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Author Topic: Stunt Plane Parameter Calculator  (Read 1355 times)

Offline Howard Rush

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Stunt Plane Parameter Calculator
« on: December 26, 2020, 04:53:32 PM »
Here's a spreadsheet to calculate some stuff that's easy to calculate, but kinda rule-of-thumby. It introduces the Buck coefficient, invented today by me, based on Brett's advice that absolute tail length is more useful than tail length relative to wing chord.  I just embellished that by dividing by circle radius, making it look more scholarly. 
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Online Dave Rigotti

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Re: Stunt Plane Parameter Calculator
« Reply #1 on: December 26, 2020, 06:18:16 PM »
Thanks Howard!
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Offline Chuck_Smith

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Re: Stunt Plane Parameter Calculator
« Reply #2 on: December 27, 2020, 08:04:13 AM »
Thanks Howard,

Pretty darned cool. What would be even cooler would be to have all of us enter our data and have the results plotted graphically. Or even better, take the winning ships from the last 50 years and see how they compare and changed over time or overlayed on the data

I suspect that with the advent of electric power and the fixed CG we'll the tail volume increasing somewhat noticeably, right Igor ;D? Or at least we'd see a divergence in tail volume of electric vs IC power choice.

But I should add that from a maneuverability standpoint and not static stability, the tail volume can be somewhat (OK, very!)  misleading. We really care about the moment generated vs. inertia tensor of the airplane.  That's where maximizing comes into play. An infinitely long tail would have an infinite pitching moment upon an infinitesimal elevator deflection, right?  But then again it would be infinitely massive so it would never move! Conversely for the infinitely short case. All other things equal, a light model turns faster than a heavy one. Keep the aerodynamic forces constant but at the same time increase the inertia tensor - things slow down.

Or how you distribute the mass. Two planes may be identical in planform and mass, but one has the battery on the CG and the other in the nose. Which one turns faster?


Peace,

Chuck
« Last Edit: December 27, 2020, 09:31:53 AM by Chuck_Smith »
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Offline Howard Rush

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Re: Stunt Plane Parameter Calculator
« Reply #3 on: December 27, 2020, 12:30:50 PM »
Yep. Graphics would be cool, and a lot of stuff is left out that could have been included without requiring any more effort by the user. For example, I should have estimated wing and tail lift curve slopes.
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Offline Igor Burger

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Re: Stunt Plane Parameter Calculator
« Reply #4 on: January 11, 2021, 10:50:50 AM »
I suspect that with the advent of electric power and the fixed CG we'll the tail volume increasing somewhat noticeably, right Igor ;D? Or at least we'd see a divergence in tail volume of electric vs IC power choice.

1/ I do not know if "the longer the better" probably not and 2/ I do not know if electric is different than IC - probably also not

However I think there is some optimum (here I do not mean to compare model with 2m long tail flying 1,5m radiuses, I mean real numbers) ... and that optimum I mean between position of CG means static stability and "maneuverability". Means there can be some optimum of tail length and horizontal tail area, elevator area etc (not needs to be only tail volume in meaning volume X arm length) which will allow to move CG so that the static stability will be highest. It will need to seat at such simulator/calculator and try some configurations ... whe know what to hunt for, we have calculator, whe know how to do it ... but .... but for me answer is still ... no time no time  n~

Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #5 on: January 17, 2021, 01:18:59 PM »
An infinitely long tail would have an infinite pitching moment upon an infinitesimal elevator deflection, right? 


   And the torque would go to zero the instant it moved, because the AoA be infinitely sensitive to rate. That's the part that everyone seems to consistently ignore, and while making it longer might increase the initial torque (while also increasing the moment of inertia...) it also limits the maximum rate to a smaller value.

    Brett

Offline Igor Burger

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Re: Stunt Plane Parameter Calculator
« Reply #6 on: January 17, 2021, 01:42:01 PM »

   And the torque would go to zero the instant it moved, because the AoA be infinitely sensitive to rate.


Yes, that is exactly what I mean, may be small example will make it clear - imagine extremely long tail (with no mass, so it does not make any inertia) which should turn fuselage in 0,2s long corner of radius 3m and on path 4m long measured at CG. If the tail is 30m long it must travel 10x longer path on the same distance, so what must be its deflection? something very close to 90 degrees ... what it will do in level flight?

And if we add some inertia, that extreme deflection will loose lift to accelerate it (the tail speed will be 10x higher than CG).

