Tuesday, March 3, 2015

Measuring Cane Density

How I Measure Cane Density

In a previous post, I outlined my method for measuring cane hardness. Although hardness and density are closely related (it makes sense that a hard piece of cane may be more dense compared to soft piece -- and my measurements mostly bear this out), I have found enough reason to measure both.

In this post, I'd like to describe my method and my findings for measuring cane density. I have been using this method in concert with measuring hardness for two years now. I feel I have amassed enough results to draw some solid conclusions from my efforts.

What I'm about to share with you is a way of selecting cane that has doubled my yield of good reeds made from blanks using this process.

Before this, I would average maybe 2 good reeds from 10 blanks. Pretty good, considering the standard I have to maintain given the musical crucible of The Cleveland Orchestra. Now I consistently get 4-5 out of 10!

First, I'd like to acknowledge the help I received in pursuing this idea from bassoonist, David Rachor and Jean-Marie Heinrich, a scientist who has devoted much of his research to the physics, botany and geometry of arundo donax (our cane).

Measuring Density

Density is commonly measured in relation to water, which is given a value of 1. Thus, something less dense than water (all cane in a dry state) will measure between 0 and 1.

D=   M 
        V (volume)

This is the equation used to determine the density of a substance.

A pycnometer is most commonly used in measuring density.

The density is measured by the amount of water displaced by a substance when it is immersed in a chamber filled with water. A more dense substance will displace a greater amount of water.

To determine the density of a piece of cane using this equation, you need a strictly constant volume of water and mass from trial to trial and piece of cane to piece of cane. Thus, the pieces of cane measured must be as close in mass to each other as possible (this would necessitate lots of minute trimming to the pieces of cane). Keeping a constant amount of water in a chamber while measuring many pieces of cane would probably prove too difficult for easy use. Just the act of taking a piece of wet cane out of the water when finished measuring would change the volume minutely, and, over time, skew the results a fair amount.

Measuring cane density this way is too fussy and time consuming.

The test I use does not directly measure the density of cane. What it measures is the specific gravity of a piece of cane and compares it with that of water.

I use a scale with a calibration of .01g. A tolerance this small is necessary to show the minute differences in density from piece to piece. A postal scale or a kitchen scale isn't accurate enough to detect differences in cane mass.

The Method

  • First I weigh a dry piece of cane. It can be gouged, shaped, profiled, simply gouged or just a split piece of tube.
  • I record the dry mass. (M1)
  • Then I submerge the cane in a pan of water suspended over the scale by placing it under a rack that sits on the scale.
  • I record the wet mass (M2) and remove the cane from the water. It spends just a few seconds in the water.
Next I use the following formula to ascertain the density of the piece of cane:

D= density, M1=dry mass, M2=wet mass

D =   M1   

What I'm measuring is could also be described as buoyancy or porosity. Cane that exerts more upward force under water against the rack than that which doesn't is more buoyant. I'm measuring the mass of a piece of cane in two different media -- air and water.

Since dry, aged cane is composed of cellulose fiber and lots of air spaces, it is reasonable to assume therefore, that cane with more air spaces per square millimeter will be correspondingly less dense than cane with fewer spaces.

This indirect way of measuring cane density takes about 20 seconds


  1. Hi Barry. Your post on density is very intriguing, but I'm having trouble visualizing this step: "I submerge the cane in a pan of water suspended over the scale by placing it under a rack that sits on the scale." Can you perhaps show us with a drawing or photo? Best, Rick Yoder www.londonfieldsreedshack.com

  2. Hi, Rick,

    Please see my post of 5/22/15 for some photos.

    Best wishes!

  3. Very interesting! By measuring the difference between M(wet) and M(dry), you can also calculate the volume of free air space (FAS) within the dry cane because 1mL of water is equal to 1 gram, though we would have to assume that “soaked” cane is fully saturated. This measures volume in grams per milliliter (g/mL).
    V(fas) = M(wet) - M(dry)

    The V(fas) implies density, as FAS increases density decreases. This test can replace the hardness and buoyancy tests if you invest in a scale to find the mass of a sample to the thousandths place (0.001). It will also help, theoretically, to infer the resistance, or resiliency, of the cane. A piece of cane, relative to your preference, with a standard deviation 3% or greater will definitely be noticeable. This property may confuse us when finishing the reed because at either ends of the spectrum a reed becomes resistant and we are dealing with yet another material property which, at this time, musicians are not measuring. A secondary option, from Soil Physics, is a calculation of soil water content and a simple reference. For our needs θ is considered an arbitrary number without a unit of measure.
    θ = ( (M(wet) + M(dry)) / M(dry) ) – 1

    The issue you described with the Hardness tester is an issue many material scientists face as well. An indentation test is not well suited for convex, concave, or rounded materials and has a very larger error- one of the reasons why multiple people conducting the test with the same sample yield different results. Another issue is that these tests are localized, destructive, and not very suitable for the material we are trying to measure. The deformation around the impression may lead to discrepancies in the results if an experimenter is trying to conduct multiple measurements too close together. The deformation around the indentation can lead to distortion of measurements conducted elsewhere on the specimen and there are a number of other factors we cannot compensate for during this test.

    Finally, cane is essentially an organic composite basically made of a hard waxy epidermis, or bark, and then a vascular system netted within a cellular matrix (thinking back to high school physics, this would have been a great design for those bridge competitions where you can only use cardboard, spaghetti, and wood glue).

    The blade of a bassoon reed is cut across this composite and when we play our instrument we apply a force through the grain of the cane, let us call this the Y axis. For reference, we conduct a hardness test in the Z axis and a flexibility test in the X axis. This into the grain testing poses a big issue for material scientists and wood scientists alike and currently there is not a standard methodology. A study published in the Journal of Wood Science showed an interesting correlation between the stiffness and FAS of hardwoods so there is hope for us cane dependent musicians. Until we develop a better process, I would recommend start noting the FAS during your current process. This is a quantifiable physical property that implies density.

    If you are looking for an easy way to calculate a precise and accurate apparent density, perform a simple specific gravity test on 20% of each batch of cane- by batch I mean a relatively uniform sample population, same brand, gouge thickness, eccentricity, etc. This process takes a little bit of time but I’ve found it yields the best relative bulk density and a resolution of 0.25mL can be estimated when using a 50mL graduated cylinder.

    Anyways, good luck with your continued research!

  4. Dear Unknown,

    Many thanks for your very helpful comments. Clearly your understanding of the issue of cane selection outstrips what I have done. I will try out your ideas and see what I find. It may be prohibitively expensive to purchase a scale that measures to the .001 gram -- mine measures in the .01gram range and cost $250. Do you have any ideas about this?
    When you calculate specific gravity do you need the mass of each piece of cane to be constant? That could be time consuming?