string tension at various scale lengths

Karlis Abolins · From: (near) Seattle, WA, USA

Recently there have been a number of posts that talked about problems with string breakage. I have used a spreadsheet that I developed to help select appropriate strings for my new guitar which has a 25 inch scale. I used the spreadsheet to chart string tension of two string sets for E9 pedal steel. Both of these sets are available from the forum. I charted the sets at four scale lengths: 24, 24.25, 25, and 25.5. The charts show tension of the open string and the string pulled to its maximum note. In the charts you can see the trouble string (the 3rd string) carrying the 2nd highest tension. On a 25.5 inch scale, the pulled tension goes up over 35 lbs. I personally don't like to have pulled tension greater than 32 lbs.
The formula I used is ((G * N * L)/(K * C))squared
where
G = String Gauge
N = Note Frequency
L = Scale Length in inches
K = 1 for plain strings and 1.098901 for wound strings
C = 20.86 (conversion factor)

Take these charts for what they are. I don't purport to know the best string gauges for scale lengths but I know what I will use for my guitar.
If anyone would like my spreadsheet for their own purposes, please email me and I will send you the spreadsheet in Excel 2003 format.

Karlis

Lloyd Green Jagwire set 24 inch scale



Gauge    Open Tension       Pulled Pension


0.013    F#   30.62463597   F#   30.62463597


0.015    D#   28.83047188   E    32.36111052


0.0115   G#   30.19418023   A    33.89182138


0.014    E    28.19012294   F#   35.51732929


0.017p   B    23.32815604   C#   29.39163484


0.022w   G#   22.87682739   A    25.67837053


0.026    F#   25.36026561   F#   25.36026561


0.030    E    26.79824044   F    30.08000786


0.034    D    27.31984759   D    27.31984759


0.038    B    24.13085075   C#   30.40296681

Buddy Emmons SIT set 24 inch scale



0.012    F#   26.09436438   F#   26.09436438


0.015    D#   28.83047188   E    32.36111052


0.011    G#   27.62567718   A    31.00877420


0.014    E    28.19012294   F#   35.51732929


0.018    B    26.15336524   C#   32.95117540


0.022p   G#   27.62567718   A    31.00877420


0.026    F#   25.36026561   F#   25.36026561


0.030    E    26.79824044   F    30.08000786


0.034    D    27.31984759   D    27.31984759


0.038    B    24.13085075   C#   30.40296681

Lloyd Green Jagwire set 24.25 inch scale



0.013    F#   31.26597220   F#   31.26597220


0.015    D#   29.43423501   E    33.03881172


0.0115   G#   30.82650193   A    34.60157849


0.014    E    28.78047599   F#   36.26112753


0.017p   B    23.81669055   C#   30.00714977


0.022w   G#   23.35591026   A    26.21612287


0.026    F#   25.89135624   F#   25.89135624


0.030    E    27.35944491   F    30.70993858


0.034    D    27.89197547   D    27.89197547


0.038    B    24.63619517   C#   31.03966088

Buddy Emmons SIT set 24.25 inch scale



0.012    F#   26.64082839   F#   26.64082839


0.015    D#   29.43423501   E    33.03881172


0.011    G#   28.20420970   A    31.65815499


0.014    E    28.78047599   F#   36.26112753


0.018    B    26.70106484   C#   33.64123365


0.022p   G#   28.20420970   A    31.65815499


0.026    F#   25.89135624   F#   25.89135624


0.030    E    27.35944491   F    30.70993858


0.034    D    27.89197547   D    27.89197547


0.038    B    24.63619517   C#   31.03966088

Lloyd Green Jagwire set 25 inch scale



0.013    F#   33.22985674   F#   33.22985674


0.015    D#   31.28306410   E    35.11405221


0.0115   G#   32.76278236   A    36.77497980


0.014    E    30.58824104   F#   38.53876876


0.017p   B    25.31266931   C#   31.89196489


0.022w   G#   24.82294639   A    27.86281525


0.026    F#   27.51764932   F#   27.51764932


0.030    E    29.07795187   F    32.63889741


0.034    D    29.64393184   D    29.64393184


0.038    B    26.18364881   C#   32.98933031

Buddy Emmons SIT set 25 inch scale



0.012    F#   28.31419746   F#   28.31419746


