Acceleration / Anchor

Gordy, I tried sending this again with the Study Group site in the address box. I?m trying it now just to the other address to try to spot the problem. Thanks Mark

From my reading about the casting analyzer I suspect that it works in a way which requires a different way of thinking about acceleration. Normally we talk about speed as a linear distance travelled over time and acceleration as change in speed. I believe the casting analyzer measures not distance but degrees (of an arc) travelled over time and acceleration in this case would refer to change in degrees travelled per unit of time. Here?s a chart I made to make sense of this.

Time Segment	Degrees travelled in segment	Cum Degrees Travelled
#1	1	1
#2	2	3
#3	3	6
#4	4	10
#5	5	15
#6	6	21
#7	7	28
#8	8	36
#9	9	45
#10	10	55
#11	11	66
#12	12	78
#13	13	91
#14	14	105
#15	15	120

The constant rate of acceleration for this example is 1⁰ per unit of time; the rod butt rotates 1⁰ in the first time segment, 2⁰ in the second time segment and so forth. If you look at a cast with an arc of 91⁰, it would consume 13 time segments. During the first half of that cast which consumes 6 ½ time segments, the rod would have travelled through only about 25⁰ of the arc, approximately 27% of the total for the cast. If you consider that the casting stroke takes something on the order of a single second to complete it might well appear to the caster that there are two separate speeds a slow initial speed that covers 25⁰ in ½ second and a fast second speed that covers 66⁰ in ½ second. There are indeed different overall speeds during the first and second half of the cast but just a single and constant rate of acceleration. No matter the size of the arc approximately ½ the time is used to cover just over ¼ of the total arc for the cast. This will also hold if the rate of acceleration is some fraction of a degree per unit of time .

Mark

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Bruce Richards answers with this message and an attachment :

Hi Gordy,

I've attached a couple charts re: acceleration. Mark is right, what the CA measures is angular speed and acceleration, measured in degrees/sec, and degrees/sec/sec (acceleration).

I've attached a showing both constant and non-constant acceleration in an automotive analogy. I've also made the same kind of chart using Marks data, assuming the "segments" were of equal time. As you can see, the acceleration his data shows is typical non-constant acceleration. I hope this helps.

Bruce

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Bruce .... Very clear.

Reminds me of Tom White and his imaginary Ferrari as he taught this in our MCCI Prep Courses.

Gordy

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Mark....

This time your message came through well.

Here is how I try to understand it:-

You are correct in that the CA does measure angular acceleration of the rod butt.

I never thought about it in terms of numerical progressions as you have done ... rather the acceleration curves which are generated. Bruce did both in his diagram.

Things to consider:

If we have a propeller such as an airplane prop. and the shaft is rotating at a constant number of revolutions per minute, the tip of the propeller blade is constantly accelerating.

That concept was hard for me to understand until one of our physicists pointed out to me that acceleration is a vector quantity ... not scalar. It is DIRECTIONAL. So every time there is a change of direction, acceleration goes from zero to a higher number. That propeller tip can be seen as constantly changing direction an infinite number of times as it rotates.

It gets more complicated when the propeller shaft turns at an increasing number of revolutions per unit of time....... That propeller tip is then accelerating at a higher "rate" or progression.

Seemed to me that this is would happen when we cast. The hand rotates as would a propeller shaft, but the rod tip would move as the tip of a propeller .... constantly accelerating by virtue of an infinite number of changes of direction ....

HOWEVER ....

That isn't what really happens when casting, because of the flexibility of the fly rod which bends in response to that very acceleration as force is applied.

Consider this:

The hand rotates the rod handle and rod butt. The CA measures rotation at the rod butt. The rod tip moves in both a linear direction and varying degrees of rotation unless the caster is theoretically capable of achieving a true SLP (which probably never really happens.)

Gets even more complicated when we look at the videos and see that the hand and rod butt actually move at one and the same time in both a rotational and linear manner and that admixture of rotation and translation (linear motion) is a changing relationship during the cast.

We can make this as complicated as possible ... the physicists could describe it with a blackboard full of calculus equations.

Makes one a bit dizzy ! Especially as I think of rotating one end of a rod to yield a straight line path of the other end !

Or we could make it simple ..............

Gross simplification in answer to a student's question on this subject :

" In order to form a small loop, the caster rapidly rotates his hand in order to achieve a straight path for the tip of his bent rod. "

Gordy

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ANCHOR

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From Craig Buckbee in response to Bill Kiester's use of the term "anchor" to apply to the point of resistance between the rod leg of the loop and the rod tip :

gordy,

i love the image/idea of the tip as anchor point. thanks bill !

and so here now is a definition of a D loop:

2 anchor points shorter in distance from each other than the length of line strung between them.

craig

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