On 7/20/2010 1:41 AM, cavelamb wrote:
Wayne.B wrote:
On Mon, 19 Jul 2010 23:18:19 -0500, cavelamb
wrote:

NOTAM:

Oakland Center (Fremont CA) [ZOA]: April NOTAM #31 issued by Gps
Notam OA [GPS]
Navigation GPS is unreliable and May BE unavailable WITHIN A 375
nautical miles RADIUS of 393101N/1175659W LOVELOCK / LLC / VORTAC
141.25 DEGREE radial at 46.65 nautical miles, at FL400; decreasing in
area with DECREASE in altitude to 290 nautical miles RADIUS at FL250;
220 nautical miles RADIUS at 10000 ft. mean sea level, and 220
nautical miles RADIUS at 4000 ft. above ground level. effective from
April 09th, 2010 at 06:00 AM PST (1004091400) - April 09th, 2010 at
11:30 AM PST (1004091930)

Those ranges quoted are for aircraft thousands of feet above sea
level. The jamming range would be much shorter for boats, probably
10 miles or less.


aSSuming it's a linear relationship, I get 202 mile radius...




Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

Those ranges quoted are for aircraft thousands of feet above sea
level. The jamming range would be much shorter for boats, probably
10 miles or less.


aSSuming it's a linear relationship, I get 202 mile radius...




Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

...and of course that assumes that the emitter is at sea level, so if it
is at any appreciable height (or in another aircraft) then you have to
add the result of the same equation again!!

Jeff

On 25/07/10 10:54, Jeff wrote:

Those ranges quoted are for aircraft thousands of feet above sea
level. The jamming range would be much shorter for boats, probably
10 miles or less.


aSSuming it's a linear relationship, I get 202 mile radius...




Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

..and of course that assumes that the emitter is at sea level, so if it
is at any appreciable height (or in another aircraft) then you have to
add the result of the same equation again!!

and ignores the surface effect that allows UK TV & VHF signals to be
picked up as far away as in the Netherlands.

In article ,
Martin wrote:

On 25/07/10 10:54, Jeff wrote:

Those ranges quoted are for aircraft thousands of feet above sea
level. The jamming range would be much shorter for boats, probably
10 miles or less.


aSSuming it's a linear relationship, I get 202 mile radius...




Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

..and of course that assumes that the emitter is at sea level, so if it
is at any appreciable height (or in another aircraft) then you have to
add the result of the same equation again!!

and ignores the surface effect that allows UK TV & VHF signals to be
picked up as far away as in the Netherlands.

Horizontal Bending doesn't work all that well at 1.6 Ghz, and is
negligible, in its effect. Temperature Inversion Refraction is also
negliable at 1.6 Ghz, and even if you could count on any specific
Inversion System to be present at any one time. Both of the above are
present for frequencies below 1 Ghz, and could contribute a small effect
but above 1 Ghz, it just isn't going to happen....

--
Bruce in alaska
add path after fast to reply

Bruce in alaska wrote:
and ignores the surface effect that allows UK TV& VHF signals to be
picked up as far away as in the Netherlands.

Horizontal Bending doesn't work all that well at 1.6 Ghz, and is
negligible, in its effect. Temperature Inversion Refraction is also
negliable at 1.6 Ghz, and even if you could count on any specific
Inversion System to be present at any one time. Both of the above are
present for frequencies below 1 Ghz, and could contribute a small effect
but above 1 Ghz, it just isn't going to happen....

I'd be willing to trust you one this (I have been a ham since 1977,
la8nw), but we are after all in a sat-nav newsgroup he

Why do we talk about pseudo-range measurements and corrections? Isn't
this due to bending of signals at 1.575 GHz?

OTOH, as long as the effect is in the sub-percent range, it really
doesn't matter when we're discussing 1.2 vs 1.0 rule-of-thumb factors. :-)

Terje
--
- Terje.Mathisen at tmsw.no
"almost all programming can be viewed as an exercise in caching"

brian whatcott wrote:
Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

That calculation follows directly from the Taylor series for Cosine:

1 - x^2/2! + x^4/4! - ...

It means that for very small angles, the height above the sea is

1 - (1 - x^2/2!) = x^2/2! = x^2/2 (when R == 1)

Insert the radius of the Earth (in nautical miles, 3500 or so) and
multiply the result by the number of feet in a nautical mile (about
6000+) and the 1.2 factor should pop out.

