On Monday 05 March 2007 20:28, Bill Hooper wrote: > I do NOT see > that "it is not very helpful". If correct it allows me to see > that 1 mm on the map represents 1.472,441 km or 10 mm =14.724,41 km > (if one does not round off sensibly). That strikes me as very > helpful. It's easier than finding how many nautical miles is > represented by 2 3/8 inches!
The people who use these maps probably have an engineer's scale. This is a stick with a sort of triangular cross section and six rulers with different ratios printed on the sides. They ought to be easily findable in metric but I haven't seen one. When I measure a map, I use a millimeter ruler and a calculator (usually bc). I suggest that the maps be made in round number scales, and for those who want to measure them in nautical miles, scales be made for that purpose. > I do NOT see > how they got that figure of 1:1.473.441. I get 1:1,455,024. > However that is a detail that I will relegate to a P.S. which you may > read if interested. > > I DO see > that the person who calculated the equivalent ratio didn't know > much about rounding off values to a degree appropriate for the > precision of the original value. Now I will admit that I do not know > the precision with which their maps are drawn. However, their figure > of "1:1,472,441" (with SEVEN digits) is apparently given to a > precision of +/- 0.000 07% (about 1 part out of 1,470,000). > I would be surprised if their maps could be that precise. Assuming a > more realistic precision, say 0.1%, then the ratio should be given > as 1:1,472,000. It would not be too far off > to call it 1:1,500,000. Although the 1:1,500,000 figure may be a bit > imprecise, it is certainly as easy to use (easier than the original > which was "1 inch:20 nautical miles"). One pixel on a plotter is 25 µm. Assuming that the chart is A0 (1189*841), there are 47560 dots on the long side. But when I'm scaling a distance off a map, I can't eyeball it finer than 100 µm. So I think that the precision should be set to 0.01%. > I also question the value of the ratio itself. I get 1:1,455,024 > which probably should be rounded > off to 1:1,455,000. That's not very close to their value of > 1:1,472,441 even if rounded to > 1:1.472,000. > > Here is how I find my value: > I found the figure of 24,901.55 miles for the equatorial > > circumference of the Earth at the "About:Geography" web site: > > http://geography.about.com/ > > and more specifically at this page: > > http://geography.about.com/library/faq/blqzcircumference.htm You should know this in metric, at least to the nearest megameter; it is 40 Mm by the original definition, assuming the meridional circumference equals the equatorial, which it doesn't. > I used this, along with the definition of the nautical mile which is > "1 NM = distance along the Earth's equator equivalent to a > longitudinal change of one minute of arc". The circumference of the > Earth is distance 24,901.55 miles. There are 360 degrees in the > entire circumference and 60 minutes in each degree. That means there > are (60 x 360) or 21,600 minutes in the entire circumference. From > the definition, that means > that the Earth's circumference must be exactly 21,600 NM. therefore, > 21,600 NM = 24,901.55 miles > or > 1 NM = 1.148 219 miles. > > Using that figure to interpret the " 1 inch = 20 NM " scale in the > message from Jeppson, I find the equivalent ratio to be > 1:1,455,024 > not the value of > 1:1,472,441 > Jeppson claims. I used two different values for the nautical mile. Using the current definition, 1852 m, I get 1:1458268. Using 100/54 km, which is what it would be if both were defined in terms of the same circumference of the earth, I get 1:1458151. Multiplying the current definition by 21600 yields 40.0032 Mm for the circumference. phma
