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distance / bearing calculator

post #1 of 24
Thread Starter 
Stuart <ddjuqw@ppoxcvqq.kud> wrote in message
news:cja5tb$6n6$1@newsg4.svr.pol.co.uk...
> I done a wee calculator to help me identify hills on my panaramas, and
> thought it maybe of intrest to some of you
> http://www.stuartstuart.fsnet.co.uk/...g/distcalc.htm
>
> I think it should be fairly accurate on small distances but not too sure

how
> it will perform on big distances (hills too far to see anyway) I believe
> these GPS gadgets do these calculations properly, maybe someone with a GPS
> could do some comparisons for me.
>


Looks very nice, but only northern prefixes allowed.... - <sob>

Tom
post #2 of 24

Re: distance / bearing calculator

On Tue, 28 Sep 2004 13:04:43 +0100, Paul Saunders wrote:

>Stuart wrote:
>
>> I done a wee calculator to help me identify hills on my panaramas, and
>> thought it maybe of intrest to some of you
>> http://www.stuartstuart.fsnet.co.uk/...g/distcalc.htm

>
>Looks handy.
>
>> I think it should be fairly accurate on small distances but not too
>> sure how it will perform on big distances (hills too far to see
>> anyway)


How are the bearings and distances calculated?

>I've photographed Snowdon from Cadair Idris, that's about 27 miles.
>I've seen Pen y Fan from the Gower at 30 odd miles. I've often seen
>Lundy Island clearly from the Gower at 35 miles and I've identified the
>Arans from Drygarn Fawr at 40 miles.
>
>I'm sure distances greater than this are possible when the light is
>clear and when line of sight permits. I'm pretty sure I've seen greater
>distances than those listed above, but those are definites.


Try the one below on a crystal clear February day.
>
>> I believe these GPS gadgets do these calculations properly,
>> maybe someone with a GPS could do some comparisons for me.


What they don't do is produce a table of possible hills in bearing
order.
>
>Ozi Explorer has a very convenient distance between waypoints calculator
>(alt-D). It lists all waypoints twice, you just select one waypoint in
>the left box and another in the right box and the results are displayed
>below, both for Great Circle distances and Rhumb Line.


Again it doesn't produce a list in bearing order so you can tick them
off as you look round.
>
>For example; Llanmadoc Hill trig point to Black Mountain (703m)
>
>Great Circle / Rhumb Line
>Distance: 92.9536 km / 92.9547 km
>True Bearing: 60.9 Deg / 61.4 Deg
>Magnetic Bearing: 65.1 Deg / 65.6 Deg
>
>My GPS gives me 92.92 km at 65 Deg.


Sgurr a Mhaoraich (1027m) to Ben Macdui (1309m)

From Ozi

Distance 100.8km
Bearings (Great Circle / Rhumb Line)
Magnetic97.6 Deg / 98.2 Deg
True91.6 Deg / 92.3 Deg

From Stuart's Calculator

Ben Macdui 63 miles 4294 ft 94 Deg

Sgurr a Mhaoraich to Creag nan Damh
(chosen to provide a reference for Grid North)

From Ozi

Distance 4.6km
Bearings (Great Circle / Rhumb Line)
Magnetic3.0 Deg / 2.9 Deg
True357.0 Deg / 357.0 Deg

From Stuart's Calculator

Creag nan Damh 3 miles 3011 ft 360 Deg

I'll leave the comments about the bearings to others....
--
Phil Cook looking north over the park to the "Westminster Gasworks"
post #3 of 24

Re: distance / bearing calculator

On Tue, 28 Sep 2004 14:18:01 +0100, Phil Cook wrote:

I know, bad form replying to self, but I've dug a picture out.

>>I'm sure distances greater than this are possible when the light is
>>clear and when line of sight permits. I'm pretty sure I've seen greater
>>distances than those listed above, but those are definites.

>
>Try the one below on a crystal clear February day.


http://www.p-t-cook.freeserve.co.uk/...haor-gorms.jpg

Full panorama at
http://www.p-t-cook.freeserve.co.uk/pans/mhaoraich.htm

>Sgurr a Mhaoraich (1027m) to Ben Macdui (1309m)


>Distance 100.8km

--
Phil Cook looking north over the park to the "Westminster Gasworks"
post #4 of 24

Re: distance / bearing calculator

"Paul Saunders" <pvs1@wildwales.fsnet.co.uk> wrote in message
news:cjbsfl$ehd$1@news5.svr.pol.co.uk...

Most of what Paul said is agreed with here, but I'm yielding to the forces of
pedantry. We can't have inaccurate ideas about photography tolerated on URW!

