The amount of leverage is determined solely by the distance of the handle from the axis of rotation of the rudder. Imagine a straight line extending up from the rudder post, and draw a line at right angles to it such that it hits the handle. (This second line will be approximately along the tiller arm.) In terms purely of leverage, i.e. how easy or difficult it is to push the rudder round, the shape of the metalwork connecting the handle to the rudder makes no difference. So, just because the swan neck takes the tiller arm "backwards" a little before coming forward to the handle, that in itself doesn't add more leverage. One way to see this is to imagine the bends of the swan neck filled in with solid metal - this imaginary metal can extend backwards, forwards, up or down - even left and right - as much as you like. The swan neck is still there, it's just got some extra metal attached. Now you could make the rigid structure connecting rudder and handle any shape you like, and then, if you wish, remove the "imaginary" metal. The ease or difficulty of pushing the rudder depends only on the distance of the handle from the axis of rotation.
Having written the above, I think I've just realised the importance of the shape. If the handle is connected to the rudder post in a straight line, which, in my treatment of the problem above is entirely feasible, then the small word "rigid" becomes especially important. Trying to move this would put a lot of force on the rudder post in a different direction to its normal rotation, and the straight connection would try to flex. If it doesn't flex, and if the rudder bearings can cope with the strain, than it would work, but it would obviously be impractical. As far as I can tell, the shape which would introduce the least unwanted stresses on the rudder bearings is a simple right angle - as on Ross Barlow. But if the shape has curves and a bit of springiness then it will absorb shocks better. Perhaps this is a good reason for the curves and the swan neckiness.
8 comments:
Rereading Dave's comments on the last post I think some of what he says is wrong. Firstly, although standing on the step is indeed the safest and most comfortable steering position, this isn't the main reason for the tiller extension(which after all is the major factor in making it dangerous to stand on the counter); the primary reason for the tiller bar is leverage. Steering a working boat takes a fair amount of force and even six inches on the tiller bar makes a lot of difference, which is why it needs to be high enough to clear the cabin top. When I used to steer Tarporley, the swan's neck had been bent slightly and the long tiller extension barely managed this - there was always a danger of catching your steering fingers on the top of the door. For that reason some people preferred to use a shortened tiller bar but I found it impossible to steer with that one exceptvat very low speeds.
Also, working boats don't (unless they are tugs) have a big deck at the front; they have a hold. And they definitely do not have a coal box behind the cabin or indeed anywhere near the tiller; the coal box is inside under the step.
Halfie, I have asked some historic boat owners about this burning question. So far I have had two replies:
Clearly there's no mechanical advantage - it doesn't give the steerer any more leverage.
But it is space saving. The tiller needs to be demountable from the rudder so there needs to be a collar with the tiller more easily connected horizontally and there needs to be a way of attaching the tiller extension necessitating a horizontal stub for it to fit over. "Folding" the tiller in to a Z shape means all this takes up little or no space - nor is it likely to foul ropes and cross straps. The royalty boats initially had C shape tillers with folding extension but whether these were found to get in the way or offended the boatman's innate conservatism I don't know - but they were all changed for the more conventional type.
and:
Having done a quick calculation, I think the swan's neck shape is to ensure balance of the rudder.
The tiller arm is quite long (approx 100 cm) but is a hollow tube and its centre of gravity is approx 50 cm from the axis of rotation of the rudder. The swans neck is solid bar (approx 125 cm long) much heavier than the tiller arm and, as it is bent back on itself, its centre of gravity is just over 10 cm from the axis of rotation. Thus the two parts of the steering more or less cancel each other out, do not put excess pressure on the rudder cup at the end of the skeg, and make the rudder easier to turn. On full-length boats with substantial rudders this is important.
Similarly, the rudder itself has a balancing plate forward of the axis of rotation which also helps to deflect the water throw.
The same effect could be achieved with a semi-circular curved bar in the swan's neck position but would look all wrong to a boatman - and might not be quite so well balanced.
If I get any more responses, I'll post them.
Sarah, many thanks for this.
I'm yet to be convinced on the space-saving argument - a vertical (all right, almost vertical) tiller with extension at right angles would take up less space and be always in the same place. An obstruction which never moves is less of a hazard than something which might be here one moment, there the next.
But I like the balance theory, and the fact that it makes separation from the rudder and fitting of the extension easier.
And, of course, as you say, it just looks better as a swan neck!
I'm probably going to make an idiot of myself now (I plan to ask an engineer tomorrow...) but actually it is starting to look to me, contra to what everyone else has said, that it could increase the leverage. Start at the bottom of the swan's neck and visualise just the first upward section, rising at an angle of approximately 30 degrees to the vertical. That in itself is a lever and it would be easier to move the rudder using that than with a completely vertical bar. Next, add the stub to which the tiller bar attaches. The end of this will be pretty much directly above the bearing where the first angle branched off from. Again, what is easier - to rotate the rudder using this stub, or using a direct vertical connection - but your hand is in the same place, directly above the bearing. I suppose that my contention is that the second angle magnifies the leverage of the first, rather than cancelling it out. Add an extension and it becomes easier still. So tell me why I'm wrong.....
I think you're wrong, Sarah, for the reason I tried to explain in the post. My understanding of physics is that the leverage depends only on the distance of the handle from the axis of rotation, not the route by which it gets there. I've just tried, and failed, to find an explanation on the web, so let's hope someone else can provide chapter and verse ...
OK, I have spoken to my tame engineer, and he agrees with you Halfie, that it doesn't make any difference to the leverage. I have also asked someone who's tried to steer with a right angled tiller, who is adamant that it does. And I thought it was economists who weren't able to see anything working in practice without asking whether it will work in theory....
The engineer does agree with my initial guess though that the stresses are less with those bends than with a right angle.
Something else we've not considered is that, at least on old boats, the rudder tube is not vertical, but angles slightly. The tiller therefore has to compensate for that, and then compensate again by bending back in the other direction.
Sarah and Halfie, I stand corrected and will keep looking for an answer.
P.S. Love both your blogs :-)
My goodness, what an interesting debate!
Post a Comment