Unfortunately there are too many inputs to the equation, so solution is not so easy as it looks.

May be picture from my SN article will show it better.

Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #7 on: January 17, 2021, 02:08:58 PM »

Unfortunately there are too many inputs to the equation, so solution is not so easy as it looks.

   It's worse than that, it's a differential equation (or series of them) with trig functions as some of the factors, so there is almost certainly no closed-form solution.

    Fortunately, you don't really need one to get the concept, and plenty of people have experimented and gotten close enough by cut-and-try.

    Brett

Offline Igor Burger

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Re: Stunt Plane Parameter Calculator
« Reply #8 on: January 17, 2021, 02:14:13 PM »
Fortunately we have excel with solver, so it is easy to make so many trials in one evening like 10 buildes can do models in life  VD~

Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #9 on: January 17, 2021, 03:12:29 PM »
Fortunately we have excel with solver, so it is easy to make so many trials in one evening like 10 buildes can do models in life  VD~

   We also have MATLAB and any number of various solvers. But fortunately, 100s of our buddies have already done it the hard way for 70 years, which makes it easy to see if we put our equations in correctly. If the answer is anything outside the range of about 16" to 19", it's probably wrong...

     Brett

Offline Chuck_Smith

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Re: Stunt Plane Parameter Calculator
« Reply #10 on: January 18, 2021, 05:39:34 AM »
It's worse than worse than that Brett, since the AoA of the tail is dependent on the downwash from the wing, which on a flapped CLPA ship is - significant. In fact, the flow field is so heavily affected that there's a non-trivial contribution to the pitching moment from the fuselage too.
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Re: Stunt Plane Parameter Calculator
« Reply #11 on: January 18, 2021, 07:44:25 AM »
Yes, that is exactly what I mean, may be small example will make it clear - imagine extremely long tail (with no mass, so it does not make any inertia) which should turn fuselage in 0,2s long corner of radius 3m and on path 4m long measured at CG. If the tail is 30m long it must travel 10x longer path on the same distance, so what must be its deflection? something very close to 90 degrees ... what it will do in level flight?

And if we add some inertia, that extreme deflection will loose lift to accelerate it (the tail speed will be 10x higher than CG).

Unfortunately there are too many inputs to the equation, so solution is not so easy as it looks.

May be picture from my SN article will show it better.

Igor, I'm not certain I agree with the changing AoA in your illustration. (I admit I maybe interpreting it wrong though.)  The curved streamline you drew is not representative of what's going on around the plane. There will be significant downwash behind the wing so the streamlines will deflect rather than stay constant with the flight path. I suppose there may be some superposition of the velocity vectors but my experience lends me to believe the downwash effect will greater. It's pretty easy to quantify the downwash.

If you look at modern sailplane you'll see that the nose is low and the aft fuselage curves downward. This is done to align the fuselage with the incoming upwash and outgoing downwash of the wings at flying speed. Given that sailplanes have really high aspect ratios and thus have much lower induced drag than other aircraft, the fact that this effect is visible in the fuselage design shows how strong the effect can be.

Finally, we need to remember that as we deflect the controls the pitching moment coefficient for for the airfoil changes too. (At the tail too!)

And for the eight hundred pound gorilla in the room - when we make a square corner there's a really strong shed vortex that hits the tail, and we never speak of it. But if you know what you're looking for, you can see it affect the dynamics at the crossing of round eights where we make our largest and fastest changes in control deflections and flight path. It's that barely perceptible timing thing we take for granted since we're used to it. But it's there. Watch closely and you'll see it.


Long story short - there are so many coupled non-linearities a theoretical solution is almost incalculable. Use what works. But - it sure is fun to muse about it.

Chuck

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Offline Igor Burger

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Re: Stunt Plane Parameter Calculator
« Reply #12 on: January 18, 2021, 08:34:09 AM »
The curved streamline you drew is not representative of what's going on around the plane.

That line is not "streamline" (hard to expect that stream goes through the wing  ;D ) it is illustrative PATH of the wing LE at fuselage.

So yes, of course I agree there is some downwash, but it does not change fact that there is also effect on picture making AoA at tail angled and extremely long tail will magnify that effect (and minimize downwash) and that is what is going on here.


Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #13 on: January 18, 2021, 10:44:30 AM »
It's worse than worse than that Brett, since the AoA of the tail is dependent on the downwash from the wing, which on a flapped CLPA ship is - significant. In fact, the flow field is so heavily affected that there's a non-trivial contribution to the pitching moment from the fuselage too.

