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Author Topic: Constant velocity or constant angular rate ?  (Read 2161 times)

Online Mark wood

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Re: Constant velocity or constant angular rate ?
« Reply #50 on: January 14, 2022, 12:24:48 AM »
One thing to keep in mind, and some of you do, is that some stuff varies with the square of airspeed and some stuff remains constant with airspeed.  I imagine a doodad hooked up to the flap control horn with a bobweight-actuated slider to work the throttle.  Details left as an exercise.   

Interestingly so does G.

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“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Peter Germann

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Re: Constant velocity or constant angular rate ?
« Reply #51 on: January 14, 2022, 05:56:26 AM »
I am following the ongoing discussion on automatic speed controllers with great interest and have great respect for the quality of the arguments put forward by the experts. It is this kind of objective discussion which maintains and promotes our common cause. Many thanks to the participants and to Stunthangar for maintaining the website.

According to what has been published here so far, it could be that after a complex development process we will see e a rather complex and not cheap system. I therefore take the liberty of proposing a first step to gain knowledge first:

A prerequisite for further steps should be that in order to design an automatic speed control system, the term speed should be defined. Whether the purpose of the controller should be to keep constant a given value for the airspeed, the angular speed or the groundspeed remains to be determined.

In order to support the opinion making on which speed to aim for, I believe that it would be useful to allow experiments on as broad a possible basis. This could be done by an adjustment of the making legal manual in-flight speed control by the pilot. For electric drives (and possibly IC motors, too) the current technology available would make it possible to make such systems available to a wide range of pilots at low cost.

I am positive that wide spread experience gained from manual in-flight speed control would be helpful defining requirements for the development of automatic speed controllers.
Peter Germann

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Re: Constant velocity or constant angular rate ?
« Reply #52 on: January 14, 2022, 10:02:04 AM »
I am following the ongoing discussion on automatic speed controllers with great interest and have great respect for the quality of the arguments put forward by the experts. It is this kind of objective discussion which maintains and promotes our common cause. Many thanks to the participants and to Stunthangar for maintaining the website.

According to what has been published here so far, it could be that after a complex development process we will see e a rather complex and not cheap system. I therefore take the liberty of proposing a first step to gain knowledge first:

A prerequisite for further steps should be that in order to design an automatic speed control system, the term speed should be defined. Whether the purpose of the controller should be to keep constant a given value for the airspeed, the angular speed or the groundspeed remains to be determined.

In order to support the opinion making on which speed to aim for, I believe that it would be useful to allow experiments on as broad a possible basis. This could be done by an adjustment of the making legal manual in-flight speed control by the pilot. For electric drives (and possibly IC motors, too) the current technology available would make it possible to make such systems available to a wide range of pilots at low cost.

I am positive that wide spread experience gained from manual in-flight speed control would be helpful defining requirements for the development of automatic speed controllers.

Actually Peter what I am doing can be accomplished with an Arduino based board. There's zero automation. Basically the output can be tuned to match what the airplane is required to do. I published my thoughts quite a bit prematurely and this precipitated something much more complex than is necessary. My original purpose of asking the question was to gain insight on what I need to present in terms of performance prediction. As it is, a simple input from a potentiometer can be read and used to create the command. I use gain as the control would have a base level output for level flight. Then any needs of the airplane would commanded by the 1 - Cos X gain which, as can be seen, is a function of drag and can be made to fit quite well. This means that the control can output the thrust as required for the airplane to not loose energy from the turning. This gain could be adapted to a feedback controller but my experience as a powerplant engineer tells me it's not necessary for what we are doing. This same architecture is what wee use in helicopter engine control as failure mode accommodation which works nearly as well or as good as the hydro mechanical control systems.

What this means is that, if the system is trimmed correctly, the exit of the turns will only decay in velocity by the change in gravitational potential energy. I did not present this quite yet as this is the portion of my article I am working on. I am working through the mathematic derivation and the illustrations to demonstrate. Basically, once we can match the drag, the analysis becomes similar to a frictionless change in total energy. The question becomes one of were does the work come from which is obviously the powerplant. It is extremely hard to describe in words and requires the illustrations and mathematic derivation. If you haven't read my thread on motor Control, please have a read there.

My initial Energy conversion yielded some 28 ish fps velocity delta. The only computation I have worked through is simple, frictionless change in altitude where the change in kinetic energy from the change in potential energy drives the velocity change. Offhand that seems like allot but I have no real intuitive feel for it initially. I know the airplane slows down allot from watching the videos now, but I never really perceived that deceleration until I went looking for it and it verifiable in my videos. This is what begets the thread title question. The following use 65' base circle.

For instance, in level flight the airplane is going 78 fps which translate to about 69 Deg/s (Dps). The delta V of 28 fps means the airplane would be flying at about 50 fps on the 45 degree azimuth. This then translate to 289/360 = 0.8, and 50 fps  / 0.8 D/ft = 62.5 Dps. Our perception of velocity is a function of the characteristic length of the thing we're watching and perceive the airplane as flying at a near constant velocity. So what I think we like is that the airplane crosses the high leg at near the same angular rate. I.e. we'd like to see i flying at a near constant 69 Dps in this case. I'm not so sure and that is the foundation of my question, because the small change I've derived is consistent with my observation, although not extensive.

In the simple version of my control, there is no need for any attitude information. However, in order to compensate for the mgh term in the energy a means of doing work to mitigate the loss is necessary. Basically we need to add or decrease thrust as a function of the pitch attitude as a function of the angle between the airplane and the gravity vector. This again doesn't need to be a complicated computation other than filtering the input from the IMU.

Take a square non tethered loop as an example. When we are in level flight we make the assumption Thrust equals Drag, T=D. In order to transit the corner we add thrust to compensate drag and maintain T=D. That compensation is the 1-cos X term. If that term is exactly correct, it won't be, then the exit would be slower by the change in altitude 1/2mV^2 = mgh leads to dV =sqrt(2*g*dh). For the non tether case during the turn the g vector changes as Sin X. It's not so simple in 3 space. In order to mitigate the gh term we simply need to add a trimming function to the gain computation Kg*Sin X so that the power gain would now be K1*(1-K2*Cos(K3*X)) + Kg*Sin X. With this we can now fine trim the airplanes velocity to suit what our perception wishes.

