Engineering advice

[DarwinStrings]

I have been thinking about the break angle of the strings over the saddle on a glued bridge a lot lately. I once though that it did not make much difference but the more I think about it the more unsure I am of it. I have knocked up this diagram and wonder if someone could answer this question regarding it. Are the forces at A and B the same in both diagrams given that the inverted T shape is rigid as well as the same size and the force X is the same in both.

bridge diag.jpg (54.24 KiB) Viewed 10526 times

Jim

[Puff]

No-demonstratively not.
The sum of the forces will be but.
The resultant overall force path will subtend the angle over the saddle. This is the torque (belly up behind the bridge and collapse in front) factor on a 'normal' acoustic/classical bridge. Your figure on the left has a lot of torque to the left on the upright. The right a lesser torque on the upright but the same on the base.
Somewhere in the distant path was "taking moments about..."
A floating bridge or the likes of that on Smoothtalker addresses this issue in trying to give a simple close to vertical pulse rather than one queered by torque.
For mine if the Batson boys went to the Smoothtalker bridge they would gain an increment. Love those boys' bracing

[jeffhigh]

This is a much more complicated situation to analyse than what you have presented and glue line stresses are greatly affected by whether you use a pin bridge or pinless, but yes the rotational forces exerted on the soundboard are the same regardless of the break angle.
Assuming of course that the string height above the soundboard remains the same and the width of the bridge remains the same.

Besides theoretical analysis, there was a fellow on one of the forums who made up a model and measured the forces involved and found they did not vary with break angle.
Most still did not believe it.

[Puff]

Sure as hell there ain't going to be a banjo builder believe it.

[jeffhigh]

Banjo is a totally different situation
You are anchoring outside the bridge so there are no rotational forces only the downwards and yes that is directly affected by break angle.
But apples and oranges.

[Nick Payne]

If the T structure is rigid then for the same X, the forces at A and B have to be the same in both diagrams. That's elementary first year engineering statics.

[DarwinStrings]

Okay, thanks very much you mathematical mob. I had always thought this would be the case but some things I have read lately did cause me to question my thoughts even though when I look at the two sketches my head tells me that the forces at A and B are the same in both cases. It is great to have real engineers confirm it.

From a repair point of view I am not a big fan of those pin-less bridges Jeff although I like the look of the way I did that ukulele where there is no pins but the strings come through from inside the box and have given it some thought on a steel string. It is possible and I reckon it would work as well as a pin bridge but it would make changing a single string mid gig a bit of a pain, so maybe a good look but not great from a practical point of view.

Jim

[Dominic]

Hey, the only difference is the force acting on the saddle within the structure. Otherwise the forces on the whole structure are the same.
Dom

[DarwinStrings]

Cheers Dominic, I have that sussed. The first would be more prone to bending the saddle and or splitting the bridge and the second would give less chance of splitting the bridge and I reckon add a bit more weight onto a UST. Do I have that right in my back yard engineering mind?

Jim

[Puff]

Yep - but perhaps 'weight' would be better termed force. Same effective stuff in the long run though.
For mine the optimum would be a development of the Smoothtalker with the back and front saddles subtending the respective break angles thereby taking all torque out of the bridge and giving a simple vertical pulse to the soundboard.

[jeffhigh]

You will have a little more vertical loading on the saddle and hence on the UST in your first diagram

[DarwinStrings]

Ahhhh...of course...silly me . I should have realised that Jeff as the second one is sort of more like the tail piece equation where the smaller angle drives less force into the sound board. Cheers again.

Jim