# NavList:

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

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Re: The magical maths of Google Maps
From: Gary LaPook
Date: 2015 Oct 8, 03:00 -0700

```
If a surveyor started at the equator and walked straight north, setting up his
theodolite from time to time to determine his latitude, when he got to the
place where he determined that his latitude was exactly one degree north when
he then looks at the distance he measured with his chain he will find that he
walked 59.701 nautical miles not the expected 60 NM exactly.
Gl

------------------------------
On Thu, Oct 8, 2015 2:12 AM PDT Gary LaPook wrote:

>I think I can see what your are missing. When we learn celnav we work with
the assumption that the earth is a perfect sphere and a degree on the
surface, as measured at the center of the earth, is everywhere 60 nautical
miles. This assumption is appropriate given the level of accuracy that is
obtainable at sea with celnav. Based on this assumption we also accept that
straight down at our position points to the center of the earth so the
horizon, from which we measure our altitudes, is exactly at right angles from
a line from out feet to the center of the earth. If this were true then, when
we take a noon latitude, we would be determining our geocentric latitude, the
angle between the equator and our position as measured by a person at the
center of the earth. This is the simplified diagram that we have been trained
on.
>However, there are two other types of latitude, geodetic and astronomic.
>What we are actually determining is the last type, the astronomic latitude.
Because of the oblateness of the earth and because of local deflection of the
vertical due to non uniform density, the horizon is not at right angles to a
line from out feet to the center of the earth but is at a right angle to the
local field of gravity as it is deflected from the tangent to the surface of
the oblate earth. As to deflection of the vertical, Frank has posted before
maybe a few tenths of a minute, is not charted so it can not be corrected for
by a navigator, If you could correct for the local deflection of the vertical
then you would be able to determine the geodetic latitude, the latitude as
measured from a horizon that is tangent to the surface of the oblate earth at
our position but because the deflection of the vertical is very small we
ignore it (in celnav) and treat our astronomic
latitude as though it were geodetic latitude. Why do we do this?
>Because charts show the positions of places on earth by their geodetic
latitude, not their geocentric latitude. That is the reason for the
meridional parts, to allow creating a chart in which the latitude determined
with a sextant will correspond to the latitude of the shoreline. (ignoring
deflection of the vertical.) That is the reason that the length of a degree
on latitude varies because it is based on the oblate earth (the Clarke
spheroid of 1866 in Bowditch). If, instead, the shoreline was placed on a
chart with a gratical  of geocentric latitude then it would be off by about
11 minutes of latitude at latitude 45 north and south so you would be
crashing into reefs all the time.
>So forget the simplified diagram of geocentric latitude, now you know the true story.
>gl      From: Lu Abel
> To: garylapook---.net
> Sent: Wednesday, October 7, 2015 12:07 PM
> Subject: [NavList] Re: The magical maths of Google Maps
>
>I have no doubt of these numbers, Gary -- and at the same time they seem
counterintuitive.   If I were to fit a perfect sphere to the curvature of the
earth at the equator it would be - as you pointed out earlier - about 11 nm
greater in diameter than a perfect sphere that matched the curvature of the
earth at the poles.  A greater diameter should imply a greater surface
distance for one degree than for a smaller diameter.   What am I missing?
>
>
>
>      From: Gary LaPook
> To: luabel{at}ymail.com
> Sent: Tuesday, October 6, 2015 10:42 PM
> Subject: [NavList] Re: The magical maths of Google Maps
>
>That made me curious so I turned to table 6 of Bowditch which gives the
length of a degree of latitude  for each degree from 0 to 90. This length
varies from 59.701 NM at the equator to 60.313 NM at the pole based on the
Clarke Spheroid of 1866. I added all the distances up and found that half
way, at 45 degrees of latitude the distance is 8.3 NM short of the 2,700 NM
it would be on a spherical earth and then the remaining distance to the pole
is 9.2 NM greater so the total I came up with was 5,400.5915 NM but I assume
the discrepancy from the perfect 5,400 NM is probably due to rounding. So to
test Google Earth it doesn't do to measure the distance from the pole to the
equator since you will get 5400 either way but you should measure from the
pole to 45 degree latitude.
>gl
>gl
>
>  From: Frank Reed
> To: garylapook---.net
> Sent: Tuesday, October 6, 2015 10:12 AM
> Subject: [NavList] Re: The magical maths of Google Maps
>
>David Pike, you wrote:
>"From this I conclude that the Google Maps projection is close to standard
Mercator’s.". You’ll find you’ve got a “Globe” presentation, which you can
tilt until the line between Boston and London is straight while the distance
remains constant. You would appear to have hit the view in with the plane of
the great circle."
>Yes, that's right. The only thing you have to double-check with an
earth-based mapping product is that they are not being too clever by
including ellipsoidal corrections to the distance calculation. If that
happens then it's not quite a great circle but awafully close. I haven't
checked, but I assume that Google Maps products use the standard spherical
great circle calculation.
>Frank Reed
>Conanicut Island USA
>
>View and reply to this message
>
>   View and reply to this message
>
>
> View and reply to this message
>
>
>
>View and reply to this message:
```
Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)