The need to know the g vector is only necessary to make the small improvement. In upset training I teach my student the importance of drag in the recovery and I demonstrate the difference between pulling 2 G's  from vertically nose down and 4 G's nose down. In the first case we increase velocity tremendously while in the second case we actually slow down.

I my perspective, the impact of the IMU is mostly detrimental. This is due to two things. First is the amount of filtering required to get a good signal which creates a lag in response. Second is the encroachment in the processor timing margin which also leads to increased lag. Actually those two combined are the source of the lag. What I am finding on the Arduino products is that the smaller ones won't load and run the calibration libraries. I'm a total amateur when it comes to code and electronic hardware and have always relied on the others in my team for that.

Thanks for brining this up and letting me have the floor to present more of this effort. After I manage to update my article with this portion, I'll present the end game concept which incudes the variable pitch propeller.
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Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Brett Buck

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Re: Constant velocity or constant angular rate ?
« Reply #53 on: January 14, 2022, 10:36:25 AM »

According to what has been published here so far, it could be that after a complex development process we will see e a rather complex and not cheap system.

   I think the hardware will not be terribly expensive, not much different from Igors or the others. The firmware will take some development, but once you have it, reproducing it is free. So I don't recurring costs will be anything unreasonable - there will certainly be less actual production cost than, say, an AAC 61 with a pipe and a carbon prop. It's almost a miracle that it only costs $500.

     I also very strongly expect that when it comes down to it, the control system itself will be vastly simpler than some of the ideas displayed here - just following the real-life experience, most users have wound up restricting the range of adjustments and features to the point that the feedback only slightly alters the system from a fixed RPM governor. Same development curve as piped engines - yes, you can make it do stuff, but overdoing it is *extremely common*. I have seen a few of these "better" systems that were wildly unstable limited only by something saturating and limit-cycling.

    I think of threads like this more like a thought experiment, but you can't design it from scratch like we had requirements to meet, because we have never defined any requirements and only have vague notions of why some settings work better than others.

   The one thing that seems to be clear (since Igor pointed it out 5 years ago and Paul and others have confirmed it) that the current system is limited by the ability to spin the prop up or down. An obvious development step is to do something to reduce or remove that restriction and then see what effect it has. That seems to be what Paul and Howard are working on. 

    Brett

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Re: Constant velocity or constant angular rate ?
« Reply #54 on: January 14, 2022, 10:48:45 AM »
   I think the hardware will not be terribly expensive, not much different from Igors or the others. The firmware will take some development, but once you have it, reproducing it is free. So I don't recurring costs will be anything unreasonable - there will certainly be less actual production cost than, say, an AAC 61 with a pipe and a carbon prop.

     I also very strongly expect that when it comes down to it, the control system itself will be vastly simpler than some of the ideas displayed here - just following the real-life experience, most users have wound up restricting the range of adjustments and features to the point that the feedback only slightly alters the system from a fixed RPM governor. Same development curve as piped engines - yes, you can make it do stuff, but overdoing it is *extremely common*.

    I think of threads like this more like a thought experiment, but you can't design it from scratch like we had requirements to meet, because we have never defined any requirements and only have vague notions of why some settings work better than others.

   The one thing that seems to be clear (since Igor pointed it out 5 years ago and Paul and others have confirmed it) that the current system is limited by the ability to spin the prop up or down. An obvious development step is to do something to remove that restriction and then see what effect it has. That seems to be what Paul and Howard are working on. 

    Brett

Possibly, but this will work on a $7 Arduino running C+. From my point of view, this is what I am working on. If it gets taken to a different place that's great. The real test is when it flies and that is a project for after I finish coding the datalogger. I actually have an operational Arduino timer now with the radio interface. It isn't a big change to get one to fly. The hardest code branch is the gain tuning input. My intent is to initially fly without an IMU. Reducing the propeller mass is always good and I'd sure like to see how they are doing the mold process.
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“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Brett Buck

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Re: Constant velocity or constant angular rate ?
« Reply #55 on: January 14, 2022, 11:08:33 AM »
Possibly, but this will work on a $7 Arduino running C+.

   Ugh, C++, the bane of my existence, and the source of the holes burned through my stomach lining? There is no utility or value to object-oriented code in an embedded processor, and if it is not object-oriented, you don't need C++ (vice C or other procedural languages).

    But yes, that was my point, the hardware is not going to be expensive.

     Brett

Offline Tim Wescott

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Re: Constant velocity or constant angular rate ?
« Reply #56 on: January 14, 2022, 11:47:37 AM »
   Ugh, C++, the bane of my existence, and the source of the holes burned through my stomach lining? There is no utility or value to object-oriented code in an embedded processor, and if it is not object-oriented, you don't need C++ (vice C or other procedural languages).

If you want to have that discussion, we should take it outside.

Folks -- even software professionals who should know better -- confuse C++ done wrong with C++ done right.  Like Fortran done wrong, or C done wrong, or Ada done wrong, or machine code done wrong, or any engineering process whatsoever that's done wrong, C++ done wrong is just crap.  C++ done right is every bit as good as those other things done right, but "done right" means, in large part, understanding what the @#$% you're doing.

And if it's done right it can let you write safe and elegant code for larger systems than you can in C (no comment on Ada or modern Fortran, because I've only debugged Ada code* and have only written Fortran for school assignments, back in the '80's).

If you're seeing bad C++, you need to fire the software engineers that are doing it wrong and hire a crew that knows how to write code for embedded systems and are willing to work to understand how compilers work -- just changing languages without swapping out the components in the process that are causing the real trouble won't fix things.

Almost every new line of code in the airborne FLIR products coming out of Portland was written in C++ starting in around 1985 1995 (edit: got my dates wrong).  By 1990 2000 or so it was nearly every line of code in the product lines coming out of FLIR Portland.  The code base was far bigger than it was when we were writing in C, the bug rate was about the same, the man hours per line of code was about the same, but the lines of code per bit of functionality was way higher -- meaning that management got way more bang for the buck.

Because we** made sure that when we adopted it, we did it right.

* Written by someone with an opinion about C similar to yours about C++, and too damned arrogant to look at her own code.

** "We" meaning me and a fellow engineer who had been writing object-based*** code for years without knowing it, and who actually know how the tools work, and who care enough to know how embedded code has to work.

