algorithm for string tension?

[santucci218]

I'm sure its dependent on how the string is made and such, but for example, D'addario has their tensions on the back of their guitar sets...how do they figure it out? I have a new ERG (extended range guitar) and I want to piece together a more even feeling set.

[knuckle_head]

T = (UW x (2 x L x F)²) / 386.4
UW = (T x 386.4) / (2 x L x F)²

T: tension in pounds per linear inch
UW: pounds per linear inch
L: scale length in inches
F: frequency in hertz

[santucci218]

I assume different companies use different core gauges and wrapes and such, so they will all be slightly different?

[santucci218]

wait, to get tension i need unit weight. to get unit weight, i need tension. This is physically impossible!

[251]

Originally Posted by santucci218

I'm sure its dependent on how the string is made and such, but for example, D'addario has their tensions on the back of their guitar sets...how do they figure it out? I have a new ERG (extended range guitar) and I want to piece together a more even feeling set.

You pull the string until it breaks. Actually you run many samples & average the results. It takes some specialized testing machines, measuring tools & a trained technician to get uniform results.

[knuckle_head]

Originally Posted by santucci218

I assume different companies use different core gauges and wrapes and such, so they will all be slightly different?

This is true, but only to a point. You should do some comparisons between my unit weight data and D'Addario's. We both have published a tension chart and the unit weight data is pretty consistent.

Circle K
D'Addario

Originally Posted by santucci218

wait, to get tension i need unit weight. to get unit weight, i need tension. This is physically impossible!

The formulas provided above let you figure for tension or figure for unit weight. You need two of the numbers to arrive at the third.

Originally Posted by 251

You pull the string until it breaks. Actually you run many samples & average the results. It takes some specialized testing machines, measuring tools & a trained technician to get uniform results.

Pulling a string until it snaps tells you tensile failure point and little else. A tension meter will inform you what the tension on a string is given a specific tuning (this, assuming you have the meter attached to a string on an instrument capable of sound reproduction or tone generation).

Most accurate way to figure unit weight is to take a big bundle of same-gauge strings, lop off tapers and ball ends, measure each string and then weigh them all. Take the weight and divide it by the total number of inches of string you've got.

This will tell you most of the story and is accurate enough. It won't compensate for draw down under tension (a string is actually thinner when it is tuned to pitch) nor will it account for the taper which reduses the overall weight of a speaking string as the taper crosses the saddle and diminishes the mass of the vibrating string.

I figure my tension based on wind formula - I know how much wire each wrap consists of and how much core there is and how much mass there is for each layer. Imperfect as well, but another way to get to a very-close approximation.

[santucci218]

Well, This work is more than i wanted to do, cutting strings and what not. Knucklehead, let me ask you this. I have the back of my D'addario back right infront of me. 9-42. Yet, the tensions for the most part are not even.

9---13.1 Lbs
11---11.0
16---14.7
24---15.8
32---15.8
42---14.8

If they know the proper tension, why wouldn't they make the set so they all had the same tension all the way across? I just dont comprehend why! All this stems from my 8 string guitar, and trying to match a Low B and Low F# string to this set. Last night I put a 56 on the B, and a 72 on the F#. The B sounds good, but the F# is HORRIBLE. It buzzes really badly, and the sound is very weak through my pickup. It is nearly unusable unless I only play the open strings. Does this equate to improper tension? Or is the string somehow too big for its job?

What it comes down to guy is this. If you can make me a pack with a low F# that doesnt sound this bad, and has an even tension, I want to buy it.

[knuckle_head]

The only thing out of whack on that set s the .011. It gets dicey that thin as the slightest difference in diameter alters tension dramatically.

Look for .058 and .080 singles for your B and F# - you may have better luck.

I am working up guitar sets and I suspect I may need a few more gauge options than I have at present. I won't know for a little while.

[251]

Originally Posted by knuckle_head

<snip>

Pulling a string until it snaps tells you tensile failure point and little else. A tension meter will inform you what the tension on a string is given a specific tuning (this, assuming you have the meter attached to a string on an instrument capable of sound reproduction or tone generation).

Most accurate way to figure unit weight is to take a big bundle of same-gauge strings, lop off tapers and ball ends, measure each string and then weigh them all. Take the weight and divide it by the total number of inches of string you've got.

