distance / bearing calculator

Stuart <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

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/hillwalking/distcalc.htm

I think it should be fairly accurate on small distances but not too sure

how

Quoted message said:

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

Stuart said:

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/hillwalking/distcalc.htm

Looks handy.

Quoted message said:

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'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.

Quoted message said:

I believe these GPS gadgets do these calculations properly,
maybe someone with a GPS could do some comparisons for me.

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.

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.

Paul
--
http://www.wilderness-wales.co.uk
http://www.wildwales.fsnet.co.uk

"Tom" <[email hidden]> wrote in message

Quoted message said:

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

Tom

Since southern prefixes start down at leeds or somewhere like that, I doubt
( infact i'm sure) you couldn't see any scottish hills!

If you want to give me a table of english hills (to my specificatoin) I
could very well do another view point calculator. for your area!

"Paul Saunders" <[email hidden]> wrote in message

Quoted message said:

Quoted message said:

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'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.

Quoted message said:

Paul

I think you may of missed my point. I was referring to the bearing
calculation, I used very basic trigonometry to calculate the bearings. This
will obviously work fine over relatively short distances, 20 miles or so,
however inaccuracies due to the earth being round and not flat, will start
to creep in as distance increases.

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.....take the following pan from Meall Ghoarodaih (warning
its about 420K) The bearing is shown in the status bar (IE only) when you
move the mouse over the image!

http://www.stuartstuart.fsnet.co.uk/hillwalking/pans/ghaordaidh.htm

Ben Nevis is correct at 312 degrees
Ben Lawers is 2 degrees out at 84 degrees
Stob Binnien is correct at 205 degrees

How annoying that it displaced a hill by such a distance.

Incidentally on the original photos the cairngorms are very visible at 50
miles!

Paul Saunders said:

Stuart said:

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/hillwalking/distcalc.htm

Looks handy.

Quoted message said:

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?

Quoted message said:

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.

Quoted message said:

Quoted message said:

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.

Quoted message said:

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.

Quoted message said:

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)
Magnetic 97.6 Deg / 98.2 Deg
True 91.6 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)
Magnetic 3.0 Deg / 2.9 Deg
True 357.0 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"

Stuart said:

I think you may of missed my point. I was referring to the bearing
calculation, I used very basic trigonometry to calculate the
bearings. This will obviously work fine over relatively short
distances, 20 miles or so, however inaccuracies due to the earth
being round and not flat, will start to creep in as distance
increases.

True, but I think you missed my point too, which is that hills can be
seen at distances much greater than 20 miles, so if the objective is to
identify hills that you can see, then you'll have to deal with distances
greater than this, whether the results are accurate or not.

Quoted message said:

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.....

Actually the sofware is correcting distortions due to the lens. It's
not the software's fault, it's the lens's fault in the first place. Due
to the fact that lenses are spherical, when light is projected from a
lens onto a flat plane there is distortion. You can easily see this
with an SLR by simply looking through the viewfinder and panning
around - the landscape distorts 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.

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.

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

Quoted message said:

take the following pan
from Meall Ghoarodaih (warning its about 420K) The bearing is shown
in the status bar (IE only) when you move the mouse over the image!

http://www.stuartstuart.fsnet.co.uk/hillwalking/pans/ghaordaidh.htm

Ben Nevis is correct at 312 degrees
Ben Lawers is 2 degrees out at 84 degrees
Stob Binnien is correct at 205 degrees

How can you claim that any one of these is correct? You'd have to
calibrate it first. If you calibrated it relative to Ben Nevis then of
course Ben Nevis would be correct. I presume it's a 360 degree pano, so
you'd only need one calibration point.

Quoted message said:

How annoying that it displaced a hill by such a distance.

Given the distortion characteristics of lenses and potential problems of
accurate stitching, I think that's pretty good.

Quoted message said:

Incidentally on the original photos the cairngorms are very visible
at 50 miles!

Given the variations in bearing pointed out by Phil, if a hill is only
out by 2 degrees then that shouldn't be a problem. I think we have a
similar situation here to GPS accuracy. We'd like a GPS to be accurate
to 1m because that's the base unit that it displays, but in practice it
isn't that accurate. It still doesn't stop a GPS from being useful, it
gets you close enough.

Likewise, whilst you'd like your photos and your calculations to be
accurate to 1 degree, an error of a few degrees isn't enough to prevent
your software giving you enough information to determine which summit is
which. It'll get you close enough to know roughly what you're looking
at and you can figure out exactly which summit is which by close
inspection of the map.

I'm not saying you shouldn't strive for greater accuracy, but personally
I wouldn't expect or trust a stiched pano to give me 1 degree accuracy.

What would give you the degree of photographic accuracy that you desire
is a proper "swing-lens" panoramic camera, when perfectly levelled. The
photograph is taken through a narrow vertical slit which rotates as the
lens rotates. This eliminates horizontal distortion (vertical
distortion still exists).

With my camera, each shot covers 120 degrees, therefore I can do a 360
degree pano in just three shots, although I'd need to use four to give
me some overlaps. These photos can be stiched directly in Photoshop, no
need for stitching software since there's no horizontal distortion to be
corrected, the edges match perfectly. There are other panoramic camera
which give 135 degrees, so three shots would be sufficient with one of
those.

