Floating tremolo: if spring tension equals string tension, then why...?

jaymenon

A set of D'Addario EXL110s tuned to standard tuning exerts a total of 46.51kg of tension

When a tremolo is floating, since spring tension equals string tension - then the tremolo springs must exert the same 46.51kg tension irrespective of the number of springs used.

So then why does the tremolo feel softer, easier to use, with two springs installed as compared to with three springs installed?

stickyfiddle

jaymenon said:

A set of D'Addario EXL110s tuned to standard tuning exerts a total of 46.51kg of tension

When a tremolo is floating, since spring tension equals string tension - then the tremolo springs must exert the same 46.51kg tension irrespective of the number of springs used.

So then why does the tremolo feel softer, easier to use, with two springs installed as compared to with three springs installed?

Short answer: Because when you move the bar, you're only pulling on 2 springs rather than 3, which is less work. 

Slight longer answer... 

What happens when you push down on the trem arm is you're pulling against the springs with whatever force is required to shorten the strings a fixed amount such that the string tension reduces by X%. Let's call that distance Ym. That distance is dependent only on the strings, the tuning, and the physical dimensions of the guitar (scale length and total string length) - the springs are irrelevant to that equation. 

Each spring requires a fixed amount of force to stretch it by Ymm - let's call that Z. If you have 3 springs you need to move all of them by Ymm, so the total force needed is 3Z. If you reduce the number of springs to 2, you only need to exert 2Z of force to stretch the springs by the same amount and produce the same dip in string tension. 

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 

It actually works the other way in case of up-bends; more springs will make an upward dive easier, but noone ever really does those so you don't notice. 

digitalkettle

stickyfiddle said:
...

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 
... 

I'd wager that springs don't have a linear response either.

ICBM

The force when the bridge is at rest is the same, but a different number or different stiffness of springs changes the spring constant, or how much the force changes as the length of the spring changes. With more or stiffer springs, the force changes more rapidly for the same movement away from the rest position so the arm feels tighter.

stickyfiddle

digitalkettle said:

stickyfiddle said:
...

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 
... 

I'd wager that springs don't have a linear response either.

They literally do unless they're *really* weird

https://en.wikipedia.org/wiki/Hooke's_law

digitalkettle

stickyfiddle said:

digitalkettle said:

stickyfiddle said:
...

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 
... 

I'd wager that springs don't have a linear response either.

They literally do unless they're *really* weird

https://en.wikipedia.org/wiki/Hooke's_law

Holy carps...wager lost...that feels really unintuitive to me!

maltingsaudio

digitalkettle said:

stickyfiddle said:

digitalkettle said:

stickyfiddle said:
...

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 
... 

I'd wager that springs don't have a linear response either.

They literally do unless they're *really* weird

https://en.wikipedia.org/wiki/Hooke's_law

Holy carps...wager lost...that feels really unintuitive to me!

You can't alter the Laws of Physics but I'm with @digitalkettle , I scanned the wiki page , and found this bit

Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.

So they are linear up to the point they fail or are about to fail

Musicwolf

stickyfiddle said:

What happens when you push down on the trem arm is you're pulling against the springs with whatever force is required to shorten the strings a fixed amount such that the string tension reduces by X%. Let's call that distance Ym. That distance is dependent only on the strings, the tuning, and the physical dimensions of the guitar (scale length and total string length) - the springs are irrelevant to that equation. 

Thinking about briefly, I'd agree.   Spring and string tension is only equal when you aren't touching the arm

Kittyfrisk

stickyfiddle said:

digitalkettle said:

stickyfiddle said:
...

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 
... 

I'd wager that springs don't have a linear response either.

They literally do unless they're *really* weird

https://en.wikipedia.org/wiki/Hooke's_law

Is this like Hook's Law where the bass guitarists strap extends to bring the guitar to below their knees?

sev112

maltingsaudio said:

digitalkettle said:

stickyfiddle said:

digitalkettle said:

stickyfiddle said:
...

I'm simplifying a bit as there's all sorts of extra maths around leverage and moments because it's all moving around a pivot point, but that should all net out to be irrelevant in the context of this question. 
... 

I'd wager that springs don't have a linear response either.

They literally do unless they're *really* weird

https://en.wikipedia.org/wiki/Hooke's_law

Holy carps...wager lost...that feels really unintuitive to me!

You can't alter the Laws of Physics but I'm with @digitalkettle , I scanned the wiki page , and found this bit

Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.

So they are linear up to the point they fail or are about to fail

It’s a bit more
they are approximately linear up to a point quite a bit before failure at which point their stress-strain curve becomes more curved than linear, many materials 50%.

they key is to strain materials well below their failure stress/load to ensure (a) “small” deflections, and (b) no plastic permanent deformation on removal of load. 

My presumption is that the loads on strings in general are sufficiently much lower than failure loads so effectively act approximately elastically,

ToneControl

OK As I understand it: I use 5 springs, I like the trem to be stiffer, but was not sure why

Fortunately, one of my best friends is a Professor of Mechanical engineering, and I asked him about this a few hours ago.

It seems as if the reason is as follows, based on his advice to me, and my understanding:

The springs used are extension springs.
They are pre-tensioned.
Therefore, for the first part of the stretch, it takes more force to stretch them per mm say, later on it becomes easier - less force to extend by each mm -  a more normal linear response.

As mentioned by others, the strings have their own relationship to Hooke's law - at the same length, they should be at the same tension. They don't care what pulls them.

So I assume that, using 5 springs, hardly stretched at all, means that a lot of force is needed to deflect the bridge enough to decrease the length and tension of the strings (which is my usual use of the trem).
Whereas with 2 springs, the springs require less force to stretch them, hence less force to decrease the length of the strings.

Voxman

I was right there up to " A set of D'Addario EXL110s tuned to standard tuning"!! Lol