I'd never seen this before

"Mxsmanic" wrote in message
...
John Mazor writes:

So now the tower is 1000' across as well as 1000' high?

The key is the angular size of the object; whether this is vertical or
horizontal matters little.

How many towers are 1000' x 1000' ?

IOW you don't know.

I do know. If it's at least 30 seconds across, it's visible.

And in the specific case cited, the answer would be...?

Show the math for the limits of resolution.

The math is based on the size of cone cells in the retina. It works out to 30
seconds of arc.

IOW you can google on limits of human eye resolution but can't do the math.

And remember, whichever tower you are using,
you must use the narrower dimension, which would be width, not height.

Why?

I was hoping you'd do your usual Anthony evasion on that one.

To keep it in terms that even you might understand, we'll do a thought experiment that
doesn't require any calculations whatsoever.

Let's take your 1000' x 1000' tower and position ourselves at the distance where it is
just barely visible at the limits of resolution for the human eye. We'll ignore curvature
of the earth's suface because you shifted away from that when you introduced the concept
of limits of resolution. We'll also ignore the fact that we ought to be using a round
object because the difference between a diagonal and a diameter is negligible in this
exercise. Since you are conversant in computer speak, let's think of 1000' x 1000' as the
minimum-sized pixel that can be seen at that distance. You can see it only because the
pixel is just above the eyeball's limit of resolution both horizontally and vertically.

Now make it a more realistic "tower" - 1000' high but, say, 200' wide. Can you still see
it? Really? No, but let's not stop there. Make it 1' wide. Can you still see it?
Really? Make it the width of a pencil, and then the thickness of a human hair. Gone,
gone, gone.

Once you decrease the pixel size below the limits of resolution in any direction, you
could no longer can see it. So "whichever tower you are using, you must use the narrower
dimension." QED.

Just for jollies, let's hold a contest on what MadMax's response will be:

1. You're wrong because there's no such thing as a 1000' tower the width of a human hair.
2. Technically, a pixel is defined as...
3. I'm talking about a 1000' x 1000' tower so I'm still right.
4. You still can see the tower in the dimension where it's 1000' because 1000' still is
resolvable at that distance.
5. Introduce an irrelevant factoid to try to change the subject.
6. Complete silence.

wrote in message ...
Mxsmanic wrote:
John Mazor writes:

So now the tower is 1000' across as well as 1000' high?

The key is the angular size of the object; whether this is vertical or
horizontal matters little.

Wrong, it is both the horizontal and vertical.

A simple example shows you to be wrong; from how far away could one
see a 1000' human hair?

IOW you don't know.

I do know. If it's at least 30 seconds across, it's visible.

Wrong.

Show the math for the limits of resolution.

The math is based on the size of cone cells in the retina. It works out to 30
seconds of arc.

Wrong; the math is based on the lens aperature (pupil for eyes) and the
light frequency and gives the theoretical maximum resolution. See any
Google article on resolution.

And the real resolution of the average 20/20 human eye based on research
is 60 arc seconds.

And remember, whichever tower you are using,
you must use the narrower dimension, which would be width, not height.

Why?

Take a 4' piece of sewing thread, hang it on a wall and back away until
you can't see it.

Make the string 8' long and repeat.

Can you now see it from twice as far away?

No.

If you had read the entire Google artical you used to come up with
your answers, you would know why.

Ahh, you beat me to it!

And I had laid that trap every so carefully.

Mxsmanic wrote in
:

writes:

Strange you could't just say that until it was already posted.

Nothing prevented me from saying it earlier. I just thought everyone
already knew. I didn't see a reference to it until I had mentioned
it.


Yeh, right.


Bertie

"John Mazor" wrote in news:nkvfj.30$qV.27@trnddc03:


"Mxsmanic" wrote in message
...
John Mazor writes:

So now the tower is 1000' across as well as 1000' high?

The key is the angular size of the object; whether this is vertical
or horizontal matters little.

How many towers are 1000' x 1000' ?


I've been trying to work in a gag about the comparitve size of his but for
ages on this thread, but I'm just gettign nowhere.

Bertie

John Mazor wrote:

6. Complete silence.




If you get that I demand that everyone add your post as a signature line
to all messages.

"Gig601XLBuilder" wrote in message
...
John Mazor wrote:

6. Complete silence.

If you get that I demand that everyone add your post as a signature line to all
messages.

I humbly accept your encomium. Does anyone know what the Vegas betting line is against
#6?

FWIW, years ago when I started posting here my sig was:

-- John Mazor
"The search for wisdom is asymptotic."