> Stuart wrote:
> > However, all this is quite irrelevant, as I said I developed the
> > program to help me identify hills on my panoramas (just got myself a
> > digi camera!) Unfortunately I have noticed that the software I am
> > using to stich my photos together Is slightly moving the posistion of
> > some of the hills. this is really annoying.....


But unavoidable, because it's extremely unlikely your lens provides a flat field
to the software.

> Actually the sofware is correcting distortions due to the lens.


"Compensating for", not "correcting". The compensation may result in more
distortion, since the software may not be able to determine where the flat field
configuration lies.

> It's not the software's fault, it's the lens's fault in the first place.


Oh, it's a little harsh to apportion blame for things that are all consequences
of the laws of optics....

> Due
> to the fact that lenses are spherical, when light is projected from a
> lens onto a flat plane there is distortion.


Unless the lens is designed for this purpose, like an enlarger lens for example.

Very few camera lenses are, since good flat field properties and good
performance at wide apertures and long subject distances are extremely difficult
to combine.

BTW, most modern camera lenses incorporate aspherical elements to reduce the
distortion and reduce the number of elements needed for the same job.

> You can easily see this
> with an SLR by simply looking through the viewfinder and panning
> around - the landscape distorts as you pan.


The distortion changes as you pan.

> This distortion is most
> acute with a wide angle lens, the effect is to stretch the image toward
> the edges and is most noticeable in the corners. The same effect
> occurs with all lenses, but less with telephoto lenses.


Wide angles are prone to barrel distortion, long focal length lenses to
pincushion distortion. The lens designers used to pick the so-called "standard"
focal length lens to be in the zone where these are both easy to avoid.

Telephoto designs are not necessarily more prone to pincushioning than other
long lenses.

> The stitching software is simply trying to correct for these distortions
> in order to make the images fit together. The fact that they won't fit
> without corrections proves that they've been distorted in the first
> place. I've yet to find any stitching software that corrects lens
> distortion perfectly, probably because each lens has unique distortion
> characteristics.


And if you can't look at the original view how would you compare?

And does the human eye suffer from zero distortion? I doubt it.

> Anyway, don't blame the software, blame the lens.


Blame the laws of physics. Lenses can't get round those.

BTW, congratulations, Paul, on neatly bringing a discussion about grid distance
calculations and Naismith's rule straight back to photography :-)
--
"Also, Craig Shergold turned 25 this year. I think everyone on the net
should send him a birthday card, just to let him know we still care."
-- Karlo X. in alt.religion.kibology
post #5 of 24

Re: distance / bearing calculator

On Mon, 27 Sep 2004 23:57:17 +0100, "Stuart" <ddjuqw@ppoxcvqq.kud>
wrote:

>I done a wee calculator to help me identify hills on my panaramas, and
>thought it maybe of intrest to some of you
>http://www.stuartstuart.fsnet.co.uk/...g/distcalc.htm
>
>I think it should be fairly accurate on small distances but not too sure how
>it will perform on big distances (hills too far to see anyway) I believe
>these GPS gadgets do these calculations properly, maybe someone with a GPS
>could do some comparisons for me.


Fantastic web page.

What source and what formula do you use to calculate the bearing? If
the source is a six digit grid reference I'd expect it to be more
accurate over a long distance than a short distance. I note in
another message you talk of distortion due to the curvature of the
Earth. Will this really make a difference?
post #6 of 24

Re: distance / bearing calculator

In article <cjc8nd$r68$1@newsg3.svr.pol.co.uk>, Stuart
<ddjuqw@ppoxcvqq.kud> writes
>
>"C L Imber" <cliff.Imber@nospam.tumble.net> wrote in message
>
>> I note in
>> another message you talk of distortion due to the curvature of the
>> Earth. Will this really make a difference?

>
>Yes... Fitting the earrths surface onto a square piece of paper dosn't work.
>Yes, locally it works very well and each ordance survey map is very accurate
>but join all britains maps together from NA to SZ and their has to be some
>corruption somewhere! I think?
>
>

There are two different aspects that affect the output. One is the scale
factor and the other is the convergence.

Scale factor.
The scale factor is the relationship of 1 unit of distance on the map
(or in the projection) to 1 unit in reality. The OS grid has a scale
factor of ~0.9996 (a metre in reality is represented by 0.9996m on the
map / projection) on the central meridian of the grid (2 degrees w). The
scale factor at a position depends mostly upon how far it is from the
central meridian of the grid. As positions move away from the central
meridian the scale factor increases - that is why a value less than 1 is
chosen for the centre of the projection as it reduces the average error
throughout the projection.

Four parts in 10000 probably does not concern most users!

Convergence.
Convergence is the angle between grid north and true north. It is zero
on the central meridian and once again increases as positions move away
from the centre.

