Clinometer Errors and Calibration

General discussions of measurement techniques and the results of testing of techniques and equipment.

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#1)  Clinometer Errors and Calibration

Postby KoutaR » Fri Jan 11, 2013 8:45 am

This thread was pulled from a different discussion on calibration of the Nikon 440 Laser Rangefinder viewtopic.php?f=235&t=4862  and contain references to that thread.

Edward Frank




But you cannot calibrate clinometer, and clinometer is a bigger error source. Correct me if I am wrong.

Kouta
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#2)  Re: Clinometer Errors and Calibration

Postby Will Blozan » Fri Jan 11, 2013 9:07 am

Kouta,

You beat me to that comment! I agree, the rangefinder's +/- 1.5' distance range likely contributes less error than a mis-read or inaccurate clinometer, especially on higher angle measurements. Bob L has posted spreadsheets on this in the past.

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#3)  Re: Clinometer Errors and Calibration

Postby dbhguru » Fri Jan 11, 2013 9:32 am

Kouta, Will, et al.

     I agree with the two of you. Clinometer error is the bigger source and hard to get a handle on. You can check on your clinometer's accuracy at different angles, but it is a laborious process, and error-prone itself.

Bob
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#4)  Re: Clinometer Errors and Calibration

Postby edfrank » Fri Jan 11, 2013 11:57 am

KoutaR wrote:But you cannot calibrate clinometer, and clinometer is a bigger error source. Correct me if I am wrong.

Kouta


Kouta, Will, Bob,

A clinometer is basically a mechanical device.  Error in calibration is related to the balance of the internal dial/wheel.  If it is off at the top angle by 1 degree, it will be off at the bottom by one degree.  So how does this affect the total height reading if you measure the angle to the top and the angle to the bottom with the same clinometer?   The following table shows the results if the distance to the top is fixed at 150 feet (for comparison purposes).  The second assumption is that the angle to the base of the tree is close to zero.

               
                       
clinometer error.GIF
                                       
               


If the top is at 150 feet at some angle, the base is closer.  The error from the clinometer being off by 1 degree at the top, and at the bottom.  If you are shooting close to horizontal at the base of the tree, the net errors in this calculation is from 0.01 to 0.03 feet because of a 1 degree calibration error in the clinometer.  If the base of the tree is at some higher angle than horizontal, then less of the error is offset.  In the values shown in red, I have split the angle to the top in half and calculated the vertical error if the base of the tree was at half the angle of the top of the tree.   In the steepest at 66 degrees/33 degrees the error was 0.48 feet, and  the net error decreased as the angle became less steep.

John Eichholz discussed the math involved here: http://www.nativetreesociety.org/measure/height/eichholz_error_spreadsheet.htm  and includes an excel spreadsheet with formulas.  He write:  My conclusion: At a given baseline, the height error due to angle measurement error is nearly the same no matter what the angle.

You can easily test the calibration of a clinometer:  http://www.nativetreesociety.org/measure/suunto_clinometer_testing.htm

You can test the level accuracy of a clinometer or instrument. Sight from a marked height at some object- tree of pole at a distance. Have an assistant mark the point on the distant object the clinometer or instrument says is level.   Move to that spot and sight back to your original position. If it is perfectly accurate the backsight will be right on the point you shot from originally. If it is reading high, then the angle it is off will be under-reading by arc tan [1/2 (error)/distance].   If it is pointing lower than the starting point, then it is reading high, calculations are the same. In this way you can tell at least if the original level line is actually level or not.


Edward Frank

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#5)  Re: Clinometer Errors and Calibration

Postby pdbrandt » Fri Jan 11, 2013 12:43 pm

This discussion is very helpful for me.  It's good to know how much to trust (or not) my measurements and it is also good to know when to obsess about accuracy and when that is futile given the limitations of the instruments.

Is the following an accurate summary of sources of error in the sine method:?

If your LRF is not correctly calibrated you could easily add up to 2 feet of error depending on the angle of measurement.

