Estimating Air Drying 

Times of Lumber With 

Multiple Regression 

William T. Simpson 

United States

Department of 

Agriculture 

Forest Service 

Forest 

Products 

Laboratory 

Research 

Note 

FPL−RN−0293 
Abstract 

In this study, the applicability of a multiple regression equation for estimating air drying times of red oak, sugar maple, 

and ponderosa pine lumber was evaluated. The equation 

allows prediction of estimated air drying times from historic 

weather records of temperature and relative humidity at any 

desired location. 

Keywords: air drying, lumber drying, red oak, sugar maple, 

ponderosa pine 

June 2004 

Simpson, William T. 2004. Estimating air drying times of lumber with 

multiple regression. Res. Note FPL-RN-0293. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 

6 p. 

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Estimating Air Drying Times of Lumber 

With Multiple Regression 

William T. Simpson, Research Forest Products Technologist

Forest Products Laboratory, Madison, Wisconsin 

Introduction 

Several recent studies have been conducted to develop methodology for estimating the air drying times of lumber, logs, 

and square timbers based on species, size, geographic 

location (which determines average daily temperature and 

relative humidity), stacking date, and final moisture content. 

The initial study (Simpson and Hart 2000, 2001) utilized 

previously published air drying data for red oak, sugar maple, beech, yellow poplar, ponderosa pine, and Douglas-fir. 

That study applied a computer drying simulation developed 

by Hart (1982) and provided good estimates of air drying 

times for these species. However, it is difficult to develop 

the simulation parameters from the experimental data, and 

furthermore, the drying simulation computer program is not 

readily available to most potential users. Simpson and Wang 

(2003) developed estimated drying times for small-diameter 

(4 to 8 in. (102 to 203 mm)) ponderosa pine and Douglas-fir 

logs using multiple regression methods. 

Not only is multiple regression easier than computer simulation for establishing the relationship between air drying 

times and the parameters that affect it, but once the regression parameters are developed from experimental data, the 

results are readily usable in simple user-built computer 

programs or spreadsheets. The purpose of this study is to 

determine if multiple regression analysis can be successfully 

applied to predict air drying times of lumber from historic 

daily average temperature and relative humidity data. The 

test will be applied to the air drying data previously analyzed 

by Simpson and Hart (2000, 2001). 

Methods 

The multiple regression relationship applied in this study 

was 

∆M = M a

T bH c (1) 

where ∆M is daily loss of moisture content (%); M, moisture 

content at the start of any day during air drying (%); T, 

average daily temperature (°F); H, average daily relative 

humidity (%); and a, b, and c are regression coefficients 

determined by fitting experimental drying data to 

Equation (1) using nonlinear regression analysis. In the log 

drying study (Simpson and Wang 2003), diameter was also 

a variable and was included as diameter raised to a power to 

be determined by regression analysis. However, the lumber 

data being reanalyzed did not include thickness as a variable. 

Analyzing air drying data with Equation (1) requires moisture content data throughout drying—not just the drying time 

to some final moisture content. Some of the data analyzed by 

Simpson and Hart (2000, 2001) were in the form of moisture 

content time curves, and some were in the form of only a 

time to some final moisture content with no intermediate 

moisture content time data. Therefore, not all the data from 

Simpson and Hart could be reanalyzed and was limited to 

1-in.-thick northern red oak air dried in Madison, Wisconsin; 

1-in.-thick sugar maple in upper Michigan; and 1- and 

1.5-in.-thick ponderosa pine in Flagstaff, Arizona. In each 

case, the data were in the form of moisture content time 

curves for four stacking dates—in January, May, July, and 

October. The data of all four stacking dates for each species 

were used in the regression analysis with Equation (1). Daily 

average temperature and relative humidity were also 

available in each case. 

Results and Discussion 

The regression coefficients a, b, and c, and the coefficient of 

determination R2

 for each species–thickness are shown in 

Table 1. The R2

 values ranged from 0.808 to 0.920, indicating that Equation (1) works well in correlating the decrease 

in moisture content each day based on the moisture content 

at the start of the day and the average daily temperature and 

relative humidity. Equation (1) allows us to develop moisture content time curves by subtracting each daily loss in 

Table 1—Regression coefficients a, b, and c and 

coefficients of determination R 2 for the moisture content 

time relationships of red oak, sugar maple, and ponderosa pine according to Equation (1) (∆M = M a

T bH c)

Species, thickness a b c R 2

Red oak, 1 in. 2.38 0.759 –2.91 0.808 

Sugar maple, 1 in. 2.18 1.89 –3.57 0.812 

Ponderosa pine, 1 in. 1.64 1.22 –2.39 0.878 

Ponderosa pine, 1.5 in. 1.27 1.84 –2.86 0.920 
2 

moisture content from the moisture content at the start of 

that day. Moisture content time curves for each species–

thickness and each of the four stacking dates are shown in 

Figures 1–4, and each graph includes both the experimental 

curves and those calculated by Equation (1). The agreement 

between the experimental and calculated curves was reasonably good in many cases, but in some cases, it was not 

good. Overall, Equation (1) seems to have good potential in 

predicting the progress of moisture content loss during air 

drying. One problem in this analysis is working with old 

data taken from the literature. The data had to be manually 

extracted from graphs of drying curves, which resulted in 

less than exact data. And, with all due respect to the original 

researchers, not all of the details or possible pitfalls and 

errors in their experiments are known. However, the results 

of this analysis suggest that Equation (1) has good potential 

as a means of estimating air drying times and that future 

research projects could be designed specifically to develop 

that potential, including thickness as a variable. 