Unlike the scale factor the convergence is significant if you are trying
to relate grid bearings to true or magnetic bearings. Convergence can be
calculated for any position in the grid but for most uses the easiest
way to determine it is by referring to the local OS map. At the top you
will find a diagram showing the relationship between true, grid and
magnetic norths.

--

Dominic Sexton
http://www.dscs.demon.co.uk/
post #7 of 24

Re: distance / bearing calculator

AndyP wrote on Tue, 28 Sep 2004 19:48:07 +0100....
> I can remember once being able to make out the snow covered peaks of South
> Wales behind Cardiff or Newport over the Bristol Channel from somewhere in
> Somerset. Can't remember where I was exactly, Blackdown the highest point
> on the Mendips possibly, I always cast an eye over that way when I go for
> early morning runs or bike rides up there.


That would make sense. From Pen-y-Fan on a good day it's quite easy
to see an island in the Bristol Channel which I'm sure is Steep Holm,
off Weston-Super-Mare (I took a compass bearing one time). Also hills
in the general direction of Exmoor.

Rumour has it that you can see Cadair Idris from Pen-y-Fan too. I've
had days when there was certainly something on the right compass
bearing, but Pumlumon lies on the same bearing and I've never been
able to decide which it was.

--
Tim Jackson
news@winterbourne.freeserve.invalid
(Change '.invalid' to '.co.uk' to reply direct)
Absurd patents: visit http://www.patent.freeserve.co.uk
post #8 of 24

Re: distance / bearing calculator

* The air of uk.rec.walking was filled with the delicate perfume
* of violets, as AndyP <AndyP@ajp100.freeserve.no-spam.co.uk> descended
* on a shaft of golden sunlight, and announced:

> I can remember once being able to make out the snow covered peaks of South
> Wales behind Cardiff or Newport over the Bristol Channel from somewhere in
> Somerset. Can't remember where I was exactly, Blackdown the highest point
> on the Mendips possibly, I always cast an eye over that way when I go for
> early morning runs or bike rides up there.


FWIW you can see Canary Warfe from Whipsnade Zoo! It's quite an impressive
sight with the sun shining on it. It pokes just above the horizon and looks
like a golden pyramid through binos. IIRC you can only see it from near the
camel enclosure.

REgards: Jim Ford
post #9 of 24

Re: distance / bearing calculator

On Tue, 28 Sep 2004 18:57:27 +0100, "Stuart" <ddjuqw@ppoxcvqq.kud>
wrote:

>Yes... Fitting the earrths surface onto a square piece of paper dosn't work.
>Yes, locally it works very well and each ordance survey map is very accurate
>but join all britains maps together from NA to SZ and their has to be some
>corruption somewhere! I think?


Interesting.

I suspect we are both right. For short distances the bearing will be
inaccurate because a 6 digit GR is only accurate to 100m.

For long distances inaccuracies slip in for the reasons you cite.

The OS grid north converges with true north along 2 degree longitude.
I suppose the grid must converge with latitude, so any distance error
will be more marked for hills to the north or south of the origin.

I think...
post #10 of 24

Re: distance / bearing calculator

"Stuart" <ddjuqw@ppoxcvqq.kud> wrote in message
news:cja5tb$6n6$1@newsg4.svr.pol.co.uk...
> I done a wee calculator to help me identify hills on my panaramas, and
> thought it maybe of intrest to some of you
> http://www.stuartstuart.fsnet.co.uk/...g/distcalc.htm
>
> I think it should be fairly accurate on small distances but not too sure

how
> it will perform on big distances (hills too far to see anyway) I believe
> these GPS gadgets do these calculations properly, maybe someone with a GPS
> could do some comparisons for me.
>
>
>

Neat!

However, I just did a 20 mile view centered on Ben Nevis and it threw up
Shalloch on Minnoch at 19 miles!!



druidh
post #11 of 24

Re: distance / bearing calculator

I noticed that Message-ID: <cjcn8i$s64$1@newsg1.svr.pol.co.uk> from Paul
Saunders contained the following:

>I shouldn't think the difference would be significant over the kinds of
>distances we're talking about, up to say 50 miles max. It may make a
>difference to height, and perhaps a little to bearing, but nothing
>major, not for purposes of identifying summits I wouldn't have thought.



I make the difference due to curvature over 50 miles about 300 yards.

But it is quite late...
--
Geoff Berrow (put thecat out to email)
It's only Usenet, no one dies.
My opinions, not the committee's, mine.
Simple RFDs http://www.ckdog.co.uk/rfdmaker/
post #12 of 24

Re: distance / bearing calculator

On Tue, 28 Sep 2004 22:51:16 +0100, "Paul Saunders"
<pvs1@wildwales.fsnet.co.uk> wrote:

>AndyP wrote:
>
>> I can remember once being able to make out the snow covered peaks of
>> South Wales behind Cardiff or Newport over the Bristol Channel from
>> somewhere in Somerset.

