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> arms (ig
Hi Steve & All, Feb 14, 2007
Not lack of interest but other demands kept me from responding
earlier. And this will have to be brief with perhaps a follow up later.
That may be a witty quotation about ideas but it does not ring
true, because we all constantly use ideas that were initially generated
by others. To paraphrase Newton (because I don't have time to dig out
the original quotation) if we are able to see into the distance at all,
it is because we stand on the shoulders of giants.
When I read Jamie's original post, and your initial reply, three
thoughts came to mind.
1) He is posing this question to initiate a discussion and it sounds
like a fun question to explore, one reply does not constitute a
discussion so why not take part ? As it turned out, a lot of interesting
approaches rose to the surface and more may come, so I think it has been
worthwhile.
2) Or it might in addition be a genuine question and his "I could
probably find a topographical map..." suggested a relatively low
elevation where a topographical map would be much less informative than
at say 200 m as you supposed.
3) And with all the recent talk about sea level rise perhaps this hill
that affords a view is really quite low, say less than 50' and the
question is of more than idle interest but as in 2) would require a
method suitable for small elevation differences.
Now I have not worked out the likely errors as a function of
elevation, but I think you would agree, in qualitative terms, that the
approach you proposed would become less precise as elevation decreased
and would be very imprecise at elevations of say 5 m (slope being 5/1000
= 1/200).
Returning briefly to the differential manometer, note that I did not
conclude it to be the superior method of the two. I said simply that
"...I looked at a second approach..." that one must work rapidly to
avoid temperature changes, that it will "... slightly or seriously
underestimate..." and suggested at the end that, as described, it might
work fairly well at up to 10-15 feet above sea level. Hardly a ringing
endorsement.of this differential manometer.
This limitation to very low elevations, and to some extent the
underestimation at higher elevations, could be overcome, I think, if we
assumed access to a few scraps of 4" PVC pipe, to increase the volume of
the closed arm, with fittings and closure of some kind. This larger
volume would also largely overcome another problem that I forgot to
mention in my original post; increase in temperature when volume of a
gas is decreased adiabatically.
I thought that one might be able to beat the ceramic out of a spark
plug and use the resultant hollow bolt as an adapter for the bicycle
valve stem. So I tried this the other day. Getting the center post out
is a piece of cake. I did learn that this ceramic is quite hard. Hard
enough to mark window glass and hard enough to gouge channels in a
center punch and a 1/4" drift.
I took an old washing machine apart several years ago and, if I
interpreted the parts correctly, the low, medium and high water settings
are controlled by a pressure transducer that is coupled to water depth
by a Tygon tube and that when triggered closes a normally open solenoid
(open at the fill segment of the cycle). Whether this would have
potential depends, among other things, on whether or not the transducer
is a sealed unit. Perhaps someone knows how these are configured.
It seems that you didn't follow the theory. And perhaps I didn't
either because it is easy to overlook the obvious. Thus the need to
always test an idea in nuts and bolts before it becomes credible. Here
is the rationale once again.
If one has a container that can either be open to the air or closed
at will, and if this container is opened at sea level for a time
sufficient to equilibrate and then closed then the pressure in the
container (po) will remain constant at any elevation, provided neither
temperature nor volume changes. If one sets the manometer at sea level
then the pressure in the closed arm will be po. When the unit is taken
to a higher elevation then the volume of air (unfortunately) does
change. Ignoring this bias for the moment, the balance of forces will
(ideally assuming no change in po due to the larger volume) be
po= h + p
where, as previously, h is the difference in water level in the two arms
and p is the pressure at the higher elevation. These forces must all of
course be expressed in the same units (cm of water or dynes/cm^2).
Returning now to that unfortunate bias, that is a consequence of
volume change in the closed arm, one can reduce this bias to any desired
small proportion by increasing the initial volume of the closed arm. But
as initial volume of the closed arm is increased, the distortion that
will be introduced by temperature changes will be increased. So initial
volume can be made very large only if temperature stability of the
closed volume is reasonably good.
No doubt glass tubing would be better than Tygon, the latter just
being more widely available (Can. Tire used to carry Tygon but not sure
they still do). I did once make a water manometer for lab use, using
glass tubing, and wetting really does not cause problems with reading.
One could readily read pressure to within 1 mm of water (about 0.074 mm
Hg). The nuts, bolts and setting were very different but I now see that
the theory of this unit, built to confirm pressure regulator function at
very low negative pressures relative to atmospheric, and the portable
water manometer are identical.
Yours truly, Dave Webster, Kentville
Stephen Shaw wrote:
> Hi Dave and other McGyverites who have got into this...