Conclusions 

This study has shown that the nonlinear multiple regression 

equation that relates the daily moisture content loss in air 

drying lumber to the moisture content at the start of any day 

during drying and the average daily temperature and relative 

humidity can be applied successfully to estimate air drying 

times. 

Literature Cited 

Hart, C.A. 1982. SIMSOR: A computer simulation of water 

sorption in wood. Wood and Fiber. 13(1): 46–71. 

Simpson, W.T.; Hart, C.A. 2000. Estimates of air drying 

times for several hardwoods and softwoods. Gen. Tech. Rep. 

FPL–GTR–121. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 70 p. 

Simpson, W.T.; Hart, C.A. 2001. Method for estimating 

air-drying times of lumber. Forest Products Journal. 

51(11/12): 56–63. 

Simpson, W.T.; Wang, X. 2003. Estimating air drying 

times of small-diameter ponderosa pine and Douglas-fir 

logs. Res. Pap. FPL–RP–613. Madison, WI: U.S. 

Department of Agriculture, Forest Service, Forest Products 

Laboratory. 14 p. 
3

0 20 40 60 80 100 120 140

Time (days)

10

20

30

40

50

60

70

80

Moisture content (%)

Experimental

Calculated

4/4 Red oak

Stacked January 19

Madison,WI

0 20 40 60 80 100 120

Time (days)

10

20

30

40

50

60

70

80

Moisture content (%)

Experimental

Calculated

4/4 Red Oak

Stacked July 28

Madison, WI

0 20 40 60 80 100

Time (days)

10

20

30

40

50

60

70

80

Moisture content (%)

Experimental

Calculated

4/4 Red oak

Stacked May 15

Madison, WI

0 40 80 120 160 200

Time (days)

10

20

30

40

50

60

70

80

Moisture content (%)

Experimental

Calculated

4/4 Red oak

Stacked October 22

Madison,WI

Figure 1—Moisture content time graphs for air drying 1-in.-thick red oak in Madison, Wisconsin, with stacking started in 

(a) January, (b) May, (c) July, and (d) October. 
4 

0 20 40 60 80 100 120

Time (days)

10

20

30

40

50

60

70

Moisture content (%)

Experimental

Calculated

4/4 Sugar maple

Stacked January 20

Upper Michigan

0 10 20 30 40 50

Time (days)

10

20

30

40

50

60

70

Moisture content (%)

Experimental

Calculated

4/4 Sugar maple

Stacked July 14

Upper Michigan

0 10 20 30 40

Time (days)

10

20

30

40

50

60

70

Moisture content (%)

Experimental

Calculated

4/4 Sugar maple

Stacked May 19

Upper Michigan

0 40 80 120 160 200

Time (days)

10

20

30

40

50

60

70

Moisture content (%)

Experimental

Calculated

4/4 Sugar maple

Stacked October 27

Upper Michigan

Figure 2—Moisture content time graphs for air drying 1-in.-thick sugar maple in upper Michigan, with stacking started in 

(a) January, (b) May, (c) July, and (d) October. 
5

0 10 20 30 40

Time (days)

10

20

30

40

50

60

Moisture content (%)

Experimental

Calculated

4/4 Ponderosa pine

Stacked January 19

Flagstaff, AZ

0 5 10 15 20 25

Time (days)

10

20

30

40

50

60

Moisture content (%)

Experimental

Calculated

4/4 Ponderosa pine

Stacked July 1

Flagstaff, AZ

02468

Time (days)

10

20

30

40

50

60

70

Moisture content (%)

Experimental

Calculated

4/4 Ponderosa pine

Stacked May 28

Flagstaff, AZ

0 4 8 12 16

Time (days)

10

20

30

40

50

60

70

Moisture content (%)

Experimental

Calculated

4/4 Ponderosa pine

Stacked October 14

Flagstaff, AZ

Figure 3—Moisture content time graphs for air drying 1-in.-thick ponderosa pine in Flagstaff, Arizona, with stacking 

started in (a) January, (b) May, (c) July, and (d) October. 
6 

0 10 20 30 40 50 60 70 80 90 100

Time (days)

0

20

40

60

80

100

120

Moisture content (%)

Experimental

Calculated

6/4 Ponderosa pine

Stacked January 19

Flagstaff, AZ

0 5 10 15 20 25 30 35 40

Time (days)

0

20

40

60

80

100

120

140

Moisture content (%)

Experimental

Calculated

6/4 Ponderosa pine

Stacked July 1

Flagstaff, AZ

0 2 4 6 8 10 12 14

Time (days)

0

20

40

60

80

100

120

140

Moisture content (%)

Experimental

Calculated

6/4 Ponderosa pine

Stacked May 28

Flagstaff, AZ

0 20 40 60 80

Time (days)

0

20

40

60

80

100

120

140

160

Moisture content (%)

Experimental

Calculated

6/4 Ponderosa pine

Stacked October 14

Flagstaff, AZ

Figure 4—Moisture content time graphs for air drying 1.5-in.-thick ponderosa pine in Flagstaff, Arizona, with stacking 

started in (a) January, (b) May, (c) July, and (d) October.