# Mast Deflection Speeds (esp dinghies)

Discussion in 'Sailboats' started by PI Design, Jun 26, 2007.

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### PI DesignSenior Member

You often here it claimed that composite masts bend quicker than aluminium ones, giving them better gust response (even for the same deflected distance ie EI value).

Is there any way to calculate the speed of deflection (time to max deflection) using beam theory? Rate of change of deflection is not something covered in any text book I have. I assume it is soley a material property thing, not geometric (ie a circular section wouldn't deflect more quickly than an I beam, given a constant EI).

Puzzled.

PI

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### Tim BSenior Member

I'm not sure that the speed of deflection has a huge amount of bearing on gust response. Certainly, a lighter mast will deflect faster (A=F/M), but I think the shape and stiffness properties (which can be tuned very carefully with composites) have more influence.

Of course, this is a non-trivial multi-physics question, and that's why few people can give a good answer at the moment.

You could get the speed of deflection from a 2nd order differential equation.

Tim B.

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### PI DesignSenior Member

I think the thinking is that the more rapidly the mast responds, the better it is - but I agree the difference must be very small and barely worth it.
A=F/M is as far as I got. I guess that a composite mast weighing 75% of an aluminium one can be assumed to reach max deflection in 75% of the time (ignoring second order effects), but what that base time is, I have no idea.

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### Steve BJunior Member

It must be a material property, given that the deflection is elastic so the moment of inertia (2nd moment of area) is unchanged. I seem to remember from uni that Youngs Modulus (E) was only approximately linear and actually changes with increasing load/strain, and of course it is different for each material.
Were you to plot a graph of load vs deflection for each material to see how the E value (gradient of graph) changes, this may give some insight to this interesting question. Intuitively I would say the material initially with the highest E value would take the longer time to bend. The areas under the two plots must represent the energy required to produce the deflection, so the higher initial stiffness material has the highest energy requirement. So long as the two masts are being tested by the same theoretical gust of wind, then the gust must take longer to supply a larger amount of energy.
Larch and Spruce are loads better than either ali or carbon fibre in this respect, and certainly have a lower Youngs Modulus. They can also be mended after a mishap and look nicer too!
Regards
Steve

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### PI DesignSenior Member

Hi Steve, interesting thoughts. If you plot load v (cantilever) deflection (as opposed to pure tensile strain) the gradient would be proportional to EI wouldn't it, rather than just E? And EI (stiffness) is the same for the two masts (to get the same deflection) so the area under the graphs would be the same?

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### Steve BJunior Member

It's not easy to explain without a pencil and paper but here goes ...
Yes, your graph's gradient is EI, by definition. Engineers assume E and I to be constants in elastic beam theory to simplify the maths. Provided the deflection remains elastic, then I will stay constant. Assuming there is no permanent bending this will be true.
E however does change and so does the flexural stiffness EI, but by an amount that can be ignored when factors of safety are built into structural designs. It's a long time ago but I'm sure we had to compare graphs of Youngs Modulus for aluminium with steel. Steel was linear then suddenly curved flat. Aluminium curved from the word go. Carbon fibre will do whatever it will. (It hadn't been invented then.)
If on a graph of cantilever load vs deflection you drew straight lines from the origin to the point at which each material's plot got to a given deflection you would get the average E value for each material. You then find I required for each material to give the same "average" figure for EI.
First however it's only an "average" value and secondly the path taken for each material to reach a given deflection will use up energy at different rates, which the same gust of wind must necessarily take different times to supply.
Clear as custard or what? And if you have a text book to hand can you remind me how to calculate the work done in elastic bending because this has something to do with it.
Regards
Steve

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response will be dependent on both the stiffness and mass. It is a complex computation that in today's world would be handled with a FEM/A simulation. However, this is also load dependent, and load prediction is more complex than modelling the structural properties.

As long as the mast does not break or deflect to a poor or non-functioning state, the rate of deflection of carbon vs. Al will have very minor impact on performance. Bigger impact on performance will be felt by weight aloft affecting the boat stability, and stiffness to hold sail shape.

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### PI DesignSenior Member

Thanks Steve - I see what you'e saying, initial E, not average E. Energy (Work done) = force * distance, so (without looking it up), I assume you can take the max deflection multiplied by some coefficient for the the distance.
Hi Water Addict - At least the load is the same for the masts being compared, so accurate load modelling isn't so critical. I have ANSYS FE, but confess I have not tried to solve this type of problem before (its not work related, just curiousity). I'll read the manual (!!!!), to see how (if) it can be done. I agree, you wouldn't think rate of deflection would be different enough to have any significant impact, but better sailors than me reckon it does. Mind you, that's not to say they know what they are talking about, or are able to understand and isolate the factors that they desire.
I'm not 100% convinced that saving, say, 2kg on a 6m mast has that dramatic effect on stability either. Every little helps, I suppose, but the effect must be pretty small.

