### Author Topic: Liquid Prismatic Compasses  (Read 9933 times)

#### Brian

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•   • Posts: 118 ##### Re: Liquid Prismatic Compasses
« Reply #15 on: June 24, 2012, 05:29:43 PM »
Brian

Quote
My question would be:  How precise must we be?  (Yes, I know the formula . . . degrees declination X distance ÷ 60 . . . to calculate the distance "off" you might be.)

I've never come across this formula, perhaps because magnetic declination in the UK is very small. Can you explain its mathematical basis and from what you are supposed to be 'off', please? (I've never had to use a compass in a country where there is a significant difference between true and magnetic north.)

Thanks!

Hugh

My source, with the formula's explanation and examples, is here:  http://tinyurl.com/6wff3nx  It's called the One in Sixty Rule and it's evidently used by pilots.

My quick and dirty formula is:  ( [distance-traveled] X [degrees-of-error] ÷ 60) = distance "off" (right or left) when you've traveled that distance.

For example:  I want to travel 500 meters to my attack point, and my bearing should be 140 degrees.  But I actually walk 500 meters on a bearing of 142 degrees.  When I've traveled 500 meters, how far from my attack point (right or left) will I be?

500m X 2o = 1000
1000 ÷ 60 = 16.7m "off" (In this case, my error would be to the right of my attack point.  Had I walked a bearing of 138 degrees, my error would be to the left of my attack point.)

Using 60 is about 90% accurate.  But it's much easier to use and remember 60 than using the actual value of 57.3.

A more precise one would be ( [distance-traveled] X [degrees of error] ÷ 57.3) = distance "off".  So:

500m X 2 = 1000
1000 ÷ 57.3 = 17.45m "off" (right or left).

« Last Edit: June 24, 2012, 07:23:24 PM by Brian »

#### Callum

• Hero Member
•     • Posts: 512 ##### Re: Liquid Prismatic Compasses
« Reply #16 on: June 27, 2012, 01:26:44 PM »
Which compass did you go for in the end Ivo?

#### Skills4Survival ##### Re: Liquid Prismatic Compasses
« Reply #17 on: June 27, 2012, 02:16:47 PM »
will go for the silva expedition 54, not bought yet though.
Ivo

#### Rescuerkw

• Guest ##### Re: Liquid Prismatic Compasses
« Reply #18 on: June 27, 2012, 09:14:24 PM »
Well, if it's any help to the debate I've been using a Suunto MC2 mirror compass for some time and I'm very pleased with it. Does the job for me.

#### Hugh Westacott

• Sr. Member
•    • Posts: 306 ##### Re: Liquid Prismatic Compasses
« Reply #19 on: June 29, 2012, 09:54:46 AM »
<My source, with the formula's explanation and examples, is here:  http://tinyurl.com/6wff3nx  It's called the One in Sixty Rule and it's evidently used by pilots.

My quick and dirty formula is:  ( [distance-traveled] X [degrees-of-error] ÷ 60) = distance "off" (right or left) when you've traveled that distance.

For example:  I want to travel 500 meters to my attack point, and my bearing should be 140 degrees.  But I actually walk 500 meters on a bearing of 142 degrees.  When I've traveled 500 meters, how far from my attack point (right or left) will I be?

500m X 2o = 1000
1000 ÷ 60 = 16.7m "off" (In this case, my error would be to the right of my attack point.  Had I walked a bearing of 138 degrees, my error would be to the left of my attack point.)

Using 60 is about 90% accurate.  But it's much easier to use and remember 60 than using the actual value of 57.3.

A more precise one would be ( [distance-traveled] X [degrees of error] ÷ 57.3) = distance "off".  So:

500m X 2 = 1000
1000 ÷ 57.3 = 17.45m "off" (right or left).>

Thanks for this, Brian!

I now understand the maths but is it of any practical value to a walker? I'm trying to think of circumstances in which it might be used. We are all familiar with aiming off to pick up a collecting feature which then becomes a handrail which will take us to our destination or the end of a leg. It seems to me that these techniques combined with pacing, timing and a square search would cover most situations.

When I mentioned that the magnetic declination angle is small in Britain I meant in comparison with the United States. I did not mean to imply that it can be ignored when there is a need to navigate accurately.

Hugh

#### captain paranoia

• Sr. Member
•    • Posts: 384 ##### Re: Liquid Prismatic Compasses
« Reply #20 on: June 29, 2012, 01:54:14 PM »
The 'one in sixty rule' comes from some simple geometry.

If we take an arc of a circle of radius R, subtending and angle theta (expressed in radians), the length of the arc is given by R.theta.

Now, there are 2.pi radians in a circle, so one radian = 360/(2.pi) degrees = 57.29577 degrees.

To a sensible level of precision, we can consider one radian to be 60 degrees.

Thus, the length of the arc can now be calculated using the angle in degrees (let's call it phi) = R.phi/60

The radius of the arc is the distance to the landmark/waypoint, and the arc length is the error,  so we have error = distance * angle / 60.

Of course, we must also consider the compass reading angular accuracy, as this also gives an error term that is also calculated by the one-in-sixty rule.

