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Hi Steve & All, Feb 8, 2007
It is curious how one question will often disclose the answer to
another question. Jamie's question has solved the Oak Island mystery.
i.e. the so-called money pit shaft was dug by a coconut-mat salesman who
wondered how high his house was above sea level and had only a shovel
and a rope for tools.
Your formulation looks good but I would expect instrument error to
be large & have consequently looked at a second approach; an improvized
differential water manometer. At least that seems like a reasonable
name. Having never used or made anything similar, it would be best to
check this method out before using it to establish runway elevation for
instrument landing purposes.
Theory: This procedure makes use of the change in air pressure with
elevation. At the initial elevation (house or mean sea level as
convenient) water height in a transparent U-tube (both arms the same) is
recorded just after one end is closed to the air such that air volume of
the closed end is not changed. As rapidly as possible (to avoid
temperature changes) the unit is moved to the other location (mean sea
level or house) and the height of water in the two arms is recorded. If
the initial point is not about half way between the two final points
then there has been a change in water volume or enclosed air volume due
to temperature changes and it may be desirable to start again. As a rule
of thumb, a 5 cm difference from sea level would represent an elevation
difference of about 3.9 metres.
[DIGRESSION: If I have thought this through correctly, the
difference in water level between the two arms will slightly or
seriously underestimate the difference in air pressure between the two
locations, because change in volume of the air on the closed side will
change air pressure on the closed side. A smaller air pressure on the
closed will be increased and a larger pressure on the closed side will
be decreased by an amount proportional the fractional change in volume.
It might be possible to correct for this it one had to. ]
From observed difference (h; cm) in water level between the two arms
(ignoring the bias described in DIGRESSION) and assuming a temperature
of 4o C, one can estimate Z, elevation (cm) above mean sea level using
Z= (ln po- ln p)RT/g
where ln is natural log, po is pressure in dynes/cm^2 at sea level
(1,013,250), p is pressure at the house (1,013,250 -(h x 980)), R is
2.87 X 10^6, T is 277o K and g is 980.
Materials: One McGyver scrap pile, or considering component parts, a
valve stem from a bicycle innertube, pine board about 3" wide and 8'
long or equivalent (hinged or in two sections so it will fit in a car),
duct tape, tacks, about 6' of 5/16 ID tygon tubing, hot water bottle
with enema tube, ruler or metre rod secured to middle of board at eye
level, rabbit wire, nail, spring clamp & calculator.
Preparation & Construction: Wash the inside of the tygon tube
thoroughly with hot water and dish detergent, heat one end in near
boiling water, spread if necessary using a tapered stick and insert the
valve stem (previously cut from the inner tube) business end out.
Moistening the tube with glycerine will help.
Boil several cups of water for at least 2 minutes (to remove
dissolved air), add a drop of dish detergent and pour into the hot water
bottle quickly but avoid entrained air (e.g. by funnel with bottle
suspended in cold water), purge any air trapped from the bag corners,
tighten enema tube stopper, fill enema tube with water slowly from below
and store in fridge after cooling in cold water. Ideally, to avoid fussy
temperature adjustments, the water should be at about 4o C when used and
measurements should be taken when weather is about 4o C.
Secure valve stem end of tube above board end using duct tape and
tacks. The tube section at ruler level should lie near the ruler edge.
Fasten rabbit wire to the other end to facilitate water addition. Remove
valve stem insert entirely or have it very loose and add water to wire
end of tube from below using the enema tube and water bottle. Adjust
water level to near middle of ruler, wrap wire of wire end over nail &
clamp wire to board. Tighten valve stem insert and press pin in gently,
if necessary, so pressure (water level) of the two arms is equalized.
As described previously, record water level, move quickly to the
second location and record level in the two arms.
For elevations above sea level up to 10 to 15 feet this might work
fairly well. Do try this at home (basement to attic) and let me know
what happened.
Yours truly, Dave Webster, Kentville
Steve Shaw wrote:
> 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