Re: Barometer for building height
- From: Richard Heathfield <rjh@xxxxxxxxxxxxxxx>
- Date: Wed, 16 Sep 2009 23:23:33 +0000
In <87tyz2ae48.fsf@xxxxxxxxxxxxxxxxxxxxxxxx>, Nick wrote:
Richard Heathfield <rjh@xxxxxxxxxxxxxxx> writes:
In <pan.2009.09.16.18.12.47.122154@xxxxxxxxxxx>, Rich Grise wrote:
Everybody's heard this one over and over again - how to use a
barometer to find the height of a building. [...]
See page 344 of "Expert C Programming: Deep C Secrets", Peter van
der Linden, 1994. On the following two pages, PvdL gives sixteen
additional methods (over and above those mentioned in the
ObPuzzle: Come up with a new one. (If anyone wants to try this and
doesn't have the above reference, I'll type up a summary thereof on
request, when I get enough clear time, which isn't now.)
q(guess, as although I've read the book I don't own it). Fill the
building with gas. Explode it. Measure the shockwave with the
barometer. Do some clever calculations based on the area and
structure of the building to work out the volume and hence the
height (the height that it used to be, of course).
Well, that's certainly a new one! Alas, it lacks detail. Also,
although I'm no engineer and could be wrong, it sounds like it would
produce a result even less accurate than the "measure the difference
in air pressure at top and bottom" answer, which is clearly the
intended answer but is nevertheless hopelessly inaccurate.
For the record, here are paraphrases of the original answers
1) tie the B to a long string, lower it off the roof till it hits the
floor, mark the string, pull it up, measure the length of the string.
2) drop the B off the roof and time the fall: s = gtt/2
3) sunny day, shadows, proportions. (My son simplified the calculation
involved by eliminating the "proportions" part; you simply wait until
the B's shadow is the same length as the B.)
4) climb the stairs, chalking up B-lengths as you go. Count them.
Multiply by length of B.
5) offer the B to the janitor in return for his telling you the height
of the building.
Sun Microsystems added these:
6) the Pressure method (obvious, woefully inaccurate)
7) the Pendulum method - tie the B to a long string and suspend it
from the roof such that it is just above the ground. Swing it. Time
the oscillations. L = gT^2/(4*pi^2)
8) the Avarice method - pawn the B to raise seed money for a chain
letter campaign. Using the money you get from the chain letters, make
a pile of banknotes against the side of the building. Multiply the
thickness of one note by the number of notes.
9) the Mafia method - similar to 5 except that you use the B as a
weapon to intimidate the janitor
10) the Ballistic method - fire the B from ground level with a mortar,
just high enough to reach the top of the building. Then use a table
of standard ballistic calculations.
11) the Paperweight method - use the B as a paperweight while looking
over the building plans
12) the Sonic method - drop the B from the top of the building, and
time the interval between seeing the B hit the ground and hearing it.
Speed of sound gives the route to the answer.
13) the Reflective method - place the B at the bottom of the building,
glass face pointing upwards. Stand at the top of the building. Shine
a light beam at the B. Time the round trip. Speed of light gives the
route to the answer.
14) the Mercantile method - sell the B and buy some proper equipment.
15) the Analog method - attach the B to a string, wind the string
round the shaft of a generator, and measure the amount of electrical
energy produced as the B falls from top to bottom. The generated
energy is proportional to the number of revolutions of the shaft.
16) the Trig method - mark a spot on the ground a known distance from
the building. Go to the top of the building with the B and a
protractor level, wait for sun to reach horizon. Using B as a mirror,
aim a spot of sunlight at the point you picked out earlier, and
measure the angle of the mirror with the level. Now trig.
17) the Proportion method - measure the height of the B. Stand a known
distance from the building. Sight past the B to the building. Move
the B until its top and bottom appear to coincide with the t&b of the
building. Measure distance from eye to B. Then trig.
18) the Photographic method - set up a tripod and camera a known
distance from the building. Hold the B a known distance from the
camera. Take a picture, then measure the relative heights in the
19) the Gravitational method (I) - Suspend the B from a yard of
string, making a pendulum. Measure the oscillation period at t&b.
Calculate g at top and g at bottom, then do the math.
20) the Gravitational method (II) - weigh the B at the top of the
building. Then weigh it at the bottom. (Use a spring balance, not a
beam balance.) F1=Gm1m2/R^2, F2=Gm1m2/r^2
21) The Calorific method - drop the B from the roof into a container
of water (covered with a narrow slit to minimise splashing). Measure
the increase in temperature of the water, from which you can get the
kinetic energy the B had on impact, from which you can get the
potential energy it had at the top of the building.
I think my favourites are 15, 19, and 21.
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
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