Mast Deflection Speeds (esp dinghies)

[PI Design]

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

[Tim B]

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.

[PI Design]

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.

[Steve B]

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

[PI Design]

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?

[Steve B]

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

[water addict]

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.

[PI Design]

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.

[Raggi_Thor]

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 :)

[frosh]

[QUOTE=water addict;

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.[/QUOTE]

This may apply to low performance dinghies but as we move up the performance scale say to Formula Sailboards, any equipment that includes an alloy mast might as well sail on a different race course as they will finish legs behind, even with an equally capable helm. Even the % carbon content and even modulus of the carbon fibres will create significant performance differences in this highly evolved very high performance boat(board). As far as sail shape is concerned, this needs to be a dynamically shifting shape at the highest performance levels, and if twisted way off in an overpowering gust, must respond extremely quickly both to the macro gust and the rapid micro wind variations. Frank Bethwaite did considerable work on the analysis of wind gusts in the 80's and there is a lot more than meets the eye. Aluminium is not in the ball park at all if highest performance levels are to be achieved, in a class that can really perform. i.e. International 14's and 18 ft. Aussie skiffs.

[Ramona]

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.

[Raggi_Thor]

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.

[Steve B]

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

[water addict]

This may apply to low performance dinghies but as we move up the performance scale say to Formula Sailboards, any equipment that includes an alloy mast might as well sail on a different race course as they will finish legs behind, even with an equally capable helm. Even the % carbon content and even modulus of the carbon fibres will create significant performance differences in this highly evolved very high performance boat(board). As far as sail shape is concerned, this needs to be a dynamically shifting shape at the highest performance levels, and if twisted way off in an overpowering gust, must respond extremely quickly both to the macro gust and the rapid micro wind variations. Frank Bethwaite did considerable work on the analysis of wind gusts in the 80's and there is a lot more than meets the eye. Aluminium is not in the ball park at all if highest performance levels are to be achieved, in a class that can really perform. i.e. International 14's and 18 ft. Aussie skiffs.

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.

[BWD]

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

[frosh]

To elaborate a bit more and particularly comment on the last 2 postings on this thread. Water addict, sorry you are not yet up to speed on this topic. I suggest that you do some more research, and see the link below for a starting point. BWD, you are much more in tune with this under appreciated concept than most of the others. Reflex response is certainly a bigger determinant of ultimate speed through varying wind and water than light weight of spar and stiffness. The proviso is that the boat or board needs to be capable of really significant high speeds, and there is no better example than a well designed sailboard. For explanation of Mast Reflex Response I include this link from Fiberspar, probably the leading windsurfing mast manufacturer in the world. http://www.fibersparsports.com/reflex.html

[PI Design]

Hi everyone. Tnahks for all your thoughts. It seems that response time is important (at least to high performance boats), and that the faster the better. Calculating the deflection rate by hand seems a little tricky, so I shall look into whether ANSYS can do this.

[Ramona]

PI,

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

The mast was stored inside during the week between races. The spruce was varnished, can't remember whether the interior of the mast was sealed. It was just the difference in humidity that effected the gust response. The mast was no heavier.

The other difference with carbon Finn masts of the later generation is they are now wing masts with a larger fore and aft cross section, they are much stiffer yet lighter sailors can use them. They are also 8 kg.s versus 12 kg with alloy masts. This combined with plastic sails which are a fraction of the weight of Dacron and the difference is enormous. It has to be rapid response times.
What is interesting is that round skinny masts can be built with the same static bend figures as a wing mast, the usual way to compare Finn/Ok masts. They perform well but whether they have the same response times as the extremely expensive wing mast I very much doubt.

