range the a/c probably is subsonic. But then what does it matter if you can have in flight refueling.

With commercial jets such as Concorde the SFC at cruise is of prime importance. Hence the reason Concorde flies in excess of Mach 2.

Yes, he did mean heat signature. Heat-seeking missiles can detect a/c at quite long range…. At least that is to say they can detect a/c within the distance they can reach typically between 30/40 miles.

In the mpeg you refer to the aircraft is still subsonic the local speed of sound at the point where the cloud is formed is M1+. The lambda shock you are talking of is actually the same shock as the one you can see during the flypast the reason it dissapears is either a change in the water content in the air or that the a/c slowed sufficiently for the shock to disappear. I am not really sure what you are talking about. The reason you can see the cloud is because the change in pressure at the shock 'squeezes' the moisture out of the air this only happens in high humidty.

 

[matt00000]

I appologies for my use of the word "he". From the 'persons' attitude I just assumed that the 'person' was male!

 

[IRstuff]

The F-22 was designed with one specific efficiency requirement: that it perform at supercruise without afterburners.

This was the first major milestone for both the YF-22 and YF-23 during the dem-val phase of the program. Both contractor teams were required to demonstrate this performance before proceeding with the remainder of the dem-val testing. TTFN

 

[matt00000]

That is not an airframe issue that is a thrust issue and is dependant on the thrust generated by the engines without reheat.

And they both had the same engines! (that is to say that the P&W engine was better than the GE one!)