Centre of Pressure (Cp) and the movement of...

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Centre of Pressure (Cp) and the movement of...

Postby ogivemeahome » Wed Sep 05, 2012 8:03 am

I wasn't sure where this one fits, anyway..

I have a book containing a series of graphs showing the movement of the Cp.
Granted, it relates to aircraft - read: aerofoil sections and, constant Angle of Attack (AoA).
As most of us would know, rockets mostly have "flat plates" for fins and they do not have a constant angle of attack.

For the flat plate, as the AoA increases, the Cp moves aft. This is good because it increases the static margin, thereby increasing the stability of the rocket. If using the Barrowman equations to determine the Cp, it is assumed that; the fins are flat plates, the speed of the rocket is << transonic, and the angle of attack is < 10 degrees.

If you plan to go supersonic, there may be some benefit in using an aerofoil section. (If only to increase the strength of the fins?)
For an aerofoil, the position of the Cp for a given AoA;
0 degrees - 0.75 of chord (from leading edge)
1.5 " - 0.5 "
10.0 " - 0.3 "
after this the Cp starts to move back again.
Everything so far is for subsonic speeds.

For an aerofoil, the position of the Cp for a 2 degree AoA;
at Mach 0.75 - 0.15 of chord
" 0.81 - 0.25 "
" 0.89 - 0.15 "
" 0.98 - 0.35 "
" 1.40 - 0.50 "

This is all general of course. If anything, it shows that for aerofoiled fins, you would need to allow a bit more static margin if you plan to go anywhere near transonic (Mach 0.7 to Mach 1.0 ?).
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Re: Centre of Pressure (Cp) and the movement of...

Postby rocket_troy » Wed Sep 05, 2012 11:08 am



Note the *EXPERIMENTAL* results in fig 9 and that's for mach numbers from 3 to 6.3.

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Re: Centre of Pressure (Cp) and the movement of...

Postby rocket_troy » Wed Sep 05, 2012 11:26 am

However, this link says the V2's centre of pressure moved forward with an increase in speed:

http://v22v.tripod.com/47.html

which backs up the software's assumptions.

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Re: Centre of Pressure (Cp) and the movement of...

Postby cryoscum » Wed Sep 05, 2012 12:05 pm

Hi Troy

So, one day when I have a spare 6 months I'll try to get that all in my head, but am I reading this correctly:
- Boundary layer separation has a profound effect on actual vs expected lift forces (i.e. essentially where the CP will be)
- Even small changes in either the Reynolds number (ratio between the inertial and viscous forces in a fluid) or AoA makes or breaks this unexpected difference
- The paper only deals with cone-frustum (truncated cone) aft sections of this projectile, not actual fins and hence it is difficult to say what, if any, form a boundary layer separation will take (ignoring the NC wavefront for the moment) on a rocket with fins
- To accurately predict the effects of such boundary layer separation on the projectile's tail flair, the exact shape of the separation must be known and this is near impossible to do through any methods other than actual wind tunnel testing.

1.JPG
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Hard to grasp, certainly for me.

Given the above, i.e. the fact that AoA has such a big effect and the fact that rockets have fins, not tail cone flairs, can it be surmised that once the NC shock wave forms, i.e. around Mach1, the air in its 'shadow', including that surrounding the fins, are pretty much a turbulent mess and the effect of the fins become less pronounced, reducing their lift and thereby moving the CP forward?
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Re: Centre of Pressure (Cp) and the movement of...

Postby rocket_troy » Wed Sep 05, 2012 12:26 pm

"Given the above, i.e. the fact that AoA has such a big effect and the fact that rockets have fins, not tail cone flairs, can it be surmised that once the NC shock wave forms, i.e. around Mach1, the air in its 'shadow', including that surrounding the fins, are pretty much a turbulent mess and the effect of the fins become less pronounced, reducing their lift and thereby moving the CP forward?"

I'm tending to agree with you Nic. I would have thought similar issues would be experienced with truncated cones if it was an aerodynamic "shadow" effect, but well, I'm tending to agree with your reasoning and conclusions.

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Re: Centre of Pressure (Cp) and the movement of...

Postby rocket_troy » Wed Sep 05, 2012 1:22 pm

http://www.rasaero.com/dloads/Aerobee%20150A%20-%20Vought%20Astronautics%20Report%20AST%20E1R-13319.pdf


is a link to some data on the Aerobee 150A, which IIRC was spun at a certain rate, but data in Figure 22 illustrates CP location data with zero AOA over a range of Mach numbers.

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Re: Centre of Pressure (Cp) and the movement of...

Postby cryoscum » Wed Sep 05, 2012 2:16 pm

Interestingly the CP location returns to almost the initial position, and then stays there, once you get to M4-ish, of course assuming the graph is accurate. If so, maybe there is something inherently different to the NC or overall design that allows the CP position to stay behind it's launch position. I'd guess that t has something to do with the NC tip which has an effect on the angle of the wavefront?
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Re: Centre of Pressure (Cp) and the movement of...

