What makes Snap Casts (Interesting)

[VGB]

Hi Dirk

I covered this time period back in Post 100 and 103.

Regards

Vince

[Dirk le Roux]

Hi Vince

QUICKQUIP:- "There is nothing more likely to start disagreement among people or countries than an agreement." - E B WHITE.

In post 100 the car hitting mud analogy was introduced along with a statement that "The acceleration vector alone does not give you the direction of net force". N2 says the acceleration vector is the result of and in the same direction as the vector sum of forces (net force) acting on an object. In answer to the question if you still think that holds true, a generalised response was provided, adding that the acceleration graph “seems to indicate multiple reversals of net force”. Answers to a request for further clarification on this last point alluded to the increases and reductions in rod leg upward acceleration between 0.3s and 0.5s and referred to posts 100 and 103, which do not explain the reading of ups and downs in positive acceleration as indications of reversals of net force direction. Reduction in positive acceleration, but still positive acceleration, is negative jerk and not negative acceleration. Its vector direction indicates the direction of change in net force in time, which relating to the graph at hand would point down, not the vector direction of net force itself, which relating to the graph at hand still points upward.

Do you have any issues with the above or can I carry on with what happens during the snap cast?

Regards,
Dirk

[VGB]

Hi Dirk

If as much effort had been expended in answering what you didn’t like about my Post 108 on the snap cast nearly 2 weeks ago, we would probably be done and dusted. If you re-read post 100, I am talking about the effects on the driver not the car. You keep talking about blocks of wood and cars which are rigid bodies, the truisms that you are using do not apply to flexible objects. If I accelerate the line quickly and then slow down, the back end of the line will not slow down with the later input. These rigid body analogies have led to other truisms such as the line always follows the rod tip which we know not to be correct.

I’m glad that you now see that we do need to consider jerk and that it’s not one derivative too far. I have been waiting for you to carry on with your explanation of the snap cast for a while now, please carry on.

Regards

Vince

[Dirk le Roux]

Hi Vince

If as much effort had been expended in answering what you didn’t like about my Post 108 on the snap cast nearly 2 weeks ago, we would probably be done and dusted.

It would have been great not to have required the detour, but we would probably then have had even more tedium because we have read acceleration and net force directions differently. I hope I’m wrong about our still reading acceleration and net force directions differently:

If you re-read post 100, I am talking about the effects on the driver not the car.

I did indeed initially read the car-into-mud analogy as referring to the car rather than the driver/occupant, sorry. When in post #120 however you referred to the instantaneous accelerations and the effect on an unrestrained occupant, I did re-read it. The contradiction remained the same however, as the description reads "my acceleration vector changes direction 180 degrees from in the direction of travel to opposing it. My velocity vector remains in the direction of travel but the magnitude reduces". For the described to have occurred, the occupant, as with the car, must have experienced a net force pointing opposite to the direction of travel, and not “However, net force remains in the direction of travel”.

You may have referred more particularly to the occupant’s head during something like whiplash, in which case the description does not fit.

If I still understand incorrectly, please post a free body diagram, stating reference frame, illustrating among all relevant vectors the net force in direction of travel and the occupant’s acceleration direction against direction of travel.

You keep talking about blocks of wood and cars which are rigid bodies, the truisms that you are using do not apply to flexible objects. If I accelerate the line quickly and then slow down, the back end of the line will not slow down with the later input.* These rigid body analogies have led to other truisms such as the line always follows the rod tip which we know not to be correct.

Flexible objects can and should be treated as systems of variable mass and it’s convenient to divide these into subsystems of variable mass. I don’t know of a better approach, do you? With variable mass systems and accounting their subsystems, including all terms relating momentum changes due to varying mass, the vector sum of forces still determines directions of the system’s and subsystems’ acceleration.

With the snap cast under discussion at t=0.17s for instance, the net force vector on and acceleration vector of the rod leg point downward while those on and of the fly leg point upward.

* As discussed before in post #75, there may be merit to investigate a delayed signal from the abrupt absence or reduction of tension at the top of the fly leg reaching the tail end of it, and its possible role regarding dolphin noses. A train analogy was discussed, which is not so particle biased. However it is doubtful that such a signal delay could be slow enough that the fly leg keeps accelerating upward along the duration of your phase 3 in the absence of a more presently acting upward force. Inertial coasting yes, but acceleration needs a force.

