NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: 0000 not 2400?
From: Charles Seitz
Date: 2004 Oct 18, 13:11 -0400
From: Charles Seitz
Date: 2004 Oct 18, 13:11 -0400
Aren't cyclic phenomena interesting? Sin(0) = Sin(n * 360) = 0 cos(0) = cos(n * 360) = 1 Where n is an integer multiplier If degrees equal to or greater then 360 then subtract 360 until degrees is less then 360. That's why Compass cards don't indicate 360 and, by analogy, why 24 hour clocks don't indicate 2400. The confusion occurs because a circle is divided into 360 angular parts but compass cards are zero based and show 0..359 (still 360 graduations, 0 mark plus 359 other marks). You steer 0 and not 360. Maybe I should have stopped here. If you don't want to be totally confused, please exit here. You are steering 90 deg and are asked to execute a 450 deg turn starboard. Don't scratch your head questioning the sanity of the order. Do it this way: Tun right and go around a full circle. Then, continue the turn until your compass indicates 180; Done. Accumulated degrees turned: 0 90 180 270 360 450 Magnetic compass: 90 180 270 00 90 180 Integrating compass (perhaps gyro driven): 90 180 270 360 450 540 Notice, the integrating compass does define 360 as a valid direction. If you still think there is a paradox, yes, it occurs when the integrating compass approaches full scale. Watching your magnetic compass, when you have turned an accumulated 270 deg, it will indicate 359.999999999999.... and finally go over to 0. No, in the real world of magnetic compasses, you don't get closer and closer to 360 but never get there. Watching you integrating compass, you can always get a magnetic reading by subtracting 360 deg until the result less than 360. Question: Isn't there an analogous situation for the cyclic behavior of clocks as elapsed time accumulates? --- CHAS