Forest mensuration

Introduction to Forestry
(According to 5th Dean Syllabus)
Dr. Shailendra Bhalawe
Assistant Professor
Department of Agro-forestry
College of Agriculture, Balaghat
Jawaharlal Nehru Agriculture University, Jabalpur
(M.P.)

Forest Mensuration:
Forest Mensuration: Forest mensuration is the branch of forestry that deals with the
determination of dimensions (e.g. diameter, height, volume etc.) form, age and
increment of single trees, stands or whole forests either standing or after felling called
forest mensuration.
Mensuration:
 It means measurement of length, mass and time etc.
 Is art and science of locating, measuring and calculating the length of
lines, areas of planes, and volumes of solids.
 Forest Mensuration deals with the determination of the volume of logs,
trees, and stands, and with the study of increment and yield (Graves, 1906).
 Forest Mensuration is the determination of dimensions, form, weight,
growth, and age of trees individually or collectively, and of the dimensions
of their products (Helms, 1998).
 It is a tool that provides facts about the forest crops or individual trees
to sellers, buyers, planners, managers and researchers.

Objectives of the forest mensuration:
(a)Basis for value estimation for sale of forest produces: Forest mensuration forms the basis
of every transaction involving sale of forests or their products. In olden days when supplies
were ample and the value of timber or any other forest produce was low, measurements may
not have been necessary but with the increasing gap between demand and supply and the
rising prices of timber or other products, it has assumed great importance.
(b) Basis of management: Sustainable utilization of forest produces requires knowledge of the
quantum of timber standing in forest and its annual increment.
(c) Measurement for research: In forest research experiments, measurements of woods are
essential to identify the best treatment and method of management.
(d) Measurement for planning: The future planning of forest management requires
estimating the demand of wood and other forest products. Forest mensuration supplies
essential basis statistical data for these planning.

Importance of Forest Mensuration:
It is the keystone foundation of forestry.
What Silvicultural treatment will result in best regeneration and growth?
What species is most suitable for reforestation?
Is there sufficient timber to supply a forest industry and for an economical
harvesting operation?
What is the value of the timber and land?
What is the recreational potential? What is the wildlife potential? What is
the status of biodiversity on the area?
What is the status of the forest as a carbon sink?
What is in the forest now? How is the forest changing?
What can we do to manage the forest properly?
How can it be assessed?
And for what purpose?

Scale of Measurement :
Nominal Scale: determination of equality (numbering and counting).
Eg. numbering of forest types in a stand map.
Ordinal scale: determination of greater or less (ranking) eg. timber and
log grading.
Interval scale: determination of the equality of intervals or of
differences (numerical magnitude of qty, arbitrary origin) eg. Fahrenheit
temp., soil moisture etc.
Ratio scale: determination of equality of ratios (numerical magnitude
of qty., absolute origin) eg. length of objects, volumes, etc.

Unit of Measurement:
Parameter Unit Of Measurement
British systems Metric systems
Height Feet without decimal Meter with first decimal
Diameter Inches with first decimal Centimetre with odd
decimal
Girth Feet and inches Meter and centimetre
Area Square feet Square meter or
centimetre
Volume Cubic feet Cubic meter

Diameter measurement and its significance.
 A diameter is a straight line passing through the center of a circle or sphere and
meeting at each end of circumference or surface.
 The most common diameter measurements taken in forestry are of the main
stem of standing trees, cut portions of trees and branches.
 Diameter measurement is important because it is one of the directly
measurable dimensions from which tree cross sectional area, surface area and
volume can be computed.
 The point at which diameters are measured will vary with circumstances.
 The most frequent tree measurement made by forester is diameter at breast
height (dbh)
The rational of DBH measurement of individual trees is to estimate the quantity of
timber, fuel wood or any other forest products which can be obtained from them.
 DBH is important variable to calculate the product quantity.
 These measurement are also necessary for making inventory of growing stock
as well as to correlate height, volume, age, increment with most easily determinable
dimension i.e. dbh

The Universal convention is to measure at a fixed height above the ground - a
point called Breast Height.
The fixed height is 1.3 m (or 4'3") in continental Europe, Australia, U.K, Canada
and some former members of the British Commonwealth.
There are standard rules to help ensure the 1.3 m height is uniformly defined
within Australia.
The breast height convention in the USA, New Zealand, Burma, India,
Malaysia, South Africa and some other countries is to measure at 1.37 m (or 4' 6")
above ground.

