The workshop

Neck straightness and Eulers Columns

I’ve been delaying this bit of writing until I can organise some simple pictures to make explanation easier, but I haven’t managed that yet, and I don’t want to keep putting it off, so here goes without pictures, which hopefully will follow later.

This first part is old news, but sets the scene for what follows.
 
We all talk about a guitar neck being “straight”, but most of us know that in practice, the word “straight” is rather misleading - a tiny curve in the neck is essential for most playing styles. This is simply because strings don’t vibrate in straight lines, and to keep the frets as close as possible to the strings we allow the neck to bend a little, following the “envelope” of the string vibration as we move up the fingerboard from fret to fret.   Generally speaking, low actions and light playing styles require straighter necks and vice versa.  

To adjust this “straightness” against the pull of the strings we use a “truss rod”- one of several different devices that apply a reverse bending force to the neck to counteract the forward bending caused by string tension.  This isn’t the same as non-adjustable neck reinforcement, although some people still use the same name.

Here is the bit that most people don’t understand.  The forward pull of strings, taken together with the backward pull of the truss rod can NEVER add up to a straight line, or even to a single smooth curve.

The mathematics of this was worked out by Leonhard Euler in the 18th century, and expressed in  “Eulers Columns” formulae - basically, a long slender shaft such as a guitar neck, when compressed but restrained in some way so that it doesn’t bend forwards, will take up a slight S shape, it will not simply shrink lengthways in a straight line.  It’s a bit like bending at the knees when carrying a heavy load on your shoulders.

I still have a simple mock up of this that I made years ago to illustrate the point in an exaggerated manner, varying the string tension and the truss rod adjustment can produce a variety of shapes, but never a straight line.

In an acoustic guitar neck with a basic adjustable rod, the closest you can get to a straight line when the strings and truss rod are under tension is actually a slight hollow from nut to about the sixth fret, then a tiny reverse curve from sixth to eleventh, the fingerboard upwards from there remaining mostly unaffected by the truss rod (although there is a complication there, which I will explain later). On an electric guitar, the same thing happens but a little bit further up the neck because of the extra length.  This problem is usually addressed by filing off the tops of the high frets where any string buzz occurs, without much thought as to why it is happening.

To get the optimum “straightness”, a guitar maker or repairer will need to allow for string tension, either simply by knowing from experience where to remove a little extra, or by setting the guitar in a device that simulates string tension before leveling the frets. There is now even a computer operated machine (Plek) that does all this for  you, measuring and plotting out the distortion that comes from string tension and truss rods then grinding down all the high frets automatically to a pre calculated curve.  The print outs from these machines show very clearly the distortion involved - the slight S shape of a neck under several different forces.

There is no way round this- all we can do is find ways of dealing with it.
 
 One way is to design the truss rod to bend the neck in a slightly uneven manner, a little more in one part of the neck than another. With the single rod design we can change the curve in the rod, or with box section truss rods we can change the internal spacers, but it isn’t so easy with most other designs.

More about truss rods at a later date.

Another way round the problem is to thin the fretboard a little in the appropriate areas before the frets are installed, and high tech makers can use a CNC machine to do this, shaping the fingerboard along its length in a slight reverse S shape before the frets are inserted, removing a little extra wood from the surface in places where it will be forced upwards when the strings and truss rod are tightened. The end result is that common white lie – a “straight” neck. The tops of the frets will look strange when first made, but a nice even curve- “straight” when strung up and adjusted.  

Clear as mud? The next bit might cause a few arguments.