# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Make a UPS?**

**From:**Gary LaPook

**Date:**2014 Oct 19, 14:29 -0700

If you are a perfectionist you would use Mmeridional Parts found in Table 5 of Bowditch. These are simply the number of nautical miles from the equator to a particular latitude, latitude listed to the nearest 0.1 NM and takes into account the oblateness of the Earth. For example 34 latitude would be 2,040 NM from the equator if the Earth was a perfect sphere. Table 5 gives it as 2158.4 NM. So to construct a perfect Mercator plotting sheet, for example covering two degrees of latitude, 33 to 35, and two degrees on longitude we look up the Meridional parts for 33 and 35, and subtract to find the number of NM between those two parallels. 2230.0 for 35 and 2086.8 for 33 makes a difference of 143.2 NM. Since this distance represents 120 minutes of latitude we divide 120
by 143.2 to find the ratio of parallels to degrees of longitude at a mid-latitude of 34. 120/ 143.2 = 0.838 so we place the lines of longitude at this ratio to parallels (if we start with parallels spaced 60 NM apart which is the normal way to do it. If you, for some reason wanted to start with longitude lines then you would place the parallels at the inverse of this ratio 1.193.) So along the mid latitude of 34 ,one degree of longitude will equal 50.279 NM.

But that is the hard, perfectionist's, way to do it. In fact, the ratio of the spacing of meridians to parallels is very closely approximated by the cosine of the latitude. So doing this simpler and much more common way, we take the cosine of the 34 mid-latitude, 0.829 which only differs from the
meridional difference ratio of 0.830 by only 0.009 so we would plot the meridians 49.742 NM apart a difference of less than 1%.

Or we could use Table 6 of Bowditch which gives the spacing of meridians and parallels. For 34 degrees on degree of latitude is actually equal to 59.891 NM while a degree of longitude is 49.885 a ratio of 0.833 so if spacing then parallels at exactly 60 NM then the Meridians would be spaced at 49.976 NM, only 1/2% difference than using the simpler cosine of the latitude method.

The easy was to construct the plotting sheet using the cosine method is to draw parallels equally spaced to represent 60 NM and one horizontal line for the mid-latidude. Then from the intersection of the mid-latitude and the mid-longitude draw a line upward from the mid-latitude line by the number of degrees of mid-latitude. Measure along this angled line by 60 units of latitude (60 NM) and draw in the meridian form this point vertically and this will space the meridian at the cosine of the mid-latitude times 60 NM. This is exactly what Hakel's method shows.

gl

**From:**Peter Hakel <NoReply_PeterHakel@fer3.com>

**To:**garylapook@pacbell.net

**Sent:**Sunday, October 19, 2014 8:51 PM

**Subject:**[NavList] Re: Make a UPS?

About two years ago NavList member Greg Rudzinski came up with a way to accomplish this task using my T-Plotter, see:

Plotting sheet construction with T-Plotter

Plotting sheet construction with T-Plotter

and links therein.

Peter Hakel

Peter Hakel

**From:**Samuel L <NoReply_SamuelL@fer3.com>

**To:**pmh099---.com

**Sent:**Saturday, October 18, 2014 5:41 PM

**Subject:**[NavList] Make a UPS?

Can you tell me how to make a UPS from a blank sheet of paper and properly scale Longitude and latitude (Mercator)?

Thanks,

Sam