I’m glad that you now see that we do need to consider jerk and that it’s not one derivative too far.

As indicator of net force vector, jerk is indeed one derivative too far. Force direction goes with acceleration direction. We do need to consider degree of jerk if we are to cast nicely though. As aside, I think that the term has a bad rep from the common use to denote sudden changes in acceleration as “jerky”. Whereas “jerk” applies to any change in acceleration, however smooth.

Regards,
Dirk

[Dirk le Roux]

Hi Vince

I have been waiting for you to carry on with your explanation of the snap cast for a while now, please carry on.

I gave explanations in posts #22, #54, #63, #87 and #98. From post #100 and a correction in #103, it appeared you are comfortable with the rod leg’s upward acceleration, the force responsible for this as pointing upward and the relationship between reducing loop propagation speed and the reducing leg length. In #120 you again express reservation about the upward force being the tension at the loop pointing upward in relation to the rod leg. We can discuss this later if you still wish. You seem to have more issues with the relation between the fly leg and tension at the loop, so I will focus on those and then to issues with your explanation from post #108.

Tension at the loop (fold):
From a basically stationary position at the top of a basically stationary length of fly line, the rod tip is accelerated rapidly downwards. Very early during this motion a loop forms in the line, now dividing rod leg and fly leg. Different leg velocities either side of the loop cause tension at the loop due to momentum changes there and centripetal accelerations of line passing through it. Half the difference in leg velocities yields loop propagation speed and this, in conjunction with linear mass (which we don’t know exactly for this case) passing through the loop, determine the tension at the loop. The loop propagation speed’s contribution to this tension is quadratic, whereas that of linear mass is not. Neglecting the line’s linear mass distribution for now, assuming it remains constant - the higher the difference in leg velocities, the higher the tension at the loop.

Around the instant that the rod leg acceleration changes from downward to upward (0.23s), loop propagation speed is at a peak of ≈ 11.75m/s. Rotation rate (angular velocity, loop propagation speed being tangential to that) has now been imparted to the system and gradually winds down as events unfold. From the peak, loop propagation speed progressively decreases to ≈ 9.5m/s at 0.55s and from there on less progressively to its lowest of ≈ 6.4m/s at 0.96s, when the loop goes into the leader and can’t be further traced (no markers there).

As described in post #105, during the dance around optimum between leg length (mass) and loop propagation speed (see its role in tension above), the fly leg’s upward acceleration peaks at around 0.34s and the rod leg’s upward acceleration peaks at around 0.5s. Both legs’ magnitude of upward acceleration thereafter tapers down.

During the legs’ respective upward acceleration periods, the rod leg’s fall velocity slows and the fly leg’s climb velocity increases, the two briefly being equal in magnitude at the loop “freeze” point. The loop starting to climb again is the result of fly leg upward velocity having overtaken rod leg downward velocity in magnitude.

Taking loop propagation speed as indicative of tension (neglecting line taper), for the fly leg:
The fly leg’s initial velocity, when the rod stroke starts, is quite low (≈ +0.57m/s) and reduces to ≈ +0.4m/s minimum. At around 0.133s, with fly leg length reduced by only ≈ 0.24m and with the still growing loop propagation speed now at ≈ 6.7m/s, the tension at the loop is high enough to reverse the fly leg’s prior downward acceleration and accelerate the long length of fly leg mass upward. The tension combined with the reduction in fly leg length increases upward acceleration to a peak at around 3.4s. Loop propagation speed now further reduces (it started reducing at 0.23s) in magnitude and fly leg length keeps reducing. Fly leg upward acceleration reduces, but still upward.

Beyond the “loop freeze” point (your Phase 3), loop propagation speed keeps reducing in magnitude as fly leg length seems to increase. Fly leg upward acceleration reduces and remains upward. Shouldn’t the acceleration reduce faster or become negative now that leg length is growing again? A few candidates for that not being the case may be: a) Fly leg fly line has left contact with the ground. Probably not the leader yet – I counted frames from the last marker entering the view and projected that distance back. b) Due to line taper, the fly leg mass is likely to reduce despite its length somewhat growing. c) It appears that the fly leg’s velocity curve has been tracking the inverse of the loop propagation speed curve for some time already (see separate post about that).

Fly leg upward velocity has now increased from a low of 0.4m/s upward to around 9m/s upward.

