How can I measure tree height?

[jeffreythree]

How can I measure a trees height fairly accurately without using specialized tools.  I have heard you can use a 12" ruler at arms length and measure the distance you are standing away from a tree when the tree is covered by the ruler.  Do I add any lengths to this and how accurate is it?  I have 5 trees that are close(but not close enough) to Texas Big Tree registry champion size, but two others are close enough to actually measure the height instead of guess.   A cedar elm and a post oak. 

[Sprucegum]

If you are going for the record you will have to abide by their standards of measurement, whatever that may be. If you just want to see how close you are the shadow trick works pretty good:

Use a post of known height(eg 6') and measure its shadow. Then measure the tree's shadow and the math is......

post height/post shadow = tree height/tree shadow

Good luck with your records.

[Dodgy Loner]

Here's a simple technique to roughly estimate height:

Hold a yardstick perfectly vertically, 36" from your eye (it's helpful to have a partner to measure the distance to your eye and make sure you're holding the stick vertically).  Now, find a spot where the yardstick just covers the tree from top to bottom while holding the stick in this manner.  Measure the distance from that spot to the tree trunk (in a straight line, don't measure up or down a slope).  This distance will be the approximate height of the tree.

Good luck, and be sure to post some pictures of the trees, along with their measurements, if you get a chance!

[Tom]

Or you can get someone of Known height to stand at the bottom of the tree.  Back off a goodly distance and hold a pencil or stick so that it sticks above your thumb. At arm's lenght, place your thumb on his feet and the top of the stick on his head. This gives you an increment approximating his height.  Then just raise the stick so that your thumb is at the top of his head and the stick is "his height" above.  Keep doing this until you reach the top of the tree.   Multiply the number of increments by the guy's height and you will come close to knowing the height of the tree.

[ADAMINMO]

shimmy up that baby with a tape measure.

[DouginUtah]

All this reminds me of the message which made the rounds years ago when a physics teacher asked the class how to use a barometer to measure the height of a building.

Numerous ways were presented, the final one was 'I would go to the building superintendent and say, "Sir, I will give you this nice shiny barometer if you will just tell me how high this building is."' 

[TeaW]

Put a mark on the tree at a known hieght . Take digital camera get  pic of tree, put image on a screen ( tv bigger is beter) measure hieght of mark and tree . Do the math.

[SwampDonkey]

The only trouble with a lot of those methods is, as the view angle increases, the length of the pencil or ruler is exaggerated because the tree is not growing in an arc. With the camera idea, the scale changes as you move away from the focal point. Same problem with aerial photography.

Your on the right tract guys, but you need to relate distance from eye to the bottom of the stick (length EA¹), and distance from eye to the base of the tree (length EA), distance from base of stick to point on the stick where the line a site passes bye to see the tree top EB¹, and length of stick from it's base to the point up the stick the line of site passes to see the tree top A¹B¹. Then solve for height AB as follows.

AB = A¹B¹ x EA
             EA¹

This is called a Merritt hypsometer, and finding height by proportion. The angles of the triangle formed from eye to stick are the same as eye to tree length. If you want to modify Dodgy's method a bit, you can use tangents of right triangles to get it. Some how you have the find the angle from the horizontal line of sight to the tree top (α1), measure horizontal distance (D) from eye to tree face. Then you can add the height from the ground to the horizontal line of sight (AB) to height from the horizontal line of sight to the top (BC). Find (BC). You could easily rig up a home made compass. Just take two yard sticks and fasten them at the drilled hole with a wood peg or pencil. Hold the bottom stick level, raise the other stick so your line of site along the stick sees the tree top. Get your buddy to pull out his trusty $0.25 protractor to measure the angle between the yard sticks. Get your distance from your eye to the tree. Do the math. Make sure to add the bottom portion of the tree height from ground level up to the horizontal . Make sure your on level ground or the same contour as the tree. Otherwise you'll have to add or subtract the bottom calculation depending on whether you uphill or down hill) Same principle as a clinometer. On steep slopes you no long have a right triangle so you have to find top and bottom angles in relation to line of site to a point on the tree or imaginary point under the tree. That's why it's best to try and position yourself so your line of site is horizontal at 0 degrees with the reference point on the tree. Make sure you have your carpenter's level to get that flat horizontal line D.

