This should be a no brainer but..

I've asked this questions numerous times: What is earth's curvature
per mile?
I've gotten numerous equations, and none of the respondents end up
agreeing with each other, and their answers are as varied as their
mailing addresses!

Another issue is answers in metric - I am mathematically challenged
and cannot convert answers from KM to Miles to save my life!

Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

Please, no more formulae. All my eyes see is Cyrillic.

Thanks,

-CC

There is no single number for the earth's curvature per mile, in the form
that you want.

The earth might fall (say) 1 inch in a mile. Doesn't mean it falls 2 inches
in two miles or 2000 inches in 2000 miles or 1/100 of an inch in 1/100 of a
mile - its not a "linear relationship".

Roughly, if you measue the fall over some distance, then measure the fall
over twice the distance, the fall will be about 4 times as much. The fall
over 10 miles will be 100 times as much as the fall over 1 mile. It goes as
the square of the distance you measure it over.

Heres another example. The earth is about 10,000 miles across. Imagine a
point 5,000 miles away from where you are now, half way around the world. If
you draw a straight line connecting you with that point it would slope down
(underground) at about a 45 degree angle. But this doesn't mean the water in
your bath slopes at 45 degrees. The rate changes as you measure over
different distances.

So there isn't a single number, its a formula.


"ChrisCoaster" wrote in message
om...
I've asked this questions numerous times: What is earth's curvature
per mile?
I've gotten numerous equations, and none of the respondents end up
agreeing with each other, and their answers are as varied as their
mailing addresses!

Another issue is answers in metric - I am mathematically challenged
and cannot convert answers from KM to Miles to save my life!

Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

Please, no more formulae. All my eyes see is Cyrillic.

Thanks,

-CC

There is no single number for the earth's curvature per mile, in the form
that you want.

The earth might fall (say) 1 inch in a mile. Doesn't mean it falls 2 inches
in two miles or 2000 inches in 2000 miles or 1/100 of an inch in 1/100 of a
mile - its not a "linear relationship".

Roughly, if you measue the fall over some distance, then measure the fall
over twice the distance, the fall will be about 4 times as much. The fall
over 10 miles will be 100 times as much as the fall over 1 mile. It goes as
the square of the distance you measure it over.

Heres another example. The earth is about 10,000 miles across. Imagine a
point 5,000 miles away from where you are now, half way around the world. If
you draw a straight line connecting you with that point it would slope down
(underground) at about a 45 degree angle. But this doesn't mean the water in
your bath slopes at 45 degrees. The rate changes as you measure over
different distances.

So there isn't a single number, its a formula.


"ChrisCoaster" wrote in message
om...
I've asked this questions numerous times: What is earth's curvature
per mile?
I've gotten numerous equations, and none of the respondents end up
agreeing with each other, and their answers are as varied as their
mailing addresses!

Another issue is answers in metric - I am mathematically challenged
and cannot convert answers from KM to Miles to save my life!

Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

Please, no more formulae. All my eyes see is Cyrillic.

Thanks,

-CC

ChrisCoaster wrote:

I've asked this questions numerous times: What is earth's curvature
per mile?
I've gotten numerous equations, and none of the respondents end up
agreeing with each other, and their answers are as varied as their
mailing addresses!

Another issue is answers in metric - I am mathematically challenged
and cannot convert answers from KM to Miles to save my life!

Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

Please, no more formulae. All my eyes see is Cyrillic.

1) World Geodetic Survey 1984 (WGS84) fits the surface of the Earth
to a 360-degree polynomial. Solve for your desired patch.

2) Assume the Earth is a sphere with average radius 6378 km. Solve
for the surface curvature to get a decent approximation.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

ChrisCoaster wrote:

I've asked this questions numerous times: What is earth's curvature
per mile?
I've gotten numerous equations, and none of the respondents end up
agreeing with each other, and their answers are as varied as their
mailing addresses!

Another issue is answers in metric - I am mathematically challenged
and cannot convert answers from KM to Miles to save my life!

Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

Please, no more formulae. All my eyes see is Cyrillic.

1) World Geodetic Survey 1984 (WGS84) fits the surface of the Earth
to a 360-degree polynomial. Solve for your desired patch.

2) Assume the Earth is a sphere with average radius 6378 km. Solve
for the surface curvature to get a decent approximation.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

Chris Florida is very flat.Still it has to curve down towards its
horizon that we can put as noticeable 12 miles where we are standing.
hmmm standing creates a problem. The higher up your eyes are the further
away goes the horizon. I think my pet cockroach "Big Moe" never worried
about the Earth's horizon. Bert

Chris Florida is very flat.Still it has to curve down towards its
horizon that we can put as noticeable 12 miles where we are standing.
hmmm standing creates a problem. The higher up your eyes are the further
away goes the horizon. I think my pet cockroach "Big Moe" never worried
about the Earth's horizon. Bert

On 26 Jun 2004 07:49:25 -0700, (ChrisCoaster) wrote:


Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

The answer to that specific question, using a circle of 7920 mile
diameter and chord of length one mile is:

The between the chord and circle is:


0.0000315656566914 miles


0.1666666673305920 feet


2.0000000079671040 inches

--Lynn

On 26 Jun 2004 07:49:25 -0700, (ChrisCoaster) wrote:


Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

The answer to that specific question, using a circle of 7920 mile
diameter and chord of length one mile is:

The between the chord and circle is:


0.0000315656566914 miles


0.1666666673305920 feet


2.0000000079671040 inches

--Lynn

"Lynn Kurtz" wrote in message
...
On 26 Jun 2004 07:49:25 -0700, (ChrisCoaster) wrote:


Now, shouldn't it be as simple as taking a slice through a 7,920 mile
diameter circle(creating something called a "chord" I think), and
measuring the highest point of that chord?? In our case, the straight
line slices through the cirle between two points a mile apart on that
circle. What the HECK is the maximum height of the segment of that
circle between the ends of that line?

The answer to that specific question, using a circle of 7920 mile
diameter and chord of length one mile is:

The between the chord and circle is:


0.0000315656566914 miles


0.1666666673305920 feet


2.0000000079671040 inches

--Lynn



Makes my estimate in the other thread of 1" in a mile look pretty good.

I must stress for the OPs benefit that 2" in 1 mile doesn't mean 20" in 10
miles - its 200" (goes as the square). And the fall in 0.5 miles isn't half
of 1 mile, its one quarter. So unless you are measuring over exactly one
mile, this 2" is no use.