Author

Topic: 314

M. C. Rowley

posted August 13, 2005 03:02 PM
OK, I am stumped on this one! We know that the true course to Brotchie Ledge LIght from buoy Y "SA" is 300T. If the wind (in subsection C) is from the northwest, I am assuming it is from 315T. Therefore, there is a 15 degree angle between our course and true wind direction. Not being a sailor, I have a limited understanding about the concept of tacking. I am assuming here that we are headed upwind at a 45 degree angle when we tack (both port and starboard) to the true wind which means we are headed half the time on a true course of 270 and 000 the other half. If this is the case then we will not end up at Brotchie Ledge but at a point east of it. Now if I tacked along the 300T bearing then the distance should simply be be the sum of all of the hypotenuses or simply 1.4142 x the rhumbline. This would give a distance of 1.4142 x 25.75 nm = 36.42nm. I am obviously off here and I am assuming it is becaue of the 15 degree difference from the rhumbline and the true wind direction and because I probably have no clue what I am doing. I would appreciate some guidance here....thank you in advance.
Mark Rowley Santa Fe, New Mexico


David Burch

posted August 16, 2005 02:24 PM
When tacking you will not necessarily be 50% of the time on each tack. This depends on the wind angle. If the target is exactly downwind (not the case in this problem) then 5050 is right. Regardless of what route you take, you will be on opposite tacks the same amount of time  assuming of course steady winds and no currents.
You will travel the same distance no matter what tack or what route you take, providing you are starting out the same distance downwind.
Also the trick of computing the tack distance using 1.5 times the rhumbline distance assumes the target is indeed dead down wind. If you are close to the layline, meaning one short hitch on one tack and then you stay on the other tack all the way to the target (as in boat C in the drawing) then you are closer to using the actual rhumbline distance as you are in effect reaching to the target.
Notice that each boat must sail 14 "units" to get there, regardless of route, and they could of course start on the other tack as well. Note too that after sailing say 4 units they are still equal distance off and again at 8. So unless one actually goes faster, it will not get there quicker.
(In the real world, if you do a lot of tacks you may lose some as tacking is not efficient, on the other hand if you tack just once or twice, you go farthest off the rhumbline and gamble that conditions might change unfavorably. To optimize efficieny, racing or cruising, one has to balance out these two factors.)
Note that Boat A is on port and starboard tack the same amount of time regardless of routes, whereas B is slightly more on port tack, and boat C is way more on starboard tack.
I think the answers in the book are right, but i will check that as well. (There was some question about this problem in the past.)
From: Starpath, Seattle, WA


