This document provides an overview of the course Forest Mensuration and Biometrics. It will be a 3 credit course offered in the 3rd semester of the B.Sc Forestry program at Purbanchal University College of Environment and Forestry. The document lists several recommended textbooks and outlines the topics that will be covered in Unit 1, including definitions of mensuration, objectives and scopes of forest mensuration, and principles of height measurement using trigonometric and geometric methods.

1. FOREST MENSURATION AND
BIOMETRICS
NRM 237
Credit hour (2+1)
B.Sc Forestry (3rd Semester)
Prabin Pandit
Assistant Lecturer
Purbanchal University
College of Environment and Forestry (PUCEF)
foresterpandit@gmail.com

2. Books
• Elementary Forest Mensuration by M R K Jerram
• Forest Mensuration by A. N. Chaturvedi and L. S. Khanna
• Forest Measurements by Chapman and Meyer
• Forest Mensuration by Donald Bruce & Francis Schumacher
• Forest Mensuration – Tree Measurement by Pravin Agrawa

3. Unit-1: Introduction
1.1 Definition and scope of forest mensuration
1.2 Bias, accuracy and precision
1.3 Principles of height measurement
1.3.1 Trigonometric principle
1.3.2 Principle of similar triangle

4. 1.1 Definition of Mensuration
➢ The word mensuration is derived from the Latin word mensura which means measure.
➢ It is an art and science of locating, measuring and calculating the length of lines, areas of
planes and volumes of solids.

5. ➢ To differentiate between quantitative and qualitative assessment
➢ To remove personal bias and error (to a great extent)
➢ For responsible use of forests and other natural resources
Why measure anything?

6. 1.1 Definition of Forest Mensuration
➢ 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 that branch of forestry which deals with the determination of
dimensions (i.e. diameter, height, volume etc), form, age and increment of single trees, stands
or whole woods, either standing or after felling (Chaturvedi and Khanna, 1986).
➢ 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)

7. ➢ Age
➢ Diameter- over and under bark
➢ Length or height
➢ Form or shape
➢ Taper or the rate of change of diameter with length
➢ Volume over or under bark
➢ Crown width
➢ Wood density
➢ …
Measurements are:

8. 1.1 Objectives of Forest Mensuration
➢ Basis for sale
➢ Basis for management
➢ Measurement for research
➢ Measurement for planning

9. 1.1 Scopes of Forest Mensuration
➢ Forest mensuration involves all stakeholders i.e. Labors, buyers, sellers, contractors, planners,
managers/foresters and researchers.
➢ So, forest mensuration has a very wide scope.
➢ It comes into play every time the wood is sold, converted or used.
➢ Applicable to any forest measurement problems of wildlife management, watershed management,
insect and disease incidence, recreation, tourism and in fact, many of the mensurational aspects of
multiple use forestry.
➢ Forest Mensuration is the application of measurement principles to obtain quantifiable information
for forest management decision making.

10. 1.2 Bias, Accuracy and Precision
➢ Bias refers to the difference between the long-run average of the observations and the true
value. An unbiased measurement technique is one which yields the correct answer on
average.
How many trees are there ?
500 m2
500m2 = 3 trees
1m2 =
3
500
100ha =
3
500
∗ 1000000 = 6000 trees
How many trees are there ?
500m2 = 1 trees
1m2 =
1
500
100ha =
1
500
∗ 1000000 = 2000 trees
Suppose area of this forest is 100 ha = 100*10000 m2
Average tree per plot = (2+3+1+2+2)/5 = 2
500m2 = 2 trees
1m2 = 1/500
100ha = 1/500∗1000000=2000 trees

11. 1.2 Bias, Accuracy and Precision
Total forest area of Nepal = 44.74%
of the total area of the country
• Calculated by Pranish = 43.11%
• Calculated by Sirjana = 43.42%
• Calculated by Nutan = 44.10 %

12. 1.2 Bias, Accuracy and Precision
Diameter of stump
Calculated by Pranish = 43.2 cm
By Linear Tape
Diameter of stump
Calculated by Sirjana = 40.1 cm
By Linear Tape
Relative diameter of the stump = 41.22 cm

13. 1.2 Bias, Accuracy and Precision
• Accuracy of a measurement is a measure of how close the measured value is to the
true value of the quantity.
• Accuracy refers to how close an observations, are to being correct.
• True value can be determined only by very careful measurements with accurate
instruments and formula used.

14. 1.2 Bias, Accuracy and Precision
Calculated by Nutan = 41.12 cm
By calliper
Diameter of stump
Calculated by Pranish = 43.2 cm
By Linear Tape
Relative diameter of the stump = 41.22 cm

15. 1.2 Bias, Accuracy and Precision
Linear Tape
Least count = 1 mm
Calipers
Least count = 0.1 mm

16. 1.2 Bias, Accuracy and Precision
• Precision tells us to what
resolution or limit, the
measurement is measured by a
measuring instrument.
• Precision refers to the closeness of
two or more measurements to
each other.

17. 1.3 Principles of Height Measurement
• Instruments used for measuring tree heights are collectively referred to as
hypsometers.
• All height measuring instruments are based on ;
i. Trigonometric Principles
ii. Geometric Principles (Principles of similar triangle)

18. Trigonometric Principles
• Two laws are applicable for this purpose and they are:
i. tangent law and
ii. sine law
i. Tangent law
➢ Applicable to right angle triangle
➢ For accurate results, trees must not lean more than 5° from the
vertical, and the fixed horizontal distance must be determined by
taped measurement.
θ
h
d
A
B
C
Tan θ =
𝑝
𝑏
=
𝐴𝐶
𝐵𝐶
=
ℎ
𝑑
Therefore, h = d * tan θ

19. Trigonometric Principles…
ii. Sine Law
➢ Applicable to lean tree or non right angle triangle.
➢ Sines of angles are proportional to the opposite sides.
θ
h
d
A
B
C
𝑺𝒊𝒏∠𝑪𝑨𝑩
𝑩𝑪
=
𝑺𝒊𝒏∠𝑨𝑩𝑪
𝑨𝑪
=
𝑺𝒊𝒏∠𝑨𝑪𝑩
𝑨𝑩

20. Geometric Principles
• Two tringles are said to be similar, when;
i. AAA (angle angle angle) All three pairs of corresponding angles are the same.
ii. SSS in same proportion (side side side). All three pairs of corresponding sides are in
the same proportion. ...
iii. SAS (side angle side) Two pairs of sides in the same proportion and the included angle
equal.

21. Geometric Principles
• Two tringles are said to be similar, when the corresponding angles are
equal and the corresponding sides are proportional.
• By knowing the two sides of a triangle and only one side of the other,
the corresponding second side of the latter can be found.
•
𝐴𝐶
𝑔𝑓
=
𝐵𝐶
𝐵𝑓
• AC (ht) =
𝐵𝐶
𝐵𝑓
* gf θ
f
A
B
C
g

22. Thank You