Changing a Beam into a Parabolic Rib

NOTE:  One of my many soundboard experiments.

Soundboard ribs have two duties to perform. Hold up weight, and move freely with that weight. In other words, to behave like a strong spring.

Let’s take a closer look at this behavior and perform a few tests.

For the sake of clarity, terms have to be defined:

  • Beam– A squared piece of wood spanning horizontally between two support points. Strength and rigidity is its purpose.
  • Rib– A squared piece of wood spanning horizontally between two support points. Strength and flexibility is its purpose.
  • Scalloping– The removal of wood from the ends of a beam to make it more flexible (increasing its deflection), and evenly distribute the load placed upon it, thus turning a beam into a rib.

 

Pictured below is a rib (on top) and a beam.

 

The following series of tests, consist of clamping a rib or beam to support blocks. A series of 9 evenly spaced dial micrometers are placed underneath, then a 10lb weight is placed on the test piece, and its deflection values are measured along its length.

The first test was to measure a simple beam. The dimensions are .84” in height, and 1.00” in width. The span is 33.75”. The weight is placed in the geographical exact center.

The result:

This chart shows how the beam deflected (in thousandths of an inch) along its length.  I added a parabolic curve for comparison. Note that the center of the beam is the most flexible (above the parabola) and that the ends are stiff (under the parabola).

 

For test number two,  I removed the beam and scalloped both sides in an identical fashion (now a rib) and replaced it back on the support blocks. The length of each scallop is approximately 3.25”.

 

The result of the second 10lb test:

The scalloping made the rib exhibit a more acceptable parabolic curve!

But now a problem presents itself. These tests were performed with a weight in the geographical center of the rib. However, that is not the normal situation in the piano. It’s more common for the location of the bridge to be off-center on the rib.

So next, is the weight off center test.

Result:

 

Amazing! Just by moving the weight 2 inches to the left there was a change in behavior. There has been a shift in the force distribution along the length of the rib. It no longer follows the parabola, indicating that one half of the rib is working harder than the other half.

So now I’ll make some adjustments to bring back symmetry and balance. Looking at the chart above, the deflection on the first dial on the short side was 42 thousandths, compared to 33 thousandths on the long side. What I did next was to lengthen the scallop on the long side (right side on chart) to 5”.  This brought it to 40 thousandths. Then I removed a little more material from from the height of the rib between the geographical center to the start of the scallop on the long side. This final step brought the entire rib back into symmetry.

Results:

 

Conclusion:

These tests show that the scalloping cannot be arbitrarily done. That they must be made in proportion to the position of the downbearing force on the rib.

Otherwise one part of the rib is working harder than another part.

And that’s inefficient.