1.37 m from ground level
Diameter Measurement Girth Measurement

DBH has been accepted as the standard height for diameter measurement
because …
 It is a convenient height for taking measurements and therefore avoids the
fatigue unnecessarily caused in taking large number of measurement at any other
lower or higher point.
 The base of the tree is generally covered with the grasses and shrubs and even
thorns sometimes and so the measurement of diameter or girth at the base is
generally very difficult without incurring extra expenditure in clearing the base.
 Majority of the trees develop root swell near the base. This results in abnormal
formation from ground level to a certain height along the bole. These abnormalities
depend upon the species and the conditions of the ground on which the tree grows.
However, in most cases, the abnormalities disappear below breast height.

 It gives a uniform point of measurement and therefore standardizes diameter
measurements of trees.
 It is preferred to diameter measurement at stump height because stumps are
never cut at uniform height and as such standardization is lost. The height of
stump also depends upon the skill of the labor and the commercial value of the
trees.
 Even if the stump height is standarized the value of such diameter or girth
measurement is completely upset by a change in utilization standards demanding
either higher or lower stump.

Log of tree: Diameter Measurement
S1 + S2 +S3 = Average Diameter
3
S1 S2 S3

Standard rules governing Breast Height measurements of trees
principles are described with figures:
Rule 1: Breast height should be marked by means of a measuring stick on
standing trees at 1.37 m (4ft 6 inch) above the ground level (Fig a).
Rules 2: The Breast height point should be marked by inserting vertical and
horizontal lines of 12 cm long, painted with white paint. This is known as cross
mark.
Rules 3: On slopping ground, the diameter at breast height should be
measured on the uphill side (Fig b & c).
Rules 4: If the tree is leaning on flat ground then DBH or GBH is measured
along the tree stem (i.e.-parallel to the stem), not vertically from the ground
(Fig d).
Rules 5: If the tree is leaning on sloping round then DBH or GBH is measured
on the uphill side (Fig c).

Rules 6: When there is an abnormality found at the Breast Height (See fig e)
then B.H mark should be shifted wither up or down as little as possible to a
more normal position of the stem, where diameter or girth is measured.
Rules 7: When the tree is forked above the Breast Height, it is counted as
single tree and diameter or girth is generally measured at Breast Height (Fig
g).
Rules 8: If the tree is forked below the Breast height, then each forked stem
should be treated as separate tree and DBH or GBH should be measured
and recorded separately (Fig h).
Rules 9: When forking renders the beast height point as abnormal, then the
foregoing rules such as rule 7 & 8 should be applied and the tree counted as
one or two depending on the place of measurement.
Rules 10: When buttress formation is found at the base of the tree which
likely to extend upwards with the development of the tree, then the Beast
height should be taken at the lowest point above which the abnormal
formation is not likely to extend.

Instrument used in diameter measurement:
The most commonly used instruments for measuring diameters at BH are:
 Diameter tape,
Calipers,
Biltmore stick,
Sector Fork and
 other optical instruments.

Height Measurement of Trees:
Tree height is one of the components for calculating tree volume. This is
required for computing volume table, form factor table and yield table. Height of trees
indirectly gives the idea about the productive capacity of site or site quality.
Total height of a standing tree is the distance along the axis of the tree stem between
the ground and the tip of the tree.
Bole height is the distance along the axis of tree between ground level and crown
point. (crown point is the position of the first crown forming branch).
Commercial bole height is the height of bole that is usually fit for utilization as
timber.
 Height of standard timber bole is the height of the bole from the ground level up
to the point where average diameter over bark is 20cm.
 Stump height is the distance between the ground and basal position on the main
stem where a tree is cut.
 Crown length -The vertical measurement of the crown of the tree from the tip to the
point half way between the lowest green branches forming green crown all round and
the lowest green branch on the bole.
 crown height - The height of the crown as a measured vertically from the ground
level to the point half way between the lowest green branches forming green crown all
round

Methods of Measurement of Tree Height
1. Ocular estimate:
2. Non-Instrumental methods:
(a) Shadow Methods:
(b) Single Pole Methods:
3. Instrumental Methods:
 By using a instruments like- hypsometer, Clinometer, Altimeters, Abneys level,
Improverised calipers etc.
 All these instruments are based either on geometric principle of similar triangles or
on trigonometric principles

1. Ocular estimate: In this method, the height of tree is assessed by visual judgment.
For this purpose, Initially few trees are measured using instruments. Thereafter, the
estimator can judge the height of trees exactly by comparison. It is also a pole of 3 m
length may be placed against the tree and then the tree is imagined to be divided in a
3 m sections for calculating tree height. This method is not very accurate and results
vary with the experience of the forester.

