Neck torque

[Larry Simonson]

With so many discussions on mandolin neck joints I wish some of the resident engineers and physicists would discuss the forces the typical mandolin neck joint endures. Currently my interest is in the torque trying to separate the joint near the bottom button. I am thinking the torque exerted on the joint is the string tension multiplied by the sine of the neck angle then multiplied by the length of the neck as measured from the end of the neck to the nut. Is this correct?

[Jim Hilburn]

I probably shouldn't comment because I don't know much about the physics, I just know that when you set the neck and have it right where you want it you shouldn't have any slop at the bottom and expect the glue to lock it in. If so, start over with shims. When it's fit well it's total overkill and will hold up forever.

[Pete Jenner]

Is this correct?

Quite possibly.

[sunburst]

...the torque trying to separate the joint near the bottom button. I am thinking the torque exerted on the joint is the string tension multiplied by the sine of the neck angle then multiplied by the length of the neck as measured from the end of the neck to the nut. Is this correct?

I don't know the answer, but if I'm reading this correctly there is something missing: the length of the neck heel. It seems to me that the force "trying to separate" the joint near the button is a tensile force, not a torsional force, so calculating torque is not all that is needed(?). The fulcrum of a lever is the heel of the neck directly below the fingerboard, one end of the lever is the neck shaft, the other end is the neck heel. Am I wrong about that, or am I wrong about your question?

[fscotte]

With so much worry about the neck, in particular a well made dovetail joint, no one seems to care about the 3 little screws that hold the strings at the other end. If three tiny screws, each no more than a 1/4" long can contain all that tension, why worry about a well made neck joint?

[Marty Jacobson]

OK, I'm not an engineer... but I think John's onto something -- to draw a valid free-body diagram, you must have the sum of the forces equal zero.
So Larry's point about the torque being related to the neck axis component of the string tension is valid. Also, John's point about the length of the dovetail (or neck heel) is important because that's where the counter-torque enters into the picture which, if the neck is not actively failing, is counter-acting the torque applied at the nut/peghead.

There's more, too- some part of the string tension as normal force on the neck block, and normal force from the neck block back on the dovetail. Then if you want to model the whole neck, you get the fretboard as a beam, the truss rod, etc., each relating to an equal and opposite force.


With so much worry about the neck, in particular a well made dovetail joint, no one seems to care about the 3 little screws that hold the strings at the other end. If three tiny screws, each no more than a 1/4" long can contain all that tension, why worry about a well made neck joint?

They don't -- the just have to keep the tailpiece from sliding upwards. The sheet metal does the heavy lifting.

[jim33]

The torque on the neck in inch-pounds would be the total string tension in pounds times the distance from the strings to the top of the dove tail in inches.

The force trying to separate the bottom of the dovetail would be the torque divided by the height of the dove tail. (top to bottom)

This assumes that the fulcrum is the top of the dove tail.

The 3 (5?) little screws are in shear and they will carry a lot in shear.

[Larry Simonson]

Thanks to all. Jim don't you have to resolve the total string tension into horizontal and vertical components? I think the horizontal component puts the compression force at the fulcrum and the vertical component provides the torque putting the heel bottom button joint in tension. If the angle is 5 degrees only 8.7% of the total tension is providing the torque.

[Larry Simonson]

John, I forgot to answer your question. Yes, the height of the heel block is important as that is the fulcrum . I should have defined the angle as that between the string tension vector and a line drawn from the top of the nut and the top of the heel block. I think is is very nearly the neck angle.

[Jim Hilburn]

All I think I have to do is what has worked for over 100 years. I really don't think of it in mathematic terms. Then I'd really be in trouble.

[jim33]

Just resolve your moments around the fulcrum. The string tension is balanced by the compression in the upper dove tail and the tension in the lower dovetail. This is a simplification of what is actually going on, but it will get you close.

[Nevin]

Correct me if I am wrong but I always thought of torque as a twisting force. The force trying to separate the neck at the button is in an arc due to it acting on a fulcrum. But it is otherwise a straight, not twisting force.

[Jim Hilburn]

What problem are we trying to solve here?

[fscotte]

We're trying to resolve Loyd Loar's equation of the derivative computation of the forces on the standard typical uncommon dovetail joint and its compression factor after being resolved in Einstein's theory of continuum and mass over the e=times square to the root of the tail.

[sunburst]

What problem are we trying to solve here?

Sometimes it's just curiosity that drives us to ask questions. It would be interesting to know how much strain a neck joint must withstand.

[Jim Hilburn]

Yeah, that's what I thought too.

[Dale Ludewig]

Me too. I think there's too many variables involved to actually come up with a number in real terms. Suppose there is no neck joint; just the neck and the headblock as one piece- now all the strain is on the neck and the parts of the body, top, sides, back, and where they join the head block (not to mention the rest of the forces trying to deform the back, sides, and top.... I suppose you can relatively easily compute the downward force on the top based on the strings used and the break angle, etc. But to calculate the stress on the neck joint involves conjecture- all of them assuming deformation in the neck joint based on different woods that aren't anchored perfectly, glue that gives or creeps, voids, etc. etc.

