20 replies to this topic

[bcncello]

I have two german or czech student cellos of about 60 years old which have the same problem: after all those years their tops have sinked along the bass side due to bridge downward pressure.

That got me thinking this evening and I did some geometric-trigonometric sketches of the forces applied on a bridge by the strings and I came to some...interesting? results

1) Tension of the strings (forward on T) is the same at both sides of the bridge Let's name T' that of the tailpice side and T that of the neck side (T'=T)
2) T (and T') can be separated into two components: one horizontal and one vertical (Th and Tv). First one is parallel to the top, the other one perpendicular to to it (same goes for Th' and Tv' on the other side)
3) Tv and Tv' are downward forces and add themselves resulting in the downward force over the bridge and top.
4) Th and Th' are opposed forces which withdraw each other being Th always greater. That generates an horizontal force on the bridge top that pulls it towards the neck side. It is canceled however by friction between bridge and strings
5) Tv and Tv' magnitude depends on the angles formed between the strings and each side of the bridge: The smaller the angle the greater the force

...In short, the downward force on the bridge and top comes from the strings tension and it depends on the angle between the bridge and the strings

Happy with that finding I went on thinking because my two cellos have a rather low neck step over the top plate and both have too a very low neck projection onto the bridge.

Doing some more geometric-trigonometric sketches of the strings tension on the neck I came to the conclusion that:

6) The smaller the angle formed between the neck and the neck root the greater the force that pulls the neck up on its end at the pegbox If the neck step over the top plate is low, that angle must be smaller to achieve the same neck projection so the pulling is greater.
7) Angles described on points 5) and 7) are related so that the smaller the one the smaller the other.

Summarizing:

To decrease both the force of the bridge over the top plate and the force that pulls the pegbox up, the neck must be fitted so that those two angles are the greater as possible

[Pete Moss]

I have two german or czech student cellos of about 60 years old which have the same problem: after all those years their tops have sinked along the bass side due to bridge downward pressure.

That got me thinking this evening and I did some geometric-trigonometric sketches of the forces applied on a bridge by the strings and I came to some...interesting? results

1) Tension of the strings (forward on T) is the same at both sides of the bridge Let's name T' that of the tailpice side and T that of the neck side (T'=T)
2) T (and T') can be separated into two components: one horizontal and one vertical (Th and Tv). First one is parallel to the top, the other one perpendicular to to it (same goes for Th' and Tv' on the other side)
3) Tv and Tv' are downward forces and add themselves resulting in the downward force over the bridge and top.
4) Th and Th' are opposed forces which withdraw each other being Th always greater. That generates an horizontal force on the bridge top that pulls it towards the neck side. It is canceled however by friction between bridge and strings
5) Tv and Tv' magnitude depends on the angles formed between the strings and each side of the bridge: The smaller the angle the greater the force

...In short, the downward force on the bridge and top comes from the strings tension and it depends on the angle between the bridge and the strings

Happy with that finding I went on thinking because my two cellos have a rather low neck step over the top plate and both have too a very low neck projection onto the bridge.

Doing some more geometric-trigonometric sketches of the strings tension on the neck I came to the conclusion that:

6) The smaller the angle formed between the neck and the neck root the greater the force that pulls the neck up on its end at the pegbox If the neck step over the top plate is low, that angle must be smaller to achieve the same neck projection so the pulling is greater.
7) Angles described on points 5) and 7) are related so that the smaller the one the smaller the other.

Summarizing:

To decrease both the force of the bridge over the top plate and the force that pulls the pegbox up, the neck must be fitted so that those two angles are the greater as possible

Your maths, (if I remember back to University) describe a system in equilibrium. This is not the case though when you play the 'cellos. Given your research, how are you going to rectify the states of your 'cellos and what results are you after? Please report.
Thanks, pete

[Bruce Carlson]

That got me thinking this evening and I did some geometric-trigonometric sketches of the forces applied on a bridge by the strings and I came to some...interesting? results

Could you post a vector diagram or simple sketches of your verbal presentation? Thanks.