*** Not to be confused with "pure" object-oriented code -- that's bad in a deeply embedded system.
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Online Mark wood

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Re: Constant velocity or constant angular rate ?
« Reply #57 on: January 14, 2022, 12:18:39 PM »
If you want to have that discussion, we should take it outside.

Folks -- even software professionals who should know better -- confuse C++ done wrong with C++ done right.  Like Fortran done wrong, or C done wrong, or Ada done wrong, or machine code done wrong, or any engineering process whatsoever that's done wrong, C++ done wrong is just crap.  C++ done right is every bit as good as those other things done right, but "done right" means, in large part, understanding what the @#$% you're doing.

And if it's done right it can let you write safe and elegant code for larger systems than you can in C (no comment on Ada or modern Fortran, because I've only debugged Ada code* and have only written Fortran for school assignments, back in the '80's).

If you're seeing bad C++, you need to fire the software engineers that are doing it wrong and hire a crew that knows how to write code for embedded systems and are willing to work to understand how compilers work -- just changing languages without swapping out the components in the process that are causing the real trouble won't fix things.

Almost every new line of code in the airborne FLIR products coming out of Portland was written in C++ starting in around 1985 1995 (edit: got my dates wrong).  By 1990 2000 or so it was nearly every line of code in the product lines coming out of FLIR Portland.  The code base was far bigger than it was when we were writing in C, the bug rate was about the same, the man hours per line of code was about the same, but the lines of code per bit of functionality was way higher -- meaning that management got way more bang for the buck.

Because we** made sure that when we adopted it, we did it right.

* Written by someone with an opinion about C similar to yours about C++, and too damned arrogant to look at her own code.

** "We" meaning me and a fellow engineer who had been writing object-based*** code for years without knowing it, and who actually know how the tools work, and who care enough to know how embedded code has to work.

*** Not to be confused with "pure" object-oriented code -- that's bad in a deeply embedded system.

Yeah, but I'm not the code guy. I can hack out a functional control using Arduino IDE which is the top of my ability. In fact I already have one. For an amateur user, such as myself, I can build what I need. I have no need for Level A, B or C software for this application. If you're willing to help me on that level, I would very much appreciate it but I'm on this road with focus and the next step is flying the control open loop on control input.
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Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Tim Wescott

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Re: Constant velocity or constant angular rate ?
« Reply #58 on: January 14, 2022, 05:51:18 PM »
Yeah, but I'm not the code guy. I can hack out a functional control using Arduino IDE which is the top of my ability. In fact I already have one. For an amateur user, such as myself, I can build what I need. I have no need for Level A, B or C software for this application. If you're willing to help me on that level, I would very much appreciate it but I'm on this road with focus and the next step is flying the control open loop on control input.

Not critiquing your choice -- first make it work, then make it work good.  The nice thing about CL is that assuming you're plane is in good condition, the worst that a software error will do is splat a pretty plane into concrete.

Just getting tired of Brett's rant, which appears to be based on some bad experiences and apparently without detailed knowledge of what he's critiquing.  I've ran into it before -- in the 1990's.  It's interesting to see it arising now.
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Re: Constant velocity or constant angular rate ?
« Reply #59 on: January 14, 2022, 06:15:24 PM »
Not critiquing your choice -- first make it work, then make it work good.  The nice thing about CL is that assuming you're plane is in good condition, the worst that a software error will do is splat a pretty plane into concrete.

Just getting tired of Brett's rant, which appears to be based on some bad experiences and apparently without detailed knowledge of what he's critiquing.  I've ran into it before -- in the 1990's.  It's interesting to see it arising now.

Thanks for that. There's some of this that I'm stretching on and code is where that is. Elliptical integrals is the other.
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“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Brett Buck

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Re: Constant velocity or constant angular rate ?
« Reply #60 on: January 14, 2022, 06:51:04 PM »
Just getting tired of Brett's rant, which appears to be based on some bad experiences and apparently without detailed knowledge of what he's critiquing.  I've ran into it before -- in the 1990's.  It's interesting to see it arising now.

    "Without detailed knowledge of what I am critiquing"?  Probably right, aside from the code review/"self-induced bug" hunting I was in 2 hours ago.

    Of course you can write proper embedded processor code in C++ - by forgetting the words "abstraction", "object" and just about everything that has ever been touted as an "advantage" of C++. Superset of C, right?

      Brett

Offline Brett Buck

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Re: Constant velocity or constant angular rate ?
« Reply #61 on: January 14, 2022, 06:55:10 PM »
Thanks for that. There's some of this that I'm stretching on and code is where that is. Elliptical integrals is the other.

   You are going to need to know basic coding to get what you need to do, done.

    What are you using elliptical integrals for - not this, surely?

      Brett

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Re: Constant velocity or constant angular rate ?
« Reply #62 on: January 14, 2022, 09:30:37 PM »
   You are going to need to know basic coding to get what you need to do, done.

    What are you using elliptical integrals for - not this, surely?

      Brett

I can write code Brett, but it's not my forte. I learned Fortran in college and can write C++ to a level. My skills are enough to build the basic control. I can hack others code into a package I can use. I find it refreshing actually, to learn more. 

Elliptical integrals - Nothing I can avoid. I think the most extensive would by integrating the work over a spherical path and that would be simply to show proof of a concept derivable via point conditions. The 2 D derivation makes intuitive enough sense to expand to 3 space. My math skills have atrophied in the 35 plus years sense I last used them on that level. From what I have been able to discern, that is something well within your umbrella of tools.
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Offline Brett Buck

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Re: Constant velocity or constant angular rate ?
« Reply #63 on: January 14, 2022, 09:49:32 PM »
Elliptical integrals - Nothing I can avoid. I think the most extensive would by integrating the work over a spherical path and that would be simply to show proof of a concept derivable via point conditions. The 2 D derivation makes intuitive enough sense to expand to 3 space. My math skills have atrophied in the 35 plus years sense I last used them on that level. From what I have been able to discern, that is something well within your umbrella of tools.

  Well, maybe, but I am very curious as to the applicability to this particular problem - you aren't attempting to come up with a closed-form equation for the airplane path, are you?  I certainly would not do that, and I don't think you need to, since you can numerically integrate more-or-less anything you need to, to arbitrary accuracy. Either that, or you are way ahead of us on something!

