PDA

View Full Version : Bad navigation, bad sundial



Craig_C
2009-Apr-21, 10:13 PM
text removed

I was surprised to learn that there's a common recommendation for finding north without a compass--a potentially handy trick, if it works. Basically: poke a 1-foot stick in the ground, mark its tip's shadow, wait 15 or 20 minutes, mark the tip's shadow again; it is claimed that a line between the marks will always run exactly east-west, any where, any time. A seductive idea, perhaps, for the kind of people who don't understand why there are seasons.

I first encountered this when my daughter was watching science videos for school children at www.krampf.com. When I complained to Bob Krampf about his video, he supported his claim (and even augmented it by claiming a personal accuracy of a few degrees) by suggesting a Web search on "tip shadow method." Sure enough, there are lots of hits, mostly referring to Army field manuals, but including the Boy Scouts, the National Emergency Services Academy, the Forrest Service, YouTube videos, WikiHow, eHow, etc. More hits on "stick shadow."

I sent Krampf various reasons his method could be highly inaccurate (except at solar noon and on the equinoxes, of course) but he wouldn't budge. I even sent him a picture of the Solarium Augusti, a huge nodal-based sundial analogous to his stick, with the hyperbolic shadow paths (declination lines) laid out on its base. I sent him links to the EarthDial-of-science project at The Planetary Society at www.planetary.org/programs/projects/earthdial/instructions.html, to www.illustratingshadows.com, and www.mysundial.ca for the math and example illustrations. I tried to make it clear that, at typical latitudes, as days approach the solstices, the difference between his morning and evening measurements (which are chords along the hyperbolic declination lines) would be about +/-30 degrees. Take a look down the Planetary Society page at the arc for 75 degrees N in Canada; looks to me like a difference of about 90 degrees between morning and evening of the summer solstice. Krampf was unmoved, maybe because I can't find a specific, direct reference to the tip shadow method being subject to error, even though there are plenty of references to the changing hyperbolic paths of a gnomon's tip shadow.

None of those sources of the basic claim explain the reasons that the "tip shadow method" gives different results at different times of the day and days of the year and different latitudes. text removed

So here's an old, surprisingly common, blunder that could be, and should be, corrected by a Real Astronomer(TM). It might also be fun to explain why the declination curves are hyperbolae instead of, say, circular arcs. Good lessons to be had.

Point to a specific reference if you know of one that debunks the tip shadow method, or even better suggest how to straighten out Robert Krampf, the Army, the US government, the Boy Scouts, and all the others who are misleading the unwashed. Thanks.

pzkpfw
2009-Apr-22, 12:32 AM
Welcome Craig_C,

First up, please note that as your post contained URLs it was held up for moderation. Don't take it personally, it's a defence against spammers.

Secondly, please note that I've removed a little text from your post. It wasn't "all that bad" but really wasn't the kind of tone we use here - especially not in post #1.

The rest of your post is very interesting and I'd like to see how it is answered - so have approved it. (It's beyond me to answer).

Please keep any further discussion "civil".

Cheers,

01101001
2009-Apr-22, 01:52 AM
Basically: poke a 1-foot stick in the ground, mark its tip's shadow, wait 15 or 20 minutes, mark the tip's shadow again; it is claimed that a line between the marks will always run exactly east-west, any where, any time.

[...] the difference between his morning and evening measurements (which are chords along the hyperbolic declination lines) would be about +/-30 degrees.

If the time between measurements is 15 to 20 minutes, where do problems with morning and evening measurements enter (besides those either side of, and very close to, noon)?

Welcome to BAUT Forum.

Edit: Or did you mean a pair of morning measurements and/or a pair of evening measurements? Yes, those would be more problematical. I thought you were referring to two measurements, one in the morning and one in the evening -- and yet only 15 to 20 minutes apart.

a1call
2009-Apr-22, 01:55 AM
Hi Craig_C,

I am not an astronomer but I am pretty confident that you are correct in that the top of a shadow of a stick does not scan WE (necessarily). However it does scan along a latitudinal circle which is parallel to the equator any time of the year and everywhere on Earth. Thus it can be used to locate true North-South direction very accurately by finding the perpendicular to it.

That was a very good question. Welcome to the board.

01101001
2009-Apr-22, 02:06 AM
When I complained to Bob Krampf about his video, he supported his claim (and even augmented it by claiming a personal accuracy of a few degrees) by suggesting a Web search on "tip shadow method."