> I forget exactly who, but think it was a German who said that the
> average
> respondent "would rather use another man's toothbrush than his ideas",
> and I'm
> therefore not unduly shocked that Dave without evidence rejects my
> proposed
> sighting method for determining height as having a large expected
> instrumental
> error, while favouring his own even more improbable alternative. In a
> winter
> contest to do just-possible thought experiments that we guess Jamie
> will never
> follow through on anyway, it's really hitting below the belt to get
> serious and
> start talking about errors, but I feel I've got to rise to the bait here.
> Dave, I couldn't follow your pressure formulation as given, but
> essentially,
> this seems to be that as you go up the hill and air pressure drops,
> the volume
> in the closed end of the manometer will rise proportionally, if
> temperature
> stays the same (I think it's Boyle's Law, PV=RT?). This is sure to
> work as a
> nice thought experiment but since you are getting finecky, the
> question is
> whether any such change would be detectable in practice. Air pressure is
> halved at about 18,000 feet which should be detectable, but it seems
> doubtful
> that Jamie lives that high up; more likely the house is (say) 200
> meters above
> sea level (~600 feet). I looked up Atmospheric Pressure on Wikipedia
> and if
> you use the second equation given there for calculating air pressure
> against
> elevation (for the lowest zone, starting at sea level), an increase in
> elevation of 200 m would generate a change in atmospheric pressure of
> only 2.4
> percent. I doubt that a change in volume (= air column height) of
> 2.4% could
> even be detected reliably never mind accurately measured with your
> Tygon tubing
> method, even if you could avoid water droplets on the wall as you jog
> up the
> hill carrying it (Tygon is quite wettable by water, which I think is
> partly why
> such instruments often use mercury in glass).
> If you go back to my suggested sighting method, the two angles are
> eminently
> measurable (unlike in your method), and the distance between the two
> rocks
> should be easily measurable to better than 1 percent with a calibrated
> rope, so
> the main expected error would be in the inaccuracy of reading the two
> angles
> from a home-made scale. Because tangents are involved, the actual errors
> depend strongly on the actual dimensions and angles involved, and I
> doubt if
> you can make, fit and read a home-made scale to better than 1 degree.
> If the
> house is 200 m up, and the first rock is 1000m out and the second 500 m
> further, a 1 degree error in setting or reading the scale on the
> telescope for
> the two angles would tranlate into a 21-34 percent error in height
> estimation
> (worst cases, where the errors run in opposite directions rather than
> partly
> cancel out). You could improve this a bit by repeatedly sighting and
> averaging
> the angles but I doubt if you could get it down below +/- 10 percent,
> because
> of difficulty making and accurately centering the scale. This would
> not be that
> bad for a first try. With your method, you too perhaps could improve
> detectability a bit by running up and down the hill repeatedly,
> carrying the
> maonometer, but I think my method of averaging is more restful.
> Commenting on methods for measuring distance, Lois' method using 3-4-5
> Pythagorean triangles that are 'similar' (not 'congruent'): this OK
> for short
> distances, as in the example given (factor of 10), but invites the
> comment that
> if you have a measuring stick 5 units long already, it would be actually
> quicker to simply tumble it 6 times to measure out the 30 units
> required than
> to set up all the sighting sticks and to make sure that they are
> vertical. How
> accurate would it be if you wanted to measure something at, say, 1000
> units
> distant, abandoning the 3-4-5 system but keeping the 4 unit baseline? --
> sighting errors over the sticks would be much more significant. The
> website
> mentioned by Ray may be interesting historically but doesn't help because
> ultimately one's paces, thumb or whatever have to be calibrated with a
> ruler to
> pull out dimensions that we currently use, like feet or meters. Can't
> estimate
> if you can't calibrate. One method not mentioned so far is that years
> ago,
> Polaroid cameras introduced a range-sensing method that worked over
> near to
> middle distances, that I think employed the reflection of an
> ultrasonic sound
> pulse from the desired object, presumably by measuring the time
> delay. Maybe
> this is how the hand-held devices used by real estate agents to
> measure the
> sizes of rooms work - I'm not sure. Not sure either how my camera
> autofocusses, either.
> Final advice to Jamie would be to listen to Peter and rent a surveying
> instrument, or if he really wants a project, make his own survey
> system with a
> laser diode (a few dollars these days), angle scales, tripod, level
> and and a
> calibrated measuring pole. Methods using triangulation on maps are
> practically
> sensible, but essentially amount to cheating in this McGyver context,
> because
> the map has already been calibrated by experts.
> Steve
>
> Quoting David & Alison Webster <dwebster@glinx.com>:
>
>> Hi Steve & All, Feb 8, 2007
>
>
>> 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
>>
>>> 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'.
>>
>
>
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