Fly rod deflection

[hshl]

Gordy,

in annex 2 of my investigations I estimated the moment of inertia ‚J‘ by deviding the fly rod up in 4 segments. You can notice that for the 1st tip segment J1 is quite small though it is referred to the grip by the Law Of Steiner: J1=1243 m*cm². J1 is siginificant smaller than e.g. J for segment 3, which is located closer at the grip: J3 =2292 m*cm².

It follows: J1 < J3 (even if I take J1 of the ridig fly rod: J1 =1687 m*cm². So the following estimation is on the saved side).

For the angular velocity w of the flexible fly rod it follows (w1 = 1st tip segment, w3 = 3rd segment):
a) at the beginning of the cast => w1 < w3
b) at the end of the cast => w1 >> w3

You can see that at the beginning of the fly cast L1 = J1 * w1 < J3 * w3 = L3.
As w3 slows down significantly at the end of the fly cast meanwhile w1 had strongly increased, w1 should be much (much) more higher than w3, so that the multiplication of J * w will turn the angular momentum to L1 > L3.

This is what I stated before...

So even if I look on the flexible fly rod sololy, a significant variation of the constribution of angular momentum could be detected. But since my investigations I always keep the (absolut) ridig fly rod in my mind, for which w1 = w3 over the whole duration of the fly cast. So for the ridig fly rod I can't see any variation of the contribution of the angular momentum. In comparison of both rods the different contribution of the angular momentum becomes more evident to me.

Thanks Walter, to me the variation of the angular velocity is the requirement for the varying contribution of the angular momentun.

Tobias

[Walter]

Tobias,

You are welcome. This an interesting and new view of the fly rod during the cast. I didn't want to see the discussion get sidetracked by a simple misunderstanding. I will be interested in your thesis when it is available.

Walter

[hshl]

Thanks again Walter,
I must pay attention not to neglect my work and family due to this discussion - as well as practiced fly fishing ... in the video I refer to in my post #24 at 2:18 I mentioned in short words what I descriped before.

Tobias

[Merlin]

Kinetic energy.JPG (57.38 KiB) Viewed 7210 times

This graphic illustrates an example of the evolution of rod kinetic energy as the swing weight changes due to the rod deflection (inertial effect). It starts from the butt and ends up into the tip. The vertical red line is the launch timing (maximum line velocity). As the cast is progressing, rod kinetic energy starts in the butt (brownish line, hard to see given the scale), followed by the middle of the rod and finally the tip, where kinetic energy concentrates (blue line). Since there is no damping for this example, all the remaining kinetic energy of the rod (green line) at max line speed is converted into counterflex (purple dotted line). In this particular case there is still some kinetic energy coming from the transfer phenomenon (rod mid kinetic energy, orange line) at launch time. The maximum tip kinetic energy is larger than the maximum elastic energy in this example, but this depends on casting conditions (arc, timing, carry).
The 2D casting model is based on energy (Lagrangian equations), the angular momentum approach is possible but at least as complicate (you handle vectors and not scalars). It is not an exact model since there are some simplifying assumptions, this is why I speak of trends, but it allows visualizing the different mechanisms involved. Powerful software exists (e.g. Abaqus) to get a more accurate solution, but it does not allow sufficient understanding; it is somehow a black box.

Merlin

[VGB]

The 2D casting model is based on energy (Lagrangian equations), the angular momentum approach is possible but at least as complicate (you handle vectors and not scalars). It is not an exact model since there are some simplifying assumptions

Thank you for that Merlin. I think that that it is worth highlighting that models contain simplifying assumptions to make them manageable and may lead to a loss of fidelity. If you haven't used Lagrangian techniques, then vectors summation is a good method to present the problem. Like Walter, I find the approach interesting and I will look at the latest paper from Tobias during the winter, to see how it has evolved.

regards

Vince

[gordonjudd]

I hope that helps clarify Tobias' statement.

Walter,
Thanks for pointing out my error.

Since this idea seems to be focused on the effect of the redistribution of the angular momentum in the rod I would still like to understand what the changing diameters of the max curvature points in the rod (the changing red circles) have to do with the redistribution of the the angular momentum change in the rod since the mass of the rod is not moving along those changing circles, but rather the rather broad curved paths that Grunde showed below.


Could you explain how the two (changing circle diameters and the redistriubtion of angular momentum) are related?

Gordy

[gordonjudd]

Since there is no damping for this example, all the remaining kinetic energy of the rod (green line) at max line speed is converted into counterflex (purple dotted line).

Merlin,
Does that imply if the line was impacting the damping of the rod (even though the affect of the caster's grip might have a bigger effect on the damping of the rod oscillations) that some of the K.E. in the rod would be directly transferred to K.E. in the line?

What would be the mechanism for that energy transfer?

Gordy

[Walter]

I hope that helps clarify Tobias' statement.

Walter,
Thanks for pointing out my error.

Since this idea seems to be focused on the effect of the redistribution of the angular momentum in the rod I would still like to understand what the changing diameters of the max curvature points in the rod (the changing red circles) have to do with the redistribution of the the angular momentum change in the rod since the mass of the rod is not moving along those changing circles, but rather the rather broad curved paths that Grunde showed below.


Could you explain how the two (changing circle diameters and the redistriubtion of angular momentum) are related?

Gordy

Gordy,

Probably best to ask Tobias. It's his paper.

[hshl]

As I mentioned before the curvation should face the complex redistribution taking place in the fly rod. There is another little video published at the end of 2014 http://www.youtube.com/watch?v=2JHo86zDbEE, which tries to get closer to this phenomenon with other words. The upmoving curvation as well as the shortening of the distance between the rotating mass and the "rotation point" should visualize, that some kinetic energy could climb up along the fly rod shaft. This ability should depend on the varying shape of the deflection (simply shown by the w1/w3 ratio of my previous post). But I fear it requires the Abaqus approach to get closer to this ...

[Walter]

Tobias,

That is interesting seeing the affect of conservation of angular momentum together with the redistribution, change in rotation point and conservation of energy. Like Vince, I am looking forward to reading the paper.

Walter