Saturday, October 24, 2009

A Table for the Mathematically Disinclined

October 24, 2009

Meredith made the 11:00 a.m. locking at Deep Creek Lock - she floated again at 10:45 just as the lockmaster was opening the gates. Actually she did not float but the tide was high enough that using our winch we were able to drag ourselves out of the mud using our anchor. [ No primordeal similes were injured in the making of this blog].

As beautiful as the Dismal Swamp is, especially now that the colours are turning, it can be tedious after the 3rd or 4th passage. Ten boats came through the lock with us yesterday and all ten tied up at the free dock at the visitor centre located mid canal. Six of those boats set off this morning for Elizabeth City. Weather on the Albemarle is snarly for the next two days and you all know what we think of the Albemarle, even in good weather.

It is a relief to be freed from the rigor of the daily destination schedule. Even better - we ran out of store bought bread this morning and Connie is baking fresh as I write.

Nothing will happen for the next couple of days.

Elaboration on Deviation from Course v Speed Needed to Equal or Better Time to Destination

A couple of people have asked for this and I am never one to avoid labouring a topic.

There is a chart toward the end for sailors who hate pedantic rambling and would prefer to just get the info.

In this age of GPS course plotting some very civilized sailing practices have fallen into disuse. Many crew are put to inconvenience and discomfort as a result.

When your direct route from A to B involves ploughing into uncomfortable waves or braving nasty wind too close to the nose for civilized sailing the proper practice is to deviate from the destination to ease the boat motion. Sailing across the waves at a 40 to 60 degree angle is usually much smoother and if you can get some wind in the sail - main or genoa - it will work wonders s for both the motion of the boat and its speed.

So why do people seem so intent on sailing the rhumb line come hell or high water?

The problem is twofold:

firstly: once you deviate from your direct course you are no longer taking the route calculated for you by the GPS or chartplotter. The helmsman cannot watch his progress against the reassuring computer drawn rhumb line. (The Rhumb line is a straight line drawn on a nautical chart from point A to B. It is not really straight but only appears so due to the scale of the chart.) This lack of computer support seems to throw a lot of people into a state of apoplexy.

secondly: Obviously when you deviate from the "direct" route you are no longer taking the "shorter" route. People then often assume the longer distance means longer travel time. This proposition is not correct.

The first and most important reason to turn off the wind and waves is to grant increased comfort to all aboard. Even if a trip takes longer why not enjoy it a bit more. A smooth ride for 12 hours is preferred to the hobby horsing bumper car ride the lead boats from Deltaville were on yesterday even if the GPS did think it would take only 11 1/2 hours.

Often diverting from a direct course can be quicker as well as smoother. Here is how it works:

The diagram was drawn in Geonext, a free geometry program and the table was prepared in Quattro Pro. The ideas came from Tom Cunliffe, Bill Siefert and the Budget Committee - especially where comfort at sea is concerned:

A boat at Point D wants to go to Point A. It is making about 5 knots pounding into that famous Lake Huron short chop.

If the skipper proceeds direct from Point D to Point B he must go 9.0 nautical miles.

If the skipper turns off the direct course and proceeds instead to Point C he must then go 10.77 nautical miles.

Both Point B and Point C are the same distance from the destination, Point A (they must be as they are both points on a circle which has point A as its centre).

The angle of deviation is 13.82 degrees.

Assume the boat is Meredith and she is making 5.0 knots on the course from Point D to Point B.

If by deviating from the straight line course the skipper can increase his speed from 5 knots to

secant (13.82 degrees) x 5.0 = 1.029812 x 5.0 = 5.15 knots

then he will be just as close to his destination. If by deviating the skipper can increase his speed more than .15 of a knot then he will be arriving early.

If he also gives his passengers a smoother ride the skipper wins twicefold.

You can check the math on the chart that follows. Find the row that says "Boat Speed" is 5 knots and look across to the 10 degree line. It says for a 10 degree deviation you must increase your speed to 5.1 knots to arrive at the same time. For a 15 degree deviation you must increase your speed to 5.2 knots. You can read between the numbers to get close to 5.15 (I mean really how accurate is your knot meter while pounding into a 5 foot short frequency sea).

On Meredith it really does not matter how much out of the way we are going. A smooth ride always wins. I mean we are only going 5 kts. What's our hurry?

When you use this to justify deviating make sure you consider the effects of having to "finish" the trip: make sure the wind and waves are bearable when you have to make your course good.

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