# How to calculate maximum neck thickness

Discussion in 'Luthier's Corner' started by Ben Rose, Dec 21, 2005.

1. ### Ben Rose

Jan 12, 2004
Oakland
I'm getting set to build my first instrument (something like a Chapman Stick). I'm very early in the design phase, and have a couple of questions related to neck thickness.

Based on projected total string tension (approx 200kg / 440 lbs) and materials used (maple), is there a way to determine the maximum thickness of a neck that will still allow relief adjustments, given an essentially rectangular neck shape? I believe that the structural rigidity of deifferent wood species is used in part to determine this, but I'm not sure how.

How do carbon fiber rods and truss rods affect these calculations?

Thanks,
Ben

2. ### mahrous

Aug 13, 2005
Egypt
i havent seen many luthiers going into such calculations ... but there is some basic common sense. You don't build a neck out of a 1/2" piece of wood. all my necks come out of at least 1" maple or other woods. i am talkng rectangular shapes as you said above.

3. ### Ben Rose

Jan 12, 2004
Oakland
True, but I'm looking for maximum thickness, not minimum. Could you leave the neck as a 2" unshaped rectangle of wood? Weight and playability aside (it will mounted on a stand and tapped only), would a neck that thick still allow for relief adjustments to be made?

4. ### Suburban

Jan 15, 2001
lower mid Sweden
d(x)=L^2/(6EI) * [T(0) (2x-3x^2+x^3) + T(L) (x-x^3)]

d(x) is deflection at x mms from one string anchorage.
x is distance from one string anchorage.
L is distance between the two anchorages.
T is the torque from stings and truss rod.
E is the MOE or Youngs modulus of the material(s).
I is the geometrical bending resistance (moment of inertia, I think).

Now you know.
The rest is just mechanical browsing of tables and calculating.

5. ### Ben Rose

Jan 12, 2004
Oakland
Thanks Suburban! Very helpful. I thought that torque was a twisting motion. Do you mean to substitute torque for bending load or string tension? (Sorry if this question sounds dumb to people with knowledge of physics)

Thanks,
Ben

6. ### Biagio139Dealer: Hipshot Products, Inc.

Dec 23, 2005
Ithaca N.Y.
wow you really getting deeper than I ever have, I leave an 8th behind my truss rodds. make sure its flat when you put the fret board on, use a couple of truss rods in you need to. I like the carbon fiber rods, mostly to help with deadspots in the finger board. dont worry to much remeber maple isnbt that expensive

7. ### Suburban

Jan 15, 2001
lower mid Sweden
As you may have noticed, the string is not quite parallel to the neck, nor are they in the bending center of the neck profile. This means that the tension force can be split into composants, one parallel to the neck and one perpendicular, using Pythagoras.
The perpendicular force is multiplied with the free lenght of the neck, which gives you one part of the torque.

The parallel composant is multip´lied with the distance from the bending line of the neck profile, which gives you the other part of the torque.

Add them and be done...so far.

Heck, I'd need you here to show you! Or, you find an engineer or an engineering professor near you and ask him/her! It's easier to understand than to explain in plain text.. :scowl:

8. ### Ben Rose

Jan 12, 2004
Oakland
Thanks, Suburban. I appreciate that you took the time to explain that. I've been researching these terms online and I think I'm making a little headway into understanding them. But you're right, I should probably find a friend with an engineering background and sit down with him for an hour.