NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Graphical solution
From: Thomas Alley
Date: 1997 Feb 14, 20:57 -0500
From: Thomas Alley
Date: 1997 Feb 14, 20:57 -0500
>Given a polar plot of the expected performance of a sailboat, given your >present position, and given the place you want to get to, is there a simple, >graphical plotting method one canue to determine the optimal course? Without going into a great amount of detail to check this, I would think the following would hold true: Given a chart on which your desired course is plotted, superimpose the polar plot over your current position on the chart and align it with the current wind direction. Using a set of parallel rules (or equivalent "rolling" ruler), align it to be perpendicular to the desired course such that the ruler is between your boat and its destination. Bring the ruler closer to your current position until it just touches the polar diagram. Draw a line from your current position to the point of tangency. This line represents the course that will give you the maximum rate of progress towards your intended destination. The second step will be to determine a limit for cross track error from the desired course and to tack back and forth when this limit is achieved. This effectively keeps the desired track centered on each leg of every tack. This approach is strictly theoretical and will be compromised by practical considerations. Examples include, but are not limited to: o Sea state may limit pointing ability or be too hard on the crew for extended beats. Easing off a bit will make for a much more comfortable ride but at the expense of a sub-optimal course. o Prudent seamanship may suggest deviations from the optimal course to avoid charted hazards or to minimize the time one is in an area with heavy shipping traffic. o As the wind direction and sea state change, the "optimum" course will change along with it and needs to be recomputed. o Following the "optimal" course for each individual wind shift may result in a course that is less than optimal when considered over the entire voyage. (Consider the racing tactic of anchoring in light winds when caught in a foul tidal current.) Hope this helps. Anybody have any other ideas? Tom ------------------------------------------------------------------------ Thomas Alley alley@acm.org KD2VH, Youngstown, New York Alberg 35, "Tomfoolery" From mail Sat Feb 15 08:37 EST 1997 Received: from dg-webo by wellspring.us.dg.com (5.4R3.10/dg-gens08) id AA29206; Sat, 15 Feb 1997 08:37:40 -0500 Received: from gw-ronin.mv.net by dg-webo.webo.dg.com (5.4R3.10/dg-webo-v1) id AA10513; Sat, 15 Feb 1997 08:37:38 -0500 Received: (from root@localhost) by gomoku.ronin.com (8.6.9/8.6.9) id IAA28081 for navigation-outgoing; Sat, 15 Feb 1997 08:20:10 -0500 Received: from prepress.pps.com (gw.pps.com [204.176.216.2]) by gomoku.ronin.com (8.6.9/8.6.9) with SMTP id IAA28076 for; Sat, 15 Feb 1997 08:20:04 -0500 Received: by prepress.pps.com (4.1/SMI-4.1) id AA15852; Sat, 15 Feb 97 08:32:19 EST Received: from harlie.pps.com(192.168.1.4) by gw.pps.com via smap (V1.3) id sma015850; Sat Feb 15 08:32:15 1997 Received: from AlphaMail.pps.com by harlie.pps.com (4.1/SMI-4.1) id AA20711; Sat, 15 Feb 97 08:32:13 EST Message-Id: <737901@AlphaMail.pps.com> Date: 15 Feb 97 08:32:13 EST From: Bob.Trenkamp@gw.pps.com (Bob Trenkamp) Subject: Re: Graphical solution To: navigation@ronin.com Sender: owner-navigation@gomoku.ronin.com Precedence: bulk Reply-To: Bob.Trenkamp@gw.pps.com (Bob Trenkamp) Errors-To: owner-majordomo@ronin.com Content-Type: text Content-Length: 895 Status: RO --- Thomas Alley wrote: Given a chart on which your desired course is plotted, superimpose the polar plot over your current position on the chart and align it with the current wind direction. Using a set of parallel rules (or equivalent "rolling" ruler), align it to be perpendicular to the desired course such that the ruler is between your boat and its destination. Bring the ruler closer to your current position until it just touches the polar diagram. Draw a line from your current position to the point of tangency. This line represents the course that will give you the maximum rate of progress towards your intended destination. --- end of quoted material --- Tom, It's elegant - thanks. You're resolving any course into components parallel and perpendicular to the desired track and selecting the course based upon maximum component in the desired track direction. Neat. Thanks. bob