I so Google searched. I visited the first hit Wikihow (http://www.wikihow.com/Find-True-North-Without-a-Compass). I don't have much complaint. It didn't support the person who suggested it, but I didn't expect it to.

Advice there was to let 10 or 15 minutes elapse, and the claim was:


This is an approximate east-west line.

It seems like it would be, approximately, at least good enough for someone hiking who wouldn't need small-degree accuracy.

Are all the hits so inoffensive, or did I just get lucky?

01101001
2009-Apr-22, 02:33 AM
Would the animation at Motions of the Sun Simulator (http://astro.unl.edu/naap/motion3/animations/sunmotions.html) be instructive?

Hit the start-animation button and observe the stick figure's head shadow move in a curved line. That should make it clear that a line connecting two tip shadows is only an approximation to east-west.

a1call
2009-Apr-22, 03:39 AM
It seems like it would be, approximately, at least good enough for someone hiking who wouldn't need small-degree accuracy.



Exactly, a line along WE would have to be a section of a great circle which is centered in the center of the Earth. The actual scan of a shadow is a latitudinal circle parallel to the equator but is not centered at the center of the Earth. On very short distances the difference between the two arcs approaches 0 and is probably beyond regular measurement in a 15-20 minutes scan. Regardless it could be used to find true north quite accurately on a level surface.

Gandalf223
2009-Apr-22, 04:23 AM
poke a 1-foot stick in the ground, mark its tip's shadow, wait 15 or 20 minutes, mark the tip's shadow again; it is claimed that a line between the marks will always run exactly east-west, any where, any time.

By extrapolation, you could poke a stick in the ground, mark its shadow at sunrise and again at any time of the day right up until sunset, and the shadow would always fall on the same east-west line.

Sounds enticing, but I suspect it's only an approximation.

Stellarium will give az-el data for the sun for any time you choose. Simple job to plug the numbers into a spreadsheet and have it calculate the shadow's
X-Y coordinates. Someone who's not as lazy as I, should do that.

a1call
2009-Apr-22, 04:52 AM
ETA:
I removed my wrong info in this post after drawing the line on a 3D sphere and I have to revert back:
*- Drawing straight lines between points on latitudinal circle is not West-EAST unless they are points equally before and after local noon. So Craig_C you are correct about EW being very wrong. It is only approximately correct for short lines across it.
*- However you can get true north by connecting any 2 points on a longitudinal circle with a straight line along the surface and finding it's perpendicular.

mysundial
2009-Apr-23, 07:53 PM
Sunny Day!

Please visit my web site at www.mysundial.ca/tsp/tsp_index.html and go to the "Declination Lines" page. Figure 1 shows the declination lines of a horizontal sundial at one specific latitude. These are the lines the shadow from the tip of a stick will follow during the year. These lines will change with latitude.

The method described in the first post will be most accurate at the equinoxes when the declination line is a straight line east-west. As you get further away from the solstices this method will become less accurate.

If you go to the "Finding True North/South" the fourth method there will give you an accurate east-west line and in turn an accurate true north-south line.

a1call
2009-Apr-24, 02:05 AM
Welcome to the board mysundial,

You have an excellent site. I find visualizing of spherical mechanics very complicated.
Studying your site made me realize that I had erred in my 3D drawing in that I had assumed the sun perpendicular to the equator (i.e. equinoxes year round).
Now I figure that on equinox days the shadow traces a straight line which is in fact part of a latitudinal circle. On other days the trace deviates due to angular deviation factor of the Nodus angling as the earth rotates.

Looking at the link that you referenced (http://www.mysundial.ca/tsp/declination_lines.html) and the horizontal trace of the shadow it seems that the opening post method is totally nonsense and depending on time of the day different East, West and North directions would be marked which would be very different and thus very wrong.
Basically North-South could be any perpendicular line to any of the hyperbolas at any point.
The method seems worthless even as an approximation.

Craig_C
2009-Apr-25, 05:43 PM
Maybe the problems with the "tip shadow method" aren't as obvious as I thought. To me they're most obvious by looking at the sundial plots on the Planetary Society site I linked in the OP; clearly the tip shadow path is curved (except on the equinoxes) and so perpendiculars to such curves, or to short chords of them, won't point due North except at solar noon. Those pages were down for several days, but are now back.

01101001, your link showed me lots of great simulators, thanks. But the Sun Position Simulator is kinda hard to interpret. You have to fiddle with the settings and carefully observe of the shadow of the little figure. I'm afraid that the Army, the government, Boy Scouts, and others won't dig out the implications. I know Robert Krampf hasn't and he's supposed to be a science teacher. The challenge is to find a quick, simple way to approximate North using only Neolithic technology.