2. Non-Instrumental methods:
(a) Shadow Methods:
AB = BD
ab bd
AB = BD x ab
bd
A pole of convenient length is fixed upright in the ground and
its height above the ground is measured. The shadows of the
pole and the tree are also measured.
Where, AB is the tree (ligt lamp), ab is the
portion of the pole (Man) above the ground
level, BD is the length of shadow of the tree
and bd is the shadow of ab.
a
b
d
A
B
D

Measurement of tree height using single pole method
AB = EB (Since ab = Eb)
AB = EB
ab Eb
AB = EB x ab
Eb
AB = tree, ac=pole about 1.5 m long

Instrumental method:
By using a instruments like- Hypsometer, Clinometer, Altimeters, Abneys level,
Impoverished Calipers etc.
All these instruments are based either on geometric principle of similar triangles or on
trigonometric principles.
Principles of the height measurement:
Many types of height measuring devices and instruments in the course of time, but only a
few have gained wide acceptance by practicing foresters.
The two of the common designs are based on trigonometric principles and geometric
principles.
.

Christen Hypsometer Smythie's Hypsometer

1. Geometric principles of similar triangles: In similar triangles, the corresponding
angles are equal and the corresponding sides are proportional. In the following similar
triangles viz., ABC and abC.
A
B C
a
b
Similar triangle
method
= AB : ab : BC :bC
= AB x bC = ab x BC
AB = ab x BC
bC
In this AB refers to the tree, ab denotes the staff and
bC designates the ground distance between the
observer and tree
Useful in rough estimation, not reliable for
precise work. Eg. Christen’s hypsometer,
Improvised calipers

Trigonometric principles:
The principles follow the basic rules of trigonometry for deriving heights of trees
from distance and angle measurements. Two laws are applicable for this purpose and
they are: tangent law and sine law.
Tangent law
Applicable to right angle triangle
Instruments based on this principle are Abney’s level, clinometers, altimeter
etc.
with clinometers give the direct height reading is possible at fixed horizontal
distances (15 m & 20 m) from the tree.
For accurate results, trees must not lean more than 5° from the vertical, and the
fixed horizontal distance must be determined by taped measurement.
Tangent Method: this method utilize the tangents of the angles to the top and base of
the tree and the distance of the observer from the tree.

1. On level ground: Let AB is the tree, EF is the observer, BF is the horizontal
distance from the tree and α is the angle to the top of the tree. Now,
AB = AD + BD
= ED tan α + BD (tan = AD/ED)
= BF tan + EF (ED = BF)
BF is the ground distance and EF is the eye height of the observer.
α α
α

2. On sloping ground
(i) The top of the tree is above the eye level and base of the tree is below the eye level.
Let AB be the tree, be the angle to the top, β be the angle to the base of the tree and ED
ground distance from the observer to tree.
AB = AD + DB
ED tan + Ed tan β
ED ( tan + tan β )
α
α
α

(ii) The top and base of the tree are at above the eye level
AB = AD – BD
ED tan - ED tan
ED (tan - tan )
= EB cos (tan - tan )
α
α
α α
β
β
β

(ii) The base and top of the tree is at below the eye level
AB = BD – AD
ED tan - ED tan
ED (tan - tan )
= EB cos (tan - tan )
α
α
α
β
β
β

2. Sine method: In this method, the ground distance and angles are used according to sine
theory:
Sin AEB = Sin ∠ EAB
AB EB
Hence,
AB = EB Sin ∠ AEB
Sin∠ EAB
= EB sin ( + )
sin (90 - )
= EB sin ( - )
cos
∠
β
β
α
α
α
α

Example: A man who is 1.8 ft tall casts a shadow that is 1.5 ft long. A nearby tree
casts a 20ft shadow. What is the height of the tree.
A
B C
a
b
Similar triangle
method 1.8
1.5
--------------------20----------------------------
Tree height X ?
20/1.5 = X/ 1.8
X = 1.8 x 20
1.5
X = 24 ft

Example: You are standing 42 ft away from a tree. Your line of sight is 5 ft from the
ground. If you measure the angle of elevation to the top of the tree to be 43 degree
how tall is the tree.
----------------------------------42 ft-------------------------------------------
5 ft
43 degree angle
X height
5 ft
H = X + 5
Tan 43 /1 = X + 42
X = 42 tan 43 degree angle
X = 39.2 ft
H = 39.2 ft + 5 = 44.2 ft

Tree Stem Form:
Form is the rate of taper of a log or stem
Taper is the decrease in the diameter of a stem of a tree or of a log from base
upwards.
The taper varies not only with species, age, site and crop density but also in the
different parts of the same tree.
Basal portion of the tree corresponds to the frustum of Neiloid, the middle
portion to the frustum of Paraboloid and the top portion to a cone.

