Evil final exam question

[Tim Wescott]

Consider a control line model aircraft.

Define the axes of rotation of the thing in the usual aerospace manner: x is through the nose, y is out the starboard wing, and z is straight down.  The right-hand rule applies.

It is perfectly trimmed, such that in level flight rotation is about the z axis only, and there is no hinging, banging, or rolling in maneuvers.

Assume that the airplane performs a rulebook-perfect set of three consecutive inside loops.

(A) What is the total rotation of the aircraft, from the start of the maneuver until the end.

(B) What is the total rotation* about each axis (x, y and z), from the start of the maneuver until the end.

Show your work.  Ignore the rotation of the earth or whatever planet you choose to frame the answer upon.  Use of quaternions is allowed, but not strictly necessary.

Answers will be shown later, after y'all have had a chance to think about this and respond.

* "Total rotation" in this context would be the cumulative rotation registered by integrating the output(s) of a perfect gyroscope.

[Mark Scarborough]

you reference the manuever, however you do not define whether you are refering the the manuever as seen from level flight to inverted level flight, or the manuever as scored...

[Tim Wescott]

you reference the manuever, however you do not define whether you are refering the the manuever as seen from level flight to inverted level flight, or the manuever as scored...

Good students second-guess the professor, and answer the question that the prof should have asked.  (Well, really good students come up to the front and ask for clarification.)

As scored, from level flight to three loops after.

[Mark Scarborough]

well I aint no math major,

for part a, if you look at the start of the manuever as zero, then as it moves through the manuever it transcribes a part of the circle but as it reaches the top of the loop it returns to zero rotation, then proceeds into negative since its below, or behind zero,, so in simplest terms it would seen that assuming the pilot does not walk the loops, the cumulative rotation ( as seen from above the pilot) is ultimatly a total ov zero, if you want to measure the total number of degrees covered by the airframe then I think the question should be worded different
 I tried to test my memory of cypherin, but I never got past Calculus, and I dont think I have the formulaic tools to attach this,, 

[Mark Scarborough]

to rotate about the z axis, it would have to be yawing, therefore there is zero about the z axis,, and if trimmed right there is no rotation about the z AXIS, there is no rotation about the x axis either unless the airplane rolls, so the only rotation is with reference to the y axis, rotating about the wing tip to tip, and there really isnt any fair way to address this because you really only want the pitch change, not the motion of the airframe through space, simple answer would seem to be three hundred sixty degrees per loop. but that is not the rotation about the y axis, that is the path of the airplane, the pitch change would be the rotation measure,,

or am I whacked out in my primitive outlook here

[Tim Wescott]

Hint, to calibrate your brain:

In level flight, the plane experiences 360^o of rotation around the z axis per lap.  Given perfect trim there's no yaw with respect to the lines, but you really do want the plane rotating as it goes around the circle.

[Mark Scarborough]

all true, but I have no tools to mathmatically define it,, and I caught later that you are asking for the cumulative, but the x axis still is about roll, not rotation,,
the y axis, then would be 1080 degrees cumulative for three loops
the z is still about yaw and well, maybe if you arelooking with respect to a spot on the ground directy under the start of the mayever, then you would have 22.5 degrees of circumfrance rotation ( bad terminology) and the same aft of the start point but it would take trig or some other magic to figure out how many degrees of rotation about the z axis you experience as you move fore and aft doing the loops,,
yeah I can talk myself into a couple ways to look at it,
if you take the "Fancher aproach" and break it down, the airplane would in fact rotate 360 degrees about z axis in one lap,, to visualize put the airplane at the center of the circle and the pilot flying around the circle,, the airplane would rotate that full 360 degrees per lap, a loop takes 45 degrees or 1/8 of a lap so in simplest terms covering 1/8 or 45 degrees each loop one would think that you would cover 135 degrees of z axis rotation,, but I feel thats not completely accurate,,

[Mark Scarborough]

and why am I the only dumb head even trying to play your game Tim, sheesh,,
oh thats right, I like to challange my brain and reach beyond my current knowledge base

[Tim Wescott]

but it would take trig or some other magic to figure out how many degrees of rotation

Yup.  That's a good starting point.

[Tim Wescott]

and why am I the only dumb head even trying to play your game Tim, sheesh,,
oh thats right, I like to challange my brain and reach beyond my current knowledge base

I know!  Where's Howard?