   Yes, there is certainly more than one thing happening at the same time, but it is generally useful to look at the elements of the system one-at-a-time, and build up the model that way. If nothing else, you get limiting conditions very easily by assuming that a particular element is the only one, and then be able to see how something like, say, downwash, affects your supposed dominant effect (vector sum of omega( r) and V))

     That's the beauty of what Igor was talking about (i.e. solving it numerically or with approximations (like a power series) instead of attempting it in closed-form), you can just start adding the elements in one at a time and see how much each one matters, and maybe find you can disregard some of them because the magnitude is negligible.

    And in any case, you have to consider how accurately you need an answer. In this case, two significant figures is about what you need, any more and the answer starts to be affected by things you have little or no control over.

    Brett

Online Ken Culbertson

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Re: Stunt Plane Parameter Calculator
« Reply #14 on: January 18, 2021, 01:43:14 PM »
.... And in any case, you have to consider how accurately you need an answer. ....

One thing that has always bothered me is the comment that comes up all of the time "but we are flying in a circle, not a straight line".  I wonder just how much that really matters when it comes to the basics of airfoil and movements especially since the plane is really trimmed to fly in a straight line more or less.  Are there any wind tunnel tests in a 120' donut?  All of Al's work with flaps and airfoils were in a straight line and even if we did get a nice curved airflow, we still have the wind changing the direction of the air mass an infinite number of times each lap.  Should wind speed be considered in formulas?  We fly most of our maneuvers at the point where airspeed most closely matches ground speed.  Since only airspeed matters, I have often wondered how much it actually changes in wind.  If it doesn't change much, and I suspect it doesn't, then neither wind or flying in a circle should have a major impact on design.  Am I wrong?

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Offline Chuck_Smith

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Re: Stunt Plane Parameter Calculator
« Reply #15 on: January 18, 2021, 01:59:40 PM »
Ken, it matters because our planes are (hopefully) continually in a sideslip. This means that the dihedral effect is always there. Most CLPA ships have the wing pretty much centered in the fuselage so that limits the effect. If  I was going to put a CLPA airplane in a section I would have the sideslip included when I adjusted the sting.


As far as the wind speed, the one that will bite you there is viscosity again. If it's blowing 10 at shoulder height it's blowing faster 75' up. I've seen some pretty decent wind gradients over the years in full size aircraft.
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Online Ken Culbertson

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Re: Stunt Plane Parameter Calculator
« Reply #16 on: January 18, 2021, 02:41:32 PM »
Ken, it matters because our planes are (hopefully) continually in a sideslip. This means that the dihedral effect is always there. Most CLPA ships have the wing pretty much centered in the fuselage so that limits the effect. If  I was going to put a CLPA airplane in a section I would have the sideslip included when I adjusted the sting.


As far as the wind speed, the one that will bite you there is viscosity again. If it's blowing 10 at shoulder height it's blowing faster 75' up. I've seen some pretty decent wind gradients over the years in full size aircraft.
I "semi" agree, especially the second part.  I was only considering the horizontal.  You are correct about the vertical.  Where I am not convinced is the sideslip's effect on the design.  I will grant you that there will be some of that when there is wind because, just like a motorboat in current, the wing is not moving through a stagnant airmass. But, when it is calm there will be very little sideslip.  Hence, it is the wind not the curvature that is the design factor to consider if any.  All of that changes if you have asymmetrically airfoiled your fuselage.

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Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #17 on: January 18, 2021, 05:46:22 PM »
Since only airspeed matters, I have often wondered how much it actually changes in wind.  If it doesn't change much, and I suspect it doesn't, then neither wind or flying in a circle should have a major impact on design.  Am I wrong?

  Yes - you definitely do care about the groundspeed, in fact that is critical,  because the centrifugal force is determined from groundspeed (inertial speed, but you can safely  ignore the rotation  of the earth in this case). And the airplane certainly does not maintain a constant airspeed as the wind vector changes or moves around, as long as it has any mass.

     Brett

Online Ken Culbertson

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Re: Stunt Plane Parameter Calculator
« Reply #18 on: January 18, 2021, 06:19:25 PM »
  Yes - you definitely do care about the groundspeed, in fact that is critical,  because the centrifugal force is determined from groundspeed (inertial speed, but you can safely  ignore the rotation  of the earth in this case). And the airplane certainly does not maintain a constant airspeed as the wind vector changes or moves around, as long as it has any mass.

