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Y
........................................................................
.<...................> house level
| . ,
| . ,
| . ,
H . ,
| . ,
| . ,
| . ,
0末末末末末帽1末末末末末乏1末末末末末帽2末末末末末R2
< - flat beach level ->
I agree with Paul, you need a GPS but also at least one angle; but, if
you must try to do it the hard way:
In the diagram above (hoping it doesn't wrap-around on your monitor
display) your house is at 'Y', at height 'H' above beach level, which
projects vertically down below you to point '0' at beach level.
Tools: get out your builder's spirit level (set it up horizontally) and
your telescope, and duct tape a straight stick to the telescope to use
as an angle pointer. Set the telescope exactly horizontal, then
rotate it downwards to focus on a nice prominent beach rock visible on
your beach at 'R1'. Measure the angle of declination (rotation) with a
simple protractor, then calculate (90-this angle), to finally get a
number for the angle (0-Y-R1) = call it angle A1.
Re-level the telescope and rotate it down again to focus it on a more
distant rock on the same beach, at 'R2' . Measure the angle of
declination (rotation) again, then re-calculate (90-this new angle), to
get new angle (0-Y-R2) = angle A2.
Quickly rush down to the beach before the tide comes in to cover the
rocks, and accurately pace out the horizontal distance from R1 to R2,
called 'X2'.
You now have measured angles A1, A2, and distance X2 from R1 to R2, but
don't know 'X1' which is under the cliff anyway.
Now consider the two (right-angled) triangles above, 0YR1 and 0YR2:
In the first triangle, taking the tangent of the angle, tan A1 = X1/H,
while in the second triangle, tan A2 = (X1+X2)/H
If you rearrange these two simple equations to eliminate X1, you should
have:
H = X2/(tan A2- tan A1), in which you've just measured all the 3
unknowns, so can now calculate the height above beach level of your
house, 'H'.
As a manufactured example used for a back-check, if X1 = X2 = 2 km
each, and measured angle A2 = 75.96ｰ and angle A1 = 63.43ｰ (tan A2 = 4
and tan A1 = 2, and X2 = 2), H = 1 km exactly above beach level. I
think this is OK and hope no stupid mistakes.
I can think of several ways in which this would not be very accurate,
e.g. how would you ensure that the telescope is exactly level before it
is rotated? A: get a laser level and focus the scope on the laser spot
reflected back off a tree or cliff or something. Maybe strap the
telescope on the laser?
Steve
On 7-Feb-07, at 5:17 PM, Jamie Simpson wrote:
> Does any one know a McGyver method of determining elevation? In an
> idle moment I decided I want to know how high my house is above sea
> level.
>
> I live on a hill with quite a good view including the Minas Basin
> below me and about 1 KM east, which would constitute sea level I
> expect.
>
> I could probably find a topographical map but I was wondering if there
> was some way to build a device from things around the kitchen - duct
> tape, paper clips, a pocket calculator...
>
> Trigonometry or Pythagorean method would probably work if I knew
> distances to points of reference which I don't, nor do I possess a
> sextant.
>
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