# NavList:

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

**Fwd: Lehmann's Rules and surveying**

**From:**Peter Fogg

**Date:**2007 Mar 17, 18:39 +1100

This message came directly to me, rather than to the group, which I assume was not intended, so have forwarded to the NavList.

Hope this is OK with you, Richard. It does not seem to be in the nature of a personal message.

---------- Forwarded message ----------

From:

Date: Mar 17, 2007 4:36 PM

Subject: Lehmann's Rules and surveying

To: peter.fogg---.com

On Thu, 15 Mar 2007 23:30:01 -0700, P F <peter.fogg---.com > wrote:

> Lehmann's Rules were used by surveyors, mainly for orienting the plane

> table

> (essentially a drawing board mounted on a tripod).

>

I'm glad that you mentioned that analogy, as I had been thinking that way

for some time. However, no analogy is perfect.

Note that even in the standard three point resection problems there are

four cases:

1. The true location is within the great triangle formed by the three

reference objects

2. The true location is outside of the great triangle, but within the

great circle running through the three reference objects

3. The true location is on the Great Circle (the indeterminate case)

4. The true location is outside the great circle.

Only in case "1." will the true location be found inside of the little

triangle on paper (cocked hat) formed by sighting and drawing with a

misaligned table (systematic error).

Case "3." will always show as one of many perfect intersections on the

Great Circle no matter what the table orientation, so find some other

reference objects or change the plane table setup location. You could try

the Italian method instead, which will show the c-B and a-B intersection

(x) to lie right on top of the b point on the paper.

Italian method, three steps: From left to right on the ground A, B, C.

On the paper, a scale plot of the objects called a, b, c. For the

indefinite case, assume you set up on P very close to the fourth corner of

a square A-B-C-P. Place the alidade on "c" and "a", pivot the table so

the alidade and table rotate together, until the alidade now points

c-a-A. Lock the table. Rotate the alidade only about the point "c", and

draw a line from "c" toward B.

Set the alidade in the opposite direction compared to step one, so as to

line up with "a" to "c". In step two, pivot the table so the alidade will

line up a-c-C and lock the table. Pivot the alidade about the point a on

the paper so it points to B on the ground and draw a line from c toward

B. The two lines, c-->B and a--> B will intersect at a point "x" on the

paper.

Step three: Draw a dotted line through x and b on the paper, set the

alidade along this line, release the table clamp and point the alidade

aligning x-b-->B (or perhaps b-x-->B) on the ground. The table is now

properly oriented, so resecting from A-a->p and C-c->p will give your true

position "p" on the paper and "P" on the ground. But, if you are on the

"Great Circle" along with A, B, and C; point "x" will land nearly on top

of "b", and it will be obvious that it is impossible to orient the table

with any accuracy in step three, and thus "p" cannot be found.

Generally, fairly good intersection angles can be obtained if you chose

reference objects and set up such that you are closest to the middle

object . . . but all this is for mapping, not navigation. You (correctly,

I think) mentioned the stars could be thought of as being all at the same

distance.

--

Richard . . .

Using Opera's e-mail client since Dialog, "the Dog", died.

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Hope this is OK with you, Richard. It does not seem to be in the nature of a personal message.

---------- Forwarded message ----------

From:

**Richard**<rmpisko1{at}telus.net>Date: Mar 17, 2007 4:36 PM

Subject: Lehmann's Rules and surveying

To: peter.fogg---.com

On Thu, 15 Mar 2007 23:30:01 -0700, P F <peter.fogg---.com > wrote:

> Lehmann's Rules were used by surveyors, mainly for orienting the plane

> table

> (essentially a drawing board mounted on a tripod).

>

I'm glad that you mentioned that analogy, as I had been thinking that way

for some time. However, no analogy is perfect.

Note that even in the standard three point resection problems there are

four cases:

1. The true location is within the great triangle formed by the three

reference objects

2. The true location is outside of the great triangle, but within the

great circle running through the three reference objects

3. The true location is on the Great Circle (the indeterminate case)

4. The true location is outside the great circle.

Only in case "1." will the true location be found inside of the little

triangle on paper (cocked hat) formed by sighting and drawing with a

misaligned table (systematic error).

Case "3." will always show as one of many perfect intersections on the

Great Circle no matter what the table orientation, so find some other

reference objects or change the plane table setup location. You could try

the Italian method instead, which will show the c-B and a-B intersection

(x) to lie right on top of the b point on the paper.

Italian method, three steps: From left to right on the ground A, B, C.

On the paper, a scale plot of the objects called a, b, c. For the

indefinite case, assume you set up on P very close to the fourth corner of

a square A-B-C-P. Place the alidade on "c" and "a", pivot the table so

the alidade and table rotate together, until the alidade now points

c-a-A. Lock the table. Rotate the alidade only about the point "c", and

draw a line from "c" toward B.

Set the alidade in the opposite direction compared to step one, so as to

line up with "a" to "c". In step two, pivot the table so the alidade will

line up a-c-C and lock the table. Pivot the alidade about the point a on

the paper so it points to B on the ground and draw a line from c toward

B. The two lines, c-->B and a--> B will intersect at a point "x" on the

paper.

Step three: Draw a dotted line through x and b on the paper, set the

alidade along this line, release the table clamp and point the alidade

aligning x-b-->B (or perhaps b-x-->B) on the ground. The table is now

properly oriented, so resecting from A-a->p and C-c->p will give your true

position "p" on the paper and "P" on the ground. But, if you are on the

"Great Circle" along with A, B, and C; point "x" will land nearly on top

of "b", and it will be obvious that it is impossible to orient the table

with any accuracy in step three, and thus "p" cannot be found.

Generally, fairly good intersection angles can be obtained if you chose

reference objects and set up such that you are closest to the middle

object . . . but all this is for mapping, not navigation. You (correctly,

I think) mentioned the stars could be thought of as being all at the same

distance.

--

Richard . . .

Using Opera's e-mail client since Dialog, "the Dog", died.

--~--~---------~--~----~------------~-------~--~----~

To post to this group, send email to NavList@fer3.com

To unsubscribe, send email to NavList-unsubscribe@fer3.com

-~----------~----~----~----~------~----~------~--~---