Lesson 2 - Measurement of Tree Volume

Question 1

What is a paraboloid, cone and a neiloid shape? What are their volume equations?

Answer 1

Paraboloid = Convex cone shape (V= Ab x h/2)
Cone = cone shape (V=Ab x h/3)
Neiloid = concave cone shape (V=Ab x h/4)

Question 2

Explain the term “volume of a solid of revolution”

Answer 2

refers to the fact that a line is rotated around the x-axis (or curve if the shape is not a cone) and we are assuming that the shape that is formed by the revolution has volume (i.e. its a solid)

Question 3

What is a frustrum

Answer 3

the base of a shape (take the top off a cone and its a cone frustrum)

Question 4

What is a xylometer

Answer 4

instrument used to measure tree volume using water displacement method

Question 5

What is total tree volume and what are three ways to measure it

Answer 5

volume of the main stem of a tree

1. measuring the volume of water displaced
2. assuming a standard shape for the tree (i.e. cone)
3. assuming standard shapes for different parts of the tree

Question 6

What is Newton’s formula for?

Answer 6

calculate volume of a nieloid, cone or paraboloid frustrum

- diameter at top, midpoint and bottom needed for this equation

Question 7

What are Smalian’s and Huber’s formula

Answer 7

both for paraboloid frustrum

• Smalians requires diameters at top and bottom
• Hubers requires one diameter from middle
• both only exact if the tree section follows a paraboloid frustrum shape, if not it will over estimate

Question 8

What is merchantable tree volume

Answer 8

volume of the merchantable part of the tree stem

Question 9

what is net merchantable tree volume

Answer 9

= gross merchantable tree volume - wood not usable for product of interest

Question 10

Describe decay, waste an breakage

Answer 10

all unusable wood

decay: wood that can be pierced by a dull object
waste: remaining volume is the log is more than 50% decayed
breakage: volume lost because the tree breaks when it impacts the ground upon felling