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Artist building a globe out of wood!

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#1
gregsd

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Just came across this posting on Google Groups - sci.geo.cartography but the guy needs some help.

Hello,
I've spent the last three months building a 23" diameter sphere out of
cherry using nothing but my tablesaw, jig saw, and sander.  The next step is
to carve the major (and some minor) land masses into its surface.  I thought
an interrupted sinusoidal map would do the trick, simply cutting it out and
laying it onto the surface of the sphere for marking.  However, the lobes of
the map are not straight-edged.  Meaning, when the map closes around the
sphere, the lobes will not meet edge to edge.
I know very little about cartography, obviously, and would appreciate any
suggestions.  If you would like to see the sphere, just go to:
Link
Thanks very much,
-Mac


Certainly looks an interesting project and I'd like to see the finished article. If anyone has any suggestions but isn't registered on Google groups then I'm willing to post a reply.

Greg.


Greg Driver

GIS Analyst
MapInfo User...!

#2
woneil

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This is the reply I sent, which I hope will clarify matters for him:

Your sphere is beautiful and impressive.


Your notion of using an interruppted sinusoidal projection puts you in
good company, as globes have been made that way for centuries. An
interrupted polyconic can give slightly better accuracy, but not enough
to matter for your purposes I should think. What is important is to
have enough gores to permit each to lie flat without too much
stretching. Of course it all has to be done with precision, but you
certainly seem to have enough talent for that!


I'm not sure why you would think that the gores should have straight
edges. Consider the following: If the gores had straight edges then
they would be half as wide at 45 deg latitude as at the Equator. Yet at
45 deg latitude the circumference of the Globe is actually 71% as great
as it is at the Equator. Not until 60 deg latitude is the Globe's
circumference 50% as great as at the Equator. Your sphere has a
circumferance at its equator of 72.3". If you were to use a projection
with 24 lobes then each would be just about 3" wide at the Equator.
They would need to taper slightly to 2.6" at 30 deg latitude, to 2.1"
at 45 deg, to 1.5" at 60 deg, and finally to 0 at 90 deg.


Good luck,
Will O'Neil


His woodworking is certainly of a high order.
Will O'Neil
Author and amateur cartographer

http://analysis.williamdoneil.com/w.d.oneil@pobox.com

#3
mdenil

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Here is a description from Snyder's Flattening the Earth (pp 42-3) of one way this was done.
[quote]
a straight line two and a half times the length of the equator of the proposed globe is divided into thirty equal parts. The middle twelve parts constitute the equator itself. Circular arcs are struck through each end of these twelve parts, with the other point of the circinus or compasses ten parts in distance along the original line, in a direction such that the arcs intersect to form twelve gores 30° wide in longitude. This construction makes the meridians 4-6% longer than their true length relative to the equator, but formation into a globe would alter this disparity.
[...]
The central meridian of each gore (whether shown or not) is evenly divided for latitudes at the same spacing used to set off meridians of the same degree interval along the equator. The parallels of latitude are apparently non con-centric, circular arcs with radii that appear to be the same as the length of the element of a cone tangent to the globe at the particular latitude. If so, this is a prototype of the polyconic projection of the nineteenth century.
[unquote]

This is for gores that run pole to pole, usually with a small patch on the poles to cover the hood ends. One can also make the gores in two sets centered on the poles and splaying like an asterisk. Globes gored like this often have a tape line applied for the equator.

M.Denil


[the passage from Snyder in full]
Gore maps, consisting of strips bounded by two meridians usually 10° to 30° apart and either bounded by the equator or extending pole to pole, were primarily drawn as sections for globes, beginning in the early sixteenth century. A number of gore maps were used in atlases and thus became flat map projections in their own right. Waldseemiiller prepared a world map consisting of twelve 30°-wide gores, with a 10° graticule, in 1507 (reconstructed in fig. 1.33), the year his modified conic world map was printed (Schwartz and Ehrenberg 1980, 26).
Glareanus described one type of construction of a set of globe gores (fig. 1.34) in Poetae laureati de geographia liber unus, first published in 1527 (Nordenskiold 1889, 74-75). According to his description, a straight line two and a half times the length of the equator of the proposed globe is divided into thirty equal parts. The middle twelve parts constitute the equator itself. Circular arcs are struck through each end of these twelve parts, with the other point of the circinus or compasses ten parts in distance along the original line, in a direction such that the arcs intersect to form twelve gores 30° wide in longitude. This construction makes the meridians 4-6% longer than their true length relative to the equator, but formation into a globe would alter this disparity.
How Glareanus drew meridians and parallels within the gores is not clear. From the appearance of contemporary gore maps, other meridians, if shown, are circular arcs equally spaced along the equator, except for a straight central meridian (if shown) on each gore. The central meridian of each gore (whether shown or not) is evenly divided for latitudes at the same spacing used to set off meridians of the same degree interval along the equator. The parallels of latitude are apparently noncon-centric, circular arcs with radii that appear to be the same as the length of the element of a cone tangent to the globe at the particular latitude. If so, this is a prototype of the polyconic projection of the nineteenth century. The latter, however, does not use circular arcs for meridians, and the concept of tangent cones does not seem to appear in the literature of the sixteenth century.
Some other gore maps are joined at the poles instead of the equator, such as sets of gores 10° of longitude wide in northern and southern hemispheres on a 1555 map by Antonio Floriano and a 1542 map by Alonso de Santa Cruz (1505-1567).102 One map with much larger gores, ca. 1550, has four 60° gores plus one of 120° with horizontal straight parallels.103 At first glance, the map resembles an interrupted sinusoidal, but the meridians are circular arcs, not sinusoids.




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