Regards,
Dirk

[Dirk le Roux]

Hi Vince

Phase 1 - the rod leg acceleration causes loop propagation velocity to increase and pulls loop front down. Fly leg velocity is slow to react to the external force of the loop tension, possibly the loop is moving too slow to overcome the fly leg inertia.

The first part I basically agreed with previously and responded on the second part that the evidence shows that the fly leg started accelerating upwards quite early, and therefore the tension at the loop quite soon overcame the fly leg’s inertia.

Phase 2 - Loop tension pulls on the fly leg causing it to accelerate, fly leg pulls back in accordance with Newton’s 3rd, slowing down the loop propagation speed. The fly leg acceleration pushes the loop face upward.

The first phrase I agree with. The second part of the first sentence though – loop propagation speed will reduce more with less restraint on the part of the fly leg, because rod leg downward velocity is higher in magnitude. An increase in fly leg upward velocity narrows the gap with rod leg downward velocity, meaning a lower leg velocity difference and a lower loop propagation speed.

The second sentence – if you mean the fly leg’s increasing upward velocity being party to the loop face’s reducing downward velocity, yes. But, “pushes” sounds a lot like your phase 3 explanation (see comments on that below).

Phase 3 - The loop propagation velocity is no longer pulling the fly leg and the begins to collide with the loop because the fly leg is traveling faster than the loop. Possible cause of DN.

Velocity difference between fly leg and loop travel was addressed in post #75 and you said I was correct in this regard in post #78. If there is any rotation at the loop, the fly leg and the loop approach each other, as explained before. If the premise does not apply during phase 2 when the fly leg is also traveling faster than the loop and, as you agree during that phase that the tension at the loop pulls on the fly leg, why should it hold for phase 3?

Line in the loop rotates and passes through the loop due to leg velocity differences. The loop is a geometric disturbance where fly leg becomes rod leg, points on the line passing through it, with the added benefit of turning over the cast. Direction changes, velocity changes, momentum changes and acceleration changes occur there, but points on the line don’t stay in the loop and move together with it, as points do move with the fly leg.

Your point since post #78 about the rate of closure between fly leg velocity and loop travel velocity not matching will be further addressed in my next post, but for now it is once again maybe necessary to repeat that loop travel velocity is just the average of leg velocities. Its curve traces the midway between the two legs’ velocity curves.

If tension at the loop does not exert upward force on the fly leg, what force is responsible for the fly leg’s upward acceleration at this stage?

Regards,
Dirk

[Dirk le Roux]

Hi Vince

Your focus on the relationship between phase 3’s loop propagation speed and fly leg acceleration upward as can be seen on its velocity curve made me think some more, thanks!

Because the loop approaches the fly leg during the cast, its velocity vector should be opposite relative to that of the fly leg. So loop propagation speed in terms of fly leg should be given a negative direction regarding the fly leg. Looking at the relationship between the inverse (mirrored) loop propagation speed curve and the fly leg velocity curve, for easy comparison I moved the loop propagation inverse up on the chart by the difference between leg velocities. It shows that up to fly leg max. acceleration the two approach each other and from shortly thereafter the fly leg velocity curve generally follows the loop propagation speed curve.

Looking at the fly leg length during this period, I placed the loop front Y displacement curve (representing leg length) tangent to the loop propagation speed curve. Here it is easy to see the relationship between the reducing leg length and increasing loop propagation speed and later the two diverging again. The two become tangent, optimum, at the point of fly leg max. acceleration and remain closely tangent for a while. The midpoint of the tangency coincides with the fly leg velocity and loop propagation inverse curve joining.

It is like nature says to the fly leg “You have now been accelerated in your catch-up to energy balance” and thereafter its curve follows that of loop propagation regardless of further changes in leg length. Why should this be so? I don’t really know and maybe it’s just a simple coincidence.

Regards,
Dirk

[VGB]

Hi Dirk

You may have referred more particularly to the occupant’s head during something like whiplash, in which case the description does not fit.

If I still understand incorrectly, please post a free body diagram, stating reference frame, illustrating among all relevant vectors the net force in direction of travel and the occupant’s acceleration direction against direction of travel.

I may have referred to the occupants head and I may have put a free body diagram up, this traditional initial step would be a first in Tech Anal history. If you had done this, you would not have come to any answer, you would have asked what comprised the system. Introducing the suspension and seat back would have given you a different answer, a seat belt would change it again. I agreed with you on multiple occasions to stop the subject turning into another bead chain fest..

