Guitar String Maximum Travel Distance

[Dejoblue]

I would like to calculate the maximum distance, crest, a guitar string will travel at it's center when plucked in order to determine how high the string needs to be on the fretboard to avoid striking parallel frets and thus avoiding "fret buzz".

Example:

0.762 mm string thickness with 6.35029 kg of tension to get A=440 Hz @ 647.7 mm string length
where a force Z provides 5 mm of string movement @ point 161.925 mm from one end of the string length and vertical movement Y occurs.

X = string length
Y = movement I am interested in
Z = initial force stroke


I need to solve for the initial force required to move the string under tension at the specific place, 1/4 of the length, and then I think I can use sinusoidal formulas? It is actually circular, since the lateral movement Z causes a vertical movement Y. What formulas should I use?

I plan to post the results I calculate for all strings of a 6 - 8 string guitars at different intervals and different initial conditions(IE frequencies, thicknesses, scale lengths, etc.) on my blog.

http://dejablueguitar.blogspot.com

Scroll down to see my balanced string tension article and calculations. I wish to do something similar for string travel at the crest for many strings etc.

Thank you in advance for any help.

 

[Dejoblue]

PS: guitarists do not actually stroke laterally they stroke across and down at the same time, as well as up with upstrokes, and the movement is actually more elliptical. Dunno if this matters or if the equations bear that out regardless. I am interested in looking at these initial conditions with an ideal perfectly lateral stroke to see if the results are even feasible, IE if the crest radius is more than 3 mm under "ideal" conditions then it is not really relevant.

Thanks again for your time.

 

[Jolb]

If you model a guitar string as a perfect classical string, then the standing modes (the natural harmonics of the string) can be excited with any arbitrarily small initial displacement. In other words, there is no lower bound on the force required to pluck a string and get it ringing very softly.

Of course a guitar string is not a perfect string and there are other effects going on, but the ideal string approximation would be a good approximation for the guitar string at very small displacements of the string (very light plucks, and thus very soft notes). So the minimum amplitude of the harmonics is not really relevant for calculating how high your strings should sit above the frets.

Really the best way to determine fret height is by seeing whether you get clatter when the guitar is being played loudly (or as loud as the player would like to be able to play). Of course if you really yank vertically on the guitar string, even if it is at the right height to ordinarily avoid clatter, then a strong enough yank will cause the string to hit the fret. Also if the player of the guitar has a very horizontal picking style, they may be able to play very loudly without any interference with the frets--the strings can (in principle) just move around in the plane parallel with the plane of the frets. All these things could happen regardless of whatever (reasonable) initial fret heights and string tensions you want. It all comes down to what the player's style is and what they would like to be able to do. (In fact many "slap bass" bass guitarists do indeed really yank on the strings--they call it "popping"--to get them to hit against a fret. e.g. )

Calculating these things from basic physical principles is a mammoth task and you would be better off just being a little more "empirical" with how you try to configure a guitar. People who work on guitars have all sorts of rules of thumb for configuring the fret height--setting your bridge height/tremolo tension, adjusting the truss rod, setting the bridge saddles, even your tuning and the kind of strings you use--all come into play in many ways that would be quite difficult to calculate.

 

[Dejoblue]

I appreciate your help and source references.

This is on electric guitar using a plectrum. I used a ruler to measure at what point I could hear the string go out of tune from being struck, this was at 5 mm on the A string and a very hard stroke. More likely I would be using 2 - 3 mm strokes. This 5 mm stroke is far beyond what will cause "fret buzz". My current "action"(string distance from the fretboard) is 2 mm at the 12th fret, ostensibly 1/2 the length of the string.

Perhaps I should have prefaced and or elaborated on my question.

I have played guitar for 24 years and have serviced my own instruments as long. I understand completely these "rules of thumb" and can cite many of the sources I have used over the years as well as my personal preferences.

I understand that neck relief is a necessity(of preference) to counteract the elliptical motion of the strings along it's length.

I also understand that this initial endeavor does not entail actual fretting.

I understand that a harder stroke WILL cause buzz.

Nut and bridge height will be determined by the crest of the string's movement.

i also realize that the crest may travel along the length of the string, I am interested in it's greatest point.

I also realize that this is a "monumental" task, but it is something I am very interested in performing. Furthermore it becomes even more monumental when I next calculate the crest distance 1" away from the nut, as it will be a smaller movement but it what actually causes the "fret buzz".

At any rate, for the current calculations let us assume a perfect lateral stroke of 5mm. I need to calculate the force needed to move a string 5mm under tension at a point that is 1/4 the length of the string away from one side.

Let us also assume no fretboard is involved, just the simple distance traveled at the crest of the ellipse.

Then I also need to calculate the crest once the string is released from that initial 5 mm starting point.

Please be aware I am not asking for anyone to do numerous calculations, if one can simply point me to a formula I am wanting to do this myself or better yet give one example calculation.

I do appreciate requesting and providing clarification. I also intend to participate in discussion here to assess what is relevant to my application as well as the potential for other applications.

Thank you for your time.

 

[Dejoblue]

Ahh i think i understand now. The initial force is arbitrary so the amplitude will vary. Doh. Hmm. Well maybe we can figure out what it would be with a maximum of 5 mm.

Would I just use the wave equation?