Mast Bend

[PI Design]

Hello,
I think that mast design is one of the most important, but least understood (by me at least!), aspects of boat design. I have a question regarding mast bend for dinghies. I am able to calculate how much any given mast will bend, but how does one know how much bend is desirable? You don’t want it too stiff, because it won’t respond to gusts well enough and will heel the boat. You don’t want it too flexible, because it will spill power unnecessarily. Bethwaite talks about the concept of a design wind, which is the wind at which the boat is powered up so that heeling moment = max righting moment. Beyond this, the mast should flex so that any extra force is spilled and the heeling moment doesn’t increase (too much). I understand the principle, but how does this work in practise? The mast must be flexing before the design wind is reached – it can’t be rigid and then suddenly bend at some magic force. So it must already be de-powering before design wind. It will continue bending in a steady, continuous manner as the design wind is reached and exceeded. The rate of change of bend will not increase significantly. So how can one tell how much mast bend is required to spill a given amount of power? Do you want a 10 degree bend at design wind? 15 degrees? This is the bit I don’t get – how much bend do you need to be de-powering effectively? It is as if Bethwaite is saying that the amount of bend you get up to the design wind is acceptable, it doesn’t de-power you too much. At design wind the mast bends by some critical amount, at which point the wind in the sails is spilled.
Can anyone shed some light? Please.

Doesn't it depend to a large degree on the planform of the main? For instance, even with a stiff mast a squaretop can depower automatically
which is different behaviour than a "normal" fully roached or triangular sail.

[PI Design]

Absolutley, yes. I think a squaretop main twists off in a gust, so does not require the mast to bend to achieve depowering. In many ways I see that as a simpler (and better) solution than the Bethwaite flexy mast. I am surprised none of the Bethwaite boats take this route.
However, I want to try to understand how the Bethwaite style mast works. Their boats use a largish roach mainsail (but not square top) and a flexible mast tip. What I don't get is how you know how much flex you want, other than by trial and error. There must be a mathematical way to at least get you in the right ball park, mustn't there?
P.S. For the purists amongst you, I know the Bethwaites are not solely responsible for this type of mast, but it is easy to refer to it this way.

[national]

If you were to imagine a graph of heeling moment vs wind strength. There is obvisouly a maximum righting moment that you can exert. in theory you would want the heeling moment to increae and then level off at you maximum righting moment. The aim of the mast and sail design is thereofore to design it so that as of your maximum righting moment the rig can be depowered so that anything above this can be reduced. The design of the mast cannot be treated in isolation as how sail interaction is paramount. not sure if that has helped at all but it came ot mind!!

[PI Design]

Thanks National, that's exactly what I was trying to describe, but you have done it much more succintly. The problem I have is - how do you get the heeling moment to remain constant once it equals the righting moment? As far as I can tell, the Bethwaite rigs try to do this automatically by letting the top of the mast bend off. But its not as if the mast could have been perfectly straight prior to the heeling moment equalling the righting moment. And it cannot suddenly bend shed loads once this value is exceeded. It is not an on/off, all-or-nothing thing. The mast will be bent slightly in 1 knot of wind, more bent in 10kts and a lot more in 30kts. Assuming that a 10kt wind produces a heeling moment equal to the max available righting moment, then the idea (as I understand it) is to let the mast flex significantly after this point, so that the sail does not produce any more force (or at least, in practical terms, much less extra force). As far as I can see then, the change in bend between 9 and 10kts should be fairly small, whilst the change in bend between 10 and 11kts should be fairly big. But this isn't possible, is it? The deflection is linear with force within the elastic region, so that each extra knot of wind produces the same change in mast bend. Therefore, the Bethwaite masts must be cunningly made so that at 10kts, the bend is just sufficient to ensure that it passes some critical value and thereby spills the sail enough to prevent it generating much more force. But how do you calculate what this critical value is - how do you know how much sideways bend you need to de-power a sail?

[national]

There is no exact formula otherwise a computer could win the olympics. The mast bends obviously from as soon as the wind blows. And this can be futher amplified with changing curvature of sail to alter the lift from the sail. You can also add bend into the mast without the need for the wind. By varying spreader angles and rig tension you can introduce mast bend. This is what people with alu masts have to do in order to de power. The main advantage of the flexy mast is the gust response. I think you are also falling into some of their marketting hype!! just because they say it doesn;t mean they are faultless. You can still capsize these boats and if their rig auto depowered like you are describing they never would!

[PI Design]

I agree exactly with what you are saying, but there must be a way of estimating how flexible you want to design the mast tip to be to respond to gusts, mustn't there? If you make it too bendy, you will lose power too soon. If its too stiff, it won't have any gust response. If I were to make my own mast, how would I decide how flexible to make it?

[Kaa]

I think it's a trade-off without a "universal" optimal spot.

I can think of a guy who says "In my area the winds are not too gusty, and I am a good skipper. I want power, not hand-holding. Give me a rigid mast.". And I can also think of another guy who'd say "Around here the winds are very gusty and I prefer to relax and not drive her hard. I will sacrifice some power for additional safety. Give me a flexy mast".