0.015    D#   31.28306410   E    35.11405221


0.011    G#   29.97577819   A    33.64667339


0.014    E    30.58824104   F#   38.53876876


0.018    B    28.37821750   C#   35.75431358


0.022p   G#   29.97577819   A    33.64667339


0.026    F#   27.51764932   F#   27.51764932


0.030    E    29.07795187   F    32.63889741


0.034    D    29.64393184   D    29.64393184


0.038    B    26.18364881   C#   32.98933031

Lloyd Green Jagwire set 25.5 inch scale



0.013    F#   34.57234295   F#   34.57234295


0.015    D#   32.54689989   E    36.53265992


0.0115   G#   34.08639877   A    38.26068898


0.014    E    31.82400597   F#   40.09573502


0.017p   B    26.33530115   C#   33.18040027


0.022w   G#   25.82579342   A    28.98847299


0.026    F#   28.62936235   F#   28.62936235


0.030    E    30.25270112   F    33.95750887


0.034    D    30.84154669   D    30.84154669


0.038    B    27.24146823   C#   34.32209925

Buddy Emmons SIT set 25.5 inch scale



0.012    F#   29.45809103   F#   29.45809103


0.015    D#   32.54689989   E    36.53265992


0.011    G#   31.18679963   A    35.00599899


0.014    E    31.82400597   F#   40.09573502


0.018    B    29.52469748   C#   37.19878785


0.022p   G#   31.18679963   A    35.00599899


0.026    F#   28.62936235   F#   28.62936235


0.030    E    30.25270112   F    33.95750887


0.034    D    30.84154669   D    30.84154669


0.038    B    27.24146823   C#   34.32209925

ed packard · From: Show Low AZ

Good stuff Karlis!

Re pounds pull...did you ever measure the tension on the wound and unwound strings? when I measure the wound string tension, it is different from the values given by the common equation(s).

The wrap is a distributed mass placed upon a core. The core carries the most tension. Cores come in different shapes and sizes. String makers are a secretive bunch and generally don't answer questions. I only know of one brand that gives tension info on the wrapper, and I have never measured theirs.

Karlis Abolins · From: (near) Seattle, WA, USA

Ed, I have not measured the pull on wound strings. D'Addario publishes values for their strings which are very close to my formula. The big issue is the relative diameter of the core. The other manufacturers must use a different diameter from D'Addario. If we can determine the relative core diameter, we can probably adjust the factor to make the calculation more accurate.

Karlis

Robert Leaman · From: Murphy, North Carolina, USA

Does this chart take into account string length from the tuner keys to the nut? Tension is equal back of the nut to the tension from the nut to the bridge (changer). Unless the guitar is gearless (keyless), string length is only equal in pairs. For example on a 10 string neck, 1st & 10th, 2nd & 9th, etc.

Apparently, my question is still valid since the chart references tension to scale length. According to various forum experts, scale length is from the nut to the bridge and I agree with that. Most certainly, tension is equal across the entire string length between its two anchor points.

James Quackenbush · From: Pomona, New York, USA

Karlis,
Very interesting measurements here ....What I am finding is that just as important as the tension put on the various strings , that equally if not more important is how the string is mounted on the steel ...I am convinced that the straighter a string is pulled, and the least amount of angle the string has to endure from end to end , the more tension the string will hold without breaking ... This is why strings will last longer on some steels and not on others .... Jim

Karlis Abolins · From: (near) Seattle, WA, USA

Robert, Total string length is irrelevant to tension. When you raise a string to, say, 30 lbs it will have a tension of 30 lbs at every point on the string whether it is between the nut and changer or between the nut and the tuner. This discussion has been explored over and over on various topics.

