On 2007 Mar 5 , at 2:51 PM, Michael Payne quotes the Jeppson
company's response to his query:
(Regarding the providing of) equivalent
information to the scale indicated on our enroute, area and
terminal charts
e.g. 1"=20NM / 1:1.472.441 . As you can see it is not very helpful
to show the scale as both values ...
That phrase, "As you can see ...", is insulting to my intelligence.
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!
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").
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
==========================
P.S.
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
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 did this by calculating how many inches there are in 20 NM. (It is
1 455 024). I started with 20 NM converted that to miles, converted
that to feet and converted that to inches.
If the map length of 1 inch purportedly represents 1,455,024 inches
on the ground, that is a
ratio of 1 inch to 1,455,024 inches or simply
1:1.455,024.)
(I can show that my calculated figure has a precision of 7
significant figures or +/- 0.000 07% but, when used to describe a map
scale, which I don't believe is that precise, this should be rounded
to about 1:1,472,000, just as the Jeppson's figure should have been
rounded.)