[Nevin]

Just to make things more complicated, the strings are under tension but are not parallel with the neck, they are on an angle and the angle changes at the nut. Thus, just as the break angle changes the forces working on the top, I would think that the break angel at the nut would have an impact on the forces on the neck.

[CedarSlayer]

Torq on a neck might apply on a Celtic style instrument. On an F style instrument it should all be done with vectors. :)

Bob

[Dave Cohen]

I have styed out of this thread because it is a statics problem. There are numerous engineers on this forum, and they can certainly handle statics problems. However, it seems that some clarification is necessary.

Torque is a vector quantity, defined by

Tau = rxF,

where Tau is the torque, r is the displacement vector, and F is the force vector exerted at the end of the vector r, and x denote the cross or vector product. It can also be expressed as

Tau = I*alpha

where I is the moment of inertia (presumably of the neck) and alpha is tha angle through which the end of the r vector has rotated. That is the rotational analog of Newton's 2nd law, i.e., F = ma. The torque vector can be visualized by the "right hand rule". Curl the fingers of your right hand. That is the direction of the rotation. Extend your thumb to the side. That will be the direction of the torque vector.

Torque is a quantity central to rotational dynamics, and therein lies the point (oops, a pun) of all this. Torque becomes a signifiant quanty when there is rotational motion. For a mandolin in the normal playing position, assuming it was rotating, the torque vector would be pointing toward the floor. Except that the mandolin is not rotating to any significant extent. Maybe if you were trying to be the Hendrix of the mandolin and were spinning your mandolin around about the heel joint,,,,. What is really needed for the purpose of this thread is a simple force vector.

http://www.Cohenmando.com

[Jim Adwell]

Sometimes it's just curiosity that drives us to ask questions. It would be interesting to know how much strain a neck joint must withstand.

It wouldn't be all that hard to build a mockup of a mandolin, with a bolt-on neck and a strain gauge like this one (http://www.smdsensors.com/Products/productView.asp?ProductID=13&Sensor=P940+Thin+Film+Pressure+Diaphragm&CategoryID=162) between the head of the bolt holding the heel on and the head block. String it up with a set of cheap mando strings tuned to pitch and measure away.

I'm not going to do this, because it's not important enough to spend any time and money on, but it could be done.

[kkmm]

build a mockup of a mandolin
This is the most practical idea and will give the actual answer.
I remembered when I was in Engineering school, there was a story (joke):
Someone brings in a vase with a nice body contour and ask the engineers to figure out capacity (volume) of the vase ?
The engineers took measure of the contour and turn that into an equation using curve fitting method. Then using complex integration method (calculus) to compute the volume of the vase.
The janitor guy who happened to be around said: why don't we fill the vase with water, then pour that into a gauge container which will tell what the volume is.
I guess this method has a very generic and familiar name: KISS.

[John Arnold]

Correct me if I am wrong but I always thought of torque as a twisting force. The force trying to separate the neck at the button is in an arc due to it acting on a fulcrum. But it is otherwise a straight, not twisting force.
Torque is force times a moment arm. For example, if you have a bicyle with a 7" long crank, and you press on it with 100 pounds of force, the torque is 700 inch-pounds. By definition, this force is perpendicular to the arm, and in a static sense, it is not a 'curving force'.
If the fulcrum is assumed to be at the top of the dovetail, then the torque is equal to the string tension times the perpendicular distance between the strings and the fulcrum. the greater the distance between the strings and the fulcrum, the greater the torque. The force at the bottom of the heel would be the torque divided by the height of the heel.

I would think that the break angle at the nut would have an impact on the forces on the neck.
It does. The greater the break angle the more force on the nut. This force roughly bisects the angle of the strings, and the torque is produced because this force is not in line with string tension at the tuners. This is separate from the torque at the neck heel, and tends to add to it.

Torque becomes a significant quantity when there is rotational motion.
How about a very slow rotation, as is the case when the neck heel pulls out of the body? IMHO, that is pretty significant.

[jim33]

If the fulcrum is assumed to be at the top of the dovetail, then the torque is equal to the string tension times the perpendicular distance between the strings and the fulcrum. the greater the distance between the strings and the fulcrum, the greater the torque. The force at the bottom of the heel would be the torque divided by the height of the heel.

You made the same simplifying assumptions that I did which is a standard engineering technique. However, there may be a more accurate way to look at this.

The string tension puts the entire neck in bending including the fret board, just like a bow (as in bow and arrow). This can be proved by checking the relief before and after stringing the instrument up. Adjusting the truss rod will prove it also. The upper neck including the fret board will be in compression and the lower neck will be in tension. The tension is trying to pull the dove tail apart. The neutral point will see no load. There are many diagrams of bending beam forces on the net.