James, You are right when you say that the way a string is routed and attached has an effect on the longevity of the string. If you minimize the bends, a string will have a decreased tendency to fail at the bends. My point is that string tension is a significant factor in string failure as well. In researching this topic, I came upon a statement that 37 lbs. tension was a failure point for strings with smaller diameter strings failing at lower tension. I think in your case 35 lbs on the pulled 3rd string is close to the failure point. That is why I would recommend going to a smaller diameter string (.0105) to help eliminate this problem. I think in your case, changing the radius of the bend on the connection point will also diminish the problem. In the meantime, try .0105.

Karlis

ed packard · From: Show Low AZ

Here is the way that I solved the sharp bend, and string tension on the BEAST. The tuner thingy could just as well have been a screw clamp (like the other end) and then no ball and wrap would be needed.

The tensile strength of the plain string is in pounds per square inch of string, so it is the pounds pull on the square inches of string = Pi*dia.

Here is a quick table showing the effect of tension and string dia. Now add the notes to it from Karlis' notes/length/tension tables.

Pounds> 33 30 28
dia. Pi*dia
0.010 0.031 1050.42 954.927 891.266
0.011 0.035 954.927 868.116 810.241
0.012 0.038 875.350 795.773 742.721

The above is just tensile strength...the shear strength comes in when the string is bent around a corner. In that case the tendency is to tear the outside of the string bend thus making the situation worse. Any abuse during/because of the ball wrap further weakens the string.

The best fix on most PSGs is what Jimmy Day did...tune down to D9.

James Quackenbush · From: Pomona, New York, USA

Karlis,
If I went to a .0105 for my 3rd string ....On a 25.5 inch scale , what is my tension, and what is the tension rating for a .0105 string ??....Not only that , but who makes such a string ?....I was not all that happy with an .011 on my steel ...I would really rather go to .0115 if possible ...?????....Thanks, Jim

Karlis Abolins · From: (near) Seattle, WA, USA

Jim, the .0105 string would be pulled to A at just under 32 lbs (31.89). I would not recommend a .0115 because the pulled tension would be over 38 lbs.
I put together my special string sets by buying single strings of the correct gauges at juststrings.com. They have SIT and D'Addario .0105's.

Karlis

James Quackenbush · From: Pomona, New York, USA

Karlis,
Thanks for the info ...I appreciate it ...Happy New Year !!..Jim

Ray Minich · From: Bradford, Pa. Frozen Tundra

On a string mfgr's website, several years ago, they calculated tensile stresses on the string by diameter & tension at note. I'll never forget that the stress on an .004 mandolin string was something like 400,000 PSI.

James Quackenbush · From: Pomona, New York, USA

Ray,
Just my luck ...I play mandolin also !!..... So far no problems with that instrument !!.... Laughing

....Jim

Jim Palenscar · From: Oceanside, Calif, USA

Do you think that the downward pressure that the string exerts on either the nut or changer affects the tone? Cool

One of the most acute angles of all guitars at the nut is the Emmons PP especially on the 1st and 10th strings. (just an early morning muse)

Curtis Mason · From: Ohio, USA

Karlis,

Your findings bring something else to surface here. I'm no rocket scientist, but it seems that the total tension needs to be minimized as much as possible to help eliminate or at least minimize the cabinet drop...isn't this correct?

I would be interested in your thoughts for the rest of the string sets. Is there a factory or customized string pack that meets your requirements??

I'm currently using the Jagwire Stainless Lloyd Green Artist series which does use the .0115 3rd string.

Thanks for the info,
_________________
Star Steel Guitar, G.D. Walker's Stereo Steel System, Hilton Volume pedal, TC-M1 Effects Processor, Peterson StroboFlip Tuner

Jim Palenscar · From: Oceanside, Calif, USA

I remember when David Wright sat at my Anapeg and played it saying that it felt "mushy" to him on the strings. While kinda taking offense I then remembered that, at the time, he was playing a Sierra with a 25" scale and the Anapeg had a 24" scale- that one inch of difference in scale length can make a world of difference in how the guitar feels to the player.