   Brett

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Re: Constant velocity or constant angular rate ?
« Reply #64 on: January 14, 2022, 10:11:21 PM »
  Well, maybe, but I am very curious as to the applicability to this particular problem - you aren't attempting to come up with a closed-form equation for the airplane path, are you?  I certainly would not do that, and I don't think you need to, since you can numerically integrate more-or-less anything you need to, to arbitrary accuracy. Either that, or you are way ahead of us on something!

   Brett

I may be way ahead of you on this or not, but it isn't because of integrating the path. That truly isn't necessary to design a control. That is the kind of thing we would do for an engine though but again that would be  more of a 3d look up table and we interpolate between points. I only mentioned it as a mathematical proof. Not for any other reason. I need to finish writing the performance analysis and present that. I've started but, as you know, written words don't convey concept well. Illustrating takes allot of time. This effort is good enough to warrant illustration better than the pictures of my white board.
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“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

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Re: Constant velocity or constant angular rate ?
« Reply #65 on: January 15, 2022, 05:42:02 AM »
There is a simple reason for using C++, that just about trumps any argument against it: the entire Arduino ecosystem is built around it.
All the libraries, hardware, examples, forums, etc are a huge resource, that (as far as I know) just is not matched in any other language.

You always have the option of using assembler with Arduino when you think it is more appropriate.

You also don't need to get into the weeds of object oriented stuff, and the code can end up looking a lot like regular C code.
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Re: Constant velocity or constant angular rate ?
« Reply #66 on: January 15, 2022, 06:37:18 AM »
There is a simple reason for using C++, that just about trumps any argument against it: the entire Arduino ecosystem is built around it.
All the libraries, hardware, examples, forums, etc are a huge resource, that (as far as I know) just is not matched in any other language.

You always have the option of using assembler with Arduino when you think it is more appropriate.

You also don't need to get into the weeds of object oriented stuff, and the code can end up looking a lot like regular C code.

For a guy like me, this is exactly why I use it. I'm not a code guy and I can hack out just about anything I wish with these resources.
Life is good AMA 1488
Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline phil c

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Re: Constant velocity or constant angular rate ?
« Reply #67 on: January 15, 2022, 01:39:00 PM »
I'm working on an electric powerplant control / timer and I'm fairly certain that a near Constant Velocity could be achieved. I'll publish that work eventually. It has been the focus of much of the testing I have been doing with the exception of the spade exercise which was a valuable distraction. In the process of the analysis, I make the assumption (simplification) of Constant Velocity, CV, in order to simplify the math involved. We always talk about that being desirable but I'm not so sure. While flying the SV videos I would swear the velocity is nearly constant but when I do the math and watch the video for verification, I see the airplane decelerating on the 45 lines. Which begs the constant Angular Rate question.

A Constant Angular Rate would make the squares look uniform and the leg time would be the same basically. With a CAR the upper level line would take the same time as the lower level line. With CV the top leg would be short time while the bottom leg would be long time. When we watch objects moving we don't necessarily see the actual speed so much as we see the characteristic length coved per unit time. A 767 on final looks like it is flying much slower than a Learjet 23 does even though both have nearly identical approach velocities. My truck going down the road at 80 MPH feels much slower than the wife's LaCross doing 80 MPH.

So, the question opened for discussion is CV or CAR as it relates to perception of the quality of the maneuvers.

I've judged quite a few PA flights with no griping from flyers.  I NEVER paid attention to the speed of the plane.  It was all about "did  the plane follow a steady, smooth flight path.  Did the plane follow the flight path that matched the maneuver descriptions, how bad were any errors.  Did they do the maneuvers in the correct order,  proper number of intermediate laps,  did the landing occur as the last maneuver.

There's nothing in the rules about keeping an even airspeed.  If the plane could hold a constant airspeed it might make the maneuvers appear more uniform.
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Offline Tim Wescott

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Re: Constant velocity or constant angular rate ?
« Reply #68 on: January 15, 2022, 04:09:30 PM »
There's nothing in the rules about keeping an even airspeed.  If the plane could hold a constant airspeed it might make the maneuvers appear more uniform.

I'd expect that some judges would see a deviation from the timing they're used to, feel disturbed about it (consciously or unconsciously) and you'd get lower scores.  OTOH, I think that the good judges wouldn't do that, and the "bad" ones would get used to it for seeing it all the time.
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Re: Constant velocity or constant angular rate ?
« Reply #69 on: January 15, 2022, 04:51:06 PM »
If the plane could hold a constant airspeed it might make the maneuvers appear more uniform.
I have been following this thread intently because I really am interested in why our planes do what they do.  I haven't commented so far because I don't speak engineerese.  This is in English!  I agree that when you are judging, or for that matter just watching, the actual airspeed doesn't really catch your attention, ground speed maybe but airspeed?  I am not sure that how it appears from the outside is as important (to me at least) as how it feels from the inside.  I would like consistent airspeed, except maybe in the down leg of the hourglass.  The active timers attempt to emulate that but the lag in when you need it, and when you get it, can be a bit annoying BUT, you at least know it is coming.  One of the more difficult times I am having adjusting to both logarithmic flaps and an active timer is the varying feel in the rounds.  Having a timer that constantly kept the airspeed the same, or close, would really help me.

Ken
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Re: Constant velocity or constant angular rate ?
« Reply #70 on: January 15, 2022, 07:42:12 PM »
I have been following this thread intently because I really am interested in why our planes do what they do.  I haven't commented so far because I don't speak engineerese.  This is in English!  I agree that when you are judging, or for that matter just watching, the actual airspeed doesn't really catch your attention, ground speed maybe but airspeed?  I am not sure that how it appears from the outside is as important (to me at least) as how it feels from the inside.  I would like consistent airspeed, except maybe in the down leg of the hourglass.  The active timers attempt to emulate that but the lag in when you need it, and when you get it, can be a bit annoying BUT, you at least know it is coming.  One of the more difficult times I am having adjusting to both logarithmic flaps and an active timer is the varying feel in the rounds.  Having a timer that constantly kept the airspeed the same, or close, would really help me.

Ken

Well, my initial intent was not to make this an engineering discussion and more about perception. But then I went said I was working on a control which I have been for quite some time and that let all us ubergeeks out to play on the drawing CAD board table.
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Re: Constant velocity or constant angular rate ?
« Reply #71 on: January 16, 2022, 05:00:13 PM »
When you say constant velocity, what is that relative to? The ground, or the air?

