# Wood Hardness Versus Moisture Content

## Introduction

Figure 1: Wood Hardness Scale.

I have long been told that wood hardens as it ages, but I have anecdotal evidence that this is not always true. I also know that some species are far harder than others (Figure 1).

I read the following forum post that I thought presented really good information on wood hardness and moisture content that I would like to research a bit more and present here. The key point of the forum discussion was that wood gets harder as its moisture content decreases, which can happen to wood as it ages. Other factors, like insects and mold, will decrease the hardness of wood. I am only concerned with moisture here – the other factors are unpredictable.

I will present two numerical models for how the hardness of wood varies with moisture content. These two models will be shown to be roughly equivalent.

## Background

### Concept

There are many wood properties that vary with the moisture content of the wood. Here are a few examples:

• hardness
• shear modulus
• tensile strength
• compressive strength

I have seen two approaches to modeling the effect of moisture on these properties: (1) a power law relationship (USDA) and a linear model (Bozkurt Y, Göker Y [1987]). I will show that the two approaches produce similar results over a narrow moisture content range.

### Definition of Hardness

My post here will focus on Janka hardness, which is a commonly used wood hardness measure. Here is the definition of the Janka measurement process and how moisture content is defined.

Janka Side Hardness
Janka side hardness is the load required to embed an 11.28-mm (0.444-in.) ball to one-half its diameter.
Moisture Content (M)
The percentage of wood mass consisting of water. It is often measured in the field using electrical test equipment. In the lab, it can be measured using by measuring the mass of a test sample before and after drying and computing $M\triangleq \frac{{{m}_{water}}}{{{m}_{dry}}}=\frac{{{m}_{wet}}-{{m}_{dry}}}{{{m}_{dry}}}$
where

• mwater is the mass of water in the wood sample.
• mwet is the mass of the wood sample before drying.
• mdry is the mass of the dried wood sample.

Figure 2 illustrates the Janka test.

Figure 2: Illustration of the Janka Test (Wikipedia).

This post is focused on hardness, but the approach can be used for many other parameters.

### Forest Products Laboratory Model (USDA)

Equation 1 shows the model from the Forest Products Laboratory (FPL). I will use data from the FPL to model wood hardness.

 Eq. 1 $P(M)={{P}_{12}}\cdot {{\left( \frac{{{P}_{12}}}{{{P}_{g}}} \right)}^{\frac{\left( 12-M \right)}{\left( {{M}_{p}}-12 \right)}}}$

where

• P a property of wood (e.g. hardness)
• P12 the property value at 12% moisture content.
• Pg is the property value under green conditions.
• M is the moisture content of the wood expressed as a percentage.
• MP is defined in Chapter 4 of the 1999 Wood Handbook as the moisture content percentage at the intersection of a horizontal line representing the strength of green wood and an inclined line representing the logarithm of the strength–moisture content relationship for dry wood. They then say to assume 25% if MP is not known. I can explain why they say assume 25% if you do not have information otherwise. The intersection statement does not seem correct. I go into detail here.

### Linear Model

Equation 2 shows a model that I have seen in many publications (example, sect 2.3) for normalizing data gathered from wood at various moisture contents to 12%, which is the industry standard for moisture content.

 Eq. 2 $\displaystyle P\left( M \right)=\frac{{{P}_{12}}}{1+\alpha \cdot \left( M-12 \right)}\approx {{P}_{12}}\cdot \left[ 1-\alpha \cdot \left( M-12 \right) \right]$

where

• P12 is estimated value of a parameter at 12% moisture content.
• P is measured value of a parameter at a moisture content of u%.
• α is a constant that in general varies with the species of the wood under test. It can be calculated using $\displaystyle \alpha =\frac{\ln \left( \frac{{{H}_{12}}}{{{H}_{g}}} \right)}{{{M}_{p}}-12}$. This relationship is derived in Figure 3.

## Analysis

### Objective

I will show how Equations 1 and 2 are related in that they produce similar results for wood hardness in the typical range of wood moisture contents.

### Calculations

For my work here, I will work with the wood hardness normalized to the hardness at 12% moisture content. Normalizing allows me to work with numbers that are in the neighborhood of 1. Figure 3 shows my analysis.

Figure 3: Comparison of Exact and Linear Approximation.

## Conclusion

I was able to show that Equations 1 and 2 produce similar results in the typical range of wood moisture contents (6% to 14%). I also see that the model states that wood gets harder as moisture content decreases, which is something that I have observed.

To centralize the data that I use for my personal work, I have included a list of the hardness parameters for common North American Species (Table 1).

## Appendix A: MP Values for Common North American Species.

MP is an important parameter for estimating wood hardness and its value varies by species. The Wood Handbook states that its value is normally near 25%. Figure 4 shows some common MP values and you can see that they are near 25%.

Figure 4: Table 4-13 from the Wood Handbook.