[Howard Rush]

You could have asked why my TUT loop kill was inconsistent when I had the radius angle set at 330 degrees  (I recently bumped it up to 340 degrees).

Here's my guess:  A: 1080 degrees, although I'm not sure what you're calling total rotation.  B: X=0, Y=998 degrees, Z = 413 degrees.  The loop is a cone with axis 22.5 degrees (pi/8 radians) from horizontal.  The y airplane axis is tilted 22.5 degrees from the loop axis; the z airplane axis is 90 degrees to the y airplane axis.  So the y rotation is cos (22.5 degrees) times the total rotation; the z rotation is sin (22.5 degrees) times the total rotation.  Another way to get the z rotation is to calculate the distance traveled, which is 1.148 laps.  That times 360 degrees also gives you 413 degrees.

*edited to fix a word

[M Spencer]

The Correct answer is " Sufficent " , otherwise it would crash .  and your calculations would be incomplete . The aeroplane might be too . 

[Tim Wescott]

You could have asked why my TUT loop kill was inconsistent when I had the radius angle set at 330 degrees  (I recently bumped it up to 340 degrees).

Eeek.

Here's my guess:  A: 1080 degrees, although I'm not sure what you're calling total rotation.  B: X=0, Y=998 degrees, Z = 413 degrees.  The loop is a cone with axis 22.5 degrees (pi/8 radians) from horizontal.  The y airplane axis is tilted 22.5 degrees from the loop axis; the z airplane axis is 90 degrees to the y airplane axis.  So the y rotation is cos (22.5 degrees) times the total rotation; the z rotation is sin (22.5 degrees) times the total rotation.  Another way to get the z rotation is to calculate the distance traveled, which is 1.148 laps.  That times 360 degrees also gives you 413 degrees.

You pass.  At the very least, if you're wrong we're both wrong identically.

One of the interesting things that I realized, when starting to think hard about the TUT, is that at a constant "airspeed" (really, at a constant speed in inertial space, because the air may be moving), not only is the rotation around the z axis constant, but the centrifugal acceleration along the y axis is constant, too.  Igor already knew this.

[Chris Wilson]

My head hurts just thinking about all of this.

[Gerald Arana]

Eeek.

You pass.  At the very least, if you're wrong we're both wrong identically.

One of the interesting things that I realized, when starting to think hard about the TUT, is that at a constant "airspeed" (really, at a constant speed in inertial space, because the air may be moving), not only is the rotation around the z axis constant, but the centrifugal acceleration along the y axis is constant, too.  Igor already knew this.

I just want to NOT hit the ground on the 2ND or 3RD loop.

Jerry

PS: I've been out of school for more years than I care to remember, so to 'L with your question! 

[Tim Wescott]

My head hurts just thinking about all of this.

Math is fun.

[Mark Scarborough]

Math is fun.

Math is fun when you know the tools to accomplish what your after,, if you dont, its just painfull,,

[Tim Wescott]

Math is fun when you know the tools to accomplish what your after,, if you dont, its just painfull,,

When that happens I go buy books and have fun studying them.

I'll admit, when I was working on the project on GPS/IMU integration, the book "Directional Statistics" pretty much stumped me.  I hate it when I get a math book and I can't tell if I'm just not smart enough to understand, or if the person doing the 'splainin' is a dolt.

[Howard Rush]

You could have asked why my TUT loop kill was inconsistent when I had the angle set at 330 degrees  (I recently bumped it up to 340 degrees).

Oops, that's backwards.  I musta reduced it.

[Howard Rush]

I hate it when I get a math book and I can't tell if I'm just not smart enough to understand, or if the person doing the 'splainin' is a dolt.

Much of my schooling involved the intersection of those two sets.

[Tim Wescott]

You could have asked why my TUT loop kill was inconsistent when I had the radius angle set at 330 degrees  (I recently bumped it up to 340 degrees).

Oops, that's backwards.  I musta reduced it.

So, asbestos* you can remember you had it set to 330 (or 340), then you reduced it some, and then it worked?

If so, and if you were doing a single loop, it may take it some time before it tells itself "oh, I'm in a loop" and starts counting degrees.  Since it doesn't start the cut-off sequence until you're out** of the loop, you probably don't need to hold it that long.

* It passed the spell checker.  It must be right.

** Except for one memorable occasion -- with Paul's Atlantis -- when I flat-topped the first loop of three, and it went into it's routine.  Did you know that you can do half a loop in a glide, if the engine had just been at full power before cutting off cleanly?

