Latitudes again!

In my above post I forgot to include a formula by NGS for calculating the quadrant distance.

In USC&GS report of 1881, Appendix #12 there is an article "ON The Length of a Nautical Mile" by J.E. Hilgard
On page 355 NGS gives: Length of quadrant of the meridian;
1/4 pi (a+b) [ 1+1/4 (a-b/a+b)^2 + 1/64 (a-b/a+b)^4 + ...] very accurate.

JOHN NOLTON

So, let me get this right. I need to take your calculations to Michigan DOT and have all these signs corrected to "Almost Half..."

Ramanujan was a genius. He is compared to Euler and Jacobi often.

My data run through an iterative process.
I had 0.000 000 5 left over.
So call me a slacker for not doing another iteration.

My formulae.

Then there is geocentric or geodetic? Is "way" a unit of distance? Half way = way/2?

Scott McLain, post: 359580, member: 6271 wrote: So, let me get this right. I need to take your calculations to Michigan DOT and have all these signs corrected to "Almost Half..."

"more or less". You always use "more or less". "å±" if you're low on room.

Scott McLain, post: 359580, member: 6271 wrote: So, let me get this right. I need to take your calculations to Michigan DOT and have all these signs corrected to "Almost Half..."

And Oregon. Possibly other states as well.

But that's all along the ellipsoid, what about the real globe..............

1st. No one has to go to any Dept. and say move your sign. Its close enough for City work/State work.

For Scott Zelenak: What you have done is take a 16 pound hammer and your computer to solve a very simple problem that can be solved using
a 2 ounce pencil and just a little brain power. In all the mapping books and other papers on Geodesy that I have read I do not see them saying that this problem is done by iteration; because its NOT the easy way. You did get the solution and that counts for something.

JOHN NOLTON

This one is less accurate...lol Nova Scotia style

Well, John I used a variant of DeLambre's 217 year old formula for solving ellipsoidal distances.
We used to do it with the TI-55 calculator but it's slightly quicker with excel.
When I want to learn something I prefer the formulas to tables or software.

If I want the answer I'll use the software. If I want the knowledge I'll work it out.

So if a 217 year old formula is a sixteen pound hammer then, oh well, guilty as charged.
And sometimes the point isn't to get the correct answer to ten decimal places, it's to inspire critical and logical thought in the generation that has the unenviable misfortune to replace us.

Wait now...isn't the earth flat?

About 10 miles north of the 45th Parallel by my crude method. Used google earth to measure in miles from 0E, 0N to 0E, 45N east of Bourdeaux, France. This was 3097 miles. From 0E, 90N to 0E, 45 N measured 3117 miles. Difference of 20 miles. So it must be about 10 miles to the north to be equidistant. Give or take a few smoots.

Mike Mac, post: 359789, member: 2901 wrote: Wait now...isn't the earth flat?

Clearly it isn't flat. I've driven over mountains that are definitely not flat! 😀

Where is halfway equator to pole?

In reality it's a fair and good question. Either as a bar bet, or a genuine test question. As we can see there are a lot of qualifiers, technical considerations, and math. There is the casual answer, and ultimate resolution. I read a really good account of the answer to that very question: French Academy of Science, circa 1792. Pierre M̩chain and Jean-Baptiste Delambre tried to do just that by measuring a portion of a meridian. And they learned just how hard that is to do. And it took seven years and several additional campaigns; nearer the pole, across the equator, as well as across France. Even Mason/Dixon's Delaware - Maryland border survey data was included.

And as we all (should) know, the meter was conceptualized as a cardinal fraction of the distance from the equator to the pole. And that was hard then, and relevant today.

So calculate it, estimate it, qualify it. It's as fun as it is educational. Bring on the hammers, 64 bit software, slide rule, or 8th grade text book.

And when you have an answer, the next question: is that true for astronomic? Geographic, geodetic, or geodesic? Can you you get there with GPS? or do you need a Zenith sector? did you account for deflection of the prime vertical? Geodesics are complicated and we get with murder these days with our software and GPS receivers. Try retracing latitudes and meridians of the western states boundaries. GPS or astronomic?

And what if the question was to monument the mid point of the California Utah border? That's real world.

There is plenty of technical questions. Well worth the thought experiment. Just ask Johann Gauss.

Good book on the subject: The Messure of All Things, by Ken Alder. A must read to appreciate GPS and classical methods.

:gammon: I meant Utah Nevada border.

Larry Scott, post: 359894, member: 8766 wrote: And what if the question was to monument the mid point of the California Utah border? That's real world.

Hmmm...That would be the [very] OLD border (pre 1861).

B-)
Loyal

Larry Scott, post: 359896, member: 8766 wrote: :gammon: I meant Utah Nevada border.

Which one?

1861?
1862?
1866?

Theoretical ("deed")?
As surveyed and monumented?
Grid or Ground?

Sign me up, sounds like a blast!
🙂
Loyal

So, if the POB of an existing parcel was the mid point of the Nevada Utah border? Would that be by latitude? Distance? Slope chaining?

Could you defend a different distance for the north and south halves? if by latitude?

Could you walk to it with RTK?