## Appendix B: MP Definition Discussion.

The definition of Equation 1 includes some phrasing that is difficult for me to figure out. I will try to provide some additional clarification here. Here is how MP is defined.

MP [is the] moisture content at the intersection of a horizontal line representing the strength of green wood and an inclined line representing the logarithm of the strength–moisture content relationship for dry wood.

I actually could not understand this statement as written, although I do think I can explain how you determine MP. Figure 5 shows my explanation, which assumes you have (1) a plot of the hardness versus moisture content of the wood in question, and (2) you know the green hardness.

Figure 5: Explanation for Mp Determination Statement.

Figure 5 shows that the if we graph Equation 1, MP is the moisture level at which the wood strength equals the green strength. Figure 6 illustrates the relationship between MP and the Fiber Saturation Point (FSP). Observe that the "green" strength is reached before the FSP. This means that Equation 2 does not hold above MP.

Figure 6: Relationship Between Mp and FSP.

## Appendix C: Table of Hardness Values (Dry/Green/Ratio) for Common Species.

Table 1 is from a US Forest Service publication, which I have augmented with a column of common tree names. The scientific names are not of much use for me – I only know the common names of trees. Note that the hardness levels are specified in units of Newtons (metric measure) and there are 4.448 Newtons in a pound. For example, the hardness of Black Cherry is rated at 4210 Newtons, which is ~950 pounds.

