Content of the material
Abney Level:
The Abney Level is an engineering instrument which can be used to determine height. It is moderately expensive and of medium size and weight. Although the Abney Level is relatively robust, the bubble tube can be knocked out of alignment during rough treatment. When used correctly, the Abney Level has an accuracy of about +/- 0.5 m for a 20 m tall tree (ie about 2.5%).
- Measure the horizontal distance from the base of a vertical tree (or the position directly beneath the tree tip of a leaning tree) to a location where the required point on the tree (e.g. tree tip) can be seen.
- Sight at the required point and move the index arm over the scale until the bubble tube is level.
- Read the percentage scale (or the degrees and minutes of the angle).
- Calculate the height by multiplying the percentage read by the horizontal distance (or by multiplying the horizontal distance by Tan of the angle).
- Site to the base of the tree and repeat steps 2 – 4.
- Combine the heights from steps 4 and 5 to determine total tree height:
- Add the 2 heights together if you looked up to the required point in step 2 and down to the base of the tree in step 5.
- Subtract the height to the base of the tree from the height to the required point if you are on the sloping ground and had to look up to both the required point and the base of the tree.
- Check all readings and calculations.
Video
Things You’ll Need
- A friend (optional for most methods, but a little help makes the process easier and more fun)
- either a tape measure or yardstick (meter ruler)
- or a clinometer or transit
- or a piece of paper
- plus a pencil (for one method)
How to calculate the height of a tree using the shadow measurement?
In case you can’t or simply don’t want to trouble yourself with the angle measurement, there is a simpler way – one based on Thales’s method of estimating pyramid height. However, it is more universal because you do not have to wait for the proper time of day. In fact, all you need to do is measure the length of your shadow, the tree’s shadow, and know how tall you are. Then you can use the following formula:
tree height = (your height * tree's shadow length) / your shadow length
.
Bear in mind that this equation tells you only how to calculate the height of a tree if it is on a level ground. If the tall object is elevated or located below you, you should opt for the trigonometrical method.
Java
// An iterative java program to find height of binary tree import java.util.LinkedList;import java.util.Queue; // A binary tree nodeclass Node{int data;Node left, right; Node(int item){data = item;left = right;}} class BinaryTree{Node root; // Iterative method to find height of Binary Treeint treeHeight(Node node){// Base Caseif (node == null)return ; // Create an empty queue for level order traversalQueue<Node> q = new LinkedList(); // Enqueue Root and initialize heightq.add(node);int height = ; while (1 == 1){// nodeCount (queue size) indicates number of nodes// at current level.int nodeCount = q.size();if (nodeCount == )return height;height++; // Dequeue all nodes of current level and Enqueue all// nodes of next levelwhile (nodeCount > ){Node newnode = q.peek();q.remove();if (newnode.left != null)q.add(newnode.left);if (newnode.right != null)q.add(newnode.right);nodeCount–;}}} // Driver program to test above functionspublic static void main(String args[]){BinaryTree tree = new BinaryTree(); // Let us create a binary tree shown in above diagramtree.root = new Node(1);tree.root.left = new Node(2);tree.root.right = new Node(3);tree.root.left.left = new Node(4);tree.root.left.right = new Node(5);System.out.println(“Height of tree is ” + tree.treeHeight(tree.root));}} // This code has been contributed by Mayank Jaiswal
Geometric principle
Christen, Merritt or JAL altimeter use geometric principle, which is based on the equation: A’C’/AC = A’B’/AB, where AB corresponds to the tree height. Before mentioned instruments that apply this principle use fixed distances of A’B’, A’C’ and AC, where A’B’ and A’C’ are given on the instrument and AC is set by some reference fixed at the tree (see the formula on the main photo).
Christen altimeter
With the Christen altimeter, the visual image of the tree or part of the tree to be measured must be fit exactly between the upper and lower ends of the scale. The height or length of a tree, a stem, or a stem section is then determined on the basis of a fixed reference length on the stem. Instruments such as Christen altimeter are relatively simple in construction, only one reading is necessary, and the measurement is not affected by the inclination of the terrain.
C#
// An iterative C# program to// find height of binary treeusing System;using System.Collections.Generic;// A binary tree nodeclass Node{public int data;public Node left, right;public Node(int item){data = item;left = right;}}public class BinaryTree{Node root;// Iterative method to find// height of Binary Treeint treeHeight(Node node){// Base Caseif (node == null)return 0;// Create an empty queue// for level order traversalQueue<Node> q = new Queue<Node>();// Enqueue Root and initialize heightq.Enqueue(node);int height = 0;while (1 == 1){// nodeCount (queue size) indicates// number of nodes at current level.int nodeCount = q.Count;if (nodeCount == 0)return height;height++;// Dequeue all nodes of current// level and Enqueue all// nodes of next levelwhile (nodeCount > 0){Node newnode = q.Peek();queue();if (newnode.left != null)q.Enqueue(newnode.left);if (newnode.right != null)q.Enqueue(newnode.right);nodeCount–;}}}// Driver codepublic static void Main(String []args){BinaryTree tree = new BinaryTree(); // Let us create a binary// tree shown in above diagramtree.root = new Node(1);tree.root.left = new Node(2);tree.root.right = new Node(3);tree.root.left.left = new Node(4);tree.root.left.right = new Node(5);Console.WriteLine(“Height of tree is ” +tree.treeHeight(tree.root));}}// This code has been contributed by 29AjayKumar
Applications of Binary Tree:
- Its used in many search applications and algorithms which constantly display and store data. For instance, map including set objects in many libraries.
- Its utilized in 3D video game to conclude which objects need to be executed.
- Its used in nearly every high-bandwidth router to store router tables.
- Its used in construction of compilers and (implicit) calculators to parse declarations.
Algorithm for Calculating Height of a Binary Tree
There are two methods to approach this problem statement. First Approach is based on Depth first seach using recursion, and the other method is based on Breadth first search using Level order traversal without using recursion.
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