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TB500
Topic Author
Posts: 10
Joined: Sat Oct 05, 2019 11:48 am

### Why does the wings center of pressure moves aft with increasing mach number?

Hello,
I've been watching a video on mach tuck recently and wondered why does the cop (center of pressure) moves aft. I saw this video of 'ATPL theory' about high speed (and altitude) flight (link: https://youtu.be/_LYU03RErTU) and at 8:55 it says that 'as the mach number increases the effective airflow has to upwash to a greater angle and the effective aoa will increase.' (I'll attach to pictures of the leading pressure wave and resulting air flow from the video)

So I was wondering why the cop moves aft as I have learned that for increasing aoa the cop moves forward.

Greetings, TB500

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Starlionblue
Posts: 20861
Joined: Fri Feb 27, 2004 9:54 pm

### Re: Why does the wings center of pressure moves aft with increasing mach number?

At transonic speeds, shockwaves form above and below the wing. These shockwaves increase pressure gradients and "concentrate" the lift towards them. With increasing Mach number, the shockwaves move aft as the aircraft "outruns" them. This means that the CoL also moves aft.

This CoL movement causes Mach tuck, a downward pitch moment with increasing Mach number.

Aerodynamics start becoming a bit counterintuitive in the transonic regime.

This old video has good wind tunnel footage. https://youtu.be/bELu-if5ckU

TB500
Topic Author
Posts: 10
Joined: Sat Oct 05, 2019 11:48 am

### Re: Why does the wings center of pressure moves aft with increasing mach number?

Starlionblue wrote:
This old video has good wind tunnel footage. https://youtu.be/bELu-if5ckU

Hello,
I've watched your video when you posted your answer and now want to phrase a question.

It's the same as before. Why does the Col move aft? I could refer to your images but I'm using Screenshots from the video.

In the picture regions where the air is being slowed down and becoming denser are shown in red. Regions where it's speeding up and becoming less dense appear in blue.
In consider those as low static pressure regions. The red regions I consider to be high static pressure. (Just to clarify, maybe there is already my comprehension problem)

The flow in front of the shock wave is supersonic after the shockwace it's subsonic.

In the first picture you can see the shicjwaves forming first on top of the wing an then below it as the airfoil passes Mcrit.

In the second picture you can see you can see the lower shockwave moving aft as soeed increases. The upper one cant move be aus it's restriced by flow seperation. (Maybe because turbilent airflow isn't going in one direction and it's speed can't be supersonic; perhaps someone explains this btw)

In the video it was said that this causes the pitch to move up for some reason. And there is the part where I can still follow. In my mind, the position of the CoL is determined by where the shockwaves are, where there is flow separation, and where the air moves sub- or supersonic.

So I thought if you look at the part of the wing between the upper shockwave and the trailing edge: The upper air moves subsonic / turbulent so the static pressure might be high.
And the air below the wing moves supersonic resulting in a low static pressure. So the air pushes from above and because it's the aft part of the airfoil the nose goes up.

Now comes the confusing part. As the speed of the airfoil/aircraft reaches mach 1 the upper shockwave moves back and eventually reaches the lower shockwave. So because the nose up momentum is disappearing. It seems like theres a pitch down momentum.

The video says that this may not happen in most aircraft (thanks for the explanation anyway) But at all aircraft the col shifts to the rear.

So my question isn't answered. Why does the center of pressure or the col move aft with increasing mach?

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flipdewaf
Posts: 4289
Joined: Thu Jul 20, 2006 6:28 am

### Re: Why does the wings center of pressure moves aft with increasing mach number?

My answer may be way out due to memory lapses over the course of ~10 years but here goes.

The CoL is effectively the point in the wing where half of the lift has been created in front and half behind, ie the point at which the integral of the lift along the chord is equal to half of the integral of the lift of the whole cord. In a ‘normal’ wing at subsonic, incompressible regimes (below Mcrit) the CoL is at about 25% chord.

In fully supersonic flow the distribution of pressure (and so lift) is basically constant so the point at which the integral of lift = half that of the full wing is at basically 50% chord.

As shown in the video the area under the supersonic flow increases between Mcrit and M1 and so more of the wing is under the constant pressure distribution and so the closer it approximates to supersonic CoL.

Fred

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AvgWhiteGuy
Posts: 35
Joined: Tue Jun 25, 2019 2:44 pm

### Re: Why does the wings center of pressure moves aft with increasing mach number?

In August of 1996, when I was in ground school, this is what the US Air Force was teaching about the subject of mach tuck: In rear-swept wing, subsonic aircraft, the shock wave is strongest at the wing root due to the profile of the wing (fatter, maybe less AR?), so when a say 707 approaches .85M, the shock wave at the root of the wing is strong enough to disrupt the flow of air behind it on top of the wing, causing less lift at the root. Consequently, the COL moves outward on the wing, and hence aft with the sweep. This aft movement causes the nose to pitch down with increasing speed as the effect increases.
That's from memory, but I know it's close to what they were teaching because I was fascinated by it and hung on every word.

TB500
Topic Author
Posts: 10
Joined: Sat Oct 05, 2019 11:48 am

### Re: Why does the wings center of pressure moves aft with increasing mach number?

Also an interesting explanation. Thank you both. Maybe it might be possible with a forward swept wing to compensate to the Col moving to 25% chord

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flipdewaf
Posts: 4289
Joined: Thu Jul 20, 2006 6:28 am

### Re: Why does the wings center of pressure moves aft with increasing mach number?

TB500 wrote:
Also an interesting explanation. Thank you both. Maybe it might be possible with a forward swept wing to compensate to the Col moving to 25% chord

Maybe but I would guess that the aeroelastics on a forward swept wing would make it a structural nightmare.

Fred

TB500
Topic Author
Posts: 10
Joined: Sat Oct 05, 2019 11:48 am

### Re: Why does the wings center of pressure moves aft with increasing mach number?

TB500 wrote:
Also an interesting explanation. Thank you both. Maybe it might be possible with a forward swept wing to compensate to the Col moving to 25% chord

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Edit: Moving to 50 % of course. My bad.

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Airliner1973
Posts: 13
Joined: Thu Mar 14, 2019 6:48 am

### Re: Why does the wings center of pressure moves aft with increasing mach number?

Starlionblue wrote:
At transonic speeds, shockwaves form above and below the wing. These shockwaves increase pressure gradients and "concentrate" the lift towards them. With increasing Mach number, the shockwaves move aft as the aircraft "outruns" them. This means that the CoL also moves aft.

This CoL movement causes Mach tuck, a downward pitch moment with increasing Mach number.

Aerodynamics start becoming a bit counterintuitive in the transonic regime.

This old video has good wind tunnel footage. https://youtu.be/bELu-if5ckU

Brilliant video. I learned a lot from watching this old video. The way it is explained is easy to understand, even for someone like me who hasn't taken any aerodynamic classes / training. I've always understood the basic principles of lift, but how that translates to trans / super sonic was always a big unknown to me.
Again, thanks!

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