Terje
--
- Terje.Mathisen at tmsw.no
"almost all programming can be viewed as an exercise in caching"

The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

That calculation follows directly from the Taylor series for Cosine:

1 - x^2/2! + x^4/4! - ...

It means that for very small angles, the height above the sea is

1 - (1 - x^2/2!) = x^2/2! = x^2/2 (when R == 1)

Insert the radius of the Earth (in nautical miles, 3500 or so) and
multiply the result by the number of feet in a nautical mile (about
6000+) and the 1.2 factor should pop out.

Terje

For a more exact result you only need to use Pythagoras.

Jeff

Terje Mathisen "terje.mathisen at tmsw.no" wrote:

brian whatcott wrote:
Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

That calculation follows directly from the Taylor series for Cosine:

1 - x^2/2! + x^4/4! - ...

It means that for very small angles, the height above the sea is

1 - (1 - x^2/2!) = x^2/2! = x^2/2 (when R == 1)

Hmm. Your working suggests that for R=1 the height is equal to 1-cos(x),
but that is not the case, it's actually equal to 1/cos(x)-1. By chance,
for very small angles, these two expressions are approximately equal.

Insert the radius of the Earth (in nautical miles, 3500 or so) and
multiply the result by the number of feet in a nautical mile (about
6000+) and the 1.2 factor should pop out.

Actually a factor of 1.0 would be a better approximation than 1.2,
since the factor which actually pops out, when I use R=6371km and
conversion factors 1852m/NM and 0.3048m/ft, is 1.064.

On 7/25/2010 9:54 AM, Ronald Raygun wrote:
Terje Mathisen"terje.mathisen at tmsw.no" wrote:

brian whatcott wrote:
Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

That calculation follows directly from the Taylor series for Cosine:

1 - x^2/2! + x^4/4! - ...

It means that for very small angles, the height above the sea is

1 - (1 - x^2/2!) = x^2/2! = x^2/2 (when R == 1)

Hmm. Your working suggests that for R=1 the height is equal to 1-cos(x),
but that is not the case, it's actually equal to 1/cos(x)-1. By chance,
for very small angles, these two expressions are approximately equal.

Insert the radius of the Earth (in nautical miles, 3500 or so) and
multiply the result by the number of feet in a nautical mile (about
6000+) and the 1.2 factor should pop out.

Actually a factor of 1.0 would be a better approximation than 1.2,
since the factor which actually pops out, when I use R=6371km and
conversion factors 1852m/NM and 0.3048m/ft, is 1.064.

Even using alpha math engine, I get 1.07 with those other conversions
that Terje gave. hehe...

Brian W

Ronald Raygun wrote:
Terje Mathisen"terje.mathisen at tmsw.no" wrote:

brian whatcott wrote:
Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

That calculation follows directly from the Taylor series for Cosine:

1 - x^2/2! + x^4/4! - ...

It means that for very small angles, the height above the sea is

1 - (1 - x^2/2!) = x^2/2! = x^2/2 (when R == 1)

Hmm. Your working suggests that for R=1 the height is equal to 1-cos(x),
but that is not the case, it's actually equal to 1/cos(x)-1. By chance,
for very small angles, these two expressions are approximately equal.

Not "by chance", I (mis-)remembered the result I needed (from doing this
calculation 30+ years ago) and didn't have paper and pen to rederive it
so I picked the first approximation that looked correct. :-(

Anyway, doing a series expansion for your formula leads to the exact
same x^2/2 value for the first term, and since x is very close to zero,
it is the only one we need. :-)

(It is probably_more_ precise than doing regular trig operations on a
calculator, due to the limited precision on said calculator: With a
height of 6 feet we get about 3.5 miles, right?

The ratio of 1.8 m to 6400 km is about 3.5e6, so the second-order term
requires 13 digits while most calculators are happy to show 8 or 10, right?

Insert the radius of the Earth (in nautical miles, 3500 or so) and
multiply the result by the number of feet in a nautical mile (about
6000+) and the 1.2 factor should pop out.

Actually a factor of 1.0 would be a better approximation than 1.2,
since the factor which actually pops out, when I use R=6371km and
conversion factors 1852m/NM and 0.3048m/ft, is 1.064.

OK, that's useful!

Terje

--
- Terje.Mathisen at tmsw.no
"almost all programming can be viewed as an exercise in caching"