We all know that bigger strings require more bending force - but I was wondering how much more bending force? I did the calcs, and thought I'd share the results. I learned a lot more than what I'd planned! Here's what I found:











This was by no means a thorough investigation, there may be mistakes and there are a couple of approximations. [Edit - because of this, it's better to only look at the trends, not the absolute numbers, which could be a bit off.]

Some of the short cuts I took are listed below:
Effect of string stretching beyond nut/bridge was ignored.
Effect of instrument/whammy bar bending was ignored.
Effect of "stiffer" string ends was ignored, full string length was used.
Change in diameter with increasing tension was ignored.
String density and modulus of elasticity are only approximate.
Force of fretting the string was ignored, only bending force was used.
Ignored that adjacent strings need to be bent with bending string too. (can be incorporated quite easily)
Calcs are only for non-wound strings.


[Edit - the assumptions made are not very good for the above plot, this result is likely quite a bit off, but I'm leaving it here for interest's sake]

If anyone is interested in the Excel file I used to calculate this, I'll share it - it just needs some cleaning up first and I won't get around to that until later.

[Edit - I don't know why the graphs are so small - zoom in by holding in Ctrl and scrolling the mouse wheel, or pressing Ctrl and +. To return to default zoom, press Ctrl and 0 (zero)]

interesting work ParadoximA, im stunned that it takes so many kg's too bend a string...
nice info to start the day... ?

The Bending difficulty at different frets plot looks different than I expected. I would have thought bending at the 12th fret would be easiest then it gets harder closer to nut/bridge?

Tyron "mity88" Deakin wrote: interesting work ParadoximA, im stunned that it takes so many kg's too bend a string...
nice info to start the day... ?

Me too, I had to pick up a 1 litre bottle of water and balance it on my finger to make sure I was in the right ball park - it felt too heavy on it's own, but then I tried it with my hand on the guitar neck and it feels about right!

ez wrote: The Bending difficulty at different frets plot looks different than I expected. I would have thought bending at the 12th fret would be easiest then it gets harder closer to nut/bridge?

I also thought that, but I think what's happening is that as you move up past the 12th fret, the geometry is playing a bigger role than the increased tension - ie the vertical string movement lengthens the played part of the string a whole lot more than at the lower frets.

ParadoximA wrote: We all know that bigger strings require more bending force - but I was wondering how much more bending force? I did the calcs, and thought I'd share the results. I learned a lot more than what I'd planned! Here's what I found:

Dude! That's well cool. Care to share with us what it is that you've learned? i.e. offer some interpretation of the graphs beyond the obvious?

I agree with EZ, shouldn't the bending difficulty vs. fret number graph be mirrored around the 12th fret?

I'm still very sleepy. The point here is that that plot shows the force needed to make the string ring out one tone higher, so, the shorter the string gets (higher fret) the less you have to bend it to make it ring higher.

The plot would be mirrored like Deefstes says if we were talking about bending a string x mm away from its equilibrium position. I agree with the plot now ?

ez wrote: I'm still very sleepy. The point here is that that plot shows the force needed to make the string ring out one tone higher, so, the shorter the string gets (higher fret) the less you have to bend it to make it ring higher.

The plot would be mirrored like Deefstes says if we were talking about bending a string x mm away from its equilibrium position. I agree with the plot now ?

Aah, of course yes. It's about the force needed to bend the string enough for a pitch change of one tone, which obviously is less the higher pitched the starting tone is. Gotcha.

deefstes wrote: Dude! That's well cool. Care to share with us what it is that you've learned? i.e. offer some interpretation of the graphs beyond the obvious?

I actually did this a week or two ago and only put it up now so it's faded out of memory a bit (I really should have written this stuff down!), but here are a few things that grabbed my interest:

• It doesn't matter what gauge strings you have on, for the same tuning and the same bend on the same fret, you will always move the string the same distance.

• A set of 10s need about 23% more force than 9s, and a set of 11s need about 49% more force than 9s (and 21% more than 10s) - this remains constant no matter what fret you're on, or what scale length you have.
• Tuning a string 1 semitone sharper will increase the required bending force by about 19%, regardless of string gauge and scale length.
• So this means that string gauge makes a bigger difference than down tuning when it comes to how difficult it is to play, but the difference is small. (I'm glad Tony Iommi didn't know that, or maybe the Sabbath sound wasn't as accidental as they claim ? )

• Putting a set of 11s on a 24.75" scale length guit (Les Paul style) will make make the strings harder to bend than 10s on a 25.5" scale length guit (Strat style) - the same is true of 10s on the 24.75" and 9s on the 25.5".

More to come next week, gotta get some real work done!

Now that I look at it again, that plot of bend distance vs fret number doesn't look quite right - but maybe the "backup fingers" are playing a big role here - these calcs assume that the bending finger is doing all the work, in reality the backup fingers are doing quite a lot to increase the tension of the string, so that the bend doesn't have to move so far up the fret, I think even more so on the lower frets. This means the bend distance will be more consistent moving up the neck, not decreasing as much as on the plot. [Edit - the length of string beyond the nut/bridge will also have a big influence here, and since this was ignored in the calculation, this particular graph is quite meaningless]

The maths only speaks for the assumptions made, not necessarily for reality... if something looks wrong, there's a very good chance it is wrong, so if you see something - speak up!

ParadoximA wrote: [Edit - the length of string beyond the nut/bridge will also have a big influence here, and since this was ignored in the calculation, this particular graph is quite meaningless]

Sorry for digging up this thread.

I would really like to understand the influence of excess string length. It occurs to me that the excess length makes the bend easier to start but needs more bend distance to achieve the same pitch increase, so the net effect is zero anyway. No?

Gearhead wrote: I would really like to understand the influence of excess string length. It occurs to me that the excess length makes the bend easier to start but needs more bend distance to achieve the same pitch increase, so the net effect is zero anyway. No?

Correct. Plus a tiny bit of force to counteract the friction over the bridge and nut (which might be why some claim stiffer feel from guitars with appreciable string length between saddle and tailpiece).

Alan Ratcliffe wrote:

Gearhead wrote: I would really like to understand the influence of excess string length. It occurs to me that the excess length makes the bend easier to start but needs more bend distance to achieve the same pitch increase, so the net effect is zero anyway. No?

Correct. Plus a tiny bit of force to counteract the friction over the bridge and nut (which might be why some claim stiffer feel from guitars with appreciable string length between saddle and tailpiece).

Surely the fact that the length of string is greater means that it must be at a greater tension to generate the same note from an open string, and thus everything is a bit stiffer?