Two years now since I first bought the plans and although I'm about £3000 poorer, I do have what is recognisably a boat in my back garden. I've also learned a great deal on the job and have an increased - and possibly ill founded - confidence in introducing modifications as work proceeds.
The centreplate has now been fitted and removed several times whilst I played about with various pulleys systems for operating it. The plate weights 50 kg and, due to the length of the lifting arm, requires a force of 63 kg to lift it: a couple of triple blocks reduces this to about 19 kg - manageable.
Now this pulley business turned out to be more complicated than I realised. First of all, the mechanical advantage of a pulley system (I think nautical people call it the 'fetch') can be seen from the number of lines leading to and from the moving block, so that a single moving block has two lines (fetch of 2 x) unless it has a becket when the mechanical advantage becomes 3 x. This, however, is only the theoretical advantage as each pulley rotates against friction: using a Barton single block I found by experimenting that about 8% of the force applied was used to overcome friction = 92% efficient. But, this friction goes up as the mass to be lifted increases and down once the pulley starts rolling. Also, ever wonder why some blocks have bigger pulleys than others? It's not to do so much with breaking strain but with the fact that the force needed to overcome pulley friction is inversely proportional to the diameter of the pulley.
With a couple of triple blocks (with the becket on the fixed block) I had a theoretical mechanical advantage of 6 x but with each of the six pulleys needing about 10% of the force applied to counter friction. The formula for calculating the force, F, needed to shift mass M therefore is given by:
- where f = the % of force used to overcome friction per pulley (so 10% would be 0.1), n = the number of pulleys and m = the mechanical advantage
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It gets worse! Because the tension in each of the lines feeding to and from the pulleys is different (by the amount needed to overcome friction) one block will tend to twist in relation to the other. This results in the tension in each line being applied at a slight angle (reducing its effect a little) and can also lead to one or more of the lines fouling one or more of the others - particularly as the blocks approach close to each other. (Fiddler blocks avoid this tendancy to twist since the pulleys are not side by side.) To reduce this possibility, some thought needs to be given to how the lines are fed through the blocks (reeving), some examples from Harken and Barton being shown below.
A related consideration is the size of the line used; I'm not sure why but a 3 mm line seemed to require less force than a 4 mm which, in turn, seemed more efficient than a 6 mm - possibly the chances of one line fouling an adjacent one are reduced with smaller lines. Of course, it needs to be borne in mind that the likely tension in a line shouldn't exceed about 15% of the breaking strain (important for shrouds) or about 25% where tensions are less likely to vary a lot (like my centre plate).
It sounds just about impossible to arrive at an accurate estimate of line tensions in pulley systems - I mean you really have to admire those Vikings - but, somewhat to my surprise, the eventual force needed to raise my centreplate was just over 20 kg - near enough to the theoretical figure of 18.6 kg.
