Myth -- Magic -- Mathematics -- The Straight Line Principle

[Tim Benware]

I get it but I may not be asking the question right. I'm referring to the below pic in your article. As it shows even with the correct complimentary angles to equal 180 degrees, if a different radius is used it raises the bridge and you state "Note that with a smaller radius the bridge level raises relative to the rim correct relationship to neck angle and FB plane is lost." So to me what that says is if the neck angle is 89 deg you should be using a 40' radius or else the bridge level raises, unless of course you thin the bridge. So there must be an ideal bridge thickness to go with 89 and 40' to get that ideal height and the right relationship. So then it would follow that if you start with a different neck, say 88.5, to get the right relationship you need the right radius and bridge thickness combination. And that's what I'm asking, is there a way to determine beforehand if you have a 88.5 degree neck angle, what radius/bridge thickness combination you need? If there is, then whenever you have a neck angle of whatever degree you can pick the right radius and bridge thickness to get the string height you want.

Edit: dang typos

[Dave Bagwill]

This is how I look at it:
1. The neck/body angle is paramount. A given. The starting point. Everything else keys on that.

2. That leaves 3 variables that key off the straight line and determine the string height.
- bridge thickness
- saddle height
- top dome
3. The top dome cannot really be 'adjusted' and is not always exact anyway.
4. So the saddle height and bridge thickness are what we have to work with. Saddles are not difficult to adjust. When it comes to bridges, even Martin keeps 3 heights of bridges so that with the variables in the top dome and other inaccuracies they will have a bridge that works. As a kit builder, I have one bridge that is usually very close to correctness, though it is easy enough to thin if need be and in fact I have done that.

I don't think it is possible to come up with a perfect formula, it's just important to have the straight line first, and know how to adjust the saddle and bridge to deal with the dome.

DaveB

[ken cierp]

There is no doubt someone could come up with a grid/table showing all of the string plane "hover height" using all the various top contours, bridge thicknesses (Martin has three or more?) and saddle heights. I personally have found that to be unnecessary since I've settled in on 40' braces. And if for some reason I wanted to experiment and say, make the braces 28' I'd simply shave (sand) some material off the bottom of the bridge. And don't forget the fingerboard thickness comes into play too when considering dimensional combinations. In a "nut shell" Bob Taylor figured it out first (on a large scale) His system is able to be adjusted and "tips" the entire "straight line" using a couple of shims.

[Tim Benware]

I agree Dave. I guess I was trying to get to: If you use a 40' radius should you start with a 89 degree neck angle to limit the "inaccuracies" as opposed to if you use a 25' radius (which is what I have) should you start with a 88.5 or say 88.7 degree neck angle to reduce the inaccuracies. Or are the differences between 25', 28' and 40' top radiuses so slight that as long as you have the straight line those differences don't matter.

[ken cierp]

I recommend a fall away angle of at least 1.3 degrees no matter what top radius (which I recommend at 52' true Martin or 40' which allows for a thinner lighter bridge). Then -- again adjust your string "hover height" with the saddle and bridge thickness.

[Dave Bagwill]

Tim - in an ideal world, we could have a chart, in which you would START with the top radius, and from there the math would determine exactly what the neck angle, top slope angle, bridge and saddle heights would be to result in a desired 'hover height'.

Enter: top radius
Enter: desired hover height

Output: bridge height, neck angle, saddle height

I should not perhaps have used the word 'inaccuracies' - 'variables' is what I meant. And because of those, we cannot really start with the top radius.
We can start with the neck angle and by careful machining get very very close to the ideal at that point, and use that same ideal for any top radius by adjusting what we can adjust - flossing the cheeks, bridge and saddle height.

It's a very interesting subject.

[Tim Benware]

I agree this is a fascinating subject and I think both words are good - variables can lead to inaccuracies. I was taught Martin style building. I sand the top flat, sand a 25' radius in the braces and 1.5 degree on the neck block. That with a Martin bridge gets me the correct string height. So that's why I'm interested to see if there are ways to get there with the other neck angles.