Distribution of torsion in a steel guitar string

[Anko]

TL;DR Summary

winding a string with one end fixed, by attaching a weight to the free end and spinning it.

This isn't a question about torsion pendulums because it goes well beyond linear physics.

The question is roughly, how many times can you rotate the end of a steel string, with the other end fixed, before it breaks? Also, how does the torsion distribute along the string? I tried to answer both questions and got some surprising results.

 

[Baluncore]

I tried to answer both questions and got some surprising results.

What were your results?

I believe the torsion is distributed evenly along the wire, as the surface work hardens first. The core of the wire is not strained as much as the surface, so remains soft.

If you axially twist nichrome wire, you will find the surface and the core have different magnetic properties and hysteresis. When the external magnetic field is changed slowly, the field will switch rapidly internally.
https://en.wikipedia.org/wiki/Wiegand_Sensor

 

[Anko]

What were your results?

I believe the torsion is distributed evenly along the wire, as the surface work hardens first. The core of the wire is not strained as much as the surface, so remains soft.

I was at first surprised that I could rotate the weight as much as I managed, and how long the period was.
All of which was eyes on, I didn't make any real record or even use a stopwatch.

The other surprise was how the torsion was distributed along the string. I monitored this with small bits of sticky tape; plumber's tape would have been nice but I ended up using sticky labels, trimmed to about 2mm width. As expected, the bit of tape near the weight showed the steel string was rotating at the same rate as the weight, and there was practically no rotation at the fixed end.

Along the string the rotations were not evenly distributed.
In fact what I observed was quite nonintuitive. I'd like someone else to at least try this; the materials are fairly accessible. I'd like some independent confirmation.

 

[sophiecentaur]

As expected, the bit of tape near the weight showed the steel string was rotating at the same rate as the weight, and there was practically no rotation at the fixed end.

I would have thought that the angles of your tell-tales would be cumulative from fixed end to free end IF the diameter of the wire was uniform along the length. however, there are various possibilities that might make the modulus of the wire vary over its length. It could have been wound onto the storage drum with uneven tension.

Surfaces on one face of the drum / hank could have been a bit more corroded than the other. What was the source of the wire? Was it an old guitar string, worn on some frets and corroded by finger sweat? I'd be inclined to use a fresh guitar string as they are made and drawn with some care - as opposed to thin fencing wire which would be cheaper and non-uniform.

 

[JT Smith]

What diameter and length of steel guitar string did you use? What weight on the end?

 

[sophiecentaur]

What diameter and length of steel guitar string did you use? What weight on the end?

And was it fresh? Was it used by a guitarist for bends?

 

[JT Smith]

Well, I just tried it and I didn't see anything surprising. What did I miss?

I rotated the weight ten times and counted the rotations at the five pieces of tape I stuck on gthe string. I guessed at the fractional part of the rotations so it's not highly precise. And the tape distances I rounded off. But it looks like it is probably linear. Isn't that what you'd expect? Or is the non-linearity that showed up in my sloppy measurements the same as what you saw?

 

[Baluncore]

The first sign of torque failure of a round wire, is when the twist is not spread evenly along the wire.

If you want to reliably rotate a suspended load, hang it from a tape or a ribbon, not from a round wire.

The outer half of the round wire, forms a torque tube, about the neutral axis core. A round wire will be more rigid than a ribbon of the same sectional area. A round wire will work harden, the torque tube will fracture from the surface, where micro-cracks form, propagating fatigue internal corrosion.

 

[sophiecentaur]

If you want to reliably rotate a suspended load, hang it from a tape or a ribbon, not from a round wire.

I have noticed that the torsion pendulum in 400 day ('anniversary') clocks usually uses a wire with rectangular section so I guess that is evidence for your statement. Securing the wire at each end is obviously easier and at a repeatable angle.

The springs in (springer) air guns are usually circular cross section but you can (illegally in UK) use a square section wire and the energy stored is significantly more. The same could apply to any wire under tortion so the OP's experiment could probably be improved on with square section wire (not as readily available, though; I wouldn't like to play guitar with square section strings - ouch).

 

[Baluncore]

I have noticed that the torsion pendulum in 400 day ('anniversary') clocks usually uses a wire with rectangular section so I guess that is evidence for your statement.

We do not know why the OP was trying to break circular wires by twisting them. The best way to avoid the wire breaking, is to replace the round wire with a thin band or ribbon.

Rugged moving coil meters use taught-band suspension rather than jewels and opposed hairsprings.

The gyroscope assembly in some gyrotheodolites is suspended on a ribbon, because that offers minimum torque, and improved reliability.

 

[Anko]

Some answers for the questions.

It was a used guitar string, probably a 2nd. I was interested in how much I could stress the string by rotating it a lot. I was getting periods that were quite long, and up to perhaps 80 rotations initially, then seeing if the string would break. I did this repeatedly for weeks.

When you give the weight many turns, so you wind up the string, eventually you can feel resistance to further turning. I suppose I could have just kept turning until the string broke, but I was interested in how many times I could do this to an old guitar string. I haven't repeated this with new strings yet.
I need the space to do it. The materials aren't a problem.

 

[sophiecentaur]

When you give the weight many turns, so you wind up the string, eventually you can feel resistance to further turning.

You could see how many turns are needed before there's permanent (plastic) deformation. You'd need to be careful with counting turns so you can tell when the wire no longer returns to its original angle.

 

[Baluncore]

It was a used guitar string, probably a 2nd.

Maybe you can tell us what the string's length and diameter were.
The untwisted length, you can measure.
The nominal diameter, will be available from a string supplier.

 

[Baluncore]

Let's assume that the wire starts out 25” long, and 0.010” in diameter.
Length = 635 mm; Diameter = 0.254 mm; Circumference = 0.8 mm.

What will happen if we twist the wire 80 turns in one direction?
Consider a filament on the surface, parallel with the axis.
Once twisted into a helix, the axial length will be;
a = √ (635² – (80*0.8)² ) = 631.76 mm

The wire has shortened by; 635.00 - 631.76 = 3.24 mm.
The suspended weight will have been raised by close to 3.24 mm.
An axial filament will then have been compressed by that same length.
100 * 3.24 mm / 635 mm = 0.51 %.
That will probably be within the elastic limit for spring steel wires.

 

[sophiecentaur]

It is interesting to note that, when a coil spring is stretched, the actual rotation of the spring wire is very little but the masses hung on the bottom (as in the school experiment) will rotate a bit as the spring lengthens. When the elastic limit, when the spring coils don't go back, then the angle changes noticeably - but only by less than 180 degrees (iirc).
The OP's experiment causes a much bigger twist than that.

 

[Anko]

It is interesting to note that, when a coil spring is stretched, the actual rotation of the spring wire is very little but the masses hung on the bottom (as in the school experiment) will rotate a bit as the spring lengthens.

That's how a Wilberforce pendulum works. Momentum is transferred from the spring to the weight, then back again.

 

[sophiecentaur]

That's how a Wilberforce pendulum works. Momentum is transferred from the spring to the weight, then back again.

That looks cool. I'm probably gonna have to make one now!!! It calls for a long spring which probably means making one. Easy to bodge but hard to make it look good and uniform or it'll have other unwanted modes for sure.

I usually to stick to the 'two potatoes on strings' toy but that takes only minutes to put together as a coupled oscillators demo.