Bruce

[Wolfjk]

Summarizing:

To decrease both the force of the bridge over the top plate and the force that pulls the pegbox up, the neck must be fitted so that those two angles are the greater as possible

Hi,
There is a sirious fault in your mathematics! The ratio of overstand of the belly to the straight line beween the nut and the saddle!

[bcncello]

Could you post a vector diagram or simple sketches of your verbal presentation?

Here's a sketch

Attached Thumbnails

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[bcncello]

Your maths, (if I remember back to University) describe a system in equilibrium. This is not the case though when you play the 'cellos. Given your research, how are you going to rectify the states of your 'cellos and what results are you after? Please report.
Thanks, pete

You were the first to answer...was it necessary to repost my entire 'post?

[Michael_Molnar]

Of course the bridge must be in equilibrium or it would move. When you do a complete vector diagram of the entire instrument you find that a and b cannot be changed willy-nilly.

Stay Tuned.
Mike

[bcncello]

When you do a complete vector diagram of the entire instrument you find that a and b cannot be changed willy-nilly.

Stay Tuned.
Mike

Hi Mike, where could I find a complete diagram?
Thanks!

[actonern]

.

[Pete Moss]

You were the first to answer...was it necessary to repost my entire 'post?

Sorry about that, my mistake.
pete

[lyndon]

it seems you have everything axx backwards, the higher the angle over the bridge the greater the downward pressure, at least thats how it was last week, this week it might be different??

[bcncello]

it seems you have everything axx backwards, the higher the angle over the bridge the greater the downward pressure, at least thats how it was last week, this week it might be different??

No, the higher the angle "a" the smaller the downward force. And the smaller that angle the greater that force.

I know this is just to spend the time or hang out, not a serious analysis. But imagine an adjustable neck could be designed (as some bridges are) so to experiment with small variations, perhaps some sound changes could be appreciated

[lyndon]

your angle a is inveresely proportional to the downbearing angle, hence the confusion

[Michael_Molnar]

Hi Mike, where could I find a complete diagram?
Thanks!

Complete what you started.

Hint: Start with the ENDS of the strings and draw the vectors for each point where the strings touch something.

It's a lot of work.

Mike

[lyndon]

edit

[lyndon]

your angles a,b are not proportional to down pressure they are inveresely proportional to down pressure, and inveresely proportional to the string angle over the bridge, when the string angle over the bridge is 0' and a and b are there maximum 90' then there is no down pressure at all, as the string angle over the bridge increases and a and b get smaller, the amount of downpressure increases.

[Michael_Molnar]

lyndon,

He's right. You are wrong. Look at his diagram. By "higher" he means "larger". He's talking about angles a and b being larger, not bridge height.

Now, be a good boy. Offer him an apology, take your meds, and go to bed.

Mike

[lyndon]

mike, do the math, the greater the angle over the bridge, the greater the downbearing angle, end of story, go back and take a physics course

the greater angle a and b, the lower the downbearing angle, the lower the down pressure

[lyndon]

a thorough reading seems to show perhaps both bcn and me are right however, michael is obviously wrong because he said i was wrong and bcn was right.

[nathan slobodkin]

bcncello, You are correct that the smaller angle below the bridge results in greater downward pressure and perhaps a greater deformation over time if all other things are equal however your asertion that lessening this pressure is advantagous is not necesarily so. The amount of pressure on the top is crucial to the sound of the instrument . I don't usually measure the string angle over the bridge but after making well over 100 cellos I can tell you that a pitch (distance to the top at bridge position from a line extended along the center of the fingerboard)of between 78 and 83 is almost always going to work. The arch hight, neck angle, overstand and saddle hight all effect this.These things are done for acoustic reasons, as far as reducing top deformation arch shape, graduation, bass bar strength and spring are the apropriate way to help with this.As a maker my job is to make great sounding instruments that are still strong enough not to deform or fall apart over the next 100 years or so, after that they're the restorers problem.