Deflection Intro
Why Deflection?
The idea behind deflection testing (also called mechanical compliance) is that the stiffness of materials impacts their resonant behavior. In the last post we saw that materials resonate differently with different density and stiffness. The range of stiffness goes from not moving at all to breaking in failure, but the range of ideal stiffness is a bit harder to pin down.
The gist of measuring stiffness is to apply a force to a material held firmly and measure how far it deflects. Two important things need to be addressed up front. First, the measurements are in 1/1000th's of an inch, so the measuring devices need to be accurate and reliable. Second, for meaningful results we want to measure only the movement from the force applied, so the instrument needs to be held very securely and the rig must be very rigid.
My Rig
My current deflection rig is made from 3/4" solid pine boards. It has 2 walls and a connecting top, roughly 12" wide x 11" tall x 10" deep, glued together with finger joints and with a sturdy maple cross bar mortised in about half way up the sides. It has a 3/4" wide ledge on the bottom of the walls to support the rim of the mandolin. Where the cross-bar joins with the sides I use wooden wedges to wedge the mandolin between the ledge and the cross bar. This holds the mandolin securely and can hold mandolins 9.5-10.5" wide and a variety of side depths, which is basically all carved mandolins.
The measuring is done with a threaded rod assembly. At the bottom of the rod is a pivoted generic bridge designed to sit how a bridge sits on the top of the arch. The rod travels up through the cross bar, though a hole in the center of the top to a wooden platform that holds the weights. I have dial indicators attached through the cross bar with the plungers in contact with the bridge on the bass and treble side. Measurements are taken from these indicators and averaged if they are different. I have not found much value in having treble and bass side readings, they are usually the same or within 1/1000"-- on the next version of this rig I will just have one dial indicator in the center to keep it simple.
My Process
I want to make sure I don't break anything in my excitement to collect this data. So, I did the math on common string gauges and used string break angle data I had already collected to calculate the downward force range from common string gauge sets. That force is between 30-60 lbs, which covers the extremes of 10-20 degrees break angle and light to heavy gauge strings.
At first, I was taking deflection readings in 2.5 lb increments from 0 to 27.5 lbs. After 20 instruments or so I noticed that the graphs made straight lines. I suspected the relationship between force and deflection may be linear then I confirmed this with some engineering friends. This linear relationship meant I only need to do one measurement, which saves a lot of time! I settled on 20 pounds out of convenience. After I had all that sorted out, I finally read about Don Macrostie's deflection jig (American Lutherie #94, summer 2008) and he also uses one weight (25 lbs) and confirmed the linear relationship between force and deflection. His rig uses a lever and a spring gauge to measure his force in lbs, whereas I use iron weights from a dumbbell set. As long as the setup is rigid and the movement is measured at the bridge, these figures should be comparable when factored down to inches of movement per pound.
To set it up I slide the instrument into the rig while pulling the rod assembly up. I set the bridge in the correct spot, then slide wedges on the sides of the mandolin to wedge it securely under the cross bar (pine is soft enough to not mar any finishes or dent anything). Once the mandolin is secure, the faces of the indicators are rotated until their needles are at 0, then tap the platform a few times to make sure the needle always lands back on 0, then add the weight and take the measurement.
Results
These are the results of 76 instruments for which I currently (June 18, 2024) have deflection measurements using this setup. The measurements are in decimal inches with 20 lbs of weight.
Observations
- Openness, airiness and pop (attack) seem to correlate positively with increased deflection in the top. Less deflection in the top correlates with tightness, focus and sounding closer (ie, less air).
- The instruments I liked the most have a top deflection of .021" or more (all the way up to .045"), but none below that
- Instruments I liked most had back deflection ranging from .015" to .032". These data have, so far, not pointed me toward a tonal pattern based on back deflection, which I was a little surprised about
The tested instruments include a wide range from entry level to holy grail, all ff holes, all tone bar braced except 2 flatirons and the Gilchrist are x-braced. They include: Andersen, Clark, Colfax, Collings x3, Eastman x7, Elkhorn, Flatiron x6 (spanning mid 80's to early 00's), Gibson x2 (1923 and early 00's), Gilchrist, Hagerty, Ibanez, iii x 20, Iwamoto, Jbovier, Kentucky, Millard, Northfield x5, Ome, Passernig, Pava x2, Tailwater x12, The Loar x2, Turkey Creek x2, Weber x2
Questions that have resulted from deflection measuring as of June 2024:
- what is the back's contribution to tone?
- How do differences, or lack of differences, between top and back stiffness relate to tone? Should they deflect similarly or differently? Is stiff top/loose back or loose top/stiff back a good strategy?
- how would different materials (more/less massive, more/less stiff) on the top and back change the voice of the instrument?
I have done follow-up explorations on these questions and will be sharing those experiences in future posts!