Using a sextant to find the height of a hill

[sarabande]

Going round in circles in the hay fields today I pondered about my sextant.

I live in a house facing West-ish. About 300metres away there is a high hill behind which the sun sets roughly an hour earlier than on the horizon.

I can find the exact postion and height ASL of the house easily enough from a paper map. If I take the Alt and Time as the sun's lower limb touches the hill, using an oil tray, can I work out the height of the hill ASL ?

If I dust off my Marc St Hilaire templates, where do I start please ?

 

[AntarcticPilot]

Going round in circles in the hay fields today I pondered about my sextant.

I live in a house facing West-ish. About 300metres away there is a high hill behind which the sun sets roughly an hour earlier than on the horizon.

I can find the exact postion and height ASL of the house easily enough from a paper map. If I take the Alt and Time as the sun's lower limb touches the hill, using an oil tray, can I work out the height of the hill ASL ?

If I dust off my Marc St Hilaire templates, where do I start please ?

No need to worry about astronomy - simply use your sextant and oil tray to measure the angular elevation of the hill. Then, you need to know the distance to the pooint you are sighting on (which may not be the summit; most hills are convex upwards, so there is dead ground at the rop of a hill), it is very simple trigonometry to compute the elevation of the hill above the elevation of your location.

The elevation above your current location is approximately D x tan(elevation), where D is the distance to the point you're sighting on.

Because you'll be sighting almost tangentially to the slope, it won't be wonderfully accurate. The main problem with this kind of observation is getting a good sighting point on the summit of the hill - unless you're sighting from a hill of simlilar elevation, it can be difficult to know exactly where the skyline you're sighting is is.

In terms of navigation, it's the inverse problem to distance off by sextant.

 

[lw395]

If you want to do it by sun or moon, then the 'dip' angle correction will change, but that is related to your altitude relative to a true horizon.
So not much use unless you can measure the elevation of a heavenly body relative to a sea level horizon, or horizon at another known height above sea level.
So, not easily then!, unless then sun sets over a known landmark or you can see the sea horizon from the hill.
I stand to be corrected on this!

 

[sarabande]

lw - I was intending to use a pan of old engine oil to provide an artifical horizon.

AP - thanks, all that makes sense. I knew I was tired and could'nt see the solution.

 

[ghostlymoron]

Have you tried looking on an OS map? Or is it maybe the technique that interests you.

 

[AntarcticPilot]

Have you tried looking on an OS map? Or is it maybe the technique that interests you.

That's likely to be a far more accurate method in this case, though contours on steep rural slopes should be regarded as indicative rather than highly accurate! Spot heights and trig points will be accurate, though. But the technique is useful; geologists use it to determine the relative elevation of outcrops when constructing vertical sections. However, they use a gadget called an Abney Level (http://www.stanleylondon.com/abneylevel.htm), which is less accurate than a sextant, but has a built in spirit level so there is no need to use an artificial horizon. That and a tape measure suffice to measure the ground profile of the rocks being studied, and other geological measurements (dip and strike of the strata) allow the profile to be constructed.

Been there, done that, but a very long time ago - 1973, I think!

 

[bitbaltic]

That's likely to be a far more accurate method in this case, though contours on steep rural slopes should be regarded as indicative rather than highly accurate! Spot heights and trig points will be accurate, though. But the technique is useful; geologists use it to determine the relative elevation of outcrops when constructing vertical sections. However, they use a gadget called an Abney Level (http://www.stanleylondon.com/abneylevel.htm), which is less accurate than a sextant, but has a built in spirit level so there is no need to use an artificial horizon. That and a tape measure suffice to measure the ground profile of the rocks being studied, and other geological measurements (dip and strike of the strata) allow the profile to be constructed.

Been there, done that, but a very long time ago - 1973, I think!

You beat me to the mention of the abney level! It was standard issue when I worked for a certain large NERC outfit in a little town outside Nottingham. We were still expected to make use of it when I left for other fields in 2008... Mine lived under the office desk. Carry that thing up a Welsh mountain, I think not.

Cheers

 

[AntarcticPilot]

You beat me to the mention of the abney level! It was standard issue when I worked for a certain large NERC outfit in a little town outside Nottingham. We were still expected to make use of it when I left for other fields in 2008... Mine lived under the office desk. Carry that thing up a Welsh mountain, I think not.

Cheers

The one I used (provided on loan from the Sedgwick Museum) would fit in a pocket - obviously you had a larger and more accurate one! But I can't imagine it being much use on a Welsh mountain - strata much too complex for simple tools like that.

 

[bitbaltic]

The one I used (provided on loan from the Sedgwick Museum) would fit in a pocket - obviously you had a larger and more accurate one! But I can't imagine it being much use on a Welsh mountain - strata much too complex for simple tools like that.

Yep it was about the size of a pair of binoculars and came in a stitched, hard leather case (well, box). Very useful for the chaps working on landforms in east Anglia perhaps but no way was it going up those grey forbidding hills in my rucksack.

 

[sarabande]

this little angle measuring device, the Abney Level...


Is it like this ?


View attachment 33718

That is a pic of one which has been sitting in a desk drawer for 20+ years since my late FiL willed it to me. It lives in a leather box approx 5" x 3" x 2".

 

[mcframe]

Been there, done that, but a very long time ago - 1973, I think!

I bet you weren't about for
http://en.wikipedia.org/wiki/Schiehallion_experiment
;-)

Annoyingly, neither my physics, maths nor geography teachers taught me about such interesting applications of the stuff they taught.

"You have: A mountain (not spherical, but assumed uniform density).
You require: the density of our planet"

Ask the kids nowadays, and they'll need an App to even get started.

 

[AntarcticPilot]

I bet you weren't about for
http://en.wikipedia.org/wiki/Schiehallion_experiment
;-)

Annoyingly, neither my physics, maths nor geography teachers taught me about such interesting applications of the stuff they taught.

"You have: A mountain (not spherical, but assumed uniform density).
You require: the density of our planet"

Ask the kids nowadays, and they'll need an App to even get started.

Well, I wasn't around for that one, but I did take part in this one: http://gravity.ucsd.edu/pub/1990_zumberge.pdf. Shame we didn't (for certain) detect any new physics - but I still think the theoretical physicists have been too quick to disregard the results of this and similar experiments.

 

[mcframe]

Well, I wasn't around for that one, but I did take part in this one: http://gravity.ucsd.edu/pub/1990_zumberge.pdf. Shame we didn't (for certain) detect any new physics - but I still think the theoretical physicists have been too quick to disregard the results of this and similar experiments.

Thanks AP, that's really interesting.

Compared with some of the stuff I deal with in my job, I do enjoy reading the work of ProperScientists - along with the MAIB & AAIB reports.

(Saved on my iPad - along with a rather eclectic collection of PDFs - for full reading later - I've /almost/ finished all 300-odd pages of the VH-OQA engine report...)