#### captain paranoia

• Sr. Member
•    • Posts: 384 ##### Re: Liquid Prismatic Compasses
« Reply #21 on: June 29, 2012, 02:02:49 PM »
> I now understand the maths but is it of any practical value to a walker?

Well, if you're navigating blind, and walk on a bearing for a given distance, deliberately aiming off by some known angle, then you can calculate the bounds (min, max) of the distance you need to walk when you get to the aiming point (combining aiming offset angle, walking error angle bounds and compass accuracy bounds), to find your true destination.  If you know how far you expect to have to walk, you should know when you've gone wrong (e.g. you've had to walk too far, so either you've missed your target, or something has gone horribly wrong...).  If all has gone well, and you've followed your intended bearing perfectly, then you should arrive at your destination after walking the the mid value of calculated distance (distance * aiming offset angle / 60, since there were no compass or walking arrors).

#### Callum

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•     • Posts: 512 ##### Re: Liquid Prismatic Compasses
« Reply #22 on: June 29, 2012, 05:13:38 PM »
Thanks Capt., and now I can see its application, thanks Brian.

Do you instruct it Brian to your SAR Responders and if so with slides? I am fishing here for help #### Brian

• Full Member
•   • Posts: 118 ##### Re: Liquid Prismatic Compasses
« Reply #23 on: June 30, 2012, 05:31:46 AM »
Thanks Capt., and now I can see its application, thanks Brian.

Do you instruct it Brian to your SAR Responders and if so with slides? I am fishing here for help Hi Callum,

Yeah, I do teach the "One in Sixty" principle.  I don't spend much time on it since it is ancillary to what students must learn to pass the Oregon State Sheriffs' Association (OSSA) examination.  And, alas, I need to teach "to the test."  So all I do is tell them what the formula is, why it's important and how to use it.

I feel that touching on "One in Sixty" is important because it provides a mathematical/logical principle fundamental to accurate compass navigation, one that is easily grasped (in the sense of "Oh!  That makes sense!") even if it is not actually remembered.

I don't teach the trig/geometry underlying the formula.  My hope is that they will at least appreciate that there is a logical basis for calculating error, and that they will have some idea of the magnitude of an error, should they be a few degrees off in walking a bearing for a given distance.

Also, I use this formula to emphasize the need for knowing your pace and keeping track of it when you're on the go. Once you've walked the proper distance, now you can begin a rational search for your attack point, if you've missed it.

I have one or two uninspired (and I mean uninspired!) slides, at most, which are not much more than the formula itself, and an example or two.  You're certainly welcome to whatever I have, though I'm sure you can produce slides as good or better than the ones I made.

Let me know if you'd like it/them.

#### Hugh Westacott

• Sr. Member
•    • Posts: 306 ##### Re: Liquid Prismatic Compasses
« Reply #24 on: July 01, 2012, 04:24:24 PM »
> I now understand the maths but is it of any practical value to a walker?

Well, if you're navigating blind, and walk on a bearing for a given distance, deliberately aiming off by some known angle, then you can calculate the bounds (min, max) of the distance you need to walk when you get to the aiming point (combining aiming offset angle, walking error angle bounds and compass accuracy bounds), to find your true destination.  If you know how far you expect to have to walk, you should know when you've gone wrong (e.g. you've had to walk too far, so either you've missed your target, or something has gone horribly wrong...).  If all has gone well, and you've followed your intended bearing perfectly, then you should arrive at your destination after walking the the mid value of calculated distance (distance * aiming offset angle / 60, since there were no compass or walking arrors).

Hmm... As I say, I understand the maths but it sounds horribly complicated. I'm a simple soul and in the unlikely event that I were in that situation I should much prefer to aim off, pace or time the distance, then make a right-angle turn and pace the distance indicated by the accuracy by which I know I can navigate over that distance, and then conduct a spiral search. The fascinating property of a spiral search is that, theoretically and given infinite time, you could always find any spot on earth from any other point.

Nevertheless, the theory on which the 'one in sixty rule' is based is interesting and I'm glad to have learnt it.

Hugh

#### captain paranoia

• Sr. Member
•    • Posts: 384 ##### Re: Liquid Prismatic Compasses
« Reply #25 on: July 02, 2012, 01:03:56 PM »
> Hmm... As I say, I understand the maths but it sounds horribly complicated. I'm a simple soul and in the unlikely event that I were in that situation I should much prefer to aim off, pace or time the distance,

Then I have made it sound more complicated than it is; possibly due to explaining the geometric origin of the technique...

> then make a right-angle turn and pace the distance indicated by the accuracy by which I know I can navigate over that distance, and then conduct a spiral search.

That's all the one-in-sixty rule is trying to achieve; to calculate the known accuracy distance that you need to walk when you turn at right angles.

BTW, my suggested application is one that simply occurred to me when I read the rule (which I'd never seen before); I don't recall ever using it in practice, and it's not one I've seen documented...  Usual problem of an engineer taking a mathematical principle and trying to use it to solve a 'problem'...
« Last Edit: July 02, 2012, 01:06:29 PM by captain paranoia »