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### Raggi_ThorNav.arch/Designer/Builder

I think it has to do with the composite vs solid material. A composite may have a nonlinear elasticy. I don't know if this apply to carbon masts with unidirectional fibres, but in a fibre/resin mix the fibres has to be straightened before they start to absorb much energy, you can imagine, I hope

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### froshSenior Member

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### RamonaSenior Member

This is an interesting subject and one that has been keeping me busy the last couple of weeks as I modify my carbon fibre Finn mast. About 1970 I was sailing OK dinghies and at that stage they were still using wooden masts. I broke one and then built another from scratch, when this failed I bought one of Frank Bethwaite's Starboard products. This was a particularly good bit of kit if the weather during the week was dry. Come Saturday this thing was just magic upwind, very fast response time. If the weather was wet during the week the mast was a dog. Carbon fibre masts are a lot like that wooden mast after a dry spell. Later OKs I owned and my first Finn had aluminium masts. These were more consistent in performance though no match for even the early carbon masts.
The new Finn carbon fibre masts are extremely stiff both fore and aft and sideways. The difference between early carbon masts and the new is enormous and most noticeable upwind in a bit of a breeze and sloppy conditions. This is simply response times and the ability to hold a decent sail shape when the boat ploughs into a wave.

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### Raggi_ThorNav.arch/Designer/Builder

Just my guesses:

Carbon masts can (if you want) be made with a softer top than aluminum, because of better fatigue properties. A soft alu top will after a year be too soft.

Weight high up is not important for stability, because dingies are sailed quite upright, BUT it's important for longitudinal moment of inertia, in the same way as the crew sit together, not far apart.

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### Steve BJunior Member

PI,
To return to your original question, I wonder if response time could be derived in some way from the natural frquency of oscillation of the spar? I think the 2nd order DE that Tim B had in mind in his reply would provide your answer but it would be an extremely complex iterative calculation. You'd need a fair sized envelope to write on the back of.
Ramona,
Your account of the performance of the weather dependent mast, was it a change in weight from being wetter that made the difference or a change in flexibility, or both - or could you not really say? I'd be interested to find out though.
Regards
Steve

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True that carbon when properly engineered will give better performance than aluminum. My point was that it is not the rate of deflection that will be the deciding factor in performance. It will be more the overall weight and stiffness that will have much more impact in the overall performance. Carbon when properly designed and built will give lighter weight and be stiffer than aluminum in most cases.

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### BWDSenior Member

I think the point Frosh makes may be under-appreciated.
I may or may not qualify as one of those "better sailors" you refer to , PI Design, but I agree with them.
The role of reflex depends on the type of rig.

To elaborate, a planing skiff or sailboard making 20-30 knots across a light 20-30cm chop in winds gusting for example 18-25 knots might encounter somewhere from 50-150 wave crests per minute, depending on course, and several major wind gusts on the order of +25%. 100 or more accelerations imparted to the craft every minute. In a light craft or a sailboard, which operates with thrust in the ballpark of 30-70lbs and has a sailing weight of 200-400 pounds, each of these little accelerations can have a dramatic impact.
To maintain control it is very helpful to have the mast deflect. The speed gain comes in the mast returning to its original shape, which powers the sail back up. Rapidly and automatically, without any input from the sailor.

Another reason this is so effective in sailboards is the aft and to windward inclination of the mast, so the force from the mast "reflexing" is transmitted from the upper bendier parts of the mast down through its stiffer base, to drive the board forward and pressurize the foil(s). In this way part of the energy used to deform the mast and sail is recaptured, boosting efficiency.

In the case of sailboards, it is undoubtedly the carbon's reflex that is more important than the overall stiffness or weight. For example, a 460cm 30% carbon mast may weigh 5.5 pounds and a 100% mast may weigh 5.2 pounds. Both deflect a similar amount when the sail is rigged and when responding to wind gusts. The 100% mast snaps back much faster and gives faster sailing even in the hands of a rank amateur. It also has a much nicer, livelier "feel."

I have no personal experience of high performance skiffs, but I can't see how the basic principles here would fail to extend to say an 18 foot skiff. From looking at masts offered for sale, it's clear various laminates with different flex properties are available to fit boat, crew weight, sail cut, etc.

Tom Wylie's designs use similar principles on larger, heavier boats (Check the video on his web site to see the gust response of freestanding CF masts). A lot of the benefits of using carbon may be overlooked by sailors/designers working within the traditional bermudan/marconi design constraints. Of course, with those design restrictions, carbon's benefits are more limited, as others pointed out.
BWD

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