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How to Measure the Diameter, Height and Volume of a Tree ?

Matter Observing timber to seek out patterns


  1. There are relationships between the peak of an object and its shadow.
  2. There’s a relationship between the gap from a tree and the angle to the highest of that tree from some extent at that distance.
  3. There are relationships amongst species of timber.
  4. There are relationships amongst conifers.
  5. There are relationships amongst deciduous timber.

Focus Questions

  1. How can we discover top? See six ways to measure height.
  2. How massive are timber?
  3. How massive is that tree?
  4. What measurements of timber are vital?
  5. What does, how tall a tree? imply?
  6. What does trunk measurement imply?
  7. What does the scale of the crown imply?
  8. Why do individuals must know sizes of timber?
  9. Are timber proportional?
  10. Is there a relationship to the diameter of the trunk and its top?
  11. Is there a relationship to the top and the trunk?
  12. ThIs there a relationship to the e top and the crown measurement?
  13. Do sure kinds of timber have distinctive proportions?
  14. What different data might be collected about timber that’s useful for individuals to know?


50 meter wire with meter marks and one meter marked in cm, protractor, clinometer, sheets of graph paper, calculator

Exercise 1

{Photograph} and acquire details about a number of sorts of timber. May measure the peak, diameter, and crown of a number of related and totally different sorts (species) of timber, report the information, arrange it, draw it to scale, graph it, and uncover patterns.

Background data

Circumference of a tree might be measured instantly with the cm and m wire.

Diameter of a tree might be calculated from the circumference or estimated with a direct measurement or utilizing a Biltmore stick.

Crown might be measured not directly beneath the tree on the bottom with the cm and m wire.

Top of a tree might be estimated a number of methods. See six ways to measure height.

Measuring top of timber, buildings, poles,

Discover a tree, constructing, pole, or different tall object.

Guess the peak.

What’s your guess? ________________

Bear in mind to label your reply as to toes and inches and meters and centimeters. A quantity by itself is meaningless.

At first your guesses is probably not very shut, however the extra guesses and measurements made the extra correct you’ll be.

There are a number of methods you may measure top with out acutally measuring it from the highest to the underside by hand.

A technique is to make use of an individual as a, measuring stick. It’s simpler to pick an individual who’s three, 4 or 5 toes tall.

Have this individual stand subsequent to a pole or tree in entrance of it.

The measurer ought to transfer 25 – 50 toes away from each, relying on the peak, the taller the additional.

Use a clear grid or a ruler.

Wanting by way of the transparency slowly transfer away from them to you discover a spot the place the coed, in entrance of the tree or pole, measures precisely a sure variety of squares on the grid, or inches on the ruler and you may see the entire tree or pole on the grid.

Rely what number of squares on the grid the individual is and what number of squares there are from the bottom to the highest of the tree.

In the event you used a ruler and the individual standing beside the pole measured one inch, what did the tree measure in inches?

If it takes six inches to succeed in the highest of the pole and one inch represents an individual, draw that to scale on a bit of paper.

If one inch = 4 toes, then the tree would = 6 X 4 or 24 toes excessive.

Measure a pole or tree each methods (grid and ruler) report the outcomes on graph paper, and embody any notes which may be useful. What data do it’s good to bear in mind?

Scientists typically write their outcomes so they will not overlook them.

Utilizing shadows to measure:

Arithmetic is essential in science and almost all scientists use arithmetic or different arithmetic to assist clear up issues. If a pole or tree is situated on flat floor and it’s a sunny day, its shadow can be utilized to determine how excessive it’s.

Take an object or individual, whose top is thought exterior and measure the size of its shadow.

Then measure the shadow of the tree or pole of unknown top.

 Pupil top: _______________________

 Pupil shadow size: ________________

 Tree shadow size: ___________________

 It’s now attainable to seek out the tree top utilizing this data and the thought of proportion. The coed’s top is proportional to the coed’s shadow in the identical approach the peak of the tree is proportional to the tree’s shadow’s size.

Establishing the issue

Use a sheet of graph paper and draw a line to scale to signify the peak of the coed and one other perpendicular to it to signify the size of the coed’s shadow.

Use the identical scale and draw one other line to signify the size of the tree’s shadow.

Draw one other line perpendicular to it to signify the peak of the tree.

Evaluate the variety of items used to attract the coed’s shadow to the scholar’s top.

Use this relationship to attract the peak of the tree. You may then use the dimensions to seek out the tree’s top.

Establishing a proportion mathematically:

Pupil top Pupil shadow size Tree top Tree’s shadow size
4 toes 3 toes ? 21 toes

Utilizing your information from the earlier web page, discover out the size of the pole (x).

Pupil top Pupil shadow size Tree top Tree’s shadow size

Utilizing a clinometer to measure top

A clinometer might be used to measure the angle of elevation of the tree or pole.