[Steve Berry]

Perhaps I missed it, but how can this be answered without line length, which defines the half hemisphere?

[Tim Wescott]

Perhaps I missed it, but how can this be answered without line length, which defines the half hemisphere?

Everything's in degrees.  How is the answer different with different line lengths?

[Steve Berry]

Upon further examination, you're right.  I misread the initial question.  Sorry about that.

[Tim Wescott]

Upon further examination, you're right.  I misread the initial question.  Sorry about that.

'sokay.  When you're doing a test that I wrote and something is strange about a question, there's an even chance that I had my head up was mistaken vs. that you misread something.

[rustler]

Sorry I don't have time to more than skim this - (that's my excuse and I'm sticking to it) -
I figure you'd need to know the line length and loop radius to answer this.
You may be able to produce an answer incorporating L and R as part of an equation.

[Brett Buck]

Sorry I don't have time to more than skim this - (that's my excuse and I'm sticking to it) -
I figure you'd need to know the line length and loop radius to answer this.
You may be able to produce an answer incorporating L and R as part of an equation.

    Not to calculate the total angular displacement in body-fixed coordinates. It's just geometry and it has no absolute scale.

    Brett

[Igor Burger]

  Igor already knew this.

Yes, he knew, you had to ask him, he wrote it aproximately 6-7 years back either here or on stuka. He also had feedback regulator using that ... used I think 2010 in Hungary, may be Dave F. or other guys will tell why he decided to use something else :- )))

[Tim Wescott]

Yes, he knew, you had to ask him, he wrote it aproximately 6-7 years back either here or on stuka. He also had feedback regulator using that ... used I think 2010 in Hungary, may be Dave F. or other guys will tell why he decided to use something else :- )))

Wasn't on Stuka -- I never warmed up to that group.  Did I ask about this, or was it someone else?

[Igor Burger]

I really do not remember, I just know I had timer with gyro and here was some speach about it (this or stuka), I also used it it shortly, but it was not satisfying, so I changed mind. You got it right ... especially all those "lets assume" which are never fulfilled and which influence functionality :- ))

[RandySmith]

Good students second-guess the professor, and answer the question that the prof should have asked.  (Well, really good students come up to the front and ask for clarification.)

As scored, from level flight to three loops after.

Tim you said manouver  as scored, if so then it is  1260 , if just 3 round loops  then  1080 , the proper  manouver requires  3.5 loops, or else you will not like the score you get

Randy

[Tim Wescott]

Tim you said manouver  as scored, if so then it is  1260 , if just 3 round loops  then  1080 , the proper  manouver requires  3.5 loops, or else you will not like the score you get

Randy

Sigh, even my second try is ambiguous.

I just double checked the rulz, and, indeed, the part of the maneuver that's scored is exactly three loops.  The half-loop to recovery shouldn't be scored (how nicely you do it probably bears on your score with a lot of judges -- bit it shouldn't be scored).

[RandySmith]

Sigh, even my second try is ambiguous.

I just double checked the rulz, and, indeed, the part of the maneuver that's scored is exactly three loops.  The half-loop to recovery shouldn't be scored (how nicely you do it probably bears on your score with a lot of judges -- bit it shouldn't be scored).

sigh....  not really  keep reading  Tim :-)  you have to do the 1/2 loop to complete the proper correct manouver, if you do not , you did not do the manouver right and you will lose many point, so 3.5  loops you can get 40 points, 3 loops you can get 10, and lose your  25 pattern points

now  if your just talking about  not doing  3 loops and not  a Pattern manouver  that, as I stated is different.   and  it was your second try that promoted my  post  :-)


don't believe me  just  do not  do the half loop at your next contest, just do  1080 degrees let me know  that score  
Regards
Randy

[RandySmith]

 "  entering or exiting a maneuver
in any way other than is illustrated in the maneuver
section, and doing an incomplete maneuver all will
result in a loss of pattern points. No pattern points
will be awarded if maneuvers are attempted but not
completed.  "

from the  AMA rules    if you do not  finish the manouver in the described manner  you will loose points...  hmmmm  More Evil than I thought


Sorry Tim , i couldn't  resist


Randy

[Brett Buck]

sigh....  not really  keep reading  Tim :-)  you have to do the 1/2 loop to complete the proper correct manouver, if you do not , you did not do the manouver right and you will lose many point, so 3.5  loops you can get 40 points, 3 loops you can get 10, and lose your  25 pattern points

   I don't think so. Once the third loop is complete, the maneuver is complete, period. You judge the maneuvers from the defined entry to the defined exit, so how ever accurately the three loops are done determines the maneuver score. If you then exit incorrectly (like flying out of it level, or doing a fourth or fourth and a half loop) is an improper exit. The penalty is loss of pattern points, but nothing else.