[frosh]

Hi Ramona, thats an interesting discussion on the Finn carbon mast. Pretty much what I would have expected. A few years ago very skinny round carbon windsurfing masts came onto the market. As sailboard race sails are very low drag pocket luff leading edge sail shapes, one might expect that a sharper leading edge might lead to higher racing performance. It wasn't borne out in practice, and the very skinny mast has become a rarity now except in waves. Something about it was causing inferior performance to larger sections. Static bend was designed to be similar. The tables for a state of the art standard diameter mast, first table, and the RDM (reduced diameter mast) second table, tell the story. From the Fiberspar web site.
Standard Racing Mast
(cm) IMCS Stiffness Reflex Indicator Carbon Content Weight KG/LBS
430 21 7000+ 100% 1.30/2.86
460 25 7000+ 100% 1.50/3.30
490 29 7000+ 100% 1.67/3.67
520 34 7000+ 100% 1.86/4.09
550 36 7000+ 100% 2.10/4.62

RDM

(cm) IMCS Stiffness Reflex Indicator Carbon Content Weight KG/LBS
370 17 4200+ 95% 1.50/3.30
400 19 4200+ 95% 1.65/3.64
430 21 4200+ 95% 1.90/4.20
460 25 4200+ 95% 2.20/4.80

[Ramona]

[QUOTE=frosh;149116] [A few years ago very skinny round carbon windsurfing masts came onto the market. As sailboard race sails are very low drag pocket luff leading edge sail shapes, one might expect that a sharper leading edge might lead to higher racing performance. It wasn't borne out in practice, and the very skinny mast has become a rarity now except in waves. Something about it was causing inferior performance to larger sections. Static bend was designed to be similar].


Sailboard masts are probably made the same way as fishing rods over a tapered spindle. I tried to stiffen on once by adding material but it was a waste of time. Larger diameter is the only way to go.

New Finn masts are made in two halves, the inside of the halves is then laid up with a carbon fibre hat which is probably about 15mm high x 20mm wide. This probably runs up to almost the top, depending on the weight of the sailor its designed for. From an engineering point the carbon masts have vast improvements over the aluminium masts which are usually extruded then cut and welded for tapers etc.

Having a core in a carbon fibre mast alters the bend characteristics also. I think with a yacht mast up to about the normal half tonner in the 30 foot range, its now feasible to construct your own carbon fibre mast using a combination of the older hollow timber mast constuction methods and the new carbon fibre methods.

[water addict]

To elaborate a bit more and particularly comment on the last 2 postings on this thread. Water addict, sorry you are not yet up to speed on this topic. I suggest that you do some more research, and see the link below for a starting point. BWD, you are much more in tune with this under appreciated concept than most of the others. Reflex response is certainly a bigger determinant of ultimate speed through varying wind and water than light weight of spar and stiffness. The proviso is that the boat or board needs to be capable of really significant high speeds, and there is no better example than a well designed sailboard. For explanation of Mast Reflex Response I include this link from Fiberspar, probably the leading windsurfing mast manufacturer in the world. http://www.fibersparsports.com/reflex.html

Frosh,
Did some looking on your above mentioned web site. It didn't really provide anything quantifiable other than the natural frequency of vibration - i.e. so what.
Did some further looking on the web, could not find any quantifiable numbers on how rate of deflection of the mast affects average speed on the race course. Help me get up to speed - if you have some documents showing how rate of deflection impacts average speed, I'd like to see them. I could not find any, and am interested in the numbers and methods if you have them.
Thanks.

[Ramona]

Rate of deflection is the tricky bit. If you were an Olympic sailor then mast manufacturers would probably come knocking on your door, begging you to sail a selection of their products and pick the good ones. Mere mortals have to rely on static bend numbers and take your chances.

Interestingly Mr Elvstrom used to compare wooden Finn masts by placing the bases of the masts together on the ground, then holding both tips just above his shoulder, jiggle both masts the same and sight along them comparing their action. Obviously he understood rate of deflection. I gave it a go and learned nothing from it.

[tspeer]

...Is there any way to calculate the speed of deflection (time to max deflection) using beam theory? ...

Linear beam theory can predict the vibration frequencies of a mast in much the same way that it can predict the static deflection under load. In many ways, a beam vibrates much like a plucked taut string. The dynamic response to a sudden application of a load will result in an initial acceleration, overshooting of the eventual steady deflection, and a damped oscillation as the beam settles down. There will be an infinite number of vibration modes at different harmonic frequencies that sum up to form the dynamic response, although only the first few modes are typically needed to get an acceptable accuracy.