It seems to me that you are asking "how flexy is too flexy?" Well, the flexiness basically auto-depowers the rig as wind strength goes up. How much power are willing to trade-off? Well, ask the client! :-)

Kaa

[Stephen Ditmore]

Recommended reading:
http://www.wb-sails.fi/news/98_2_SideBend/SideBend.htm

[Andy P]

Originally Posted by PI Design

Hello,
I think that mast design is one of the most important, but least understood (by me at least!), aspects of boat design. I have a question regarding mast bend for dinghies. I am able to calculate how much any given mast will bend, but how does one know how much bend is desirable? You don’t want it too stiff, because it won’t respond to gusts well enough and will heel the boat. You don’t want it too flexible, because it will spill power unnecessarily. Bethwaite talks about the concept of a design wind, which is the wind at which the boat is powered up so that heeling moment = max righting moment. Beyond this, the mast should flex so that any extra force is spilled and the heeling moment doesn’t increase (too much). I understand the principle, but how does this work in practise? The mast must be flexing before the design wind is reached – it can’t be rigid and then suddenly bend at some magic force. So it must already be de-powering before design wind. It will continue bending in a steady, continuous manner as the design wind is reached and exceeded. The rate of change of bend will not increase significantly. So how can one tell how much mast bend is required to spill a given amount of power? Do you want a 10 degree bend at design wind? 15 degrees? This is the bit I don’t get – how much bend do you need to be de-powering effectively? It is as if Bethwaite is saying that the amount of bend you get up to the design wind is acceptable, it doesn’t de-power you too much. At design wind the mast bends by some critical amount, at which point the wind in the sails is spilled.
Can anyone shed some light? Please.

That's what the skiff type double spreader rig does - the rigging prebends the mast, so the mast bend is relatively constant up to a wind speed of 10 kts ( or 15 kts etc - depending on the tensions, stiffnesses etc ).
The mast is more flexy than a single spreader rig would be, but is held up better and more controllably by the extra rigging to the mast head.
The mast is more rigid up to the design windspeed, but then tends to act automatically to increase in wind. Side bend is reduced, and gusts create aft bend at the tip, opening the leech.
Combined with square head sails, if tuned correctly, much better than conventional single spreader rigs.
The mast can be lighter ( total (inc rigging )weight and inertia is lower.

[gggGuest]

Originally Posted by PI Design

In many ways I see [ a square top] as a simpler (and better) solution than the Bethwaite flexy mast. I am surprised none of the Bethwaite boats take this route.

They work in exactly the same way. The Bethwaite boats still have lots of roach at the top comparted to a traditional rig. The more the roach the stiffer the topmast has to be to get the same bend response and vv.

Its worth noting that the downhaul on a two spreader rig changes the preload on the mast and thus changes the triip point when the caps start unloaduing and the rig yields.

[PI Design]

Thanks for all the replies.
My work PC prohibits access to the WB Sails site, so I've not had the chance to read thier article, but thanks for the link, I'll check it out when I can.
Andy P - are you saying that these masts bend fore/aft in a gust, not sideways? I hadn't realised that. ggg - I'm not sure that they do, do they? The square top sail will twist off significantly, even if the mast remains straight. It acts a little like a gaff due to the discontinuity in the leach profile. The Bethwaite rigs require the mast to bend to depower the sail. Sure, you can still twist their sails by letting off the kicker, but this is not the 'automatic' depowering that Bethwaite claims. For his auto gust response to work, the mast must bend. For the square top sail to auto depwer, there is no need for the mast to bend (although some bend probably helps). I think this a fundamentally differenty approach to design, where the Bethwaite rig requires more attention to the mast design and the squaretop requires more attention to the sail design.
Kaa (and others) - but how do you translate a clients request for "I want the rig to depower at x kts" into a known amount of flexibility? How do you calculate that a certain amount of flexibility equals a certain amount of power? For example, two people sail Finns. One weighs 100kg, one weighs 70kg. It is a windy day and the 70kg sailor is overpowered all the time. The 100kg sailor is overpowered in some of the gusts. The 100kg sailor would want a stiffer mast. But how much stiffer? Presumably he wants the same amount of mast bend in the gusts as the 70kg guy is getting in the normal winds - but how much is that? Do you just do trial and error, or can you do some sums to work it out?

[gggGuest]

Originally Posted by PI Design

The square top sail will twist off significantly, even if the mast remains straight. It acts a little like a gaff due to the discontinuity in the leach profile.

You're forgetting that these rigs use very stable sailcloths. They can't twist off unless something gives, and the mast gives more than the leech! And if you lay a Bethwaite style sail over a squaretop you'll find there is only a small area that's much different. In practice too there is no absolute difference, they're just points on a curve. Look at the two boats in this pic where you can see the whole rig, one is square top, the other is halfway between that and Bethwaite's kind of rig. In all cases there needs to be a very precise match between mast and sail, I'd struggle to say that you need to pay more attention to one or the other.



What's going on with a cap shroud twin spreader rig is that the caps are holding the mast very rigidly sideways, but its free to bend fore and aft. But as it bends fore and aft the tension in the caps reduces. So in a really big gust the mast bends back and sideways as the windward cap goes slack. But up to the point at which the cap shrouds go slack enough to stop keeping the mast sideways its only really moving fore and aft.

[gonzo]

Your style of sailing determines, to a great extent, the mast setup and stifness. For example, a heavy, athletic crew will benefit from a stiffer mast. A light or out of shape crew will use a softer one. There are several mechanisms to adjust and control mast bend. The most usual are: boom vang, mast ram, stay tension and spreader angle. The shape of the sail also determines what kind of mast you need. There is no magical formula. However, there are ranges within which a certain type of boat sails best.