On squares, the top leg IS shorter than the bottom leg.  Don't know how you could get to the same time by either method.

Only because I've got nothing better to do today I thought I'd make a short response to the above short bit of Paul's previous post:  while  Paul is correct with reference to how we do things in "stunt" I wonder if we're doing the right thing.

Stunt Pattern Madness

"Snip!"  "On squares, the top leg IS shorter than the bottom leg."   "Snip"

Oh, dear.  I'm gonna get my butt kicked...nonetheless...into the breech.

That the stunt community's absurd insistence of describing a correct pattern maneuver based on the point of view of the Judges (who might be observing said maneuver from any damn place during a flight) has been dithered about ad nauseam for decades on and about the CLPA community drives me nuts.  Trying to address the stunt pilot's utilization of the flight sphere from the point of view of judges is the consummate definition of insanity.

There is only one place where the accuracy of the performance of “figures” on the surface of a sphere is accurate: in the center of the circle.  The only person in a position to accurately determine the success or failure correctly is the pilot…for whom every point on the surface “is” “identical”!  Round is round, square is square, a straight line a straight etc. etc.

A square loop can be accurately seen, performed and evaluated only from the one seat in the auditorium…one already taken…where the pilot is standing.  Where the surface of the performance (hemi) sphere is the the same everywhere and thus the display and view of straight lines (hemispheres), perfect loops (circles) and figure eights (two adjacent perfect circles), etc. etc. etc. are viewed by the pilot.

A straight flight path…although a great circle arc on the sphere’s surface…from the pilot’s view is, in fact a straight line…etc. etc. etc.  A perfect clover is four perfectly round and sized loops neatly “just” touching each other(from the pilot’s view) , etc. etc.

The pilot should be charged with doing just that: i.e. making the tricks look exactly like their titles describe from the only point they can be viewed so as to determine that perfection!

The judges are called judges because it is their responsibility to view the maneuvers and…to the best of their ability…try to mentally place themselves at the pilot’s location and, to the greatest degree possible make an educated assessment of how well the pilot has performed the prescribed maneuver.

The Pilot is paid to fly the tricks (as described by an elementary school teacher to his/her students) from his singular critical observation point.  We pay (yea right!) the judges the big bucks for doing their absolute best to put themselves in the pilot’s shoes and, as best they can, assign a value to how well the pilot has done his/her job.  Neither job is easy but both should be doing their best to do their best.  (Notice the large number of the words “their best” are included in that description of the tasks involved)

IMHO The worst thing we’ve done in assigning the responsibilities of Pilots and judges is to try to require the pilot to distort the shapes of their tricks--viewed from the perfect location—and to do so accurately so as to be “wrong” in just the right manner to the point that the trick will look more or less OK to the judges (from wherever they might be viewing the result).

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Re: Constant velocity or constant angular rate ?
« Reply #72 on: January 16, 2022, 09:46:09 PM »
I'm in total agreement, Ted.

dg

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Re: Constant velocity or constant angular rate ?
« Reply #73 on: January 16, 2022, 09:54:20 PM »
IMHO The worst thing we’ve done in assigning the responsibilities of Pilots and judges is to try to require the pilot to distort the shapes of their tricks--viewed from the perfect location—and to do so accurately so as to be “wrong” in just the right manner to the point that the trick will look more or less OK to the judges (from wherever they might be viewing the result).
[/color]
Who *are* these people we call judges?  For the most part they are *us* and we should know better.  I have been told that I needed to distort maneuvers so that the judges could see them correctly.  But, when I am judging do they think I don't know what they look like so they have to do them wierd just for me?  I think a lot of this a hold over from the old Navy days where the judges really didn't know what they were looking at!

Ken - And I am in total agreement with Dale!
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Re: Constant velocity or constant angular rate ?
« Reply #74 on: January 16, 2022, 10:38:36 PM »
Who *are* these people we call judges?  For the most part they are *us* and we should know better.  I have been told that I needed to distort maneuvers so that the judges could see them correctly

   I can guess who that might have been, however, you have to get that *right out of your head*. Even if it was a good idea - which it isn't - most people cannot even do the undistorted maneuvers well enough to be recognizable, much less put in tiny distortions that you might imagine "correct" the shapes. In the unlikely event we can reliably fly accurately to about 3" - instead of, very commonly, 10-20 feet - there's no point in worrying about putting in intentional distortions.

     Brett

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Re: Constant velocity or constant angular rate ?
« Reply #75 on: January 16, 2022, 11:40:18 PM »
I put in the corrections.  For example, when there are three judges spread out, I often put one outside loop directly across from each judge. 
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Re: Constant velocity or constant angular rate ?
« Reply #76 on: January 17, 2022, 12:06:32 AM »
I pretty much just fly and don't worry about the judges. Draw my best figures and let it be at that.
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Offline Tim Wescott

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Re: Constant velocity or constant angular rate ?
« Reply #77 on: January 17, 2022, 09:54:08 AM »
... I have been told that I needed to distort maneuvers so that the judges could see them correctly ...

... In the unlikely event we can reliably fly accurately to about 3" ...

The biggest contest I've gone to has been the NW Regionals in Oregon -- there, out of a field of 15 to 20 pilots flying Expert, it's really only the top two or three who fly well enough that they hit that close.  These are people who regularly win the Nationals and/or the Worlds, and it is out of a field of pilots dedicated enough that they're driving hundreds of miles to a contest that's conveniently timed to be two months before the Nationals.

So -- don't worry about it until you're getting into the top 5 at the Nats, or think you have a serious chance of winning the team trials.
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Re: Constant velocity or constant angular rate ?
« Reply #78 on: January 17, 2022, 12:16:19 PM »
The biggest contest I've gone to has been the NW Regionals in Oregon -- there, out of a field of 15 to 20 pilots flying Expert, it's really only the top two or three who fly well enough that they hit that close.  These are people who regularly win the Nationals and/or the Worlds, and it is out of a field of pilots dedicated enough that they're driving hundreds of miles to a contest that's conveniently timed to be two months before the Nationals.