Your question about the time to maximum deflection seems to assume the response will be over-damped and only approach the steady-state value asymptotically from the same direction - this is generally not the case as structural damping tends to be pretty low. There are several parameters you might want to use to describe the response to a sudden step change in the load, including rise time (time to, say, 90% of the steady-state deflection), % overshoot (compaared to the steady-state value), and settling time (when the deflection stays within, say, 5% of the steady-state value). But while these might be easy to calculate for simple beams and measure in a lab, real loadings are not as sharp-edged as this and are more complex. So you might not see overshoot in real life simply because the loading comes on slower than the response time of the mast.

The typical way of calculating the dynamic response is with a finite element method. The elements themselves can be simple beam elements, with the mass of the beam lumped at several nodes along the length connected together by springs that represent the stiffness of each segment of the mast. This forms a matrix equation of the form

M*x_ddot + D*x_dot + C*x = F

where x, x_dot and x_ddot are the vectors of displacements, velocities and accelerations at each node, M is the mass matrix (which also includes mass moments of inertia as well as plain masses), D is the damping matrix, and C is the stiffness matrix. F is the vector of applied loads. The steady-state solution is

C*x_ss = F_ss

So the problem starts out much the same as calculating the static deflection, but now the biggest change is the addition of the mass matrix and acceleration. The stiffness matrix is the same one you use for calculating the steady deflection.

The natural frequency is going to depend on the construction of the mast itself, which will determine how the mast would vibrate if it were floating in space (the free-free modes), and the ways the mast is constrained by the mast step, partners, spreaders, stays, etc. In general, the more the mast is constrained, the higher its frequency is going to be, and the faster its going to reach its deflection due to the load. Of course, the more constrained the mast is, the smaller that deflection is going to be, too.

If you're trying to characterize a mast's dynamic response, probably the best measure is the mast's lowest natural frequency, constrained in some standard way. As you make the mast stiffer and lighter, the natural frequency will go up and it will respond quicker to dynamic loads. For example, you could clamp the mast at the mast step and the hounds, twang the head of the mast and measure the frequency of its vibration. You'll need to do this for both major axes of the mast, since the vibration frequencies will be different in the two axes. If you had an aluminum mast and a carbon-fiber mast of the same stiffness, for example, the carbon mast would be lighter and have a higher natural frequency.

Getting the frequencies and mode shapes right for a complex structure is tricky, even if you have the most sophisticated tools. For example, every new type of aircraft is subjected to a ground vibration test before its first flight. In the GVT, it is suspended by air bags to isolate the landing gear from the ground (so it's constrained as it would be in the air), and shakers are attached to the structure to vibrate it at different frequencies. Accelerometers are liberally applied all over the structure to measure the deflections. The shakers are typically driven either with a frequency sweep (chirp) or with pseudo-random noise that contains a wide band of frequencies continuously. From the structural response to the shakers, it's possible to calculate mode shapes and frequencies, and even back out the mass and stiffness matrices. These are compared with the pre-flight predictions and the models adjusted to match. This is critical for predicting things like flutter speeds and aeroservoelastic instabilities of the control system.

Take a look at
Budiansky, Bernard and Kruszewski, Edwin T, "Transverse Vibrations of Hollow Thin-Walled Cylindrical Beams", NACA Technical Note 2682 (http://naca.central.cranfield.ac.uk/reports/1952/naca-tn-2682.pdf), April 1952.

Benscoter, Stanley U and Gossard, Myron L, "Matrix methods for calculating cantilever-beam deflections", NACA TN-1827 (http://hdl.handle.net/2060/19930082512), 1949.

[PI Design]

Thanks Tom - bonus points for you!
Well, the calcs look a little time consuming for little benefit. So I'll jsut sleep easy knowing that lighter mast respond more quickly, and not try to quantify the effect.

Still, if I get some spare time I might look into tis a bit more.

[tspeer]

I think you might use natural frequency as an indicator, without actually calculating the transient response. Rather like gyradius is used now for transient motion in waves, and measured with a simple swing test.

However, I suspect that mast natural frequency is going to be correlated with so many other factors, that it's going to be difficult for it to stand out in racing results. Take the aluminum vs carbon mast mentioned earlier. If the two have the same stiffness, the aluminum mast will be heavier (not to mention probably larger in cross section). So if the carbon mast proves faster around the race course, is it because it reacted faster to gusts, or because it provided significantly lower pitching & rolling moments of inertia for the boat as a whole? I suspect the latter is going to be the case.