Postby rocket_troy » Wed Sep 05, 2012 2:27 pm

cryoscum wrote:Interestingly the CP location returns to almost the initial position, and then stays there, once you get to M4-ish, of course assuming the graph is accurate. If so, maybe there is something inherently different to the NC or overall design that allows the CP position to stay behind it's launch position. I'd guess that t has something to do with the NC tip which has an effect on the angle of the wavefront?

Dunno, it's the closest thing to the geometry of the HPR rockets we're discussing here that I could find. I'm assuming it's the results of wind tunnel testing as they mention that also for the 10deg AOA data, so I can't see any reason why the zero AOA data wouldn't be from empirical results also.
I might post the question to the folks on ARocket.

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Re: Centre of Pressure (Cp) and the movement of...

Postby OverTheTop » Wed Sep 05, 2012 3:36 pm

If you check out page 12 (figures 10, 12, 13) of the document Nike Apache Performance Handbook":
http://hdl.handle.net/2060/19630003845
you will see that the Cp moves forward (further from base) as Mach number rises for the Nike Apache sounding rocket (Apache sustainer stage).

Figure 10 shows about a 5" forward shift for each Mach increase (approximate numbers) in the short length Apache. Long Apache (40" longer) almost doubles the rate of Cp movement forward. That is on a 6.5" airframe.
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Re: Centre of Pressure (Cp) and the movement of...

Postby cryoscum » Wed Sep 05, 2012 3:44 pm

I did a sim of the Aerobee 150 and scaled it down to a 3" inner diameter, put a big motor in it and then simmed it with different NC's. The NC's weights were all overridden to be the same to ensure that didn't have any effect on the sim. The resulting graphs show CP location (as measured from the NC tip) relative to Mach number.
1.JPG

NC's_all-5-to-1.jpg


Looks like:
- the NC shape does make a difference as to how much the CP moves for the same rocket, but this seems to be just a function of the difference in speeds achieved with the different NC's
- The max CP variance is no more than 0.3 calibres, but the performance of the rocket is hugely affected but the type of NC you use. They all had a max vel of between M3.18 and M3.20, but the Ogive sims almost 2k' higher than the Conical with the others in between.
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Re: Centre of Pressure (Cp) and the movement of...

Postby rocket_troy » Wed Sep 05, 2012 4:50 pm

OverTheTop wrote:If you check out page 12 (figures 10, 12, 13) of the document Nike Apache Performance Handbook":
http://hdl.handle.net/2060/19630003845
you will see that the Cp moves forward (further from base) as Mach number rises for the Nike Apache sounding rocket (Apache sustainer stage).

Figure 10 shows about a 5" forward shift for each Mach increase (approximate numbers) in the short length Apache. Long Apache (40" longer) almost doubles the rate of Cp movement forward. That is on a 6.5" airframe.

Interesting, although these numbers look theoretical? I'd like to see actual measured results.

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Re: Centre of Pressure (Cp) and the movement of...

Postby OverTheTop » Wed Sep 05, 2012 5:19 pm

Interesting, although these numbers look theoretical? I'd like to see actual measured results.


I got the impression they were empirically determined from actual measurements and flights. I need to confirm that though.
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Re: Centre of Pressure (Cp) and the movement of...

Postby Lamp » Thu Sep 06, 2012 9:13 am

cryoscum wrote:Given the above, i.e. the fact that AoA has such a big effect and the fact that rockets have fins, not tail cone flairs, can it be surmised that once the NC shock wave forms, i.e. around Mach1, the air in its 'shadow', including that surrounding the fins, are pretty much a turbulent mess and the effect of the fins become less pronounced, reducing their lift and thereby moving the CP forward?


I presumed this was what happened to my 38mm min diameter that went unstable at Williams as it had all fins with the body when recovered (one was almost broken off, but I think this was from the high speed landing). It had 1.0 caliber of stability at launch but quite a narrow fin span. I think the boundary layer turbulence in the Mach transition combined with the narrow span caused the CP to move forward of the CG.

In the end I concluded that a stability margin of 1 was not enough for Mach transition but also I think it depends on the fin span....The fins have to be wide enough to clear the turbulent air that must form around the body.
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Re: Centre of Pressure (Cp) and the movement of...

Postby cryoscum » Thu Sep 06, 2012 9:27 am

Hi Pete

I, in retrospect, also think my 2011 Mach Madness entry fell foul of this. The staibilty was good up to Mach 2, but the NC exited stage left at Mach 2.2. Those who saw it thought a fin had come off, but that was not the case. I suspect the topic of this whole discussion is what caused the wobble that broke the NC, not the broken NC causing the wobble. This theory to be tested soon :shock:

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