Dan's mysundial site is excellent. I linked to it in the OP and it's great that he has posted here. But his site has the same problem: too much information density that requires too much interpretation. His shadow method for finding North works well; I've used it myself. The problem is that it takes several hours in the middle of the day, which wouldn't work for a lost Ranger or Scout.

I think a great solution to the problem of debunking the "tip shadow method" would be for Dan to put a page on his site called "Why the tip shadow method for finding North seldom works." It would show up in a search for "tip shadow method" or "finding North." He could show plots of the "North"s that would be found during the solstice days for a few latitudes; he's already got declination plots that are very close. Or even a curve of angular errors similar to the Equation of Time. Or both. The data are there and Dan has the smarts; it just needs to be put in a format that's blatantly obvious to non-scientists. I'll help with the writing, if that's useful.

Plus, Dan could offer a simple explanation of why the curves are hyperbolae. :-)

Robert Krampf
2009-Oct-06, 05:25 PM
I was researching a different experiment and stumbled across this posting. I have to say that I am somewhat amused at Craig's comments, considering the actual words of our email conversations.

At no time did I claim that the shadow tip method would produce an exact east-west line. The premise that Craig objected to was that if you were in an unknown area, without a map, compass, watch, or GPS, and you knew that you were looking for a trail that was north of your position, the shadow tip method could help you find the general direction to travel.

If anyone would like to see the original material that Craig is commenting on, please contact me. I would be glad to send you a copy.

Robert Krampf

mugaliens
2009-Oct-07, 02:13 AM
The challenge is to find a quick, simple way to approximate North using only Neolithic technology.

Face the rising sun. Do a left face.

I'm sure any one of our hominid ancestors or cousins over the last 2.5 million years could have been taught to do a left face.

djinn
2009-Oct-13, 12:43 AM
Face the rising sun. Do a left face.

Hmmm. Well, I'm a complete amateur and am probably completely wrong but, unless your definition of "approximate" is a LOT broader than mine ~

1) Doesn't the sun appear to rise from a different direction every day of the year? (Otherwise Megalithic sites wouldn't have been built to show where the sun would rise at (eg) the vernal equinox)
2) Doesn't that get less and less accurate as you get further from the equator?
3) Wouldn't that only work at sea, or on a flat plain ? Eg, If you were lost in a deep valley you'd have to guess where the sun rose, introducing yet more error. (And I imagine you're more likely to get lost on uneven ground than flat anyway).

Wouldn't these factors introduce such variation as to make the "approximation" virtually useless?

01101001
2009-Oct-13, 01:25 AM
Hmmm. Well, I'm a complete amateur and am probably completely wrong but, unless your definition of "approximate" is a LOT broader than mine ~

How narrow is yours? Within what range of degrees is approximate north?

If there is a river north of you, what range of directions might you head to reach it?

mugaliens
2009-Oct-13, 02:23 AM
Hmmm. Well, I'm a complete amateur and am probably completely wrong but, unless your definition of "approximate" is a LOT broader than mine.

Ok, here's a better method:

1. Hang a rock from a string.

2. Shortly before the sun sets, trace the setting shadow line in the dirt.

3. Shortly after the sun rises, trace the rising shadow line in the dirt.

4. Bisect the angle in the general direction of North obtained by the "left face" method described earlier.

5. Draw a big letter "N" at the top of the bisection, as that's True North.

Questions:


1) Doesn't the sun appear to rise from a different direction every day of the year? (Otherwise Megalithic sites wouldn't have been built to show where the sun would rise at (eg) the vernal equinox)
2) Doesn't that get less and less accurate as you get further from the equator?
3) Wouldn't that only work at sea, or on a flat plain ? Eg, If you were lost in a deep valley you'd have to guess where the sun rose, introducing yet more error. (And I imagine you're more likely to get lost on uneven ground than flat anyway).

Wouldn't these factors introduce such variation as to make the "approximation" virtually useless?

1. Yes.

2. Yes, and nearing the Arctic Circle it's next to useless.

3. No. As long as you can see the rising sun, it works with approximate accuracy. Obviously, being in a valley would render it useless.

4. No. I grew up in Florida, next to some rather large woods in which we spent a lot of time as kids. I used the sun as an aid to navigation all the time. On cloudy days we just didn't stray as far.

djinn
2009-Oct-14, 11:48 AM
How narrow is yours? Within what range of degrees is approximate north?

