Evaluating the Haul

[gordonjudd]

I realize that mathematically speaking, using a 2D representation underestimates the haul distance but overestimates haul speed by comparison to 3D.
and
Wouldn’t it be the case that if it underestimates distance then it also underestimates speed?

Paul,
No. As is generally the case, Merlin has it right.

The z offset just adds a constant distance value to the d=sqrt(x_diff.^2+y_diff.^2 + z_offset.^2) distance equation given by the Pythagoras theorem. The speed is related to how that distance changes with time. The fixed z offset value was assumed to be constant with time so there is less change in the distance vs time values and thus less speed.

The point was for Lasse's cast the difference was around 7% (much less than 15 to 20 percent) so it is not a very big effect.
Gordy

[VGB]

I didn’t post this in teaching because it was too technical

[Paul Arden]

Hi Gordy,

But surely the hand path curves in a quarter circle from the chest to straight arm?

Won’t the haul distance be (2pi.r)/4, which would make a difference of 1.57 for the forearm movement?

r being the length of the distance from elbow to thumb. The side measurement would show the haul travelled distance r, but if we track the thumbnail it travels 1.57r Also simplified of course.

Cheers, Paul

[Merlin]

Hi Paul

Here is an illustration of your back cast record:

Paul BC haul vs line hand.JPG (30.28 KiB) Viewed 197 times

You can see the change in haul distance as the line hand moves forward in a kind of semi circle.

Merlin

[Merlin]

The same illustration for the forward cast. In this case, the difference in haul distance is approximately equal to the "diameter" of the (more than) a half circle:

Paul FC haul vs line hand.JPG (41.26 KiB) Viewed 185 times

Merlin

[gordonjudd]

the difference in haul distance is approximately equal to the "diameter" of the (more than) a half circle:

Merlin,

Could you plot a comparison of the actual haul distance measured in those two cases? I don't see where circular paths (half circle) enter into the actual haul distance (or its derivative to get the haul speed) calculation.

Here is the haul distance curve measured for Lasse's back cast. I would think Paul's curve would be similar.

Won’t the haul distance be (2pi.r)/4, which would make a difference of 1.57 for the forearm movement?

Paul,
The path of the haul hand may be circular in nature, but the distance from the haul hand to the stripper guide will not have much to do with circles.

Gordy

[gordonjudd]

Here is the haul speed curve that is calculated in Tracker by taking the derivative of the haul distance curve shown above for Lasse's back cast.

Gordy

[Merlin]

Gordy

Haul distance is measured between line hand position and stripper guide position. My point about the « diameter » of the circular path refers to the « r » value mentioned by Paul. With simplifying assumptions, and for a FC only, the haul distance may equal (in value) 2r (and not r).

Merlin

[gordonjudd]

With simplifying assumptions, and for a FC only, the haul distance may equal (in value) 2r (and not r).

Merlin,
I don't understand what assumptions you are making to come up with a haul distance difference of 2r on a forward cast. If r was equal to .4 m that would give a haul distance difference of around .8m

On Lasse's forward cast Tracker gives a starting haul distance of around .63 m as shown below.

haul_dist_start_forward.jpg (32.51 KiB) Viewed 142 times

At release the distance between the stripper guide and his haul hand was around 2.28 m

haul_dist_end_forward.jpg (35.47 KiB) Viewed 142 times

That gave a haul distance change of around (2.28-.63)=1.67m which is around 4r. Are Paul's values that much different to come up with a 2r value?

Gordy

[Paul Arden]

You can see the change in haul distance as the line hand moves forward in a kind of semi circle.

Ok from that angle the difference won’t be so great. If we were to look perpendicular to the hauling plane the circle would be wider. I believe the forearm mostly stays in one plane.

Cheers, Paul