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 Post subject: Things all sailors should know - Radian Rule
PostPosted: 17 Nov 2007 12:06 

Joined: 20 Oct 2006 16:10
Posts: 684
Location: Out of Waukegan, IL
This is a Bowditch classic. I won't go into the deep math of things, (the broccoli) I'll just give you the end rule (the candy). This a game of approximation. All things are rounded off so you can figure things out in your head as you're passing time on the mid-watch.

Some givens...
Round of a Nautical Mile to 2000 yds.
D = Distance
S = Lateral Separation
A = Angular Difference in degrees

D/60 = S/A
DA/60 = S
etc... you can form it to fit your purposes.

Situation 1. You're 6 miles from your next port sailing due North. The wind shifts and you have to sail 010. How far off course will that make you.

S is what we're figuring out. So (6 x 10)/60 = 1 nm. Use whatever units for distance are handy, just keep it consistent.

What's really handy about that is that when you're doing some "what if" work when trying to reach a destination, just figure out the distance for 1 degree. So the distance divided by 60. 6 miles = 12000 yds. 12000/60 = 200 yds. Then as you choose your course you can multiply by the degrees off course. If you can only make 015, you have 15 x 200 yds = 3000yds - 1.5 NM.

Situation 2. Turn that around and make is something you want to avoid. We're looking at the chart and see that the lighthouse on the starboard bow at 030, 3 miles away, marks a point with hazardous waters. Lets say we want to give it wide berth and stay 1000yds (half mile) from the thing. You can get the plotter going or just do some quick head math.

3 Miles = 6000 yds. Divide by 60 = 100yds separation for each degree off of 030. 1000yds desired separation divided by 100 yards per degree = 10 degrees. So we need to steer 020 or left of that to stay clear .

Sure it's not all 6 and 12 mile figures, but with sailing there's usually time for a little long division in your head. Also this gets less accurate as the angle gets larger because in reality each degree would be slightly larger separation. But under 45 degrees angle the difference is negligible and we're just trying to get in the ballpark.

Any of this making sense? Not sure if this is news to anyone, but please post comments.

SMMO/First Mate aboard High Flight #299
1981 - Full Keel - Furling Main (A boat for the lazy crew...)

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