[Gill the Piano]

As someone whose knowledge of physics is confined to a hazy mermory of Fleming's Left-Hand Rule, can you tell me if there's more torque on a string whose coil is a long way from the plank, as opposed to one whose coil sits almost on the plank? Went to a piano whose owner complains that his tuner can never tune two particular notes, (big Kawai brand new upright) and the only difference I could see was that there seemed to be more torque on those particular pins. All the pins seemed to have the coils a long way from the plank, but those were furthest. Anyway, I belted 'em and set 'em, and they seemed to settle happily. His usual tuner is less brutal than me when he tunes, apparently!

[PianoGuy]

Torque required to turn the pin will be greater with the coil further from the plank, but only if the embedded section of pin is the same length (so in practice probably not!). If the piano is pinned tightly a lot of effort will be wasted in the twisting of the pin section that is exposed before the pin actually turns in the plank.

There are other factors to consider, namely the tightness of pinning which will be slightly random anyway and the length and uniformity of the pin set.

[Gill the Piano]

Pins seemed to be no tighter/looser than any of the others. Twisting the top of the pin and not the bottom seemed to be the only explanation...?

[Barrie Heaton]

[Gill the Piano]

Never thought of that. If I get called back, I'll take a squint at it, but when I walloped it, that seemed to settle it down.
Which may be why my husband looks nervous...

[Tom Tuner]

Wrestpins with no bushings that stand a long way out of the plank are much more subject to "flagpolling", bending slightly, which does not conduce to tuning stability. Very tight pins can twist at the top of the embedded section, with respect to the bottom of the pin. When or if this subsequently untwists the string tension is certainly affected.

[Otto]

I'm now going to confuse you all!

A piano tuning pin has a turning force (couple) which tries to release the tension of the string. This is proportional to the the tension on the string and on the distance from the centre of the string in tension to the centre of the pin.

This couple (force times distance) is counteracted by the pin's stiction in the wrest plank times the radius of the pin.

Stiction is short for static friction, a resisting force that is greater than a frcitional force. You have experienced stiction many times before. You notice it when you find you have push hard to get something moving, but once moving the force required to keep it moving is much reduced. The initial effort overcomes stiction, while the lesser subsequent force overcomes friction.

Stiction is proportional to the perimeter of the pin, so double the size of the pin and you double the stiction. But you also double the radius so the couple you can resist will be four times as much.

You can increse the stiction by whacking the pin into the wrest plank, roughening up the surface of the pin or increasing the temperature (don't ask me how you do that short of moving to the Kalihari desert).

So to answer your question, if you reduce the excess off the end of the string and retighten it you will reduce the couple on the pin.

Finally, torque is applying a couple as you turn the pin. I'm not sure it's a useful concept for piano tuning, but for car engines it's brilliant - it's that which determines how fast you can accelerate.
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Otto