.Parts of a tree stem tend to approximate truncated parts of some known
geometrical shapes. The base of the tree tends to be neiloid while the tip tends to
be conoid. The main part of the bole tends to be paraboloid

Stem or bole form
• Rate of taper of a log or stem
• Development of the form of stem depends on the mechanical stresses to which the
tree is subjected
• stress come from dead weight of stem and crown and the wind force
• Wind force causes the tree, to construct the stem in such a way that the relative
resistance to shear is same at all the points on the longitudinal axis of the stem.

Tree form - theories
Nutritional theory
Water conducting theory
Hormonal theory
Mechanistic theory or Metzger's beam theory

Nutritional theory and Water conducting theory are
based on ideas that deal with the movement of liquids
through pipes. They relate tree bole shape to the need of
the tree to transport water or nutrients within the tree
The hormonal theory envisages that growth
substances, originating in the crown, are distributed
around and down the bole to control the activity of the
cambium. These substances would reduce or enhance
radial growth at specific locations on the bole and thus
affect bole shape.

Metzger’s Theory
• Has received greatest acceptance so far
• Tree stem - a beam of uniform resistance to bending,
anchored at the base and functioning as a lever as a
Cantilever beam of uniform size against the bending force
of the wind
• Maximum pressure is on the base so the tree reinforces
towards the base and more material deposited at lower ends

Metzger’s Theory : This is also called as girders theory. This theory explains the
variations in taper of tree which is developed by Metzger.
Assumption: Tree stem should be considered as a cantilever beam of uniform size against
the bending force of the wind.
The wind pressure acts on the crown and is conveyed to the lower parts of the stem in an
increasing measure with the increasing length of the bole.
Thus, the biggest pressure is exerted at the base and there is a danger of tree snapping at
that place, to counteract this tendency, the tree reinforces itself towards the base.
Tapering increases if it is an isolated area, an area where largest density, in those area
tapering decreases.
Though tapering is the natural processes which can be controlled by human interference.
If competition increases, tapering decreases.

This can be proved mathematically as follows:
Let force P is applied to a cantilever beam at its free end, 1 is the distance of a
given cross section from the point of application of force, d is the diameter of the
beam at this point and then the bending stress (S-kg/cm2) is calculated using below
formulae;
S = P x 1 x 32
d3 x π
The force P on trees depends upon wind pressure per unit area (W) and crown area(F).
S = W x F x 1 x 32 (Since P = W x F)
d3 x π
d3 = 32 x W x F x 1
π x S
Thus, the diameter is increased with lengthening of the distance from the central point of
wind force.

1. Form Factor: Form factor is defined as the ratio of the volume of a tree to the
volume of a cylinder having the same length and cross section as the tree.
Simply it is the ratio between the volume of a tree to the product of basal area
and height. Form factor is useful in estimating the actual volume of standing
tree. Form factor give an idea about the laws of growth. The following are the
classes of form factors.
Types:
1. Artificial form factor
2. Absolute form factor
3. Normal or true form factor
The form factor is described in equation form as;-
Form factor (F) = V
Sh
Where, F is the form factor,
V = is the tree volume
S = is the basal area at breast height
h = is the height of the tree.

1. Artificial form factor: It is the also known as breast height form factor. In this,
the basal area is measured at breast height and the volume refers to the whole
tree both above and below the point of measurement. The artificial form factor is
not so reliable as the diameter varies at different height. But is universally used
because its computation is easier and standard one.
2. Absolute form factor: In this form factor, basal area is measured at any
convenient height and the volume of tree refers only to that part above the point
of measurement. It is the ratio between the volume of the tree above the point of
diameter or basal measurement with the cylinder which has the same basal area
and whose height is equal to the height of the tree.
3. Normal or true form factor: In this, form factor, basal area is measured at a
constant proportion (1/10th, 1/20th etc.) of the total height of the tree. The volume
designates the whole tree above ground level. Its is a cumbersome procedure
because it required height measurement at first followed by diameter at different
height.

Forest mensuration

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