Karlis Abolins · From: (near) Seattle, WA, USA

Curtis,
The guitar I am building is a 25" scale.
These are the calculated gauges that I will be using:

James Quackenbush · From: Pomona, New York, USA

Jim,
I don't know about too much downward pressure, but not enough would give you string buzz ....Think of downward pressure or lack of on a Reso ....This may be a an excessive example , but you get the idea ...Jim Q

Curtis Mason · From: Ohio, USA

Karlis,

Thanks for the reply, Wow, a .062 for the 10th string, do you have a problem fitting that in the hardware?? And no D string, so you're probably liking the really big major chords with a lot of low end. That's what I like about the Pedal Steel, you can create your own copedant based on your personal needs, and make it do what you want.

Here's a link to a site containing strings for PSG, and I found the tension's which appear to be quite a bit lower than the specs you've encountered. Are these just wrong?? It don't specify the Guitar length.

http://www.juststrings.com/dad-xls490.html
_________________
Star Steel Guitar, G.D. Walker's Stereo Steel System, Hilton Volume pedal, TC-M1 Effects Processor, Peterson StroboFlip Tuner

Karlis Abolins · From: (near) Seattle, WA, USA

Curtis,
I make my own gauged rollers and can adjust the groove depth to accomodate any size string.
As far as the D'Addario chart is concerned, I checked out the calculation for the top F# .013 using my spreadsheet. Using a scale of 24.25" I calculated 31.266 which seems pretty darn close to 31.2. D'Addario uses the same formula that I use.

Karlis

Curtis Mason · From: Ohio, USA

Karlis,

Please forgive me, I was looking at the pulls side of your chart, and comparing it to the open string side of theirs...I stand corrected, your calculations are absolutley correct.

_________________
Star Steel Guitar, G.D. Walker's Stereo Steel System, Hilton Volume pedal, TC-M1 Effects Processor, Peterson StroboFlip Tuner

Curt Langston · Posted 14 Dec 2007 9:23 pm **Good!**

richard burton · From: Britain

I'm having a bit of a brain fart at the moment Whoa!

Can anyone tell me what the tensile strength of music wire is, either in pounds per square inch, or kilograms per square millimetre ?

I've looked on the net, but got a lot of wildly varying figures.

Brint Hannay · From: Maryland, USA

When it is said that "total string length is irrelevant to tension", that confuses me.

Karlis's charts at the beginning measured different tensions for different scale lengths. Understood that total tension for the string is unaffected by the presence or absence of a non-speaking portion, but (assuming the dimensions of keyheads are not adjusted to compensate for different scale lengths) the total length of the equivalent strings is different, by the difference in scale length. On a keyless, the total tension accordingly would be different from that of a keyed because of the different total length, wouldn't it?

That is, a different tension is required to raise a shorter string to a given pitch than to raise a longer string of the same thickness to the same pitch. Would that be correct?

Curt Langston · Posted 16 Dec 2007 4:57 pm !

David Doggett · Posted 16 Dec 2007 8:58 pm

Brint, you and Curt are confusing stretch or throw with tension. If the scale length (bridge to nut) and gauge are the same, it will take the same increase in tension to pull the string to the same given pitch, regardless of how much string is behind the nut. But the instrument with more string behind the nut will require a longer stretch to get to the new tension. This extra stretch will require more flexing where the string rotates over the changer. So that extra stretch and flex can cause more string breakage, even though the tension is the same. Thus, a keyless head may be albe to withstand a longer scale without increased breakage, or even less breakage. If the gauge and pitch are the same, the longer scale will actually have more tension, possibly with less breakage. This extra tension is why keyless instruments can feel more solid. But the possibly decreased breakage is because of less stretch and flex at the changer, not because of less tension.

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