Casting mechanics cont'd 2

Walter & Group....

Some of this gets pretty deep as we read input from members with engineering / physics backgrounds.  For those interested in that much detail, put on your hip boots and wade in.

Don't dispair.  We'll get back down to Earth in a message or two.

I placed information on the Laplace Transform (a mathematical concept) in an attachment for those who feel they can follow this string of very advanced information.    G.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From Ally Gowans :

Hi Gordy,

 

Would you be kind enough to ask Walter to consider this before publishing?

 

Stupid perhaps but I am left wondering what is being discussed. Are the ?force? and its associated acceleration being considered at the rod handle or at the rod tip? If it?s at the rod handle the F=Ma is correct only for translation and is inappropriate here. Rotation is determined by torque where t=aI where a is angular acceleration and I is the moment of inertia.

 

In casting both are used simultaneously and in varying degrees according to style. Tangential acceleration at any point of the arc (rod tip) can be derived from the product of angular acceleration and r (radius). In the case of fly casting the radius would have to include body movement which increases this dimension to well beyond rod length and the origin of the system may well occur well outside the extremities of the casters body. So far I have ignored the fact that rods bend and that the line inertia angle relationship with the rod tip and the origin changes. If a cast started at a cord angle of 45deg to the line and finished at a cord angle of 90deg and the rod did not bend the torque would have to increase by a factor of root(2). Once the cord angle is beyond 90deg it becomes increasingly more difficult to accelerate the line. The rod handle at a 90deg cord angle of course would have travelled much further due to the flex.

 

I imagine that the extent of Walter?s ?kick back? is dependant on the inertia of the system and the amplitude of impulse. A smooth ?start up? is ideal and as Walter rightly says translation helps greatly. Not only directly but also to ensure that a practically straight line is being pulled. If the line is not straight and especially if it?s not straight close to the rod tip ?kick back? is likely.

Best regards,

Ally Gowans

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Ally...   I did ask Walter.  His message, below :

 

Hi Gordy,

 

Some great discussion happening!

 

I'm in a bit of a rush at the moment but I thought I would take a bit of time and explain what I did using

the Laplace transform.

 

Basically the transform lets us understand certain (i.e. limited) things about a system without having

to fully understand the system. In this case we have an input - a force which is zero for some time and

then is constant. We also have an output - the rod tip traces a straight line.

 

For Laplace this is enough to determine the transfer function, i.e. if I have a known input what is the

function that gives me the known output? Once I have the transfer function I can substitute a different

input and see what the new output is. In Laplace terms the function of zero force followed by fixed

force is a standard input called a step input. In this case I substituted a ramp input and an exponential input

to see how the output was affected. The result is that if we have a system for which a constant force

generates straight line movement then any other input is going to result in some sort of curved path.

 

Of course we could imagine that a differently structured rod will have a different transfer function but

we also have Bruce's experimental data (and from talking to Bruce I understand he has done a lot

of experimenting) that says a step input gives us a straight line for a very broad range of casters,

distances cast, rods, and casting styles. Since I doubt that all rod manufacturers design rods with this

criteria in mind it must mean that if we take a shaft that looks like a fly rod (i.e. similar but not

necessarily identical length, taper, and elasticity) and apply a step input, within the normal range

capabilities of a human being, then we can expect the rod tip to follow slp or near slp for some

casting arc.  A radical deviation from the step input is going to give us a different tip path.

 

Thanks

 

Walter

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More from Ally Gowans.  My comments in his text in italics   G.:

Hi Gordy,

 

I have never seen ?kick back? in a cast either but it can be demonstrated by taking a rod without line (I have never tried with line but it would probably work too) hold it horizontally close over a horizontal surface (table) and lift the rod quickly as if starting a cast. Often this will energise a response from the 2^nd harmonic that flips the tip downward (Table Top Test). To see the 2^nd harmonic otherwise hold a rod by the butt and waggle it, note the stationary node and that the tip travels opposite to the butt force. Starting a cast should be done with slow movement and if you repeat the Table Top Test with a slow start the rod will not hit the table.

 I tried it a few minutes ago. Performs as you described.  Then did it with a line strung.  Much blunted effect.  However, it appears that while the tip section is bending downward, the tip itself is none the less moving upward .  Rod bend gives it the impression of downward movement. G.

