Naked Science Forum

General Discussion & Feedback => Radio Show & Podcast Feedback => Topic started by: David on 06/05/2010 09:30:02

Title: Triangulation needs three reference points
Post by: David on 06/05/2010 09:30:02

David asked the Naked Scientists:
   
ummm, not quite... the "triangulation" you suggest is actually bisection- triangulation involves three back-bearings and not two... if you are out on one or both of the two back-bearings as you suggested, then any rescue crew could in fact be quite a distance off course and would not know whether to cover left or right to make up for the inaccuracy (or east/west, etc.), however by using three back-bearings and not just two you actually create a triangle (!) and you MUST be located within this triangle, never outside the "lines", hence "triangulation"...

(David, formerly 45 Cdo, Royal Marines)
What do you think?

Title: Triangulation needs three reference points
Post by: Bored chemist on 06/05/2010 19:45:42

I'm not sure what you are on about.
A diagram might help but anyway, as I look out of my windows I can see two notable buildings. Exactly due North of me is the church of St Example. The tower of the new supermarket is exactly East of me.
As far as I can see there's only one place on the Earth's surface I can be that is consistent with that information. 2 bearings tell you exactly where I am.

Title: Triangulation needs three reference points
Post by: imatfaal on 08/05/2010 15:43:33

Hello BC and David

It seems that this may be a conflict between theory and practice. 

BoredC is, of course correct that theoretically an observer can take bearings on two points that form a triangle with him/her at the third angle and determine his position.  David, bearing in mind his experience in the armed forces is probably considering the observer as a human being who is inaccurate, tired and perhaps even injured.

If you have two points at 90 degrees to each other at 5km away from observer and we assume 1 degree error in either direction then the rough max error of position is 123metres. A third observation (at best) would lower this possible error to 88metres.  However in an extreme case if your two points are 120 degrees apart the error from two points would be possibly 175metres - the third observation would (at best) lower this error to 100metres.

I can see why David would advise that the recommended method is to use three measurements.  Additionally this would provide a check on ones one readings.  if your three bearings drawn on a map did not meet at a point you would know you had made a mistake, there is no similar way of knowing this with only two bearings.

My figures are based on an approximation and I would provide diagrams but I don't know how to.

Cheers
Matthew

Title: Triangulation needs three reference points
Post by: David on 08/05/2010 17:11:32

Using the term "exactly" is a little bit dangerous here... if one were only using grid bearings, a great degree of accuracy could be expected, however we're talking about taking bearings in the field which would be dependent upon magnetic and not grid bearings (and the previous comment by Bored Chemist is actually using the third "type" of north, true north, which varies from both grid and magnetic!)- depending on the age of your map, the magnetic declination could be inaccurately assumed and the adjustments normally estimated on ordinance survey maps are just that, estimates- the inaccuracies involved concern whether you are even using the current magnetic variation for that year and location (magnetic declination changes every year and the degree to which it changes is also not constant), and whether you are actually able to accurately measure the bearing using something like a prismatic compass where weather, technique, compass accuracy all become variables- my point essentially is that one will usually be less accurate taking field bearings, and when only using a bisecting technique, your location could, as exemplified by Matthew, be considerably off and rescue crews or fellow travelers, etc. would have to search a relatively unknown area to find you, whereas using three back-bearings, even if your back-bearings were slightly off, any searching team would know that you must be within the triangle created by slightly inaccurately measured bearings and therefore know exactly where to search...

Title: Triangulation needs three reference points
Post by: chris on 08/05/2010 20:25:27

Thanks, David, for your insights and thanks, imatfaal for an interesting perspective.

Chris