BC = tan α1 x D

[jeffreythree]

Thanks for all of these ways to measure height.  I think I will try Dodgy's and SD's since they both require yard sticks.  Measure the angle and do it SD's way and then turn it around and use it to make sure I am sighting it 36" away and vertically like Dodgy Loner suggested.  They are both umbrella shaped, so I hope I can actually see the top.  If it is close enough I can get someone out with real equipment. 
     I have not been lucky enough to find a champ in my woods yet.  The 5 that are close are a 42" dbh cedar elm with half its crown gone, a 32" 50' tall honey locust that is not any where near the champs height of 93', 2 hickories with the dbh and spread but the tops were knocked out (unless one is a mockernut which has no champ in Texas), and my biggest post oak so far has a height of ~90', crown spread of 105', but only 138" circumference(champ is 206" circ).  The cedar elm I am measuring only has a circumference of 92"(st. champ is 131"), but this tree has got to be close to 100' tall since the first branches are above all the 60-70' trees around it and the spread is ~75'.  The post oak is 201" circ and has a 125' spread because it has 3 main stems.  All of this is on 17 acres of land .  I wonder if the state forester will still push for clearcutting to plant pine when he finally makes it out like he suggested over the phone?

[Kevin]

http://www.rosevilletrees.org/pdf/treeHeightGauge.pdf


This is the tool I use ...

http://www.forestapps.com/cross_sight.html

[SwampDonkey]

Here is a drawing to demonstrate the hypsometer method with tangents.



This time we are up on a hill and to find distance D, we must slope correct length EA.

D = COS (α₂) x EA

Total Height AB = BC + CA

Where BC = D tan α₁ and CA = D tan α₂

So,

AB = D(tan α₁ + tan α₂) after simplification

If the observer where down slope then,

AB = D(tan α₁ - tan α₂)

It's the same as what a clinometer does for ya, usually calibrated for percents or chains or metric (1:20).

[STUMPKICKER]

Cut r' down! 

[Dodgy Loner]

Without a proper hypsometer, any estimate of height will be very rough, no matter how complicated the math.  We could go into great detail about all of the pitfalls that could influence the accuracy of your estimate.  If the tree is leaning, you must be standing in a specific spot to get a good estimate.  Of course, there is no practical way to determine what that spot would be, so you must estimate.  If the crown is umbrella-shaped, it will be difficult to determine what the uppermost branch is, because lower branches may appear to be higher than they are due to your point of perspective.  Just get a rough estimate, and if your trees are close enough to the champions, get someone with a clinometer out there to take a more accurate measurement.

[Lanier_Lurker]

I seem to remember someone calling SD a dweeb in another post somewhere...

(I hope winter breaks up there pretty soon)

 

Actually, it was techniques similar to those that yielded the earliest measurements of the height of Mt. Everest.  They started at sea level and worked their way to (or near) it with a giant protractor that had a sighting scope on it - leaving stakes in the ground as they went with the elevation at that point emblazoned on them.  Then, aiming the scope at the summit of Everest from the last two or three staked points allowed them to solve for its height.  They apparently nailed it to within less than 10 feet or so, although the actual height has increased since those days due to tectonic forces.

Geometry is cool...

[Dodgy Loner]

Bet they wouldn't have nailed it to within 10 feet with a yardstick .  But yes, geometry is cool.  When I was in high school, I actually made myself a crude clinometer with a protractor, a straw with a cross-hair on one end of it, and fishing weight on a thread.  I used simple trig functions to determine the height, because with my "clinometer" I could determine the distance to the tree, the angle to the top of the tree, and the angle to the bottom of the tree.  When I got a real clinometer, I tested my homemade rig and determined that it was actually remarkably accurate.

[SwampDonkey]

