I have been enjoying the comments on estimating wall declination,
especially those which have the ring of experience about them.
I am prompted to offer the following Consumer Guide to the
methods I have used over the years (and two I haven't). I
am sure that many readers will be able to add to my list:
1. Architect's Drawings
A typical Architect's site plan includes a very convincing
ornamented letter N enfolding an arrow. The arrow usually
points at some arbitrary angle with respect to the sides of
the paper. Alas, the angle is also pretty arbitrary with
respect to true north. I have known errors up to 15 degrees.
Verdict: Avoid like the plague
2. Large-Scale Maps
Good maps may well stem from very careful surveys but the
representations of buildings are often more suggestive than
accurate. You can often determine latitude and longitude
to high precision but should treat the orientation of a
depicted wall with great caution. You also have to worry
(in the U.K.) about distinguishing grid north from true
north.
Verdict: Avoid
3. Magnetic compass
Subject to numerous caveats you ought to be able to get good
results. You have to be sure that there isn't a hidden iron
drain or some such nearby and, of course, you need to know
the local magnetic variation. The method is no use if the
magnetic dip is too large.
Verdict: Avoid
4. Using Solar Azimuth - General
Carol Arnold, John Davies, Tony Moss and Bill Gottesman have
described variants of the same idea: use the sun! I have
used all these and more. I am not keen on plumb lines [they
don't keep still and if you use a bucket of water to dampen
the swings you just get a bowed string!]. If you make many
observations widely spaced in hour-angle you can get a
result better than 10 arc-minutes.
Verdict: Fair to Good
5. Using Solar Azimuth - Window Ledge Method
If you simply place a sheet of paper on a window ledge with
one edge firmly against the inside of the bottom of the window
frame you can often get the vertical edge of the window frame
or a vertical glazing bar to cast a shadow. You draw a line
just ahead of the (moving) shadow and note the time that the
shadow reaches the line.
Typical window ledges are close to horizontal and the sides
of windows are approximately vertical so this can be quite
accurate.
Verdict: Fair
6. Using Solar Azimuth - Letting the client do it
What do you do if you have to rely on someone else? The
instructions I have given overseas clients (for example)
are as follows:
Find a flat board, a sheet of squared paper, a
spirit level, a wooden pencil and a digital clock
(preferably one that is radio-controlled and shows
the date as well as the time).
Place the board against the wall and place the squared
paper on the board with one edge against the wall.
Place the clock on the piece of paper.
Check that the board is level and stand a pencil so
that it balances on its blunt end (this is an added
check that the board is level). Arrange that the
pencil casts a shadow that falls across the squared
paper.
Take several digital photographs (preferably over
several hours) which show the paper, the pencil,
the shadow and the clock. E-mail me the results
the same day.
By counting squares I can get a reasonable estimate of
the angle the shadow makes to the wall. The rest is
as for 4 and 5. Make sure that you know how the time
on the clock relates to UTC.
Verdict: Fine if there is no other way
6. Using GPS
An up-market approach using GPS kit exploits two GPS
receivers each slaved to the other so that the relative
phase-angles of the signals received from each satellite
can be compared. You let the system run for 6 hours or
so and via a good deal of software you can determine the
position or one receiver relative to the other to about
5mm. Their absolute positions will not be known to
such precision but that doesn't matter.
Using a 50m baseline, a 5mm error means you can determine
the azimuth of the baseline to about 20 arc-seconds.
You then use standard surveying techniques to find the
declination of your wall.
You have to take care not to get stray reflections so
you should be high up on something solid. Scaffolding
will not do!
This works splendidly even if it is cloudy. The snag is
the cost. The kit costs about $80,000 and is obviously
expensive to hire. It is suitable for high-budget
sundials only!
Verdict: Wonderful if you have a rich client
7. Cassini Method
When setting out camera obscura noon marks a technique,
which I think is due to Cassini, is first to note the
point on the floor perpendicularly below the hole in
the roof (immensely difficult to determine accurately)
and then draw concentric circles round that point.
Next you plot the hyperbolic path followed by the
image of the sun on a given day and, with luck, the
image will cross some of the circles twice, once
before and once after noon.
Taking these crossing points in pairs, find the
mid-points. They should align with one another
and with the point perpendicularly below the hole.
This is your north-south line.
Verdict: Fine if you are Cassini; I haven't tried it!
8. Using Stars
A technique used by the surveyors responsible for
digging railway tunnels in the 19th century was to
follow a circum-polar star round the celestial pole
and note its most easterly and most westerly points.
Half-way between is due north.
This sounds easy in theory but needs the right kit,
the right kind of experience, a clear night, thermal
clothing and considerable skill. I cannot imagine
how they avoided freezing to death in the U.K. winters!
Verdict: Not for beginners
Incidentally, real walls can be a right pain! They aren't
flat and they aren't vertical and you can easily come to
grief. For large wall dials, a good deal of practical
dialling amounts to a hard slog analysing survey data
and undertaking laborious error analysis, but that's
another story.
Frank King
Cambridge, U.K.
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