So -- don't worry about it until you're getting into the top 5 at the Nats, or think you have a serious chance of winning the team trials.
I don't worry about it at all because I don't subscribe to it as either a competitor or a judge.  I can understand the controversary though.  The rule book is very unclear on anything with corners.  A simple statement at the beginning stating that all maneuvers are described as viewed by the flier and projected on a flat surface.  Then you can properly use words like square.  Anybody that has bent solder over a bowling ball knows this.  I am trying to see how any of this relates to the thread subject, and I can't.

ken

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Re: Constant velocity or constant angular rate ?
« Reply #79 on: January 17, 2022, 01:02:18 PM »
It shouldn't be any controversy, just a conversation about perception. If it's the top 5, 10 or twenty or just a local person, it shouldn't  matter. What are the aesthetics involved. My personal thinking is that a constant velocity would look odd on any level. I think up high going slower and subscribing a comparative angular rate as the lower side is potentially aesthetically more pleasing.
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Offline Ted Fancher

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Re: Constant velocity or constant angular rate ?
« Reply #80 on: January 17, 2022, 02:31:22 PM »
I put in the corrections.  For example, when there are three judges spread out, I often put one outside loop directly across from each judge.

Howard,

Do they frequently come up to you afterward and say thanks??? ~^ ~^ n~

Ted

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Re: Constant velocity or constant angular rate ?
« Reply #81 on: January 17, 2022, 02:32:44 PM »
I pretty much just fly and don't worry about the judges. Draw my best figures and let it be at that.

There ya go, Mark.  That's pretty much all we can do, isn't it!?

Ted

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Re: Constant velocity or constant angular rate ?
« Reply #82 on: January 17, 2022, 03:00:00 PM »
I don't worry about it at all because I don't subscribe to it as either a competitor or a judge.  I can understand the controversary though.  The rule book is very unclear on anything with corners.  A simple statement at the beginning stating that all maneuvers are described as viewed by the flier and projected on a flat surface.  Then you can properly use words like square.  Anybody that has bent solder over a bowling ball knows this.  I am trying to see how any of this relates to the thread subject, and I can't.

ken

Right on, Ken.  The rule book and pattern pundits are predictably unclear as they attempt to describe the indescribable.  Perhaps, even, not so much the rule book as the acres and acres of faux computer paper spent on trying to do so!

Just as a simpler for instance, I (and I'm sure many others) did pretty well for a pretty long time by flying the tricks where the air best advantaged trying to make them look right "only" to me...and trusted the judges to grade them to the best of their ability from their point of view.

Ted

p.s. If we included a vertical "square figure eight" in the pattern would the resulting rule book description require that the topmost half of the figure consist of a single corner...an angular tilted up leg reversed to a matching diving tilted down leg.  Sorry, just being a smart arse.

 

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Re: Constant velocity or constant angular rate ?
« Reply #83 on: January 17, 2022, 03:38:44 PM »

p.s. If we included a vertical "square figure eight" in the pattern would the resulting rule book description require that the topmost half of the figure consist of a single corner...an angular tilted up leg reversed to a matching diving tilted down leg.  Sorry, just being a smart arse.
 

I think it would be a cool maneuver to add. I would have to think about the wording, but it would be bounded by a rectangle that is defined by 45° worth of flight at the bottom of the circle, 45° worth of flight along the "wingover path", and straight-looking connecting paths. Those connecting paths would then have to not be great circle paths so you'd get all sorts of interesting things with the angles not being 90° blah blah blah.

I think I would make a really impressive looking and pretty maneuver. You could put it right between the vertical eights and the hourglass, and then the order of the vertical a eights would be exactly like the order of the loops.
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Re: Constant velocity or constant angular rate ?
« Reply #84 on: January 17, 2022, 05:52:40 PM »

On squares, the top leg IS shorter than the bottom leg.  Don't know how you could get to the same time by either method.


The AMA square loops do not require that the side legs be 90o (perpendicular) to the ground, so the top leg does not necessarily need to be shorter than the bottom leg.  The  thing that the AMA rules require is that the top leg be at a constant 45o elevation.  Otherwise, if that top leg could be a great circle path as are the bottom and side legs, the maneuver could be flown with all for sides being the same length (all great circle paths) and all four corners being the same angle (which would be slightly less than 90o on the plane tangent to the circle at each corner.)  Unfortunately, the rule requires the 45o constant elevation for the top side.

Keith

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Re: Constant velocity or constant angular rate ?
« Reply #85 on: January 17, 2022, 06:22:08 PM »


p.s. If we included a vertical "square figure eight" in the pattern would the resulting rule book description require that the topmost half of the figure consist of a single corner...an angular tilted up leg reversed to a matching diving tilted down leg.  Sorry, just being a smart arse.

 

That would be an interesting figure to be sure but it would not be flown on the cardinal ordinates of the sphere it would have to have some odd great circle elements to it. It definitely would be fun to explore. What about an overhead square eight? As long as we're inventing maneuvers, how about a diamond eight or a bowtie (hourglass on it's side).
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Re: Constant velocity or constant angular rate ?
« Reply #86 on: January 17, 2022, 06:36:08 PM »

As far a a square maneuver being the same length on all four sides, use the engineers favorite check by taking things to the limit.  A square maneuver by definition has vertical sides that are perpendicular to the ground.  Now, consider a 90 degree tall square loop. It is 90 wide. Follow those sides vertically to 90 degrees, and what do you get? They intersect, forming a three sided square. Oops..three sides?  If the "square" is limited to 45 degrees, the top horizontal leg IS shorter than the bottom level flight leg.  If you use timing, to do your square, it will not be correct.  Gravity against you going up, shorter leg on the top, gravity with you going down, and the bottom leg longer than the top.  All contribute so one shouldn't use your internal metronome for this maneuver.


As has been mentioned before, the AMA rules do not require that the sides be perpendicular to the ground.  (The FAI rules do require the sides be vertical to the ground which results in the top side being noticeably shorter than the bottom leg.)  So, the AMA rules allows the top leg approach the same length as the bottom leg, the side legs need not be perpendicular to the ground.  The bottom corners are not required to be 90o to the ground.  The AMA square can be flown with all sides being equal length, are all great circle paths and the corners are slight less than 90o.  I maintain that much a maneuver will look very nice to the judges as the timing will appear/sound more consistent and the dip in the top leg due to parallax (from the judges perspective) will much less noticeable.


You have described a perfect triangle traced on our hemisphere where all three sides are equal length (great circle paths), the upright sides are vertical to the ground, and all three corners are 90o.

