# Density ρ=M/V

We have used two methods to measure the density ρ=M/V

## Volume displacement

For this method we need a big plastic barrel with an adapted tap in the upper part, and another bucket to recover the displaced water.

We fill the barrel and let the water overflow till the last drop comes out.

Weight the dry wood wedge.

Insert the wood wedge and maintain it carefully sunken with the help of a thin metal stick and let it remain sunken until the last drop has come out.

Weigh  the displaced water and the wet wood wedge.

The volume of the wedge will be the sum of the displaced water plus the difference between the weights of the wedge (We have to consider the absorbed water by the wood)

## Geometric method

Plane the wedge til it fits perfecly with the geometric figure. Planes must be as regular as possible.

Weigh the wedge.

Measure it in different places to obtain a mean value and use the formula to calculate the volume.

The formula will give us the density ρ=M/V with the mass or weight of the wedge.

## Environmental conditions

Be aware of the weather conditions.

With relative air humidity variations the measurement of the density will be pretty different.

This relative air humidity can be calculated with a psichrometer (dry bulb temperature minus wet bulb temperature) and its corresponding psichrometric chart.

Some defined environmental temperature and humidity  conditions can be fixed to calculate the density and make it comparable.

We know that the Equilibrium Moisture Content  stabilizes in all woods under  some specific enviromental conditions. This value could reach 18% in a wet week and descend to 5% in a dry one, crosing a usual value of 11%. We will have very different values of the density in the same piece of wood.

Wedge weight at 11%  375.2gr, with a volume of 0.972xE-3 m3

EMC     weight          density

18%      399 gr          410 kg/m3

11%      375 gr           386 kg/m3

5%      355 gr          365 kg/m3

A  close cabinet with a controled moisture and temperature gives us 33ºC and 44% air humidity measured with the psichrometer.

This enviromental conditions can be obtained with UV-A and incandescent lamps.

The wood reaches an Equilibrium Moisture Content of 8%. We can consider this value as a standard value, as the wood has to be worked with a quite low value of moisture content.

## Density on maple (kg/m3)

Reference         Water displ.       Geometric.

12317-A                  558                  561

12318-B                  573                  588

12319-C                  565                  580

12322-D                  560                  569

12571-E                  572                  576

12575-F                  570                  571

## Density on spruce (kg/m3)

Reference         Water displ.      Geometric.

20/1-A           380                  383,1

20/2-B           390                  386,0

20/6-C           370                  371,9

20/7-D           370                  377,3

20/ 8-E          360                  363,4

20/ 9-F           370                  364,7

# Soundvelocity C on wood

We have used two methods to measure the sound velocity C on wood: the Lucchi Meter and the longitudinal waves method.

## LucchiMeter

The Lucchi Meter measuring equipment  is very sensitive to the place where you put the sensors.

The C value also changes with the force yapplied to the sensors.

We measured all the CNC machined plates with the sensors at the same point and with the same force, driven by the weight of a 2,9 kg piece of iron, positioned above the top receiver sensor

## Longitudinal waves

We know that the frequencies of the longitudinal waves in an air column have an harmonic relation, as well as in wood columns (the length almost ten times the diameter of the column)

We plane one wedge to have the same section over the length L(it’s not exacly a column…)

We hit one side with a hammer and measure with a microphone on the other side the stationary waves. The FFT software gives us the frequency f of the first longitudinal mode.

We calculate C=2*L*f

It is not an easy task to find similar.

The search of a suitable set of wood was complicated because they had to be similar between them on their physical characteristics and these had to fit in the ones required for this project (apart of being aesthetically alike to the Huberman)

## C 0n maple (m/s)

Reference       Long. wav.   LuchiM wedge        LuchiM back routed

12317-A             4468            4801                        4447

12318-B             4623            5130                        4474

12319-C             4431            4784                       4373

12322-D             4391            4826                       4363

12571-E             4355            4702                       4272

12575-F             4511             5000                       4534

## C 0n spruce (m/s)

Reference         Long. wav.    LuchiM wedge        LuchiM top routed

20/1-A                 5326            5514                      4622

20/2-B                 5508            5786                      4803

20/6-C                 5598            5797                      4448

20/7-D                 5530            5788                      4916

20/ 8-E                 5468            5656                      4856

20/ 9-F                 5490             5660                     4876

We can observe the inferior value of C measured in the CNC tops, in which the wave travels the arching crossing the grain with certain angle.

This doesn’t happen in the wedge in which the wave travels parallel to the grain. The C value decreases in the spruce with the crossing angle.