Instructions to create a clinometer


Massive plastic protractor or (paper print of a protractor glued to cardboard), straw, 30 cm string, washer or different weight.

  1. Use the plastic protractor or the paper and cardboard protractor and tape the straw to the straight fringe of the protractor.
  2. Use the opening within the protractor or rigorously make a gap by way of the middle of the protractor the place it meets the straw.
  3. Push the string by way of the opening and tie a knot on the opposite facet so it will not pull by way of.
  4. Tie your weight to the different finish of the string.

To use a clinometer, you       will need two peopl

To make use of a clinometer, you will want two individuals: one to look by way of the straw and web site the highest of an object and one to learn the levels that the string makes with the protractor.

  1. Measure a distance, on the bottom, 50 m (for tall timber) or 25 m (for small timber) from the trunk of the tree that you just wish to measure.
  2. At 50 or 25 m from the tree stand going through it along with your associate. Certainly one of you sight the highest of the tree by way of the clinometer whereas the opposite reads the levels.
  3. Choose a bit of graph paper and draw a final analysis to scale for the 25 or 50 m distance you stood from the tree.
  4. On one finish of the 25 or 50 m scaled line draw one other line perpendicular (90 levels) to it. This line represents the peak of the tree.
  5. On the opposite finish of the 25 or 50 m scaled line draw a line that is (90 levels minus the angle measured with the clinometer).  You will in all probability want to check the diagrams beneath and persuade your self of what angle you measured and the way to attract a scale drawing to seek out the peak of a tree.
  6. The line drawn at this angle might be prolonged till it intersects (crosses) the road that represents the tree.
  7. That line phase represents the peak of the tree much less the top of the viewers eye.
  8. Use no matter scale that was used to scale the 25 or 50 m to find out the precise top of the tree.

Extension information:

Extension data:

Biltmore Stick – A Tree Measurement Tool

The Biltmore Stick is a intelligent instrument used to measure trunk diameters, heights of standing timber, and logs to estimate lumber. It was developed in regards to the center of the 18th century based mostly on proportionality and related triangles. It appears like a meter stick or yardstick. Nevertheless, the gap between the increment marks, to measure the diameter or top, lower because the diameter or top will increase. It’s used for estimates whereas different strategies could also be used for extra exact measurements. Nevertheless, the Biltmore Stick remains to be very a lot part of a timber proprietor’s instrument equipment and might be bought at any forestry provide middle. You may even make your personal.

It’s also used to measure the board foot quantity of a tree with two measurements: 1. The merchantable top in 16-foot logs and a pair of. The diameter at 4.5 toes off the bottom. The precise quantity desk is printed on the stick.

To measure diameter – Maintain the stick 4 and one-half (4.5) toes off the bottom, perpendicular to the tree trunk, towards the tree, and about 25 inches from the attention. Align the zero mark to at least one facet of the trunk. With out shifting your head, web site the opposite facet of the trunk and see what increment on the stick is closest. The variety of areas on the stick that the trunk spans is the measurement of the trunk.

How It Works – Make a diagram. Draw a line to signify the stick. Draw a circle to signify the tree. Draw one other line to signify the primary line of sight. It ought to be perpendicular to the stick line at its zero mark and tangent to at least one facet of the tree circle. Draw one other line to signify the road of sight to the correct fringe of the tree. It ought to be 25 inches from the stick line and intersect the tangent line. It ought to lengthen in order that it’s tangent to the opposite facet of the tree circle. The place the road crosses the stick line represents the diameter of the tree. For the reason that radius will not be in a direct line, an adjustment have to be made. In any other case the studying could be a lot too excessive (the purpose on the tree diameter the place the strains intersect out past the trunk).

If we decide a tree that has a diameter of 20 inches we all know the radius is ten. We additionally know the gap from the attention to the stick is 25 inches, the usual distance. The gap from the attention to the middle of the tree is the radius plus 25 inches. Utilizing this data the angle might be discovered. For the reason that two triangles are the similar, we all know that the tangent of twice the angle is the stick measurement divided by the gap from the attention to the stick (tan 2a = d / 25). Now we simply substitute the worth of twice the angle into the system and clear up d = 25 * tan (2 * (arctan [R / (R + 25)]). you may work out learn how to use an digital system to resolve the equation. In case your arm is a special measurement than 25 inches it’s possible you’ll wish to change that worth to match your arm size so it will likely be extra comfy.

The chart beneath comprises the stick measurements in inches for a 25-inch attain.

Measure and mark the tree diameters in your stick that matches your values alongside the size of the stick. If you find yourself completed, coat the whole persist with a transparent end corresponding to a transparent spray paint or polyurethane varnish, for sturdiness.

