Help determining force vectors?

[Guitar-Roy]

I'm tossing around an idea in my head, but I'm outside of my knowledge base.

A guitar string is suspended between two points (nut and a bridge) and tightened to a certain tension. I assume most of the stress is in line with the strings, but force can do funny, counterintuitive things.

I want to find how much downward pressure, perpendicular to the strings, is acting on the bridge. Or how much upward pressure the bridge is exerting against the strings. Or whatever.

I don't have test equipment, I'm hoping for some math and principles so I can figure out a realistic range of real world possibilities.

What variables and formulas do I need?

Website/book recommendations are awesome. I can RTFM. I just don't know where to begin.

 

[MarcusAgrippa]

The tension will be the same along the entire string, assuming that there is zero friction at the bridge. Friction at the bridge might cause a difference in the tension on the two sides. The rest is a simple vector problem. You need to measure, or estimate, the angles made by the string on the two sides of the bridge with the bridge direction.

 

[Guitar-Roy]

The tension will be the same along the entire string...The rest is a simple vector problem...

I appreciate the response, but I don't know much about determining vectors (outside of some specific applications I've worked on before). That's my problem.

Tension equality makes sense, which I imagine can be determined by some math on string diameter, material type, frequency it is tuned to, etc.

What do I need to learn to figure out the magnitude and direction of the forces within this context?

 

[MarcusAgrippa]

Elementary vector mechanics. Try a book like Serway, Physics for scientists and engineers, or any freshman Physics text.

 

[Guitar-Roy]

Try a book like Serway, Physics for scientists and engineers, or any freshman Physics text.

Thank you very much. That's what I'm looking for. I'll go to a library.

I didn't know where to begin.

 

[billy_joule]

I appreciate the response, but I don't know much about determining vectors (outside of some specific applications I've worked on before). That's my problem.

Tension equality makes sense, which I imagine can be determined by some math on string diameter, material type, frequency it is tuned to, etc.

Many string manufacturers provide tension tables for all their strings, they show what tension (often in lbf, pound force) a given string exerts for given pitches and scale lengths. Here Daddario's chart:

http://www.daddario.com/upload/tension_chart_13934.pdf

The angle you are looking for is called the 'break angle' and is the topic of some contention (google 'top wrapping' for an example).
The downward force acting on the bridge varies from zero when the break angle is zero up to the total tension force when the break angle is 90 (ignoring friction).
I would think friction can be ignored as any significant friction at the break points leads to tuning instability and makes the guitar unplayable (in the sense that no one wants to play a guitar that doesn't stay in tune).

Some further reading:
http://www.frudua.com/guitar_strings_tension.htm

 

[Guitar-Roy]

Many string manufacturers provide tension tables...

Thanks, Billy Joule.

Those tension tables are great.

I'm familiar with break angle as a musician, but not from an engineering perspective.

Between those tables and reading some books like Marcus mentioned, I should be able to figure out what I'm looking for.