It is possible to construct an equangular triangle of any size up to where the top is at the 90o point above the center of the circle on our hemisphere where all three sides are the same length (great circle paths) and all three corners are the same.  This can be of any size from infinitesimally small with three 120o corners to the one just described with all three side being equal with three 90o corners.  Interesting exercise because this shows that the AMA triangles have all three sides being equal length (great circle paths) and the corners will be something less that 120o.  It would be interesting to see the math involved to actually calculate what the angle is for these three turns on our hemisphere for the AMA triangle that has the top at the 45o elevation.  These turns are definitely less than 120o.

I would like to find a good test book on the basics of spherical geometry.

Keith

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Re: Constant velocity or constant angular rate ?
« Reply #87 on: January 17, 2022, 06:55:29 PM »


It is possible to construct an equangular triangle of any size up to where the top is at the 90o point above the center of the circle on our hemisphere where all three sides are the same length (great circle paths) and all three corners are the same.  T

I would like to find a good test book on the basics of spherical geometry.

Keith

The answer is yes, an equilateral triangle is not only possible but the fundamental derivation the trigonometry on the sphere. The length of a side is the radius time the angle in radians. So three side of equal length by definition have three equal angles.

Fortunately my recent endeavors have caused me to brush off some very old math cobwebs in spherical geometry. There's lots of good references in the world. Duck Duck Go it for Spherical math or trigonometry. 
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Offline Paul Walker

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Re: Constant velocity or constant angular rate ?
« Reply #88 on: January 17, 2022, 09:28:22 PM »
As has been mentioned before, the AMA rules do not require that the sides be perpendicular to the ground.  (The FAI rules do require the sides be vertical to the ground which results in the top side being noticeably shorter than the bottom leg.)  So, the AMA rules allows the top leg approach the same length as the bottom leg, the side legs need not be perpendicular to the ground.  The bottom corners are not required to be 90o to the ground.  The AMA square can be flown with all sides being equal length, are all great circle paths and the corners are slight less than 90o.  I maintain that much a maneuver will look very nice to the judges as the timing will appear/sound more consistent and the dip in the top leg due to parallax (from the judges perspective) will much less noticeable.


You have described a perfect triangle traced on our hemisphere where all three sides are equal length (great circle paths), the upright sides are vertical to the ground, and all three corners are 90o.

It is possible to construct an equangular triangle of any size up to where the top is at the 90o point above the center of the circle on our hemisphere where all three sides are the same length (great circle paths) and all three corners are the same.  This can be of any size from infinitesimally small with three 120o corners to the one just described with all three side being equal with three 90o corners.  Interesting exercise because this shows that the AMA triangles have all three sides being equal length (great circle paths) and the corners will be something less that 120o.  It would be interesting to see the math involved to actually calculate what the angle is for these three turns on our hemisphere for the AMA triangle that has the top at the 45o elevation.  These turns are definitely less than 120o.

I would like to find a good test book on the basics of spherical geometry.

Keith

Check out AMA  CLPA rules, section 13.10.  HS8..
It says vertical sides are 90 degrees from level, and the top segment IS shorter than the other legs.

Sounds like more work on the rules is required....

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Re: Constant velocity or constant angular rate ?
« Reply #89 on: January 17, 2022, 09:53:48 PM »
Check out AMA  CLPA rules, section 13.10.  HS8..
It says vertical sides are 90 degrees from level, and the top segment IS shorter than the other legs.

Sounds like more work on the rules is required....

I thought they made that change a few years ago, to match up with the FAI definition.
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Re: Constant velocity or constant angular rate ?
« Reply #90 on: January 17, 2022, 11:00:32 PM »
Check out AMA  CLPA rules, section 13.10.  HS8..
It says vertical sides are 90 degrees from level, and the top segment IS shorter than the other legs.

Sounds like more work on the rules is required....

Interesting.  13.10 describes the square eights.  The turns/vertical paths for the square eights are defined differently than the turns/vertical paths of the square loops 13.6 and 13.7.  Again, the description for the square loops do not require the sides of the maneuver to be perpendicular to the ground which allows the maneuver to be flown such that the tops and bottoms can be equal or nearly equal

Your friendly Control Line Aerobatics Contest Board would certainly entertain suggestions/proposals for improvements.  A new two-year rules change cycle has just started.

It seems that every time I read through the rule book, I find things that could be improved. It only took nearly 20 years to get the four leaf clover correctly defined from the time when the description was changed from the start of the maneuver to be at the 38o elevation to a 42o elevation which was still incorrect.  The new rule says nothing about a constant 42o elevation anywhere in the maneuver.  That 38o start point goes back to the early 60's.  (Some people still seem to fly it that way.)

Keith



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Re: Constant velocity or constant angular rate ?
« Reply #91 on: January 17, 2022, 11:08:47 PM »
I thought they made that change a few years ago, to match up with the FAI definition.

Actually, I think the AMA Control Line Aerobatics Contest Board deliberately did not change the rules for the inside and outside squares to be like the FAI rules.  This allows the AMA squares to act more like square loops than the trapezoids defined by the FAI rules with their truncated top legs being noticeably shorter than the bottom legs.  Having attended several World Championships, I do not think the top FAI pilots do that anyway.  (My personal observations, other opinions may differ.)

Keith

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Re: Constant velocity or constant angular rate ?
« Reply #92 on: January 18, 2022, 06:54:33 AM »
Actually, I think the AMA Control Line Aerobatics Contest Board deliberately did not change the rules for the inside and outside squares to be like the FAI rules. 
Keith
Personally, I do not like the FAI definitions for the squares either, but they are headed towards a full "great circle" definition which makes sense given that we do fly on the surface of a hemisphere.  Nothing describes an event better than a picture.  What would be wrong with rewriting the entire maneuvers section using accurate drawings on a half globe other than finding someone with the software and nothing better to do.  The rules section could show the maneuver from the pilots' position and the judges guide show it from the judges' position.  We have the technology to do that, and it is *not* the English language.   It would save a lot of conflicts.  For example, we do not specify that the top and bottom corners be the same on the squares.  That definition allows the square to be flown but in the same definition the word square is used which, by definition, has equal radius corners and equal sides, again making the maneuver impossible to fly on a hemisphere.  Plus we are left assuming that you don't consider the top and bottom as sides, which they actually are.