>
>Ah yes, I recall recently making a positive ID on the Quantocks from
>Swansea, 46 miles.


The Earth's circumference at the equator is 40,000,000m; its radius is
therefore 6,366,198m.

At 100m altitude you are 6,366,298m from the centre.

sqrt(6336298^2-6366198^2)=35,598m

So at 100m you should be able to see nearly 36 Km to sea level.

100m - 36 Km
200m - 50 Km
300m - 62 Km
400m - 71 Km
600m - 87 Km
800m - 101 Km
978m - 111,330m
1000m - 113 Km
1085m - 117,236m
1200m - 123 Km
1344m - 130,512m

A person who's eye level is at 1m 75cm can see about 4,709m out to
sea.

Things are complicated when looking at objects further away, but not
at sea level.

However, if two people on two distant mountains can see the same bit
on land between them, they should be able to see each other.

If I am on Ben Nevis, can I see my friend on the top of Scarfell Pike
284 Km away. The answer is no by about 42 Km. However, my friend on
Skiddaw (931m) can clearly see his friend near the summit of The
Cobbler (881m).

I trust someone will put me right if my calculations are a little (or
even way) off.

Please don't bother correcting my assumption that all the Earth's
radii are uniform.
post #13 of 24

Re: distance / bearing calculator

On Tue, 28 Sep 2004 23:13:40 +0100, "Paul Saunders"
<pvs1@wildwales.fsnet.co.uk> wrote:

>C L Imber wrote:
>
>> The OS grid north converges with true north along 2 degree longitude.
>> I suppose the grid must converge with latitude,

>
>Lines of longitude converge, I thought it did the opposite, to
>compensate for that. The whole point of the OS grid is to keep the
>distances more or less correct, so one square is 1km, all over the grid.
>(Not exactly 1km but close enough.) So I'd expect that basic
>trigonometry should work equally well all over the grid, with errors
>mainly down to distance and curvature, rather than any northern
>convergence.


Either I didn't explain very well or you misunderstood.

The OS grid north is different from lines of longitude everywhere
except the 2 degree west longitude line where grid north converges
with the line of longitude. That is at 2 degrees west there is no
difference between grid north and true north. Maps of the Peak
District show this convergence beautifully.

Lines of latitude are parallel so I see no reason why the OS east -
west grid lines should not converge (or run parallel) with lines of
latitude.
post #14 of 24

Re: distance / bearing calculator

I noticed that Message-ID: <0jqjl0thujl6t713nnspad57dse1s8qdg5@4ax.com>
from Geoff Berrow contained the following:

>I make the difference due to curvature over 50 miles about 300 yards.
>
>But it is quite late...


Oops...used diameter instead of radius

550 yards

--
Geoff Berrow (put thecat out to email)
It's only Usenet, no one dies.
My opinions, not the committee's, mine.
Simple RFDs http://www.ckdog.co.uk/rfdmaker/
post #15 of 24

Re: distance / bearing calculator

In article <0fujl0tjgfpmpqq1fcut6l96ljsjiakvra@4ax.com>, C L Imber
<cliff.Imber@nospam.tumble.net> writes
>On Tue, 28 Sep 2004 23:13:40 +0100, "Paul Saunders"
><pvs1@wildwales.fsnet.co.uk> wrote:
>
>>C L Imber wrote:
>>
>>> The OS grid north converges with true north along 2 degree longitude.
>>> I suppose the grid must converge with latitude,

>>
>>Lines of longitude converge, I thought it did the opposite, to
>>compensate for that. The whole point of the OS grid is to keep the
>>distances more or less correct, so one square is 1km, all over the grid.
>>(Not exactly 1km but close enough.) So I'd expect that basic
>>trigonometry should work equally well all over the grid, with errors
>>mainly down to distance and curvature, rather than any northern
>>convergence.

>
>Either I didn't explain very well or you misunderstood.
>
>The OS grid north is different from lines of longitude everywhere
>except the 2 degree west longitude line where grid north converges
>with the line of longitude. That is at 2 degrees west there is no
>difference between grid north and true north. Maps of the Peak
>District show this convergence beautifully.
>
>Lines of latitude are parallel so I see no reason why the OS east -
>west grid lines should not converge (or run parallel) with lines of
>latitude.


But lines of latitude are at right angles with lines of longitude and
you have accepted that only on the central meridian is the line of
longitude parallel with grid north.

As you move away from the central meridian the lines of latitude and the
east / west grid lines diverge.

This can be seen on the following page:

http://www.gps.gov.uk/natgrid/page7.asp

--

Dominic Sexton
http://www.dscs.demon.co.uk/
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