     Brett

[RandySmith]

I have seen on more than 1 occasion at the NATs  people  being hit and loosing  maneuver points on improper exit, some time NO sometimes  YES  which is why I said may lose points,  25 points is a certain  loss.
If you do just 3 loops you will finish right side up, and  not  in position  to do the inverted flight, I for 1 would not want to test that in an official flight.  It could go either  way ,  my post was just to tweek Tim , just a tiny  bit  about the  extra  180 degees   "IF"  you do a  proper maneuver

Regards
Randy

[Steve Helmick]

Jeez, Randy, you haven't even met Tim. How did you know he needed tweeking?   Steve

Edit: You were right, he does. Please continue...

One thing about that, however...if one was to pull out of the inside loops upright, fly level for 10' and then do a half inside loop to inverted (or half a square loop!), would that warrant a 10 and loss of PP's? 5'? 20'? 30'? As a machinist, I learned there are tolerances on everything.

[Brett Buck]

Jeez, Randy, you haven't even met Tim. How did you know he needed tweeking?   Steve

Edit: You were right, he does. Please continue...

One thing about that, however...if one was to pull out of the inside loops upright, fly level for 10' and then do a half inside loop to inverted (or half a square loop!), would that warrant a 10 and loss of PP's? 5'? 20'? 30'? As a machinist, I learned there are tolerances on everything.

   Of course, that's why it is called "judging" and not "measuring".

     Brett

[Ted Fancher]

Jeez, Randy, you haven't even met Tim. How did you know he needed tweeking?   Steve

Edit: You were right, he does. Please continue...

One thing about that, however...if one was to pull out of the inside loops upright, fly level for 10' and then do a half inside loop to inverted (or half a square loop!), would that warrant a 10 and loss of PP's? 5'? 20'? 30'? As a machinist, I learned there are tolerances on everything.

How, exactly, would the judges be able to tell it was 10' of level flight and not just another of my previous two flat loop bottoms, hmmmmm?!...and some people think it's easy judging "precision" aerobatics.  Thus the big $$$$.

Ted

[Tim Wescott]

... and not just another of my previous two flat loop bottoms, hmmmmm?!...

One of our local pilots (in Expert, no less) last year had a tendency to do his loops with flat spots.  Perfect flat spots, as if the loops were constructed with a compass and a ruler.  If the rulz said to do the loops with flat spots they'd be in Paul Walker territory.  And I had to tell him why I was so hard on them...

[Mark Scarborough]

One of our local pilots (in Expert, no less) last year had a tendency to do his loops with flat spots.  Perfect flat spots, as if the loops were constructed with a compass and a ruler.  If the rulz said to do the loops with flat spots they'd be in Paul Walker territory.  And I had to tell him why I was so hard on them...

Only ONE of my loops had a flat spot so it wasnt me,, and my flat spot was a half circle worth preceded by a loud pop and a skidding noise,,, Pretty sure the judges had no issue noticing my flat bottom manuever,, sigh

[Ted Fancher]

Shouldn't you boys be out mowing the lawn or shoveling snow out of the driveway or something?  This is no way to earn your allowances!

[Fredvon4]

Awe Ted Come on...I was just starting to understand some of this even tho the X/Y/Z axis stuff hurts me head

Took a bit for brain to engage and understand Mark's now infamous flat bottom loop as a bit of fuselage in dirt vs tongue in cheek

[Tim Wescott]

Only ONE of my loops had a flat spot so it wasnt me,, and my flat spot was a half circle worth preceded by a loud pop and a skidding noise,,, Pretty sure the judges had no issue noticing my flat bottom manuever,, sigh

Someone else.  It's not all about you, Mark.

[phil c]

Hint, to calibrate your brain:

In level flight, the plane experiences 360^o of rotation around the z axis per lap.  Given perfect trim there's no yaw with respect to the lines, but you really do want the plane rotating as it goes around the circle.

'nother hint-  it appears that all three axes undergo rotation in a loop.  If you want total rotation you have to use absolute values since x and z oscillate.