If you really wanted to find out the effect of mast response, you'd probably have to do a lot of two-boat testing with a carelfully designed dynamic experiment. For example, it may be possible to ballast the carbon mast, say by adding weight at the hounds, so that it didn't affect the boat's gyradius, but still had the difference in natural frequency compared to the aluminum mast. You might have to mount light-weight (styrofoam?) fairings to it to match the cross sections for aerodynamic similarity. Then do a lot of sailing, switching crews to even out the differences there, to get statistically significant results between the two configurations. Naturally, I don't think this is a feasible or even worthwhile program, but it's the only way I can think of to truly answer your original question.

[frosh]

Hi Water Addict, with due respect to your design qualifications and Tom Speer's Mathematical Analysis, there is much in the high performance sailing arena that relies on empirical semi-scientific method. For instance what was it about Alinghi using calculus or other mathematical model that allowed it to win the latest America's Cup Competition? Sometimes the most effective proof is what actually works on the water reads something like this:

Now, to answer the question "What is the scientific method?" - very simply (and somewhat naively), the scientific method is a program for research which comprises four main steps. In practice these steps follow more of a logical order than a chronological one:

Make observations.
Form a testable, unifying hypothesis to explain these observations.
Deduce predictions from the hypothesis.
Search for confirmations of the predictions;
if the predictions are contradicted by empirical observation, go back to step (2).

[water addict]

Hi Water Addict, with due respect to your design qualifications and Tom Speer's Mathematical Analysis, there is much in the high performance sailing arena that relies on empirical semi-scientific method. For instance what was it about Alinghi using calculus or other mathematical model that allowed it to win the latest America's Cup Competition? Sometimes the most effective proof is what actually works on the water reads something like this:

Now, to answer the question "What is the scientific method?" - very simply (and somewhat naively), the scientific method is a program for research which comprises four main steps. In practice these steps follow more of a logical order than a chronological one:

Make observations.
Form a testable, unifying hypothesis to explain these observations.
Deduce predictions from the hypothesis.
Search for confirmations of the predictions;
if the predictions are contradicted by empirical observation, go back to step (2).

OK, but I was wondering if you have any documentation showing methods of computation, whether empirical or first principles, relating rate of mast flexure to boat speed?

[frosh]

Hi Water Addict, in simple terms the answer is that I have never seen a mathematical proof for reflex response being directly proportional to higher boat speeds in very high performance craft. (This is not to say that one does not exist). But why is it necessary? Anyhow my point is that if every empirical observation made in high performance sailing development needed a mathematical model to confirm it, we would all be sitting in university ivory towers, in front of our super-computers, becoming generally very frustrated, with the lack of progress we are making. Instead we can observe what happens on the water, propose a hypothesis as to why is it so, observe if practical events support it most circumstances, and generally enjoy ourselves a hell of a lot more than doing it your way.
I will take the opportunity however of making another point which is very relevant to the discussion; and that is, even if no-one can come out with a mathematical proof as to why Finian Maynard still holds the outright speed sailing record on a sailboard, nothing can not possibly take away the fact that it is so, and that is beyond dispute. BTW, he does not use an alloy mast, nor would he even contemplate doing so, for very good reason, along the lines of my argument. Weight difference is not a factor, I promise you.
I think that you are simply trying to win your argument for no practical purpose, except that you believe that if the other party cannot produce an academically rigorous proof, then their contention has little merit. Sorry, but I have no intention of playing that game with you or anyone. Life is too short for that sort of nonsense.