It would be possible to calculate the forces given the neck profile dimensions and the total string tension.

[Michael Lewis]

With all this calculation going on maybe someone will come up with the minimum sizes of parts and gluing surfaces to hold it all together.

I'm with Jim Hilburn, and just use what works well.

[David Houchens]

Wow, my brain is tired.

[kkmm]

Yep, on the practical sides, "use what has worked" and leave the calculations stuff to scientists, people who want to know why things work a certain way. I was a mathematician, but I love practical things so I chose Engineering as my career (and happily retired recently).

[Larry Simonson]

Many years ago someone told me that it is the little button's attachment at the neck heel that kept the neck on a violin, so I have been interested in how that applies to mandolin. With this in mind I have done an experiment of simulating a mandolin neck heel button joint, then seeing how much torque it can withstand. In the pictures below I used a fulcrum of 1.56 inches which is the height of the neck block (1.375") plus plate thickness (about 0.2"). There can be different opinions on this choice ranging from just the neck block 1.375" to the top of the neck of about 2" , depending on how much one thinks the under fretboard extension is supporting. My choice of 1.56 seemed reasonable. The button tab was glued on with tight bond glue. The size of this glue patch was 1.5" by 0.6" with one end rounded off. These dimensions were taken from Simonoff's original book. I allowed to simulated neck to to extend well past the 8 inches of neck to nut and hung a 5 gallon pail at 12 inches from the simulated joint. I then added water to the pail. Results: The joint held when the pail contained about 5 gallons of water. The pail and its contents weighted about 42 pounds. After 24 hours it was still intact and the experiment was terminated.

I don't know what all this means but it seems that that little button joint can resist 42 foot pounds of torque for some period undetermined. Since the torque arising from the string tension on a mandolin using J-74's is on the order of 10% of 182 lbs at 8 inches or about 12.2 foot pounds, it is tempting to conclude that the little heel button is sufficient to stabilize a mandolin's neck. Of course there are other glued surfaces in a real neck and there is the problem of glued joints creeping that need to be considered in the long term.

[kkmm]

I love this experiment, it does give the answer that one need with proper parameters set in the experiment.
This morning, I did an experiment to convince me that the "under the saddle" transducer works on a silent guitar (which I am building from scratch). It does not need a resonating body as the string vibrations are picked by the transducer and thru a preamp then an amp, the sound is produced. This is the same transducer seen on acoustic / electric guitar which has a resonating body.
The silent guitar does not, and the experiment allows me to proceed with my little project (I don't have all the parts yet, they are being shipped).

[Bernie Daniel]

Many years ago someone told me that it is the little button's attachment at the neck heel that kept the neck on a violin, so I have been interested in how that applies to mandolin. With this in mind I have done an experiment of simulating a mandolin neck heel button joint, then seeing how much torque it can withstand. In the pictures below I used a fulcrum of 1.56 inches which is the height of the neck block (1.375") plus plate thickness (about 0.2"). There can be different opinions on this choice ranging from just the neck block 1.375" to the top of the neck of about 2" , depending on how much one thinks the under fretboard extension is supporting. My choice of 1.56 seemed reasonable. The button tab was glued on with tight bond glue. The size of this glue patch was 1.5" by 0.6" with one end rounded off. These dimensions were taken from Simonoff's original book. I allowed to simulated neck to to extend well past the 8 inches of neck to nut and hung a 5 gallon pail at 12 inches from the simulated joint. I then added water to the pail. Results: The joint held when the pail contained about 5 gallons of water. The pail and its contents weighted about 42 pounds. After 24 hours it was still intact and the experiment was terminated.

I don't know what all this means but it seems that that little button joint can resist 42 foot pounds of torque for some period undetermined. Since the torque arising from the string tension on a mandolin using J-74's is on the order of 10% of 182 lbs at 8 inches or about 12.2 foot pounds, it is tempting to conclude that the little heel button is sufficient to stabilize a mandolin's neck. Of course there are other glued surfaces in a real neck and there is the problem of glued joints creeping that need to be considered in the long term.

Great experiment!

[sunburst]

The experiment (and a strung-up mandolin) subject the glue joint to sheer force. Here's another plug for hot hide glue; hot hide glue resists sheer force (the force that causes creeping) better than just about any other common glue or adhesive. To further the experiment, one could glue up similar pieces with various different glues, then leave them for months or years. During those months and years, subject them to the extremes of heat and cold that a mandolin is likely to encounter, and maybe even subject them to a few bumps and shocks like a mandolin is likely to encounter in use.
It is known that a good joint between the neck heel and the back plate strengthens the neck joint, especially in violin where there is usually no mechanical joint (like a dovetail), just the glued mortise and tenon, but there are plenty of examples of neck joint holding well without that feature. Most flat top guitars, some mandolins, others.

[Larry Simonson]

Thanks John, I had the same thoughts about shear force and creeping. You are right, its another reason to use HHG.