"Except for Internet newsgroups, where it is divergent..."
-- R J Carpenter

I don't know if the Richard Carpenter who posts here is the same chap, but he kindly gave
me permission to add his witty retort to my initial observation. I may revive it since
nothing has changed in the ensuing years except the names of some of the divergers.

"Tina" wrote in message
...
The equation in error was written as

sqrt (R^2 + d^2) = R + h

I demonstrated this is an error by setting R and d to 1. The square
root of the sum of those squares is 1.414, yet the equal sign would
indicate it shoud be 2.

That is straightforward.

Never the less, the final answer that was posted was correct. As it
happens, that identity was not used later when the correct answer was
derived.

But both that post, and mine, provided the correct final equation, for
the geometric line of sight, but as to the visual one, it's subject to
both the assumptions that were llisted, and some that were not.

The good news is, ain't no pilot gonna worry about this stuff. No
airplane pilot, anyhow,but those who pilot boats on blue water think
about those things pretty often, We use them, for example, to
estimate distances off shore.

Back in radar school, the horizon was said to be approx 1.25 X
sqrt(altitude)

10,000' cruise means 125nm to the radar horizon(line of sight)

To see a tower 1,000nm out, you'd have to be around 640,000'

Good luck.

Al G

Al G wrote:


Back in radar school, the horizon was said to be approx 1.25 X
sqrt(altitude)

10,000' cruise means 125nm to the radar horizon(line of sight)

To see a tower 1,000nm out, you'd have to be around 640,000'

Good luck.

Ah yes, the radar horizon.

Since this topic has gone on so long, might as well add a bit of general
information.

There is the geometric horizon, which assumes the Earth is a big
billiard ball.

Then there is the optical horizon, which because the atmosphere bends
light, is around 10% greater than the optical horizon with the same
billiard ball assumption.

Now since both light and radio signals are electromagnetic radiation,
there is the radio horizon.

Because the atmospheric bending is roughly proportional to wavelength,
the lower the frequency, the more the bending.

So, the radar, or microwave, horizon is a bit farther out than the
optical horizon.

And the VHF horizon, as in aircraft COM, is a bit farther out yet.

If you go down low enough in frequency, there is no horizon, as the
bending is sufficient to cause the signal to follow the curve of the
Earth all they way around if you have enough power to overcome the
losses along the way.

Generally, such things are only of interest to those that do radar
or microwave tropospheric scatter communications, but I feel there
may be some readers interested in some random tidbits of knowledge.


--
Jim Pennino

Remove .spam.sux to reply.

wrote in message ...
Al G wrote:


Back in radar school, the horizon was said to be approx 1.25 X
sqrt(altitude)

10,000' cruise means 125nm to the radar horizon(line of sight)

To see a tower 1,000nm out, you'd have to be around 640,000'

Good luck.

Ah yes, the radar horizon.

Since this topic has gone on so long, might as well add a bit of general
information.

There is the geometric horizon, which assumes the Earth is a big
billiard ball.

Then there is the optical horizon, which because the atmosphere bends
light, is around 10% greater than the optical horizon with the same
billiard ball assumption.

Now since both light and radio signals are electromagnetic radiation,
there is the radio horizon.

Because the atmospheric bending is roughly proportional to wavelength,
the lower the frequency, the more the bending.

So, the radar, or microwave, horizon is a bit farther out than the
optical horizon.

And the VHF horizon, as in aircraft COM, is a bit farther out yet.

If you go down low enough in frequency, there is no horizon, as the
bending is sufficient to cause the signal to follow the curve of the
Earth all they way around if you have enough power to overcome the
losses along the way.

Generally, such things are only of interest to those that do radar
or microwave tropospheric scatter communications, but I feel there
may be some readers interested in some random tidbits of knowledge.
--
Jim Pennino

At least some of us love the random tidbits of information that can surface here,
especially when the conversation wanders a bit. Good post, thanks.

-- John Mazor
"The search for wisdom is asymptotic."

"Except for Internet newsgroups, where it is divergent..."
-- R J Carpenter

"John Mazor" wrote

At least some of us love the random tidbits of information that can
surface here, especially when the conversation wanders a bit. Good post,
thanks.
Yes, the tidbits are nice, but the cost is so high, don't you think?

Would it be possible to agree that the twit has been shown as foolish and
ignorant as needs be for the current time, and let him have the inevitable
last word on this subject?

It would be nice to move on without him in any of the discussions on the
subject, and try to ignore him and his irrelevant comments for a while,
perhaps?

Just a thought to consider, I thought.
--
Jim in NC