 Type Common Name Species Dry Hard. (N) Green Hard. (N) Dry/Green Ratio Hardwood ALDER, COMMON ALNUS GLUTINOSA 2940 2220 1.32 ALDER, RED ALNUS RUBRA 2620 1950 1.34 ASH, BLACK FRAXINUS NIGRA 3770 2310 1.63 ASH, EUROPEAN FRAXINUS EXCELSIOR 6140 4270 1.44 ASH, GREEN FRAXINUS PENNSYLVANICA 5320 3860 1.38 ASH, OREGON FRAXINUS LATIFOLIA 5140 3500 1.47 ASH, WHITE FRAXINUS AMERICANA 5850 4260 1.37 ASPEN, QUAKING POPULUS TREMULOIDES 1550 1330 1.17 BEECH, AMERICAN FAGUS GRANDIFOLIA 5760 3770 1.53 BEECH, EUROPEAN FAGUS SYLVATICA 6410 4270 1.50 BIRCH, BLACK BETULA LENTA 6520 4300 1.52 BIRCH, PAPER BETULA PAPYRIFERA 4040 2480 1.63 BIRCH, YELLOW BETULA ALLEGHANIENSIS 5590 3460 1.62 BUTTERNUT JUGLANS CINEREA 2170 1730 1.25 CHERRY, BLACK PRUNUS SEROTINA 4210 2930 1.44 CHERRY, SWEET PRUNUS AVIUM 5780 4140 1.40 CHESTNUT, AMERICAN CASTANEA DENTATA 2390 1860 1.28 CHESTNUT, SWEET CASTANEA SATIVA 3070 3160 0.97 COTTONWOOD, BLACK POPULUS TRICHOCARPA 1550 1110 1.40 COTTONWOOD, EASTERN POPULUS DELTOIDES 1910 1510 1.26 CUCUMBERTREE MAGNOLIA ACUMINATA 3100 2310 1.34 GUM, BLACK NYSSA SYLVATICA 3590 2840 1.26 HACKBERRY, NORTHERN CELTIS OCCIDENTALIS 3900 3100 1.26 HONEYLOCUST GLEDITSIA TRIACANTHOS 7010 6160 1.14 HORNBEAM, EUROPEAN CARPINUS BETULUS 6980 5470 1.28 HORSE CHESTNUT AESCULUS HIPPOCASTANUM 3340 2580 1.29 MAGNOLIA, SOUTHERN MAGNOLIA GRANDIFLORA 4520 3280 1.38 MAPLE, BIGLEAF ACER MACROPHYLLUM 3770 2750 1.37 MAPLE, BLACK ACER NIGRUM 5230 3730 1.40 MAPLE, RED ACER RUBRUM 4210 3100 1.36 MAPLE, SILVER ACER SACCHARINUM 3100 2620 1.18 MAPLE, SUGAR ACER SACCHARUM 6430 4300 1.50 MAPLE, SYCAMORE ACER PSEUDOPLATANUS 4850 3830 1.27 OAK, AUSTRIAN QUERCUS CERRIS 8270 6180 1.34 OAK, SCARLET QUERCUS COCCINEA 6210 5320 1.17 OAK, SWAMP WHITE QUERCUS BICOLOR 7180 5140 1.40 OAK, WHITE QUERCUS ALBA 6030 4700 1.28 PECAN CARYA ILLINOENSIS 8070 5810 1.39 PLANETREE, LONDON PLATANUS ACERIFOLIA 5650 4270 1.32 POPLAR, TULIP LIRIODENDRON TULIPIFERA 2390 1950 1.23 SWEETGUM LIQUIDAMBAR STYRACIFLUA 3770 2660 1.42 SYCAMORE PLATANUS OCCIDENTALIS 3410 2710 1.26 TUPELO, WATER NYSSA AQUATICA 3900 3150 1.24 WALNUT, BLACK JUGLANS NIGRA 4480 3990 1.12 WALNUT, PERSIAN JUGLANS REGIA 3600 2970 1.21 POPLAR, CANADIAN POPULUS CANADENSIS 2220 2050 1.08 POPLAR, SILVER POPULUS CANESCENS 2360 1730 1.36 Hardwood Average 4474 3343 1.34 Softwood BALDCYPRESS TAXODIUM DISTICHUM 2260 1730 1.31 CEDAR, ALASKA CHAMAECYPARIS OOTKATENSIS 2570 1950 1.32 CEDAR, ATLANTIC WHITE CHAMAECYPARIS THYOIDES 1550 1290 1.20 CEDAR, PORT ORFORD CHAMAECYPARIS LAWSONIANA 2790 1690 1.65 FIR, BALSAM ABIES BALSAMEA 1770 1290 1.37 FIR, CALIFORNIA RED ABIES MAGNIFICA 2220 1600 1.39 FIR, DOUGLAS PSEUDOTSUGA MENZIESII 2930 2260 1.30 FIR, GRAND ABIES GRANDIS 2170 1600 1.36 FIR, NOBLE ABIES PROCERA 1820 1290 1.41 FIR, PACIFIC SILVER ABIES AMABILIS 1910 1380 1.38 FIR, SILVER ABIES ALBA 2850 1910 1.49 FIR, SUBALPINE ABIES LASIOCARPA 1550 1150 1.35 FIR, WHITE ABIES CONCOLOR 2130 1510 1.41 HEMLOCK, EASTERN TSUGA CANADENSIS 2220 1770 1.25 HEMLOCK, MOUNTAIN TSUGA MERTENSIANA 3020 2080 1.45 HEMLOCK, WESTERN TSUGA HETEROPHYLLA 2390 1820 1.31 INCENSE CEDAR LIBOCEDRUS DECURRENS 2080 1730 1.20 LARCH, EUROPEAN LARIX DECIDUA 3770 2450 1.54 LARCH, JAPANESE LARIX KAEMPFERI 2940 2140 1.37 LARCH, WESTERN LARIX OCCIDENTALIS 3680 2260 1.63 PINE, AUSTRIAN PINUS NIGRA 2890 1910 1.51 PINE, CLUSTER PINUS PINASTER 2670 1690 1.58 PINE, EASTERN WHITE PINUS STROBUS 1690 1290 1.31 PINE, JACK PINUS BANKSIANA 2530 1770 1.43 PINE, LOBLOLLY PINUS TAEDA 3060 2000 1.53 PINE, LODGEPOLE PINUS CONTORTA 2130 1460 1.46 PINE, LONGLEAF PINUS PALUSTRIS 3860 2620 1.47 PINE, MONTEREY PINUS RADIATA 3330 2130 1.56 PINE, PONDEROSA PINUS PONDEROSA 2040 1420 1.44 PINE, RED PINUS RESINOSA 2480 1510 1.64 PINE, SCOTCH PINUS SYLVESTRIS 2980 2220 1.34 PINE, SHORTLEAF PINUS ECHINATA 3060 1950 1.57 PINE, SPRUCE PINUS GLABRA 2930 2000 1.47 PINE, SUGAR PINUS LAMBERTIANA 1690 1200 1.41 PINE, VIRGINIA PINUS VIRGINIANA 3280 2390 1.37 PINE, WESTERN WHITE PINUS MONTICOLA 1860 1150 1.62 REDCEDAR, EASTERN JUNIPERUS VIRGINIANA 4000 2880 1.39 REDCEDAR, WESTERN THUJA PLICATA 1550 1150 1.35 REDWOOD, COAST SEQUOIA SEMPERVIRENS 2130 1820 1.17 SPRUCE, BLACK PICEA MARIANA 2310 1640 1.41 SPRUCE, ENGELMANN PICEA ENGELMANNII 1730 1150 1.50 SPRUCE, NORWAY PICEA ABIES 2110 1420 1.49 SPRUCE, RED PICEA RUBENS 2170 1550 1.40 SPRUCE, SERBIAN PICEA OMORIKA 2710 1470 1.84 SPRUCE, SITKA PICEA SITCHENSIS 2260 1550 1.46 TAMARACK LARIX LARICINA 2620 1690 1.55 WHITE CEDAR, NORTHERN THUJA OCCIDENTALIS 1420 1020 1.39 Softwood Average 2470 1722 1.43 Grand Average 3472 2533 1.38
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