Re spiral, hex, octagon, and stiffness - Wally Murray

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I'm jumping in here to fulfill a promise to list the Orvis Battenkill, 8',
2/2, for an 8wt.  Serial # 77,xxx. (tip to butt, 5" stations)  0.085,
0.104,  0.120,  0.140,  0.150,  0.160,  0.175,  0.180,  0.190,  0.205.
0.220,  0.230,  0.235,  0.245,  0.260,  0.280,  0.290,  0.320.  Winding
check at 38".  I suppose the following remark isn't strictly necessary, but
it struck me.  This particular rod has some wicked glue lines.  I hope this
taper is useful to someone.  Wally.

 

  _____  

From:  [mailto:rodmakers-bounces@goldrush.com]
On Behalf Of Al Baldauski
Sent: Friday, March 16, 2007 10:19 AM
To: rodmakers
Subject: [RODMAKERS] spiral, hex, octagon, and stiffness

 

Gentlemen,

 

Here is my take on this ongoing discussion:

 

Here are the formulas directly from a "strength of materials" text:

 

Deflection ~W / MOI  (i.e.  Deflection is proportional to load applied
divided by the Moment of Inertia)

 

MOI for various shapes:

 
For a rod 1 inch (flat to flat)

Square (flat to flat)                    = 0.0833 8 d^4
= 0.0833

Square (corner to corner)           = 0.0833 8 d^4
= 0.0833

Hex (flat to flat)                         = 0.06 * d^4
= 0.06

Hex (corner to corner)                = 0.06 * d^4
= 0.06

Octagon (flat to flat)                  = 0.055 * d^4
= 0.55

 

Where "d" is the dimension flat to flat in all cases

 

Since MOI is in the denominator or the Deflection equation, the larger the
value the less deflection.  If you assume the 

Amount of deflection for a constant load is a measure of stiffeness then the
following is true:

 

if ALL rods compared have THE SAME flat to flat dimensions the square rod is
stiffer than a hex by 38.8% whether 

flat to flat or corner to corner (at the expense of 15% more weight).  The
octagonal rod will be 8.3% less stiff than the hex.

 

There are so many variable in making a rod that a subjective evaluation of a
couple of rods is chancy at best.  Even a 

carefully structured experiment is fraught with difficulties.  For instance:
if you evaluated a hex rod of 0.100 diameter versus 

a hex of 0.102 diameter, the larger section is 8% stiffer!  Imagine what the
difference in bamboo from culm to culm will do!

 

Regarding spiral rods:

Since the stiffness is the same flat to flat or corner to corner then the
spiralling will have no effect due to orientation of aprices.  

If any one can MEASURE a difference, then it will be because of a change in
cross section.

 

 

Al Baldauski

Hackettstown, NJ