Monday, September 16, 2013

Where is south?

You, too, can be a space alien!  All you'll need are a stick, some sun, string, and a way of making marks.  At the end of this, you'll be able to perform feats that have caused many over the decades to say that the ancient Egyptians and others 'must' have been visited by space aliens.

What you'll do is construct a very accurate definition for north+south.  From there, you can build your own pyramid aligned accurately to north/south.  Technologies involved are all 6000+ years old.

So, first step is to get a long, straight stick.  You can verify that it's straight by checking against the string in your which way is up apparatus.  (Notice that it, too, only uses 6000+ year old technology.)

Next, put the stick in to an area of flat ground.  It's best if you plant it straight up and down.  You can use your terribly advanced up-down apparatus for guidance on which way is up.

Now for the hard part.  Tie the string around the stick and your marker.  Pull the string taut and mark a circle around your stick.  Retie the string to marker and shorten or lengthen the distance from stick, to make another circle.  Repeat a few times so that you have a variety of circle sizes.

Back to easy.  A little patience is required.  Each time the sun's shadow from your stick hits one of the circles, mark the location.  If you're in a cloudy place, you really want a bunch of circles.  What we're looking for is the shadow to hit the same circle twice -- once earlier in the day and once later.

Next to last: after you have a nice pair of marks on one of your circles, find the mid-point between the pair.

Finally: Draw a straight line from your stick to this mid-point mark.  This line is the north-south line for your location.

There are some elaborations you can do here, for accuracy and for large scale construction.  But you're now done with the basics.  And can construct your own objects aligned accurately to north-south, just like the 'space aliens'.  Well, more seriously, just like our ancestors from several thousand years ago.
Some elaborations:

You can find the midpoint between your marks by eye pretty well.  You'll be most accurate if the distance between marks isn't very large.  This means you'll want a circle that's not much larger than the shortest shadow of the day.  So for accuracy, you'll want to try 2 days.  On the first day, do the procedure above, but also mark the shortest shadow.  On the second day, draw a new set of circles, starting with one a bit larger than this and then getting larger.

You find the midpoint even more accurately by straight edge and compass angle bisection.  Name sounds imposing, but the application is simple enough that even clumsy me was doing it by age 10.

If it's summer, and especially if you live at low latitudes, the shortest shadow can be very short.  That makes it hard to have a long baseline for your north-south line.  After you've marked north-south, one way to make it as long as you'd like is to take a long roll of string and tie it to your stick.  Then walk it far from your stick and have a friend move you left and right until the string passes straight over your mark.

You can also compare your north-south line to magnetic north.  For almost all the world, magnetic north isn't the same as geographic north.  (Plus, magnetic north moves year by year.)  The difference between your line and magnetic north should be about the same as the magnetic declination calculated at

9 comments:

Oale said...

:-) , but how d'you know the ground is flat?

Robert Grumbine said...

:-) Knew I forgot something.

One could be fancy and carry a level around.

I prefer the marble test. Tennis and other balls could be used instead.

Put the marble on the ground in many spots in the vicinity of your circles. If the marble stays put, the ground is flat.

I use this technique for levelling my portable telescope.

Anonymous said...

Do it in winter on a frozen pool.

stone said...

@Anonymous
"Do it in winter on a frozen pool."
Good idea!

penguindreams said...

Agreed, two good aspects to one you have to be careful with.

On the good side, if it hasn't been windy, the ice surface will be very nearly level. It it has been windy, and you're still freezing, pour some water out on the non-level parts, and it'll freeze to make things level.

Second good point -- doing this in winter means the sun is lower in the sky, and you have longer shadows to work with.

The point to be careful of -- you don't want to walk out on to ice that isn't thick enough to support you. Falling through the ice can be deadly.

Still, with appropriate caution, this takes care of two of the largest challenges to the approach.

Kevin O'Neill said...

It's oftentimes not technology that's lacking, but the knowledge required to use it properly.

As an exercise in math class we were broken up into groups of 3, given a piece of graph paper and a pencil and allowed use of a yardstick and a protractor for 5 minutes, then sent outside to measure the height of the school building.

Most of the groups just guessed based on estimating the size of the bricks and stone and counting them. Unfortunately the building (approximately 30 feet high) wasn't made of uniform size bricks or stone and there were numerous areas of stone molding at various heights. Only two used theory. My group was one of them.

Inside the classroom we had made a rough copy of the protractor on the graph paper and measured the average 'step' of each member. Outside we moved away from the building until we could sight a 45 degree angle from the ground to the top of the building using our paper protractor. From that point we all paced off the distance to the base of the school, multiplied by our measured step lengths, and used the average of our results as our answer since.

If the space aliens had visited, knowledge would be their most important contribution.

Chris Nedin said...

But it doesn't tell you where is south.

The method gives you the direction to the rotational poles - geographic constructs. North and south are magnetic constructs. Granted, magnetic poles are generated by circulating fluid at approx. 90 degrees to the geographic poles, but you cannot identify north and south by identifying the geographic poles, since, as a space alien, that alone would not give you the magnetic field direction.

D.J. Andrews said...

I would argue knowing the direction to the rotational poles is the real north and south. I consider the magnetic poles to be the "false" direction because they move, and even trade places every few thousand years or so.

If you align your building with magnetic poles, it'll be out of line very quickly. If you align with geographic poles then your building will stay aligned because those poles aren't going to change appreciably.

Chris Nedin said...

Yes, knowing the direction to the rotational poles is the real north and south. But this method will only give you the direction to the poles. It will not tell you which pole is north and which is south.

In order to identify north and south, you would have to know beforehand either where north and south roughly were, or that you were in the northern or southern hemisphere.

A space alien wouldn't know these things, and so the method would tell them the axis of rotation, but not which pole was north and which was south.