What does Al mean by ?mass profile?? Is not that determined by line diameter? I?m afraid that I don?t understand his statement. Without question hi density lines of small diameter maintain speed better than large diameter lines. Worst of all are these ?hi float? lines. A heavy object starting off at the same velocity as a lighter object of the same dimensions will travel further simply because of its momentum. Is that what Al is saying?

 I think that is what he means.  I first ran across the term, "mass profile" when Bruce Richards gave a talk on fly line design and performance a few years ago.  I look at it as the distribution of mass within a structure.  As I see it, two lines could have exactly the same outline including diameter and shape.  One could be made with much heavier material placed forward.  The two would look exactly the same and have the same diameter and optical profiles but have different mass profiles.  The one with the heavier material would yield greater momentum.  G.

I?m still trying to figure out where this constant acceleration occurs. Acceleration is a vector quantity and to be constant it must travel in a straight line. Angular acceleration moves in circles and to be constant it must move in a circle driven by torque. As far as I can see a fly rod moves differently to either of these pure movements and so the acceleration cannot be constant even if the magnitude of the driving force remains the same because its direction is changing. This is the same sort of rubbish as the ?constant tension? cast where the direction of the tension is constantly changing! In truth the important part of the fly rod ? the tip ring moves in a path that would require a combination of angular and linear accelerations to describe it and no two casts are the same so providing we have a qualitative understanding of how good casts are made that is sufficient. A detailed quantitative analysis would be of interest to some of us but in all probability the instrumentation needed to take the measurements would influence the outcome and introduce inaccuracies.

 

I recall learning that the tip of a rotating propeller the shaft of which is turning at a constant number of revolutions per minute is actually accelerating.  Reason ?  As you point out, acceleration is a vector quantity (linear) so every time you change directions you have a different vector.  One can see this as the rotating propeller tip moving with an infinite number of direction changes. 

 You present an interesting question on CONSTANT ACCELERATION.  Especially as I wonder about the relatively straight portion of the acceleration curve in mid cast as seen on the Casting Analyzer graphs in light of the fact that the sensor measures rotation at the rod butt .... NOT at the rod tip.

Interesting that if we really could have a straight line path of the rod tip that this would be the result of a combination of applications of force in a straight line as well as in a curve; the latter being torque at the rod handle.  Couldn't happen without the rod being flexible. (My words to describe what you did.) 

Your last sentence reminds me of a statement credited to Albert Einstein :  "The very act of measuring changes the measurement."     G.

 

Best regards,

Ally Gowans

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From Troy Miller :

Mass doesn?t really play into drag itself.  Mass is what determines momentum that will be used to defeat drag.  Drag is mainly a function of surface area and shape/texture of the surface.  I know what Al means, but you can have two lines with the exact same drag characteristics, but perform differently due to mass.  Conversely, you can have two lines with exact same mass profiles, but different drag characteristics.

 Sure. Increase in mass will provide increased inertia....Drag needs to overcome that in order to move the rod tip/line.  G.

I love Don?s book.  Wish I could remember who I loaned it out to.  I?ve been without it for 6 or 8 years now?  wonder if it is still in print?  May have to buy another copy.

 I often go back to it as one of my valuable references.   Don't know if it is still in print (10 years old, now).  Bob Rumph might be able to track that down for us.   G.

I think that the term ?kick back?  is maybe a misnomer.  I don?t believe that the rod tip will EVER go backward as you begin a stroke forward.  For the tip to move backward, there would have to be a force acting on the tip in that direction.

 Right.  To some it might APPEAR to go backward as it bends due to the rod tip travel lagging behind that of the remainder of the rod because of rod bend .... but it doesn't "go" backward.....     G.

 The main force acting on the line is due to the line?s inertia, hanging stationary in the air after unrolling.  NOW ? if you make a backcast with such energy that it unrolls with signigicant excess energy, then that can cause the rod tip to be pulled in that direction.  But that has nothing to do with acceleration of the rod in the forward direction.  You could let that loop fall to the ground and it would give that tug anyway.  I think what people are trying to describe when they say ?kickback? is the DOWNWARD movement of the rod tip as the ERL shortens ?too rapidly? as you accelerate very early in the stroke.  It should probably be called ?kick down?...  That clearly exists and can be one of the major causes of tailing loops.

Yep.... down then returning up.   A concave rod tip path.    G.

Regards,
Troy Miller

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Attachment: LAPLACE TRANSFORM.doc
Description: Binary data