It is *tongue in cheek* but by using accurate drawings, the definition of a maneuver could be as simple as "Do this (See Pilots' Picture)"
The Judges guide - "Didn't Do that (See judges' picture)

We should not be performing to make it easy on judges, yet that does seem the logical road to success.  IMHO, the answer is to use technology to draw accurate pictures of our maneuvers and learn to recognize a properly flown maneuver from EITHER position.

Do I think that the current crop of leadership would support such a radical change -  LL~ LL~ LL~ 

Ken
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Re: Constant velocity or constant angular rate ?
« Reply #93 on: January 18, 2022, 09:11:33 AM »

For example, we do not specify that the top and bottom corners be the same on the squares.  That definition allows the square to be flown but in the same definition the word square is used which, by definition, has equal radius corners and equal sides, again making the maneuver impossible to fly on a hemisphere.

Ken

I think it has long been understood that the rules require that the figures flown defined as square are actually "sort of square" or "squarish" though not explained that way.  As soon as the rule says that the top leg is to be flown at a 45o constant elevation, the figure cannot have all four legs to be the same.  That requirement also does not allow the "top and bottom corners be the same" which is NOT required.  At least, the rule states that "The two (2) bottom corners are equal and so are the two (2) top corners."    The rules for all of the square maneuvers as well as the triangles and the hour glass does specify that that the corners "shall be of a tight radius" which clearly (and thankfully) does not specify either the angular change or a specific "radius" of the turns for any of these maneuvers.

By contrast, the triangles and the hourglass can be flown with equal turns and equal legs, all of which are great circle paths.

Keith

Offline Trostle

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Re: Constant velocity or constant angular rate ?
« Reply #94 on: January 18, 2022, 09:40:15 AM »

IMHO, the answer is to use technology to draw accurate pictures of our maneuvers and learn to recognize a properly flown maneuver from EITHER position.

Ken

There are simulations that show in 3-D how each of the maneuvers appear on a hemisphere when flown according to the rules.  (The work on this by Keith Renecle from South Africa being notable and probably the first to do so which also eventually led to the rule change that redefines the four leaf clover.)  Keith's simulations show how the complete pattern appears on the hemisphere from any perspective outside of the hemisphere including where a the judge's eyeballs would be positioned.  His graphics clearly shows the hemisphere and how the maneuvers described by the rule should appear.  It even shows how the five foot radius would appear on those maneuvers that now only require a "sharp turn".

It is just that no one has taken the steps to develop the drawings that would be suitable to put in the rule book.  This would show the hemisphere and the path for each maneuver on that hemisphere if someone would want to take on that task, I am sure the Contest Board would favorably accept that work to change the rule book.

I would think that a set of drawings from the judge's perspective is all that is necessary.  To represent each maneuver from the pilot's perspective in a meaningful manner would be a bit more difficult and not necessary.  It still remains that the goal of the pilot is to fly each maneuver so that it appears correct to the judges.

Keith
« Last Edit: January 18, 2022, 01:02:39 PM by Trostle »

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Re: Constant velocity or constant angular rate ?
« Reply #95 on: January 18, 2022, 01:24:50 PM »
There are simulations that show in 3-D how each of the maneuvers appear on a hemisphere when flown according to the rules.  (The work on this by Keith Renecle from South Africa being notable and probably the first to do so which also eventually led to the rule change that redefines the four leaf clover.)  Keith's simulations show how the complete pattern appears on the hemisphere from any perspective outside of the hemisphere including where a the judge's eyeballs would be positioned.  His graphics clearly shows the hemisphere and how the maneuvers described by the rule should appear.  It even shows how the five foot radius would appear on those maneuvers that now only require a "sharp turn".

It is just that no one has taken the steps to develop the drawings that would be suitable to put in the rule book.  This would show the hemisphere and the path for each maneuver on that hemisphere if someone would want to take on that task, I am sure the Contest Board would favorably accept that work to change the rule book.

I would think that a set of drawings from the judge's perspective is all that is necessary.  To represent each maneuver from the pilot's perspective in a meaningful manner would be a bit more difficult and not necessary.  It still remains that the goal of the pilot is to fly each maneuver so that it appears correct to the judges.

Keith

 With our modern graphics tools that is not impossible to do. Might even be helpful. If it weren't a bucket load of work when I'm already so diverse in my efforts, I'd do it.
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Online Ken Culbertson

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Re: Constant velocity or constant angular rate ?
« Reply #96 on: January 18, 2022, 02:21:45 PM »
With our modern graphics tools that is not impossible to do. Might even be helpful. If it weren't a bucket load of work when I'm already so diverse in my efforts, I'd do it.
Here is what the same hourglass looks like from the perspective of the pilot and the judge.    These are crude examples but they do illustrate the point.  I am not sure that it is a really difficult task to draw both.  I think that Keith R.'s latest version has this built in.  I can remember playing with it before our fire.  The version I have now is quite old.  Problem is that it is programmed for the FAI version not the AMA.

Notice that the picture taken from the inside makes the figure look like it was drawn on a flat surface.  The one from outside shows the curve of the hemisphere.  That is what a judge sees.

Ken
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Re: Constant velocity or constant angular rate ?
« Reply #97 on: January 18, 2022, 05:32:59 PM »
With our modern graphics tools that is not impossible to do. Might even be helpful. If it weren't a bucket load of work when I'm already so diverse in my efforts, I'd do it.

There are only about 14 months left to make a formal proposal.

Keith

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Re: Constant velocity or constant angular rate ?
« Reply #98 on: January 18, 2022, 05:49:45 PM »
There are only about 14 months left to make a formal proposal.

Keith

Oh I don't have any intent on making a rules proposal. My input is only a potential graphics contribution. I'm not so serious about competing such that I wish to start making rules proposals on figures. If I were to get serious about competing and bringing any proposals it would be much more extensive than simply making "better" different figure graphics. In the 4/4 arena we use Aresti figures and they are even less well exact in their diagrams. They are a short hand language on their own. I've tested that water a bit and it isn't anything I think would be well received.

I'll attach link to a condensed version and a snippet for comparison.

http://www.iac52.org/2012/Catalog2012ChangedPagesFinal.pdf


Life is good AMA 1488
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Re: Constant velocity or constant angular rate ?
« Reply #99 on: Yesterday at 08:06:00 PM »
I have a friend who does a single entendre.  I didn’t see a single entendre in the catalog.  Is that a humpty bump variant?
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