Ed gives some numbers above to show the error that can occur if your clinometer dial is off, but human measurement error is also an issue.  It seems to me the clinometer can only be read accurately to within 0.25 degrees.  This human error can lead to many inches of error.  For example:
    A 64 yard LRF measurement at 45 degrees or 45.25 degrees is a difference of 0.6 feet over the ~130 foot measured height.
    A 50 yard LRF measurement at 64.5 degrees or 64.75 degrees is a difference of 0.3 feet over the ~130 foot measured height
Therefore being closer to the tree (larger angle) is better to decrease clinometer error, but on hardwoods, the closer to the tree you are the less likely that you will be to hit the top most sprig.  This is of course assuming that the clinometer scale itself is 100% accurate and the only source of clinometer error is human error in reading the angle.

Not being able to step back to "click-over" in dense undercover adds error.  For example, if you only have a tiny window through which to measure you may be stuck with the documented LRF error of 1.5 feet (for a Nikon 440), which, depending on the angle of measurement will add some fraction of that error.  Additionally, it may not be possible to step back to click over at both top and base LRF reading points.  I believe it was Ed Frank who posted in another thread that it is better to step back to click-over on the top measurement if only one is possible since the crown LRF reading is usually longer.  In fact, stepping back at both points in an effort to increase accuracy will actually introduce error if you are not on level ground.

Non-ideal atmospheric conditions such as high humidity or bright sunshine can, according to the Nikon instruction manual, introduce an unknown amount of error.

So, I think it is safe to conclude that even under ideal situations with a seasoned measurer, tree heights taken using the sine method with a Nikon 440 and Suunto clinometer are accurate to within 6 inches or so.  That's still very impressive for a ground based measurement!  In difficult measuring conditions LRF-derived heights could be off by a foot or two.
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#6)  Re: Clinometer Errors and Calibration

Postby dbhguru » Fri Jan 11, 2013 2:02 pm

Patrick,

   The attached Excel spreadsheet gives a simple way of calculating the height error incurred from distance and angle errors when using the sine method. The spreadsheet automatically calculates the error from the variable values you enter. You can play what if games.

  I've saved the spreadsheet under your name. If this approach works for you, there are plenty more spreadsheets that I can send your way. I've analyzed the sources of measurement error and their impacts from just about every angle you can imagine to include head or tripod swivel. The impact of different combinations of errors can be determined quickly through automating the calculations through spreadsheets. I've posted this stuff before, but I fear the math has been a turn-off. So, if the process described in the attachment isn't clear, I'll expand the explanation. Happy to.

   In terms of your general understanding, you're doing well. So often in cluttered woods, the desirable measuring protocol cannot be followed. So we end up improvising with one of the measurements (top vs bottom) often being subject to much more error than the other. You've correctly grasped this reality, which is a big step forward. Also, most instruments have idiosyncrasies, and yes, atmospherics matter. And as you've indicated, beyond calibration considerations, there are human errors. If you would like to set range limits on the possible error, based on the assumptions you make, then the spreadsheet allows you to easily do that. Hope it helps.

Bob
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#7)  Re: Clinometer Errors and Calibration

Postby edfrank » Fri Jan 11, 2013 2:40 pm

Patrick,

Yes there is error in how you read the instrument.  But the error values you are calculating are the maximum errors +/- if you are off by 0.25 degrees.  Bob's spreadsheet will calculate this for you.  Stepping back will negligibly increase the error from the clinometer reading as the angle will be barely perceptibly lower, but the error from the  rangefinder will decrease because the height error is the sin of the angle x height.  so as the angle decreases the effect of the length error decreases on the total height value.  

It really doesn't matter if you move backward to a clickover point or forward to a clickover point, you must be consistent every time you do it, because stepping forward finds the minimum range at which that number is displayed, while stepping back finds the maximum position where that number is displayed.  The difference is the stated precision of the instrument for example either 1.5 feet or 3 feet.

I say that in a mechanical clinometer that the error is the same at all angles because the instrument is a scale printed/etched on a weighted wheel.  The wheel rotates about a pivot point with the heaviest side pointing down.  The same point ALWAYS points down.  When using the instrument, the vertical orientation of the balance scaled wheel is not being changed, you are essentially just rotating the case around the wheel.  It moves back and forth during the movement process, but when it stops it is always the same side pointed down.

