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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Circle charts
From: Richard M Pisko
Date: 2009 Feb 04, 00:19 -0700
From: Richard M Pisko
Date: 2009 Feb 04, 00:19 -0700
On Sat, 31 Jan 2009 13:34:18 -0700,wrote: > I attached another picture that shows grid of circles on the first page > and set > of scales for same stations on the second page. > Oh my, those grids are pretty! Shows where the sextant must be located for good intersections, and gives an idea on how carefully the sextant readings must be taken, too, for a given ground accuracy. > Also, instead of printing scales on map, how about having several > T-shaped > rulers, short horizontal edge having 2 marks for stations and long > vertical > edge having graduated ticks for centers. Align marks with stations and > long > edge will show location of a center. It is even more work, plus you have > to > have special ruler for each different distance between stations, but the > map > itself remains completely uncluttered. I like that concept too; but in practice I would be required to carry a large draughting table, *and* worry about maintaining the alignment of the graduated T squares. I think I would prefer a penciled T, or perhaps a low tack adhesive on the back of the paper T square, similar to that used in "Post It" note pads. > Same approach may work with grids of circles: if you print them on > transparency > then it is possible to overlay only those 2 that you currently use, so > that grids > from unused pairs are not in the way. For the real world base stations, and the various scale distances and offset required to generate each circle, I believe that would work. I think only one chart would be saved though, if working along a riverbank using succeeding pairs of what you called "bases". The main field problem would be to align the mapped shore base points with the "Generator" base points of each overlay, and to keep them aligned. Using a transparent chart combining three base points would allow better alignment, and it still might be possible to use a pair of these triplet charts if the observation of one of the normal base points is blocked. This concept of one circle chart for each seemingly useful pair of base points would be even more desirable if the shore station points were set a uniform distance apart, so only one circle (and duplicates) would be required; but this is unlikely. But going back to your purpose-drawn circle chart from three base points: if a small rectangle of the proper size and location were to be electronically "cut" from this chart, then enlarged and mounted at the top edge of the A2 sheet; this section could be used for quite rapid plotting of the observation points at a large scale. No need to prick through the overlay, a little circle on the overlay and one or two trials on the sheet below will mark the position nicely. I think the position of the A2 sheet would have to be premarked on the large circle graph before cutting out that section, however. I belive this must be similar to some of the circle charts Nicol�s used for dredging operations on the Niger. As you say, pairs of the transparent overlays could be used on the original topographic chart without damage to the chart. But if I have to use the large topo map *for a small number of plottings*, I think a traditional station pointer, or a transparent three layer station pointer would be of comparable accuracy with less preparation time, and still be of minimal cost. One layer a full circle with an index line and degree scale ticks, having a pair (clockwise and counter-clockwise) of markings at a radius of about twelve inches, the other parts to be two sectors with only an index line on a transparent vane . . . similar to the Knight transparent station pointer, but with the degree scale circle enlarged so as to be able to pick out tenths of a degree, or preferably ten minute subdivisions. Perhaps a vernier could be added to the two smaller indexing sectors to get accuracy comparable to a plastic sextant. A good metal station pointer has a vernier, can probably be read to a minute of arc or better, and the legs fold out to cover more than a foot distance on the chart; but the cost is not small. It seems to me that Computers (of the modern electronic kind) are what makes this enlarged, oriented and "positioned" transparent circle chart practicable. > If you are going to actually try this in real world, I volunteer to make > either > grids or scales for your actual distances between stations in a form of, > say, PDF file. Would that help? I appreciate your offer, and I will ask if I get stuck; but I'll be trying to work out a series of scales or grids printed out on a Google Earth image of a small area. I have had a problem with Google Earth and my computer for the past couple of months, but I can get some pretty detailed images (somewhat out of date) from a local source. All I would have to do is print the scales to the right size and mount the whole onto a larger background paper so as to be able to draw the circles. If I can use a transparent partial grid over a good satellite image, that would be near to ideal, I think. The chart and a light plastic sextant would be very easy to carry. It's early days so far: the temperature is still below freezing, and the snow drifts have not disappeared. I am now a fair weather surveyor only. :-) > I used formula > x=h/tg(a/2)-h/sin(a) > where a is observation angle, h is HALF of a distance between stations > and x -- > distance from midpoint between stations to a center of a circle. > It is a difference between h/tg(a/2), which is distance from midpoint to > the > farthest point on a circle, and h/sin(a), which is radius of a circle. Thank you for the information. > Whether or not it is equivalent to what you wrote, I do not know. No, I was wrong on two things. I wrote h/tg(a) instead of h/tg(a/2) using your notation. My careless mistake, sorry; I know better. Second: I had not thought ahead far enough, and had not subtracted the radius from that far point on the perpendicular bisector. Manually, from what I did, I would have had to make a trial and error approach with the compass to find the proper radius and center. In setting up a computer drawing program for the circles, I would have had to continue to your more complete formula. Again, your (snellius-grid2.pdf) does look good, even printed out in just black and white. Is the switch in circle spacing from 10 minutes to 30 minutes at 15 degrees, and then from 30 minutes to 10 degrees at 50 degrees a manual setting? The way this spacing changes when the lines get too close together for printing must be an automatic setting in GhostScript . . . or is it? All these choices are what make the end product individual. I notice you have the circle spacing changing at different angles on the "T scale" construction: 5 minutes from 4 to 6 degrees, 10 minutes from 6 to 10 degrees, 30 minutes from 10 to 20, 1 degree from 20 to 35, and finally 5 degrees from 35 to 90. Interesting, and looks like a more uniform spacing. Thanks again, -- Richard . . . Using Opera 9.2.4 after the "Dog" died --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---