Dodgy, why wouldn't it be accurate? It's using the same math as the clino. A clino isn't doing anything any different at all. When you look through it at the tree and see 0 on the scale bar, that is the horizontal line from your point of view, death flat, to the tree face, or into the side of the hill. When you take a top shot on that leader and you have a percent clino, for instance, and it reads 100 %, you are standing at a position where the angle is 45° above that horizontal shot. That means the opposite angle is also 45 °, so if your 80 feet from the tree, the length of that tree from the horizontal (0 reading  on clino) to the top is the same. We assume the tree is straight up and down, and the angle between the horizontal line D and the tree axis is 90°. Then add the extra length from the horizontal to the tree base for total height. If the clino is in chains, when you see 66 as a top shot, you have a 45° angle, if you have a metric 1:20, and the top is 20 on the clino reading, you are have a 45° angle. You still have to either tape the slope distance to the tree at the point you took your bottom shot to correct for horizontal distance D, just like any engineer who surveys land or pull a tape along that horizontal line to the tree on the spot the horizontal distance D (0 reading on clino) hit. Just make sure you pull out the level from your hip pocket if using protractors and yard sticks. The math is the same whether done by calculator or computerized gadget. It's no easier to see the top with a clino than when a yard stick, nothing magic about it. No matter what gadget you use it's only and estimate and the precise height can only be determined by climbing the tree or cutting it down. It's not rocket science and once you've done it once or twice with your yard sticks you'll actual see how easy it is and think nothing of it. A little math and someone gets sweaty palms. I sure wouldn't want use the long way to cruise a forest, but we are talking one tree. All that those fancy gadgets do is put all the rulers, the level and the scale into one handy little gadget. The problem with a ground observation is being sure whether you are actually looking at the top no matter what gadget you use. The "accuracy" of your estimate comes in making sure you measure D and the angles properly. It will never be "precise" unless the tree is physically measured from ground to tip. Using a clino, with top shots over 100 % (percent scale for this example) the accuracy goes down. Not so bad maybe in eastern trees, but when trees are twice as tall it's almost impossible to see the top with over 100 % reading anyway.

[SwampDonkey]

Sure is easy to find the position E from the tree where the angle between horizontal to the top of the tree is 45 degrees when your carpenter's square has a level bubble in the base.




Nothing complicated here, I just got a straight piece of squared cherry to make a longer sight for my square. I'm finding the position E away from the tree where I have 45 degrees (angle α1 in my pencil drawing) from the horizontal (eye level - point C) to the top of the tree B. I mark the horizontal shot on the tree with flagging tape.




Now I measure that distance with a logger's tape from that previous determined position E. The tape is held at 0 degrees to the horizontal. That was determined with my level on the carpenter's square, then marked with orange tape on the tree. That horizontal distance D is found to be 10.6 meters.



The driveway is level, so here I show that my carpenter's square is very accurate in finding eye level on the tree. The distance AC is measured and found to be 1.8 meters.



Now for the math.

Since the horizontal distance D is easy to measure on level ground, we know that to be 10.6 meters by measuring with a tape. Simple enough. We also have the height from the ground point A up to that horizontal distance at point C, it is 1.8 meters.

Now we need to find the remaining height from point C to point B as illustrated in the pencil drawing above.

BC = D tan α1
     = 10.6 x tan (45°)
     = 10.6

Well, what do you expect when you know D by measuring from your standing position E where the sight angle makes 45°? As you know tangent of 45° is one, well you do now.

So, total height is:

AB = CB + CA  (from sketch)

     = 10.6 + 1.8
     = 12.4 meters

Who can't add two numbers?    

[tonich]

Have been using this tool most of the time: http://www.benmeadows.com/search/Blume-Leiss/1307/?type=brand

SwampDonkey just explained how it works. 

http://sres-associated.anu.edu.au/mensuration/BrackandWood1998/BLUMELEI.HTM

[SwampDonkey]

I try my best Toni, but nobody believes me when I show'm how simple stuff is.  Those fancy encased wheels are just graduated in tangents as a function of units, like a D-tape is graduated in Pi increments as a function of inches or centimeters.

[Phorester]

Cut the tree down, then you can accurately measure the length instead of estimating the height. 
Seriously, if your tree is close to being a champion, someone will be out to check the measurements  with a clinometer anyway.

[chep]

The most accurate way to measure is to go to Treebuzz.com and put up a post that offers any arboristin hte area to come climb your trees and drop a tape from the top. That is definetly the best way to get a height. If these trees are as big and neat as they sound, I am sure that some squirrel would love to be part of a measurement mission. You can always offer them cold refreshments once they are done.  If I lived near ya I would be up those trees asap!
Good luck with the math

chep

[Dodgy Loner]

Here is a visual demonstration (not to scale) of why my method is better.  It gives you the same results as SD's method, with no math.  It is based on similar triangles, a fundamental principle of geometry.

