A trigonometry puzzle … perhaps

[Michael GilliganParticipant @michaelgilligan61133]

I have a particular interest in this 4G cellphone tower

**LINK**

https://earth.app.goo.gl/RhxwpW
#googleearth

… I want a reasonable estimate of the height, above ground, of the antennae

Physical access is limited, but I could do some trig from the pavement.

Before going there with the Disto [or whatever] … I would welcome any clever suggestions from the forum.

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”Cheating” is permitted … so if you happen to have access to the design drawings, please just tell me the dimensions.

I suspect that we could do a passable job by scaling from the ‘Street View’ images.

Over to you, if anyone fancies a try.

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

[Nick Clarke 3Participant @nickclarke3]

I would say the antennae height is approx 4 to 4.5b times the height of the blue vehicle or 5 times the eaves height of the building between the silo and the mast.

Only a rough guess of course

[EmgeeParticipant @emgee]

Check with the Local Planning authority, the application for planning permission will include the mast height.

Emgee

[peak4Participant @peak4]

Using Google earth & streetview only, both of which might show height distortion, I'd say 12m to the top of the mast roughly.

3G aerials are about 1.5m long, I've thrown away my BT Radio Training notes now.
The base station cabin is about the same height as a shipping container 2.6m

Blowing the two pictures up on screen, using a ruler, and doing the calculations four times, all come up with about 12m

Bill

[DiogenesIIParticipant @diogenesii]

Go there with a stick of known height, measure the shadow of the mast, and then measure the shadow of your stick…

Or if it is in the same 'plane of distance' as the fence, say, measure the height on the picture with a ruler, then mark off that same distance horizontally along the fence and go out and measure that..

[JourneymanParticipant @journeyman]

It's about 8 fence posts high so about 8' x 8 64' in old money

John

[peak4Participant @peak4]

Posted by DiogenesII on 09/07/2022 11:27:46:

Go there with a stick of known height, measure the shadow of the mast, and then measure the shadow of your stick…

Or if it is in the same 'plane of distance' as the fence, say, measure the height on the picture with a ruler, then mark off that same distance horizontally along the fence and go out and measure that..

I haven't got time now, but using Google Maps Satellite imagery, you can measure distance.
Street lights are likely to be a set height, as are other things like telephone poles, which can be estimated from StreetView.
Then compare that with the overhead view and measure the shadow lengths.
The mast comes out about 15.5m shadow

I'm sure an astronomer could use the date and shadow angle from North to work out the time, and thus the sun's inclination above the horizon.

Bill

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Emgee on 09/07/2022 11:00:51:

Check with the Local Planning authority, the application for planning permission will include the mast height.

Emgee

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Thank you

Why didn’t I think of doing that before asking here ?

[ please resist the temptation to answer ]

Sadly there are no drawings accessible, but the summary is near enough and I’ve learned some new jargon.

MichaelG

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[JourneymanParticipant @journeyman]

Apparently the fence posts are only 6' high…

Unless of course it was the old ones at 14m and the new one is taller… That doesn't help much, sorry

John

Edited By Journeyman on 09/07/2022 13:34:15

[JasonBModerator @jasonb]

Even to do it with trig you would need to be able to measure how far you are from the pole which if you can't access it won't work. Then the angle between the top and bottom of the pole from your view point would give you an answer

[Michael GilliganParticipant @michaelgilligan61133]

Posted by JasonB on 09/07/2022 13:36:16:

Even to do it with trig you would need to be able to measure how far you are from the pole which if you can't access it won't work. …

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That’s why I mentioned the possibility of using the Disto

[ a laser-based distance measurer made by Leica ]

MichaelG.

[V8EngParticipant @v8eng]

Bit too far away for an iPad to measure I think.

Don’t ya just love the effect modern technology is having on landscapes!!!

Edited By V8Eng on 09/07/2022 14:40:48

Edited By V8Eng on 09/07/2022 14:42:30

[duncan webster 1Participant @duncanwebster1]

Posted by JasonB on 09/07/2022 13:36:16:

Even to do it with trig you would need to be able to measure how far you are from the pole which if you can't access it won't work. Then the angle between the top and bottom of the pole from your view point would give you an answer

You can establish 2 points outside the fence a known distance apart then use trig on horizontal bearings to work out how far one point is from the mast. Then vertical bearing from that to get the height. Looking up the planning application is too easy

[duncan webster 1Participant @duncanwebster1]

Posted by JasonB on 09/07/2022 13:36:16:

Even to do it with trig you would need to be able to measure how far you are from the pole which if you can't access it won't work. Then the angle between the top and bottom of the pole from your view point would give you an answer

You can establish 2 points outside the fence a known distance apart then use trig on horizontal bearings to work out how far one point is from the mast. Then vertical bearing from that to get the height. Looking up the planning application is too easy

[Michael GilliganParticipant @michaelgilligan61133]

Posted by V8Eng on 09/07/2022 14:40:35:

Bit too far away for an iPad to measure I think.

