Thursday, 19 July 2012

Rainy Afternoons and Rudder Angles

Here is a tale about how a simple mathematical musing can uncover daunting new tasks requiring skills you don’t have to fix a problem you never suspected.

It all started rather innocently, as these things always do, when I was looking for things to do on the boat while waiting for the rain to stop.  I remembered that one of my books on sail trim suggested calculating the rudder angle while the boat was in dry dock, and this sounded like a great rainy-day activity.  As we say back home, “you may as well dance when it’s too wet to plough.”  Now admittedly, it is difficult to liken rudder angle calculations to dancing even by the most enthusiastic math nerd, but I was happy to find something that felt like a useful task on such a dreary day.  And, truth be told, it sounded like fun.

When you are under sail, you set and trim the sails according to the wind direction and the direction you want to go.  On a well-trimmed and well-balanced boat, the rudder stays more or less straight, in line with the boat.  Joshua Slocum’s Spray was a boat that was so well-balanced that he could simply tie a rope to the tiller to keep it centered and let her go for days at a time without adjustments (in steady winds, of course).  This was quite a feat in the days before auto-pilots, and was a major factor contributing to his successful solo-circumnavigation of the globe. 

When it is necessary to hold the rudder at an angle to maintain your bearing, it means that your sails are not well-trimmed.  Beyond a certain angle, the flow of the water against an angled rudder turns your rudder into a brake.  This is bad, and depending on the expert you consult, occurs between 6° and 9°.

Most boat steering wheels will have the center point marked so that you know when the rudder is straight.  Now the trick is to mark the point corresponding to 6° of rudder angle on either side the center mark to know when you are braking and need to re-trim the sails. 

If the rudder could turn 360°, the radius of that circle is the distance from the central pivot point (the rudder stock) to the trailing edge of the rudder.  On Spray, this distance is 37 cm.  Of course everyone remembers that the circumference of a circle is calculated using the equation:  c = 2 π r    (confession: I googled it.)  At MIT, where the sports teams were rarely the school’s strongest point, there was a cheer to amuse the crowd: “Cosine! Secant! Tangent! Sine! 3 point 1 4 1 5 9 ! ” so it’s easy for me to remember the value of π.  For my rudder with a radius (r) of 37 cm, this gives a circumference of 232 cm for 360°, and by a simple ratio calculation, the 6° of rudder angle I seek is located 3.9 cm from the center position.

With numbers in hand, we moved to the practical-application step.  With Patrick up top at the wheel and me beneath the rudder (no dummy, me… he got rained on while I was protected underneath the boat), I measured off 3.9 cm on either side of the center point and had him slowly turn the wheel until the rudder was lined up with my marks.  We did this a couple of times in each direction and he marked the 6° points on the wheel with a marker. 

“How’s it look?” I shouted up to Patrick.  The response was the worrisome French expression “Ooh laaa…”.  This is not to be confused with better known “Ooh la la” which is generally a happy expression of appreciation.  “Ooh laaa” is most appropriately translated as “uh oh” or, in certain cases such as this, “oh shit”.

I climbed up on deck and looked at the two marks on the wheel.  They were not symmetric from the center.  By a long shot.  One was a full 10 cm further away from the center than the other.  “Ooh laaa” indeed.  This was a clear indication of something we knew already but had not fully appreciated:  there was considerable play in the wheel.  When we took the boat out for a test sail, we noticed that there was some play, but it didn’t seem particularly bothersome.  Clearly, after lifting the boat out of the water a second time and 2 months in dry dock with various assaults inflicted on the rudder, the play had increased significantly. 

Back at home, I looked up how to stiffen up a limp steering wheel.  The forums all suggested it was something that could be done easily, but this sort of statement always leaves me a bit queasy.  The next day on the boat, we took advantage of a brief visit from the head mechanic to ask him what he thought about the situation.  He spun the wheel slowly, watching the quadrant rotate from side to side and pointed out that most of the play seemed to be coming from the rotator pin connecting the quadrant to the steering chains (rotule, in French; see photo).

The rotator pin connected to the steering quadrant.
This reminded me that Antoine, the boat’s previous owner, had left us a spare rotator pin in case we needed to change it.  The mechanic assured us that it was a simple affair to remove the old one and attach the new one.  When he had gone, Patrick, emboldened, started looking more closely at the situation and rapidly ran up against the first hurdle:  he didn’t have the right size of wrenches. 

As with so many things that we attempt to do on the boat, my simple “mark 6° of rudder angle on the wheel” has now become:
  •  Buy new set of wrenches.
  • Mark the current position of the rotator pin and bolts.
  • Remove the damaged rotator pin and install the new one.
  • Test the play in the wheel; if acceptable, proceed to next step; if not, turn the bolt on the connecting pin by 2 turns to tighten the chains; repeat as necessary
  • …and then, mark 6° of rudder angle on the wheel.