Sunday, June 20, 2010

Hit or Miss: the Baseball Approach to Navigation

June 20, 2010
London, ON

Learning that the Budget Committee and I crossed the entirety of Lake Ontario spending all of our time below and only checking for conflicting traffic every 15 minutes many of our friends asked if this was safe.

Some went further.  There seems to be an inexhaustible supply of people who Know-It-All-But-Have-Never-Done-Any-Of-It.  One of these mounted his high horse and saw fit to lecture us on our irresponsible navigation practices.

Poppycock and bulltwiddle. 

There is no need to scan for conflicting traffic on Lake Ontario any more often than every 15 minutes.  There is nothing on the lake that I can hit in 15 minutes.

If an object on the lake is not visible on a scan there is no way my boat can hit whatever that thing is before the next 15 minute scan.  This includes other sailboats, rocks and even lake freighters.

Here is a chart that attempts to explain this:

                             Distance  Closing  15 Min    Margin
                             Seen      Speed   Distance 

Freighter   14.5 km    38     9.5 km    5.0 km
Powerboat    7.7 km    32     8.0 km    0.0 km
Sailboat    15.0 km    24     6.0 km    9.0 km
Rock         4.5 km    12     3.0 km    1.5 km

A scan every 15 minutes ensures we have lots of warning of all threats except for powerboats.  

eg.  We can see a lake freighter when it is about 14.5 km away.  If the lake freighter was just out of sight on the first scan, ie. just more than 14.5 km away we would not see it of course.  When we performed the second scan the lake freighter would have traveled 9.5 km and when we did the second scan that freighter would still be 5 km away.  

In working the chart we made some assumptions on the height of the object: lake freighters were 15 m high, sailboats the same, powerboats were 3 m and rocks 0.  Speeds are the worst possible case, ie. the sum of Meredith's speed plus the speed of the object coming head on toward us.  If the object were not on a head on collision course its speed would be less.

For all objects save a powerboat there is ample safety margin.  If a powerboat with a horizon of 7.7 km was just over the horizon when a scan was done and it then proceeded directly towards Meredith at a speed of 10 knots then Meredith and the powerboat would actually collide just before the second scan was done.  If the powerboat were travelling faster than 20 kph then the collision would occur sooner.

This risk was one we were prepared to accept in the circumstances.  For an accident to occur the following would have to happen:

1. a powerboat would have to be in midlake, travelling at speed, and on a head on collision course with Meredith and be just barely out of sight on the first scan.
2. the powerboat would have to proceed at speed directly towards Meredith's bow with no alteration of course at all, ie. it would have to maintain its head on collision course at full speed for the entire 15 minutes.
3. the skipper of the powerboat would have to completely ignore what was coming (like we were doing on Meredith)
4. No one on Meredith would hear the engines of the powerboat.

We accepted this risk. 

The Math:

How Far Away Can You See an Object?

formula: distance in kilometres at which a person on one object can see a second object: SQRT [12.7 x (height in metres of first object + height in metres of the second object)],

How Fast Do Objects Close?

Two objects moving towards each other are moving towards each other at their combined speed.  A sailboat travelling 12 kph moving towards a freighter going 26 kph will find the distance between vessels closing at  a rate of 38 kph.

The speed of the lake freighter, 12.8 knots or 26 kph is the max speed of English River, the only freighter we have ever encountered on Lake Ontario.,

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