     Brett
Of course it does.  I must have made my point poorly.  I am only concerned about how these things affect design.  Since we don't have any practical way to measure the airflow over a flying PA plane we are stuck with the straight ahead methods.  My point is that they are sufficient.

Ken
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Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #19 on: January 18, 2021, 09:36:13 PM »
Of course it does.  I must have made my point poorly.  I am only concerned about how these things affect design. 

   A large factor in the latest "best airfoil" thread was how it worked in the wind. In the good old days, how it would work in the wind dominated most of the aspects of how the airplane was designed, from Aldrich and his limited power/thin wing/giant flap, to Al's thick wing, giant flaps,  and far forward CG, then the west coast long tails and small flaps and then radically aft CGs. Only when we got overkill power did flying in the wind stop being the primary design driver.

   Even in this thread, talking about torque response and tail moment, is indirectly driving how big a flap you can use, what CG you can use, and how those affect the whip-up.

    Brett
« Last Edit: January 21, 2021, 06:47:34 AM by Brett Buck »

Offline Howard Rush

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Re: Stunt Plane Parameter Calculator
« Reply #20 on: January 19, 2021, 02:14:00 PM »
   It's worse than that, it's a differential equation (or series of them) with trig functions as some of the factors, so there is almost certainly no closed-form solution.

It's easier than it looks.  One can linearize it about an operating point.  Stunt planes don't have that many operating points, and fly at pretty constant speed and at constant altitude. 

Igor, I'm not certain I agree with the changing AoA in your illustration. (I admit I maybe interpreting it wrong though.)  The curved streamline you drew is not representative of what's going on around the plane. There will be significant downwash behind the wing so the streamlines will deflect rather than stay constant with the flight path. I suppose there may be some superposition of the velocity vectors but my experience lends me to believe the downwash effect will greater. It's pretty easy to quantify the downwash.

If you look at modern sailplane you'll see that the nose is low and the aft fuselage curves downward. This is done to align the fuselage with the incoming upwash and outgoing downwash of the wings at flying speed. Given that sailplanes have really high aspect ratios and thus have much lower induced drag than other aircraft, the fact that this effect is visible in the fuselage design shows how strong the effect can be.

I worried about downwash a lot as a kid, so I put long tails on my combat planes.  The benefit I got was also due to pitching moment due to pitch rate (Igor's picture).  Low-aspect-ratio combat planes have lots of downwash, but they have q out the wazoo.  It's different from putting the flaps down on a Cessna and retrimming to keep flying level.  There, one has downwash, but no pitch rate at all. 

I think that the sort of question that a stunt plane designer asks is, "what happens if I take a given design and make the tail longer?"  The pertinent parameters may be rate of change of downwash or Cmq with tail length. As Igor said, downwash decreases and Cmq increases (absolute values), both of which call for more elevator deflection.    A curious consequence of this stuff is that elevator required for a given loop size changes with air density.  This effect may increase with tail length (TBD (by me, anyhow)).  Those of us with long-tail combat planes had to cut way down on elevator travel at the hot-and-high 1984 Reno Nats.  I blamed Reynolds number at the time, but now I think most of it was Cmq.  Was downwash part of it, too?

Interesting tidbit about sailplanes.  That figures if they are optimized to fly level, but they are probably optimized to fly in a turn with pretty high pitch rate.  I'm too lazy to calculate anything, but I can ask guys who did. 

One thing that has always bothered me is the comment that comes up all of the time "but we are flying in a circle, not a straight line".  I wonder just how much that really matters when it comes to the basics of airfoil and movements ...

Me, too.

Are there any wind tunnel tests in a 120' donut? 

Yes, sorta.  Early aeronautical guys like Langley tested wings on whirly things.  Data were confounded by the wake from the previous lap, so folks didn't pay much attention to it, not realizing the important application to control line airplanes.   

Should wind speed be considered in formulas? 

Wind velocity should, specifically the sideslip component, as Ken said.  You can see the effect from old NACA reports. 

Then there's the issue of control line airplanes being part kite. 

Ken, it matters because our planes are (hopefully) continually in a sideslip. This means that the dihedral effect is always there. Most CLPA ships have the wing pretty much centered in the fuselage so that limits the effect.