Don’t ya just love the effect modern technology is having on landscapes!!!

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Not quite sure I get your point, V8

This is a screen-grab from the zoomed-in ‘Street View’

[ click the image for a bigger version ]

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Once calibrated, you could probably build a credible scale model from that.

MichaelG.

Edited By Michael Gilligan on 09/07/2022 16:48:35

[SillyOldDufferModerator @sillyoldduffer]

Just home from a family jolly, without reading any of the answers, I used the fence posts (2.4m), as per Journeyman, and got a low estimate of 13m and a high estimate of 16m. The average is 14.5m, pleasingly close to the planning application.

If the length of a tall object's shadow can be measured, the height is directly proportional to the length of a shadow thrown by a pole of known length at the same time. Provided the shadows are clear, the method is accurate and doesn't need trigonometry or measuring angles. A traditional Abney Level or Theodolite both work in poor weather but involve sums. If the object is a known distance from the observer positioned with a large-scale ordinance map, the stadia calculation could be rearranged to give a reasonable answer. Significantly better by laying out an accurate baseline with a surveyors chain, measuring the angle to the top, and doing the trig. The baseline must either be levelled or have the slope compensated for in the maths.

'Last of the Summer Wine' methods: Michael and I will fly a quadcopter fitted with GPS around the tower, fall in a cow-pat, and be chased through nettles by dogs and an angry farmer. Or we will climb the tower with a plumb line, only to discover it's not quite long enough. Then we'll go viral on the web after being filmed wetting ourselves due to having to wait beyond bladder endurance for an air-sea rescue helicopter. Michael will get the measurements right and I will cock-up the maths.

Dave

[V8EngParticipant @v8eng]

Posted by Michael Gilligan on 09/07/2022 16:45:55:

Posted by V8Eng on 09/07/2022 14:40:35:

Bit too far away for an iPad to measure I think.

Don’t ya just love the effect modern technology is having on landscapes!!!

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Not quite sure I get your point, V8

This is a screen-grab from the zoomed-in ‘Street View’

[ click the image for a bigger version ]

.

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Once calibrated, you could probably build a credible scale model from that.

MichaelG.

Edited By Michael Gilligan on 09/07/2022 16:48:35

Michael.

I was thinking in terms of the iPad measure feature which I tried on our big trees (20m+) without success.

That was a rather tongue in cheek experiment anyway.

[Anonymous]

There appears to be a bloke standing beside it. If he's there next time you go, you could call him over and ask him how tall he is.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by V8Eng on 09/07/2022 17:31:51:

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Michael.

I was thinking in terms of the iPad measure feature which I tried on our big trees (20m+) without success.

That was a rather tongue in cheek experiment anyway.

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Ah … I don’t think I’ve ever used it

There are plenty of other Apps that do measuring

The one that I particularly like for measuring photos is :

**LINK**

https://apps.apple.com/gb/app/ep-calipers/id982313078

Not an intuitively obvious choice, as it’s targeted at a niche market …

But, if you put a little effort in, it works very well indeed.

MichaelG.

[Jon GibbsParticipant @jongibbs59756]

Blimey this is a blast from the past – as a Scout we used to use similar triangles to estimate the height of trees.

If you position a vertical pole 11 horizontal units from the base of the mast and sight from the ground a further unit away from the pole, the intersection of the top of the mast on the pole allows an inch to feet conversion – one inch on the pole = one foot on the mast.

Edited By Jon Gibbs on 09/07/2022 20:35:55

[Michael GilliganParticipant @michaelgilligan61133]

We’ll do our best, Jon

MichaelG.

[David CauntParticipant @davidcaunt67674]

Using Goggle Earth for distance it shows 95.24 metres

[Michael GilliganParticipant @michaelgilligan61133]

Nice try, David … but unfortunately you overshot the tower !

I made the same mistake when I first looked at it on Google Earth.

… I have found a whole new level of respect for the people who analysed aerial reconnaissance.

MichaelG.

 

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**LINK**

https://en.wikipedia.org/wiki/Aerial_reconnaissance

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Edited By Michael Gilligan on 10/07/2022 05:31:49

[David George 1Participant @davidgeorge1]

Somewhere I have a laser measuring device as long as you have line of sight it would give you the length. I used it in the factories when measuring for machine moving etc.

David

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