Such a 360 degree pano should give precise compass bearings. I suppose
I should now go out and create such a pano to prove my theory.

Just a though, that 2 degree error you mentioned, how much difference in
distance was there between the correct bearings and the incorrect one?
Could the error have been due to the calculation rather than the lens
distortion/stitching?

Paul
--
http://www.wilderness-wales.co.uk
http://www.wildwales.fsnet.co.uk

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.

Quoted message said:

Quoted message said:

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/temp/mhaor-gorms.jpg

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

Quoted message said:

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

Quoted message said:

Distance 100.8km

--
Phil Cook looking north over the park to the "Westminster Gasworks"

"Paul Saunders" <[email hidden]> wrote in message
news:[email hidden]...

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!

Quoted message said:

Stuart said:

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.

Quoted message said:

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.

Quoted message said:

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....

Quoted message said:

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.

Quoted message said:

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.

Quoted message said:

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.

Quoted message said:

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.

Quoted message said:

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

On Mon, 27 Sep 2004 23:57:17 +0100, "Stuart" <[email hidden]>

Quoted message said:

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/hillwalking/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?

Mark South said:

Quoted message said:

Actually the sofware is correcting distortions due to the lens.

"Compensating for", not "correcting".

Yes, that's what I meant.

Quoted message said:

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

Of course.

Quoted message said:

Quoted message said:

the landscape distorts as you pan.

The distortion changes as you pan.

LOL! Yes, that's what I meant!

Quoted message said:

Quoted message said:

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?

Well a swing-lens panoramic camera would probably provide the best basis
for comparison IMO. There'd still be vertical distortion as I
mentioned, but the horizontal spacing of objects within the image should
be accurate.

A panoramic photograph taken at the same time as a series of images to
be stiched later would provide a good basis for comparison I reckon.
I've done this a number of times actually, but haven't yet compared any
of them closely for the kind of purposes talked about here. Most of my
panos haven't been summit panos though.

Quoted message said:

BTW, congratulations, Paul, on neatly bringing a discussion about
grid distance calculations and Naismith's rule straight back to
photography :-)

Thanks Mark, that's what I'm here for!

Paul
--
http://www.wilderness-wales.co.uk
http://www.wildwales.fsnet.co.uk

"C L Imber" <[email hidden]> wrote in message

Quoted message said:

Quoted message said:

I done a wee calculator to help me identify hills on my panaramas, and
thought it maybe of intrest to some of you

Quoted message said:

What source and what formula do you use to calculate the bearing?

Take a look at the source code for the page, All the hill details are held
in a two dimensional array, and every time you click on calculate some very
basic javaScript uses basic triganometry to calculate the distance and
bearing of every hill from the posistion entered. The distance is calculated
in exactly the same way that you utilised on your excel sheet for
naithsmiths, the bearing uses that Tangent formula to calc the bearing.
I expanded the six figure grid ref to an 8 figure by substituting the second
letter for a number. The for corners of all Northern grid referances would
change as follows.

Bottom Left NV000000 becomes 0000 0000
Bottom Right NZ999000 becomes 4999 0000
Top Left NA000999 becomes 0000 3999
Top Right NE999999 becomes 4999 3999

Quoted message said:

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?

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?

"Paul Saunders" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Stuart said:

I think you may of missed my point. I was referring to the bearing
calculation, I used very basic trigonometry to calculate the
bearings. This will obviously work fine over relatively short
distances, 20 miles or so, however inaccuracies due to the earth
being round and not flat, will start to creep in as distance
increases.

True, but I think you missed my point too, which is that hills can be
seen at distances much greater than 20 miles, so if the objective is to
identify hills that you can see, then you'll have to deal with distances
greater than this, whether the results are accurate or not.

The distance of 20 miles on the web page is changeable from 1 to 999miles

****Snipped lots of interesting stuff worth reading!****

Quoted message said:

Just a though, that 2 degree error you mentioned, how much difference in
distance was there between the correct bearings and the incorrect one?
Could the error have been due to the calculation rather than the lens
distortion/stitching?

No

Quoted message said:

In article <[email hidden]>, Stuart
<[email hidden]> writes

Quoted message said:

"C L Imber" <[email hidden]> wrote in message

Quoted message said:

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/

"Paul Saunders" <[email hidden]> wrote

Quoted message said:

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 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.

AndyP wrote on Tue, 28 Sep 2004 19:48:07 +0100....

Quoted message said:

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
[email hidden]
(Change '.invalid' to '.co.uk' to reply direct)
Absurd patents: visit http://www.patent.freeserve.co.uk

* The air of uk.rec.walking was filled with the delicate perfume
* of violets, as AndyP <[email hidden]> descended
* on a shaft of golden sunlight, and announced:

Quoted message said:

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

On Tue, 28 Sep 2004 18:57:27 +0100, "Stuart" <[email hidden]>

Quoted message said:

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...

AndyP said:

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.

Paul
--
http://www.wilderness-wales.co.uk
http://www.wildwales.fsnet.co.uk

"Stuart" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

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/hillwalking/distcalc.htm

I think it should be fairly accurate on small distances but not too sure

how

Quoted message said:

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