Flexible objects can and should be treated as systems of variable mass and it’s convenient to divide these into subsystems of variable mass. I don’t know of a better approach, do you? With variable mass systems and accounting their subsystems, including all terms relating momentum changes due to varying mass, the vector sum of forces still determines directions of the system’s and subsystems’ acceleration.

My post 107, that you seem to have missed:

Edit: ... the net force experienced by the respective legs, according to the graph reverses direction between upward and downward at the red dotted points

So we are in agreement to treat the rod leg, loop and fly leg as connected sub-systems?

* As discussed before in post #75, there may be merit to investigate a delayed signal from the abrupt absence or reduction of tension at the top of the fly leg reaching the tail end of it, and its possible role regarding dolphin noses. A train analogy was discussed, which is not so particle biased.

Using terms like particle bias makes you sound like Gordy's glove puppet, if you are acting as the mouthpiece of his study group at least be honest about it. A train and it's carriages are much more firmly coupled than a fly line so the comparison is fine very tenuous, if you get right down to it FEA is only a series of particles joined together so any analysis exhibits particle bias.

However it is doubtful that such a signal delay could be slow enough that the fly leg keeps accelerating upward along the duration of your phase 3 in the absence of a more presently acting upward force. Inertial coasting yes, but acceleration needs a force.

I'm not sure why you consider it doubtful that a positive acceleration at the front of the line, followed by either negative or less positive acceleration would not result in the back of a flexible object catching up with the front. Go and try it with a fly line; make a stroke without rotation at the end, just stop the rod.

There is no acceleration after 0.82s on the graph, the red dotted line I have added in Phase 3 to your chart below is parallel to the axis lines. I believe that you have agreed this before.

Returning to another question that I have asked multiple times; why do you think the loop is pulling the fly leg when the fly leg is travelling at a greater speed than the loop propagation speed?

Regards

Vince

[VGB]

Hi Dirk

I've read your post 145 a few times now and I don't understand it's intent, it appears to be a description of the graph. I'll try and pick out the substance.

For phase 1, I have said:

Phase 1 - the rod leg acceleration causes loop propagation velocity to increase and pulls loop front down. Fly leg velocity is slow to react to the external force of the loop tension, possibly the loop is moving too slow to overcome the fly leg inertia.

This appears to be your phase 1 description, where we seem to agree:

The fly leg’s initial velocity, when the rod stroke starts, is quite low (≈ +0.57m/s) and reduces to ≈ +0.4m/s minimum. At around 0.133s, with fly leg length reduced by only ≈ 0.24m and with the still growing loop propagation speed now at ≈ 6.7m/s, the tension at the loop is high enough to reverse the fly leg’s prior downward acceleration and accelerate the long length of fly leg mass upward.

My Phase 2:

Phase 2 - Loop tension pulls on the fly leg causing it to accelerate, fly leg pulls back in accordance with Newton’s 3rd, slowing down the loop propagation speed. The fly leg acceleration pushes the loop face upward.

and yours:

The tension combined with the reduction in fly leg length increases upward acceleration to a peak at around 3.4s. Loop propagation speed now further reduces (it started reducing at 0.23s) in magnitude and fly leg length keeps reducing. Fly leg upward acceleration reduces, but still upward.

I propose a reason for loop propagation speed reduction, you do not. You see a reduction in upward acceleration, I see something that is reasonably constant given the error bands of practical measurement. I do not see any fundamental differences in opinion.

If you are content, we can bank Phase 1 and 2?

Regards

Vince

[VGB]

Hi Dirk

I have no idea what your last post is trying to say about Phase 3 but you do not seem to reach a conclusion:

It is like nature says to the fly leg “You have now been accelerated in your catch-up to energy balance” and thereafter its curve follows that of loop propagation regardless of further changes in leg length. Why should this be so? I don’t really know and maybe it’s just a simple coincidence.

I would rather not believe in coincidences and would prefer to look at the effects of the laws of motion. We agree that it is preferable to divide a flexible mass into sub-systems and we have a subsytem of the fly leg with a greater velocity/speed than it's adjoining subsystem of the loop in Phase 3, they both have mass. The fly leg sub-system will catch up to the loop sub-system, both sub-systems have mass and some sort of collision will occur. Physicists use the term collisions, Gordy doesn't like that, I tried pushing, you don't like that. Maybe we need a SL invented term to describe this interaction which occurs in Phase 2 and 3?

Regards

Vince