Swingweight alternative - for Magnus

[Torsten]

Hi Magnus,

Also your method has the problem that you have to fix the fulcrum at a certain point - only a different grip length and you have uncertain results. I'm not a fan of all these methods I've read so far.

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So here is an alternative:

I think our main goal is to identify rods that feel tip heavy. Ideal is for this purpose something that I call the "Mass Density Graph" (MDG)

Definition: Mass Density Function md(x) = dm / dx,
that is the first derivative, the overall mass can be determined by integrating this function with the integration limits x=0 and x=rod length.

Now we have the problem that this function is hard to measure, we need an approximation.

First, we can measure the overall mass and the balance point (BP) - this way we can determine the average mass density in front and behind the BP.

AMD1= delta m / delta x = (m_overall / 2) / x_BP
AMD2 = (m_overall / 2) / (length_rod - x_BP)

AMD1 is the average mass density from tip to the balance point and AMD2 the average mass density from the BP to the butt end.

OK, the advantage is that the BP is very easy to measure accurately - and because we normalize the mass with the length it's better for comparsions where AMD1 could be used.

Two cases:
(a) Both rods have the same weight but have a different balance point, the rod with the balance point nearer the butt gets a lower AMD1;
(b) Both rods have the same balance point but a different weight, the one with the smaller overall weight has a lower AMD1.

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Now we can reapeat the same thing recursively (like Bill has done for the Bending Index Graph) for each rod section to get a more detailed approximation for the mass density function.

One example is my Sage XP #4/9ft :

length = 2,74 m
balance point = 2,23 m
weight = 92,9 g
IP=117,8 g => ERN=5,9
AA=74

AMD1=20,84 g/m AMD2=90,33 g/m

Sections:

S1
length=0,72 m
balance point=0,4 m
mass=3,38 g

AMD1=4,2 g/m AMD2=5,25 g/m


S2
length=0,72 m
balance point=0,42 m
mass=8,67 g

AMD1=10,42 g/m AMD2=14,07 g/m


S3
length=0,73 m
balance point=0,4 m
mass=15,53 g

AMD1=19,41 g/m AMD2=23,82 g/m


S4
length=0,73 m
balance point=0,57 m
mass=65,28 g

AMD1=57,26 g/m AMD2=206,58 g/m


You can see that the average mass density is progressively increasing from tip to butt - but it would be unusual otherwise.
It should be possible to calculate a approximation of the mass density graph with e.g. curve fitting methods like LMS (least mean square).

Bye..
Torsten

[Magnus]

Hi Torsten

Sounds good - nice and simple - can we run a comparison alongside the XP Z-Axis tomorrow?

[Magnus]

Measured a few rods and converted it to a graph - is this the type of thing you had in mind Torsten. (your figures are series 1)

[Eric]

That's good Torsten I like using the BP as well since it's easy and accurate.

I'm not sure, but with your method could there be a case where AMD1 for a light tipped 6wt would be the same as a heavy tipped 5wt? Maybe that make sense since they'd both feel similar to swing (might not happen with actual data)

For simplicity, how about we try to have just the BP distances as a ratio? Then leave overall weight as a scale factor.

(1) BUTTtoBP distance divided by BPtoTIP? Theoretical range 0 to infinity, but in reality never more than 1...

or...
(2) ButttoBP distance divided by Total Length? Theoretical range 0 to 1.

For both methods, a lower number would imply a lighter tip.

For you 4wt XP...
BUTT to BP: 0.51m
TIP to BP : 2.23m
Total : 2.74m

Balance Ratio method 1: 0.23
Balance Ratio method 2: 0.19

Unfortunately, neither of these methods nor yours communicates rod length well... A long rod could have certainly have a similar/identical AMD1 or BalanceRatio to a shorter one, but they'd feel much different in the hand.

I would like to suggest a multiple of the two.

BUTTtoBP distance times Mass : RodTorque

As BUTTtoBP increases so does RT
As Mass increases so does RT
As rod lengthens (increasing BUTTtoBP) so does RT
(do they increase at a proportion that seems similar to feel... I dunno)

For you 4wt XP...
BUTT to BP: 0.51m
Mass: 92.9g
RT: 47.4 g-m

[Torsten]

Hi Eric,

I'm not sure, but with your method could there be a case where AMD1 for a light tipped 6wt would be the same as a heavy tipped 5wt? Maybe that make sense since they'd both feel similar to swing (might not happen with actual data)

I've yet to find such an example - the few rods I've measured had always a higher AMD1 when they feel more tip heavy.

Normalization of the length is possible too, but I've found the mass density better - because it has a useful unit.

Of course a 10ft. rod could have a similar average mass density - but I think that's OK - usually you don't compare rods with a different length.


Magnus: Yes, I mean such a graph, but your x-axis is not scaled correctly. The x-coordinate needs to be in the middle (balance point to tip or butt) for each section.

I've done a graph of the Echo UD vs. Sage XP.

Bye..
Torsten

[Torsten]

The graph (I've removed the last 2 points):

[Torsten]

Values from the Echo UD #5 / 9ft:

legth: 2,75 m
mass: 139 g
balance point: 2,23 m
AMD1: 31,2 g/m
AMD2: 132,6 g/m
ERN: 7,5
AA: 67

Similar balance point, but much higher AMD1.

[Magnus]

Torsten

I'll fix the scaling. Yeah I've dropped the last section and the readings get more interesting. Have you compared the balance points for the sections?

Was I right in measuring the total length of the section - including spigot - one of those has spigot joints.

I'd like to be able to put three piece rods on the same graph - any suggestions?

Magnus

[Torsten]

Hi Magnus,

Comparing 3-piece rods to 4-piece could be a problem (because you're calculating the average MD and not the true MD) - but I think as rough guide it should work. I'll try that.

I've simply included the ferrules - that's a measuring error - but for a simple comparsion I think that's still OK.

Bye..
Torsten

[mpukas]

Magnum & Torsten - great work here - long time since I've been out of school & actaully had to use formulas, so I'm rusty in following this, but I get it...

Here's a question -

Comparing 3-piece rods to 4-piece could be a problem

why take measurements of each section? Why not measure the rod as a whole regardless of sections?

[Zoran]

Great work Torsten and Magnus !
Thank you guys.

Cheers,
Zoran

[Torsten]

Hi Mpukas,

why take measurements of each section? Why not measure the rod as a whole regardless of sections?

Well, I had this idea too - in theory you could suspend one end on a bearing measure at the other and dirive the mass density over some equations. But I fear this isn't easy to measure accurately.

Magnus, I've tried a graph from a 3-piece rod vs. a 4-piece ( Sage XP / Ron Thompson Axcellerator). Seems to be OK, at least you can see a trend.

Bye..
Torsten

[Rich Knoles]

Sorry I'm sleeping back here. Which one is stiffer in the tip and is the graph indicative of what you feel Torsten? Rich

[mpukas]

Which one is stiffer in the tip and is the graph indicative of what you feel Torsten? Rich

good question - I thought this was about mass distribution and swing weight? does this deal w/ stiffness? mpp

[Magnus]

Tosten

What program are you using to create the graphs - I can't seem to format that way in Excel