NORTHEASTERN FOREST EXPERIMENT STATION 

Upper Darby, Pennsylvania 

r 1 

4 

No. 46 . 

1955 - ' 

Relationship Of Stump Diameter To D.b.h. 

For Northern Red Oak In The Northeast 

This is the fifth report on a series of studies to 

show the relationship of stm~ diameter to diameter breast 

high (d. b. h. ) for cokercially important tree species in the 

 ort the as t ." This report is for northern red oak (~uercus 

rubra ) . 

In this study 1,240 stump-diameter measurements were 

used, ranging from 4 inches to 37 inches. Both stump diameters and d. b. h. were measured to the nearest l/l0-inch with 

a diameter tape. To obtain diameter inside bark, bark thickness was measured with a Swedish bark gage. Stump heights 

were measured on the uphill side to the nearest l/lO-foot. 

It was found that 74 percent of the stumps left on 

logging operations were between 0.6 and 1.8 feet high; 12 

percent were higher than 1.8 feet; and 14 percent were lower 

than 0.6 foot, 

In the computations, inside-bark stump diameters were 

used, to avoid inaccuracies due to unequal bark thickness, 

logging damage to bark, and bark peeling off. Stump diameters were sorted into 2-inch classes, Stump-height measurements were sorted into 0.6-foot classes within each stumpdiameter class. 

To develop an equation expressing the stump diameter--d.b.h. relationship for red oak,-the method described 

by DemingY4' was used. The following equation was obtained: 

D.b.h. = 0.739 (stump d.i.b.) + 2.072 (stump height) - 0.773 

The relationships developed from this equation were worked 

out as a graph (fig. 1). 

To determine the 2-inch d.b.h. class of a red oak 

stump from this graph, you merely plot the intersection of 
I. 

the vertical ordinate (stump height) with the horizontal 

ordinate (stump diameter). For example, for a stump 18.9 

e 

inches in diameter and 1.4 feet high, the two lines intersect about halfway between the two limits of the 16-inch 

deb.h. class, 

Comparison of actual d.b.h.Ps and those calculated 

with the equation showed an average weighted difference of 

less than 0,2 inch, The standard error of estimate for all 

data was 0.594 inch, At the mean of stump diameters, you 

can expect 91 percent of the estimates of d,b.h. to fall in 

the correct 2-inch d.b.h. class. The other 9 percent can be 

expected to fall one elass above or below the correct one. 

None will fall outside this range. These errors are compensating. As the stump diameters increase beyond the mean of 

these data, the error will also increase. 

(1f you use the graph by 1-inch d.b.h. classes, this 

is what you can expect: 60 percent of the estimates should 

fall in the correct 1-inch d.b.h. class; 39 percent should 

fall one class above or below it; and 1 percent should fall 

outside this range.) 

For all practical purposes this graph is expected to 

give reliable d.b.h. estimates for red oak anywhere in the 

Northeast, 

a 

--FREDERICK Ee HAMPF 

Forest Economist 

Division of Forest Economics 

Northeastern Forest Experiment Station 

Forest Service, U.S. Dept. Agriculture 

2 

r 

'%h For earlier reports on these studies see Forest Research Note No, 38 (white pine), No. 42 (sugar maple), No. 

43 (~merican beech), and NO. 45 (yellow birch) -7 

,, - ,, 

,\ rh 

Deming, W. Edwards. Statistical adjustment of data. 

261 pp,, illus. Wiley & Sons, New York, 1938. 

Agriculture-Forest Service-Upper Darby 
STUMP DIAMETER- D. B.H. RELATIONSHIP FOR 

NORTHERN RED OAK 

IN THE NORTHEAST 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 

STUMP HEIGHT, IN INCHES 

Figure 1