This will tell you most of the story and is accurate enough. It won't compensate for draw down under tension (a string is actually thinner when it is tuned to pitch) nor will it account for the taper which reduses the overall weight of a speaking string as the taper crosses the saddle and diminishes the mass of the vibrating string.

I figure my tension based on wind formula - I know how much wire each wrap consists of and how much core there is and how much mass there is for each layer. Imperfect as well, but another way to get to a very-close approximation.

If you say so Knuckle Head. I'm sure you know more about strings than I do. 8-)

[santucci218]

The more i think about this, the more I think my low F# string has a defect. Maybe there is something wrong with the core that i cant tell, but affects it badly. It sounds intensely throaty and bad. When I pluck hard its REALLY bad. when i pluck very softly i can actually hear the fundamental note. I have never heard of a string being too thick to sound correctly. Even when i tuned it up a whole step, it still sounded bad.

[knuckle_head]

Bad strings happen - but you really ought to be closer to .080.

[LowB-ing]

If you know the exact unit weight at pitch (any stretching accounted for), you can always calculate tension as described by knucklehead. Type of string, manufacurer etc. won't matter at all. This is simple physics.

The trick is figuring out unit weight from published gauge numbers. That's where string type, materials, wire core gauge, wrap gauge, number of wraps and such come into play. Not to mention the fact that published gauge isn't necessarily accurate. It's sometimes rounded. Other times it's simply wrong.

[santucci218]

OK! Guys, I figured out the problem, and wow do i feel stupid.

Mind you I own another Ibanez RG, with a floyd rose. So I strung it as i strung any other floyd rose. Ball end goes to the headstock, and the end of the strings goes in the bridge to be tightened.

Well, I wasnt even thinking, as this is have I have done it for three years. I just came to notice that the string tapers at the end, and, since I installed it backwards, the taper was right between the pickups and it made it sound horrible. How dumb. Live and learn guys!

[ixlramp]

Originally Posted by knuckle_head

T = (UW x (2 x L x F)²) / 386.4
UW = (T x 386.4) / (2 x L x F)²

T: tension in pounds per linear inch
UW: pounds per linear inch
L: scale length in inches
F: frequency in hertz

Please excuse me correcting this

T: tension in pound-force (lbf)

The rest is correct (EDIT: see below)

For years I thought that tension was in pounds, but pounds is a measure of mass, and tension is a force, two different things. 1 pound-force is the force exerted on your hand by 1 pound of mass in earth gravity (EDIT: see below)

[cassius987]

A pound is not a force or a mass, it is a mass times a force. A "pound-force" would be mass times force squared. Doesn't make sense to me.

[knuckle_head]

Force acting on a mass....

[cassius987]

If pound only refers to mass then it makes sense. If pound refers to weight, it doesn't. I guess that's where I'm confused.

[All_¥our_Bass]

http://www.bangzero.org/stringtension/#

[GregDunn]

Pound-mass and pound-force are identical in Earth gravity, but tension is measured in lb-f when using FPS units, or newtons in MKS units.

http://en.wikipedia.org/wiki/Tension(physics)
http://en.wikipedia.org/wiki/Pound(mass)
http://en.wikipedia.org/wiki/Pound-force

[ixlramp]

With more research, it seems that 'pounds' can mean either pound-mass lbm or pound-force lbf depending on context, causing confusion. Best to be specific and use lbm or lbf.

Quote from Wikipedia that is confirmed by the physics sites:

"Since most masses on earth have weight, and because this relationship is usually highly proportional, the term “weight” typically describes both properties in everyday use. In the physical sciences however, mass and weight are distinct. Mass is an inertial property; that is, the tendency of an object to remain at constant velocity unless acted upon by an external force. In turn, weight is the force created when a mass is acted upon by a gravitational field."

So the term 'Unit Weight' is also sloppy, it should be 'Unit Mass', it's measured in pound-mass per linear inch. So...

T = (UM x (2 x L x F)²) / 386.4

UM = (T x 386.4) / (2 x L x F)²

T: tension in pound-force ( lbf )
UM: unit mass in pound-mass per linear inch ( lbm/in )
L: scale length in inches ( in )
F: frequency in hertz ( Hz )