Surveying

Seems to me you would need a Laser Range Finder.

Then measure the distance to the base of the tower at ground level.

Then measure the the distance to the top of the tower.

Then measure the angle to the top of the tower using a theodolite.

Then do the math.

Just a thought.

A laser range finder would be a great help but the theodolite comes from a time before lasers. I have been meaning to buy a laser ranger when I can get the money together but it will have to be a decent one. Eventually I will check them out but for the moment we are stuck to the older models of theodolites. Thanks for the reply.

One simple and one involved way.

• Surveying processes.
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• THE THEODOLITE: MEASURING AN ALTITUDE ... - UGAstro

Have fun.I think there's a smart phone app for this too, if you want to check your work.

Thank you for your well thought reply. We will use it and should be able to get our answer.

My dumpy level is not a theodolite admittedly but i would expect the more sophisticated instrument to be at least as good as the dumpy. The dumpy level has a graticule on the vertical crosshair. This graticule relates to distance away from the dumpy. I am sure you could also use it to work out height by focussing on the tower and counting the divisions. Without moving the focus knob take the instrument to a place, such as a long straight road and using a staff (or tape measure ) go down the road until the staff is in focus. Then tell your assistant to stop and hold up the staff, mobile (cell ) phone helps. You can then read off the graticule metres per division at that distance etc.

Jim

Thank you for the reply. It might be possible to do it that way but kind of defeats the aim of learning about the theodolite. We might try it though and see if the two different methods agree.

It is good to hear from an OP, thanks. I know it must be possible as i watched a TV program about a surveyor mapping out a valley about a hundred years ago with incredible accuracy. He and his assistants built cairns of known height on top of prominent points ( hilltops ) and worked the angles from left and right and up and down. He worked his way along the valley plotting as he went. He included the height of the mountains as well as the shape and length of the valley. I am sure you could do a similar thing. As i said in my first post you could 'shoot' down a road or paddock from point A to a staff of known height and distance, point B. Without moving the theodolite shoot the tower and measure the angle, point C. Now move the theodolite to the point B and shoot the tower again. You now have two angles and one length of side. From this you can work out the distance to the tower. By now you know the relationship of divisions on the vertical graticule to distance ( either empirically from point B measurement or from instruction book ) so you can work out the height.

Alternatively you can measure the angles to the top of the tower from both point A and B and once you have worked out the length of sides you can work out the height. You will have to allow for the in/declination of point B. You only need one but two will be confirmation.

I have always wanted to get a theodolite myself but none come up in my price range. I will have to enjoy it vicariously through you.

Have fun, Jim

Just reread my post and i realise that i didn't make myself very clear. I am talking about triangulation on the ground to obtain points A,B, and C. C being the tower. This way the distance to the tower from A and/or B can be worked out. Using my level i would 'shoot' from the high ground and using a staff measure declination to point B. I only need to know the measurement, not the angle. The divisions on the vertical graticule would then also give me distance from A to B, giving me the length of one side.

One thing still worries me. If you can't see the base how do you know it's not sited in a deep depression?

Jim

Easy. Use an aerial photo on a sunny day, noting the date, the time and the latitude. Measure the length of the shadow. The rest is trigonometry.

Yes, that would certainly work but sort of defeats the object of the exercise of learning to use a theodolite. On that basis though, making these measurements would need to assume the ground was flat, something we can not show to be the case. Take the case of a very tall tower on a small sphere. the tip of the shadow could be at infinity. If the terrain were right it could possibly work.