[SwampDonkey]

It's actually the same as my method 1. However in mine the math I typed is simply the proof, just to show it's not necessary at all if 45 degree angles are used. Only requires adding the horizontal distance from the observer to the tree to the height from the ground up to the horizontal distance line. Your using a fixed angle of 45 degrees which has a tangent of 1. Your forming an isosceles triangle (two angles and two sides equal). Just have to make sure it's dead level.

[jeffreythree]

If I hold my yard stick at the 27" mark because my arm is holding it 27"s from my eye, I will be achieving the same measurement, right?  And then I would need to make sure my arm is perfectly level so I am measuring straight up the tree, and add the height of my arm to the distance from the tree?  I tried Kevin's tree height gauge, but I managed to mangle it in transit to my place.  Or maybe the state forester finally coming out next week for my free state forestry plan has a clinometer and doesn't mind a few minutes measuring a tree or 2.

[SwampDonkey]

Not precisely, you need to measure at eye level or add the height from shoulder to the eye onto that vertical stick. Everything has to be level both horizontal and vertical. Stand back until top of stick sites on tree top. Your arm is level and the vertical stick is level (up and down). More accurate with a square and a level. This assumes you or flat ground like in my pictures. On a strong slope, for example, horizontal distance from the observer eye could be 10 feet up the tree or 5 feet below, depending if your up or down hill on the slope from the tree. Neither position you can directly measure because they are out of reach, unless in short segments of measuring horizontal distances and add them up or use slope correction by finding the angle of the slope line, find it's COS and mult. by slope distance measured.

[jeffreythree]

Well,  I am going out to try both the angle and stick methods this weekend.  Evidently the old Texas nutmeg hickory champ last measured in '74 is no longer around and the new one is smaller than my tree and mine may score bigger than the national champ .  I measured 84" circumference and it has a good crown spread.  I will get pics.

[pappy19]

I measured thousands of trees on a 2 year contract job for a large land excahnge between the USFS and Boise-Cascade using an angle guage and a Sunto. With heights, the most important thing was to use a steel tape and measure to your eye. A cloth or nylon tape will stretch and will be inaccurate. On the check cruisers from both FS and B-C, I was in the 98%. They all used a Relascope.

[Beweller]

With a clinometer measure the angle to the base of the tree.  Take one-half of this angle and add it algebraically to 45 degrees.  Move toward or away from the tree until the top of the tree sights at this angle.  Re-measure the angle to the base of the tree and if the angle has changed, repeat the procedure.  Rarely will you have to do this more than once.  The slant distance from the tree to your eyeball is the height of the tree.

Many methods require you to be standing a known distance from the tree.  This can be established with a prisim or gap gage.  For example, with a 10-to-1 prism or gage, when the tree just fits the prisim or gage,you are 33 diameters from the tree.  Walk up to the tree and measure the diameter and you have the distance.

[SwampDonkey]

With a clinometer measure the angle to the base of the tree.  Take one-half of this angle and add it algebraically to 45 degrees.  Move toward or away from the tree until the top of the tree sights at this angle.  Re-measure the angle to the base of the tree and if the angle has changed, repeat the procedure.  Rarely will you have to do this more than once.  The slant distance from the tree to your eyeball is the height of the tree.

Yeah, that will work assuming your on constant slope. Might be the quicker method for sloped ground in some instances, assuming your not standing on a bench/ground break in the hill. Or the hill isn't like a cow bell.
 

Many methods require you to be standing a known distance from the tree.  This can be established with a prisim or gap gage.  For example, with a 10-to-1 prism or gage, when the tree just fits the prisim or gage,you are 33 diameters from the tree.  Walk up to the tree and measure the diameter and you have the distance.

Horizontal distance yes, not slope distance. Known as Limiting Distance of the tree.

[Beweller]

Swampy,  No.  Using the prism or gage returns the distance along what ever your line of sight is.  If you sight on the tree at your eye height, it gives the slant distance (including the special case where the slant angle is zero).

Note that this eliminates the problem of un-even slopes, mounds or gulleys, between you and the tree.

[SwampDonkey]

Ah, yes true. Hopefully you can reach up to where the gauge hit the trunk to measure the diameter when there is a hump in front of the tree.

[jeffreythree]

I just wanted to thank everyone on this matter.  Finally got the nutmeg hickories measured, both beat out the 160 point state champ with the bigger at 68" circumference, 91' height, and 45' average spread for 170 points.  The other is 168 points.  Now if I could just find the 84" circ one again.  Now I need to go fill out that entry form .