For electronic clinometer instruments essentially the same procedure outlined above can be used to check the accuracy of the clinometer.  Instead of just a horizontal reading, a point can be selected at some angle and shot and back-shot.  The vertical distance between the two readings is then measured.  The difference in height perpendicular to the angle measured is sin(shooting angle) x (measured vertical distance) then as above this distance perpendicular to the measurement line can be used to calculate the error in the angle measurement = arc tan [1/2 (perpendicular error)/distance]

Ed
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#8)  Re: Clinometer Errors and Calibration

Postby pdbrandt » Fri Jan 11, 2013 3:49 pm

Thanks for your explanations Bob and Ed.  Your level of understanding is humbling...

edfrank wrote:I say that in a mechanical clinometer that the error is the same at all angles because the instrument is a scale printed/etched on a weighted wheel.  The wheel rotates about a pivot point with the heaviest side pointing down.  The same point ALWAYS points down.  When using the instrument, the vertical orientation of the balance scaled wheel is not being changed, you are essentially just rotating the case around the wheel.  It moves back and forth during the movement process, but when it stops it is always the same side pointed down.

Ed

   
It makes sense to me that the intrinsic error of the clinometer is the same at every angle, but the further you get from the tree, the more that error is magnified by the longer distance.  Here's a screen shot from Bob's spreadsheet showing readings corresponding to an imaginary ENTSer moving toward a 70 foot tree, measuring the height as he gets closer to it.
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#9)  Re: Clinometer Errors and Calibration

Postby dbhguru » Sat Jan 12, 2013 10:03 am

Patrick,

   I've attached an updated Excel workbook for you and others. The first spreadsheet is the one that was sent before. The second gives a method for determining the accuracy of a clinometer shooting to the top and base of a target. Determining level is not involved.

The third spreadsheet illustrates Ed's procedure for checking on whether a clinometer reads true on level. The process can be a little hard to visualize.

               
                       
clinometer error2.GIF
                                       
               


   On the second spreadsheet, I've included data from an actual test conducted last evening on my TruPulse 200. As you can see, the error is slightly less than a tenth of a degree. I used a Bosch red laser to measure the distances from the TruPulse to the top and base of the target. I used a regular tape to measure the height of the target. The advantage of this type test is that it can be performed in your basement.

Bob
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#10)  Re: Clinometer Errors and Calibration

Postby edfrank » Sun Jan 13, 2013 10:24 am

pdbrandt wrote:It makes sense to me that the intrinsic error of the clinometer is the same at every angle, but the further you get from the tree, the more that error is magnified by the longer distance.  Here's a screen shot from Bob's spreadsheet showing readings corresponding to an imaginary ENTSer moving toward a 70 foot tree, measuring the height as he gets closer to it.


Yes Patrick,  but the error from the clinometer isn't the only error in the equation.  For illustrative purposes, if you assume an error of 1 foot in your distance measurements - you are underestimating the distance by that amount. The distance error is the hypotenuse of a right triangle. The the error from being short is:

height error = sin(angle) x distance error

(The horizontal error therefore is the cos(angle) x error distance.)  

at 15 degrees = 0.25 feet
at 30 degrees = 0.50 feet
at 45 degrees = 0.71 feet
at 60 degree =  0.87 feet
at 75 degrees = 0.97 feet

So error resulting from distance measurements from increasing the angle increases as you approach the tree.  Also as you get closer to the tree it is more difficult to pick out which top is higher as you are seeing if from a steeper angle.  This is particularly true of broad topped trees. From a closer perspective you may not even be able to see the true top let alone be able to hit it with your laser.  Not finding the actual top will result in a much bigger error than any generated by instrument errors or from the degree to which you can interpolate the clinometer readings.  One other note is that many laser rangefinders will swap scales at some distance going from readings nominally to within 1.5 feet to within one yard.  The goal of the calibration of the rangefinder is to get better  accuracies than what are displayed on the scale.  Your reading with calibration at click-over points should be less than the 1 foot I used in the example.  

It is always a trade-off between different types and sources of errors.  I try to shoot at angles around 45 degrees or so if possible, but move closer or farther as needed to get the job done.  I explore the structure of the tree shooting pretty straight upward from beside the trunk to see if I can find a higher point from underneath than I  am finding from shooting from a distance away. If I do, then  have not identified the real top in my  side measurement and need to do it again with more intensive searching from a different location.  Good luck, practice make better.

Ed
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