Tree Stick Tree Stick
10 8.6 30 21.8
11 9.3 31 22.4
12 10.1 32 23
13 10.8 33 23.6
14 11.5 34 24.2
15 12.2 35 24.8
16 12.9 36 25.4
17 13.6 37 26
18 14.2 38 26.5
19 14.9 39 27.1
20 15.6 40 27.7
21 16.2 41 28.3
22 16.9 42 28.8
23 17.5 43 29.4
24 18.1 44 30
25 18.8 45 30.5
26 19.4 46 31.1
27 20 47 31.7
28 20.6 48 32.2
29 21.2

Top Measurements

You may simply add top measurements to your stick, making it straightforward to estimate tree top. The system for that is very straightforward. Use the identical "attain," or distance from eye to stay. Additionally, you will must know the gap from you’re standing from the tree. A distance of 100 toes is usually recommended as a base. Some sticks have scales for 100 and for 66 toes (one chain).

To find out the peak of the tree (or different object) maintain the stick vertically at your regular attain. Align the zero level with the underside of the tree. Learn the peak on the level the place the highest of the tree seems to intersect the stick.

To calculate the measurement on the stick (S) at a base distance of 100 toes:

S = 25 * (H / 100)

For a base of 66 toes:

S = 25 * (H / 66)

In case you have a attain that is larger or lower than 25 inches, you may range the system accordingly. Now measure your stick, and mark it. You should definitely label the scales as 100-foot base or 66 foot base.

As a remaining characteristic in your stick, mark off commonplace inches. This is usually a nice. You needn’t put all of the scales on one side- there are a number of sides and even edges to make use of. Drill a gap in a single finish and fix a leather-based or nylon thong as a wrist strap. And end with a transparent coat.

To measure tree merchantable top Merchantable top refers back to the size of usable tree and is measured from stump top to the cutoff level within the prime. The cutoff level will range relying on locality, product and the variety of limbs.

Stand 66 toes (roughly 12 paces) from the tree you wish to measure. Maintain the stick within the upright vertical place 25 inches out of your eye with the "variety of 16 foot logs" facet of the stick going through you. Normally that is on an edge of the stick.

The variety of logs might be learn instantly off the stick beginning upward from the estimated stump top. You’re truly not measuring complete top however are estimating 16 foot log sections. With this merchantable top estimated in logs, plus the diameter, you may estimate tree quantity.

To measure tree quantity:  Maintain the stick towards tree at diameter breast top (DBH) 4.5 toes and 25 inches out of your eye. Shift keep on with proper or left facet of the tree till the zero or left finish of the quantity facet of the stick strains up with the left fringe of the tree. Sighting the correct facet of the stick the place it touches exterior bark (solely shifting your eyes) offers you the diameter on the highest line and beneath this the quantity of board toes for timber of various numbers of logs.

To measure quantity of logs:  Place the "log diameter" scale throughout the small finish of the log by inserting the stick throughout the place that seems to be common diameter (or take a number of readings and common). Log volumes for various diameters and lengths from 8 to 16 toes might be learn on the flat facet of the stick marked "log scale".

Logs over 16 toes lengthy are scaled as two logs permitting for taper on logs 22 toes or longer.  A 20 foot log, for instance, 15 inches in diameter, could be scaled as two 10 foot logs, every 15 inches in diameter

The bottle-opener dendrometer:

A really low cost instrument for estimating top and a few stand parameters. Engaged on the precept of comparable triangles, you maintain the dendrometer between you and the tree and transfer again or forwards till the tree seems to lie precisely between the highest and backside overhangs on the left facet. The purpose that corresponds to a mark one-tenth up the left facet of the dendrometer is then recognized on the tree. The peak from the bottom to the recognized mark is multiplied by 10 to find out the full tree top.


The way to discover the peak of an object utilizing trigonometry? – examples

As we acknowledged beforehand, our tree top calculator is multifunctional and we’re about to current an instance that’s meant to show it.

Think about that you just wish to renovate your backyard. After some typical modifications, corresponding to seeding fresh grass, you resolve to construct a treehouse – in spite of everything, did not most of us wish to have one in some unspecified time in the future in our childhood? To verify for those who selected a great place and estimate the quantity of materials required, it’s good to know the way tall the tree is. It’s situated on a small slope upwards, so you progress 26 toes away and, utilizing your telephone, measure the angle between the bottom and the highest – 54 levels – and the angle between your eyes and the bottom – 13 levels. Inputting this into the tree top calculator offers you the results of 41.79 toes – this tree ought to be excellent to have a treehouse constructed on it (assuming it’s also strong sufficient).

Nevertheless, you’re involved that it might obscure the view out of your bedroom. The home is on the similar degree as you, so that you measure the angle between your eyes and the highest of the window (handled as β). It’s 39 levels as you stand 20 toes from the constructing, and since you’re 5 toes 6 inches tall, your eye degree is roughly at 5 toes 2 inches. Utilizing our instrument as a constructing top calculator, you discover out that the window is situated on the top of 21.74 toes. Maybe the treehouse ought to be moved elsewhere, as to not block the window.


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