# Week 1

**Lab 1 Forestry NAME________________________________________**

**Forest Mensuration Techniques**

For this lab you will need a tree, a yardstick (a measuring tape may also help), paper and pencil, this worksheet, and a stick of any sort.

If you do not have a tree (desert deployment, etc.) you may use any tall object – a building, flagpole, utility pole, etc. The principles remain the same.

You are to complete 3 exercises (I, II, & IIIa or IIIb)– each measures trees using variations on the same technique. Download this lab sheet to your computer and fill in the answers. Then use the worksheet to complete the Lab 2 assignment under Tests and Quizzes.

**Answer the set of questions following each exercise**.

If you do not get a sunny day where you are located, please use Excercise IIIb below as an alternative to Exercise IIIa. **Otherwise, you MUST do Exercise IIIa.**

Be SAFE and do not measure trees if thunderstorms are nearby.

USE THE SAME TREE FOR ALL THREE EXERCISES.

USE THE SAME TREE FOR ALL THREE EXERCISES.

**Answer the following questions**:

- What was the length of the stick you used to help measure the tree?

- What was the distance from you to the base of the tree?

- How did you measure the distance from you to the base of the tree (e.g. paces, yardstick, tape measure, etc.)?

- How tall did you calculate the tree to be?

- What are possible sources of error with this technique?

**II.****Tree Height Measurement **by Bizarre Labs:

The heights of trees (or any other tall object) can easily be found using a device called hypsometer. A hypsometer is basically a long stick divided into even units used to find height by triangulation.* A yardstick or meter stick will work just fine.

http://bizarrelabs.com/tree.htm

**Material: **A yardstick

**Procedure:**

1. If you are using a yardstick, stand exactly 25 feet from the tree being measured. Hold the yardstick, with the zero end downward, 25 inches from your eye. Line up the bottom of the yardstick with the base of the tree. Without moving your head, look to the top of the tree. Where it crosses the yardstick, read off the measurement in inches. Each inch will equal one foot in the tree’s height.

2. If the tree is taller than your hypsometer will measure, stand 50 feet away. Again hold it 25 inches from your eye, as before, only this time multiply your result by 2 to get the correct height. If it is taller still, then step back to 75 feet, multiplying your result by 3, or 100 feet, multiplying the result by 4, etc.

3. If you are using a meter stick, the procedure is basically the same. Stand 5 meters from the tree. Hold the meter stick 50cm from your eye. Each 10 centimeters will equal one meter of the tree’s height. If standing at 10 meters, double the result; at 15m, triple it, etc. Granted, a five-meter tree isn’t very tall, but it is a convenient scale to start with for the sake of mathematical progression.

*Note: there are other types of hypsometers, all of which measure height or altitude. Another type of hypsometer measures elevation by noting what temperature water begins to boil; this boiling point decreases with an increase in elevation.

**Answer the following questions:**:

- How did you measure your distance to the tree?

- How many inches tall on the yardstick did the tree appear to be?

- How tall did you calculate the tree to be?

- What errors may be made using this technique?

- How far back did you have to stand to measure the height of the tree?

****CHOOSE ONE OF THE TWO METHODS BELOW – FOR A TOTAL OF THREE METHODS FOR THIS ASSIGNMENT****

**IIIa.****Tree Height Measurement **by Bellnet

You will need a sunny day to do this exercise. If you are in a location where you do not have a sunny day to produce shadows, do Exercise IIIb below instead.

**Data Sheet**

**Answer the following questions.** (**SHOW YOUR CALCULATIONS USING UNITS)**

1. What is the average length of the yardstick shadow?

2. What is the average length of the tree shadow?

3. What is the height of the tree?

4. What are two **major** sources of errors associated with this technique (see data table for one source)?

5. Explain the variation between the three tree height measurement **methods**.

**6. **In your experience, which do you think was most accurate and why?

**IIIb.****Tree Height Measurement **(Alternate to Shadow Lab.)

ENRICH Team (http://nrich.maths.org/public/viewer.php?obj_id=2434)

Use this exercise ONLY if you are in a location where you do not have a sunny day to produce shadows.

Loggers learned a great deal from people who lived in forests for generation. They might be cutting down trees that are over a certain height and it is important that they have an easy way to estimate which of the trees around them are to be cut. You can estimate the height of a tree or a building using their method.

**Material:** A partner and a pencil

**Procedure: **

1. Let your partner standt the base of the tree. Move a distance away from the tree then, holding your pencil at arms length, between your thumb and forefinger so that it brackets the height of your partner (the top and bottom of the pencil coincide with the top of the head and the bottom of the feet of your partner).

2. Now, use this length to step out the height of the tree in “pencil lengths”. You can now measure the height of your partner and multiply this by the number of pencils high the tree is.

3. Repeat **three** times from different distances and calculate an average to improve the accuracy. Report the **average** of your three trials below in # 2.

**Answer the following questions to be turned in for grading**:

1. How did you measure the height of your partner? What was his or her height?

2. How many pencil heights did the tree appear to be (average of your three trials; show calculations)?

3. How tall did you calculate the tree to be? Use the average value from #2.

(**SHOW YOUR CALCULATIONS USING UNITS)**

4. What are two potential sources of errors associated with this technique?

5. Explain the variation between the three tree height measurement methods.

6. In your experience, which do you think was most accurate and why?