If there is a river north of you, what range of directions might you head to reach it?

Answer to Q1) My definition of "narrow enough" is "accurate enough to be useful". If I was lost somewhere, and my life depended on establishing the only direction in which I could find safety, I would want that approximation to be very close to true north (or east, or whatever, doesn't matter which ofc). I would hope to be accurate to within a few degrees. Anything else might lead me into more trouble, or I might have to keep walking until I reached the coast of whatever landmass I was on (and that assumes I was walking in a straight line, which wouldn't happen if I was getting it wrong in estimating my orientation each day - I'd probably be walking along a curved path).

Answer to Q2) Within what range of what? I'm afraid I don't understand the question.

Answer to Q3) Once again, I have trouble understanding the question, but I presume that depends on how far away the river is, and how long it is. If it was one mile away and was a thousand miles long then heading almost anywhere northish would mean that I would eventually find it. I might have to walk up to 500 miles even if I was due south of the middle of the river, but otherwise maybe I'd have to walk anything up to the full thousand miles before my path intersected that of the river, depending on the line of sight.

Personally, I'd try and use the stars, not the sun. I lived in the Southern Hemisphere until I was 18, and I know how to use the Southern Cross for orientation. (To my shame, I don't know how to do that in the areas of the Northern Hemisphere where the Southern Cross is invisible - but I'm now about to go and Google to find out how :) ).

djinn
2009-Oct-14, 12:16 PM
PS to my last post.
re my "Answer to Q3"
It would also, ofc, depend on the orientation of that river. My example assumes a straight river that flows directly east > west (or vice versa). If it was "angled" then it is possible that half the time I might never meet the river, even if I was only a few degrees out with my original "approximation".

hhEb09'1
2009-Oct-14, 01:25 PM
If anyone would like to see the original material that Craig is commenting on, please contact me. I would be glad to send you a copy.I wager that it's the Finding Your Way video (http://thehappyscientist.com/science-video/finding-your-way).

Unfortunately, you have a pay-for-viewing site, so we can't check the claims directly.

djinn
2009-Oct-14, 01:51 PM
I wager that it's the Finding Your Way video (http://thehappyscientist.com/science-video/finding-your-way).

Unfortunately, you have a pay-for-viewing site, so we can't check the claims directly.

Heres's a free site that explains it so simply that even I can follow it. Good old Scouts :)
http://www.142group.net/scouts/Skills/Findin%20North.htm

Edited quote -
"1. Set up your shadow stick and mark the first shadow in the morning.
2. Use a piece of string to draw a clean arc through this mark and around the stick.
3. ...In the afternoon.... at the point where it touches the arc, make a second mark.
4. Draw a line through the two marks to get an accurate east-west line."

And it showed me how to find north using the Plough and Cassiopeia. I'm sorted now :)

01101001
2009-Oct-14, 02:16 PM
I would hope to be accurate to within a few degrees.

You won't get that in a few minutes without special circumstances. If it's an emergency, you probably don't have the time to get that sort of accuracy.

Fortunately it's rarely needed. If you do need that high accuracy and can afford the time, then use a more luxurious method.

Otherwise use the quick method and locate an estimated direction to start walking to find that path, road or river that will guide you to a target. (Or stay where you are, according to most advice to the lost.)

djinn
2009-Oct-14, 02:44 PM
You won't get that in a few minutes without special circumstances. If it's an emergency, you probably don't have the time to get that sort of accuracy.

Fortunately it's rarely needed. If you do need that high accuracy and can afford the time, then use a more luxurious method.

Otherwise use the quick method and locate an estimated direction to start walking to find that path, road or river that will guide you to a target. (Or stay where you are, according to most advice to the lost.)

I agree that if time is of the essence it would be better to use another method but as this thread is more about establishing true north than surviving when lost.... (and, anyway, I just wanted to know how to orient myself as accurately as possible).

I have been thinking some more about what you said about sighting the sun at sunrise (valleys etc). If the visible horizon is not at the same altitude as the observer you could get quite an inaccurate result. It doesn't matter whether you are in a valley or on top of mountain. We've probably all stood on a mountain and seen that the sunlight only hits the land level with the horizon much later, sometimes hours later. Roughly speaking, (depends on time of year and latitude ofc) for every hour you "mis-estimate" sunrise you would be 15 degrees out, no? (180 degrees/12 hours of daylight). That's quite a lot.