Centering the wing vertically makes the dihedral effect more symmetrical in inside and outside loops, but it's still there, and I think it's important.  Modern combat planes have swept-forward wings to reduce or eliminate dihedral effect. 

   A large factor in the latest "best airfoil" thread was how it worked in the wind. In the good old days, how it would work in the wind dominated most of the aspects of how the airplane was designed, from Aldrich and his limited power/thin wing/giant flap, to Al's thick wing, giant flaps,  and far forward CG, then the west coast long tails and small flaps and then radically aft CGs. Only when we got overkill power did flying in the wind stop being the primary design driver.

Did I tell you my Brett Buck flying-in-the-wind story?  At the October Golden State Stunt Championships, the West's biggest stunt contest, we have a banquet Saturday evening.  Traditionally this includes the Address of the National Champion.  Said Champion was away at work or something at the last GSSC banquet, so Brett was drafted to speak.  He talked about how to fly in the wind.  It was a good talk.  He stressed the need to keep the airplane from blowing down after the the first loop of the clover.  The next day, it was breezy for my second flight.  The clover will be no sweat, I told myself.  Not only had Brett advised me what to do in his lecture, but the wind was blowing at the sun, and the sun elevation app on my telephone told me that the sun would be at about 42 degrees during my flight.  I did the first loop, then observed my airplane flying the level part.  "What's it doing way down there?" I asked myself.
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Online Brett Buck

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Re: Stunt Plane Parameter Calculator
« Reply #21 on: January 20, 2021, 09:37:58 PM »
Did I tell you my Brett Buck flying-in-the-wind story?  At the October Golden State Stunt Championships, the West's biggest stunt contest, we have a banquet Saturday evening.  Traditionally this includes the Address of the National Champion.  Said Champion was away at work or something at the last GSSC banquet, so Brett was drafted to speak.  He talked about how to fly in the wind.  It was a good talk.  He stressed the need to keep the airplane from blowing down after the the first loop of the clover.  The next day, it was breezy for my second flight.  The clover will be no sweat, I told myself.  Not only had Brett advised me what to do in his lecture, but the wind was blowing at the sun, and the sun elevation app on my telephone told me that the sun would be at about 42 degrees during my flight.  I did the first loop, then observed my airplane flying the level part.  "What's it doing way down there?" I asked myself.

       I am glad people got something out of that. They hit me up to do it at about 11 in the morning, and I came up with that entirely off the top of my head, and spent most of the afternoon looking around for supplies at various art or office supply stores. It wasn't totally terrible, but preparation was not to my usual standards.

     Brett

Offline Chuck_Smith

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Re: Stunt Plane Parameter Calculator
« Reply #22 on: January 21, 2021, 06:02:44 AM »
Cool comments Howard.

About Cmq, pitch rate moment is the one stability coefficient that is hard to predict and to measure - at least for me on slow flying, light airframes.

Once you get to the point where you're past thinking in the classic 2D, infinite wing mode (which isn't reality on an airplane) you start thinking more in terms of circulation and Prandtl. That's where it gets really iffy and the predicted results start to be less than the theoretical predictions.  BTW, this is all for slow flying planes. Once they go fast life gets easier.

On something like your Nemesis the wing shape is fixed so the Cla and Cma are fairly easy to predict.

Compare that, however; to a CLPA ship with large flaps and  large deflections. The change in circulation after the vortex is shed because of the flap movement is comparatively quite large because of the non-trivial change in camber and AoA due to the flap's deflection. That means a larger vortex shed, and hence a large change in circulation. The wildcard now becomes viscosity and how far away from wing the circulation propagates. And, since air has mass it

1) takes (ultimately) thrust to replace the  airplane's momentum lost to the air movement
2) needs to be tucked away in our analysis that Sir Isaac still applies, and any change in the angular momentum of the air needs to be balanced out to net zero plus thrust impulse during the turn. [And that's the big wet blanket that gets thrown over the infinite wing model.]


Now add in that the same effect is happening in the reverse direction at the tail, and that the shed vortex of the wing gets superimposed upon that of the horizontal tail and well, I warned you leaving infinite wing 2D analysis can be fun!

Lucky for us, we have mountains of empirical results. And with an understanding of circulation and lift lines, we can all appreciate why canards suck at subsonic speeds.

Peace,

Chuck

« Last Edit: January 21, 2021, 10:08:19 AM by Chuck_Smith »
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