[water addict]

Hi Water Addict, in simple terms the answer is that I have never seen a mathematical proof for reflex response being directly proportional to higher boat speeds in very high performance craft. (This is not to say that one does not exist). But why is it necessary? Anyhow my point is that if every empirical observation made in high performance sailing development needed a mathematical model to confirm it, we would all be sitting in university ivory towers, in front of our super-computers, becoming generally very frustrated, with the lack of progress we are making. Instead we can observe what happens on the water, propose a hypothesis as to why is it so, observe if practical events support it most circumstances, and generally enjoy ourselves a hell of a lot more than doing it your way.
I will take the opportunity however of making another point which is very relevant to the discussion; and that is, even if no-one can come out with a mathematical proof as to why Finian Maynard still holds the outright speed sailing record on a sailboard, nothing can not possibly take away the fact that it is so, and that is beyond dispute. BTW, he does not use an alloy mast, nor would he even contemplate doing so, for very good reason, along the lines of my argument. Weight difference is not a factor, I promise you.
I think that you are simply trying to win your argument for no practical purpose, except that you believe that if the other party cannot produce an academically rigorous proof, then their contention has little merit. Sorry, but I have no intention of playing that game with you or anyone. Life is too short for that sort of nonsense.

You claimed that I was not up to speed on the topic, so I was looking for your enlightened view to learn more about the topic myself. That's all.

[frosh]

Water addict, If you read and absorb the material in my postings and also the stuff about the Finn dinghy masts, and the Fiberspar web site, it is all there for all the interpretation that is necessary to understand the concept. I don't get what the difficulty is with it all? Any way in summary, it goes something like this: A really efficient rig on a high performance dinghy or sailboard needs to be self adjusting and very rapidly so. This means than when the sail is temporarily in a higher than mean wind strength which potentially could produce heeling force that would overcome the human ballasted righting moment, heeling does not occur. You understand that there are gross gusts that can be detected easily by an experienced sailor by seeing cats paws on the water or feeling the higher wind velocity on your face, but also there is an unseen but measurable roughness to what might feel and look like a fairly constant wind. This could be graphed as a low amplitude reasonably high frequency sine wave, graphing actual wind velocity against time. When already fully powered up what then happens when we are on the upper section of the sine wave of wind strength? What needs to happen is that the upper sail twists off very momentarily flattening the upper sail section, and lowering both drag and drive in the upper third, which means that no noticable additional heeling occurs, and the boat accelerates. Possibly a second or two later the sine wave has moved to a point less than the mean wind strength. The mast starts to straighten out in the upper section rapidly, (and this is the entire crux of high speed reflex response), and the sail powers up in the upper third again and the sailor feels almost no change in the heeling force but boat speed barely drops as the rig is suddenly generating more power due to less twist and slightly more camber in the upper third of the sail. This needs to happen very quickly and in harmony with a fairly constant hiking force, i.e righting moment exerted by the sailor, who does not need to rapidly move his body further or less further to windward. I hope that this descriptive but non-mathematical explanation sort of clears up the mystery for you now.

[BWD]

Amen. But that's just the macro scale.
It works on the shorter time frame/smaller impacts too, as I wrote above, with the boat/board running over chop/waves/ripples, 50 or 100 or 200 times a minute.

With good windsurf rig it really is like having a crew who can trim and tune your rig several times a second. I think anyone interested in speed who doesn't know this from experience should at least look at slow motion video of windsurfers in choppy water.

The spars are a bow the wind and sea are constantly bending to shoot the board and the sailor forward.
The board is an arrow that carries its own bow.
Unstayed carbon (on the windsurfer scale at least) allows the "bow" to unbend in a fraction of a second and shoot the board forward before the next gust or wave bends it again.
I eagerly await the genius who can succesfully scale this up to a 40 footer. Wylie is part of the way there at least... but there are power to weight problems and materials limits, so it may be a long wile.

[water addict]

Water addict, If you read and absorb the material in my postings and also the stuff about the Finn dinghy masts, and the Fiberspar web site, it is all there for all the interpretation that is necessary to understand the concept. I don't get what the difficulty is with it all? Any way in summary, it goes something like this: A really efficient rig on a high performance dinghy or sailboard needs to be self adjusting and very rapidly so. This means than when the sail is temporarily in a higher than mean wind strength which potentially could produce heeling force that would overcome the human ballasted righting moment, heeling does not occur. You understand that there are gross gusts that can be detected easily by an experienced sailor by seeing cats paws on the water or feeling the higher wind velocity on your face, but also there is an unseen but measurable roughness to what might feel and look like a fairly constant wind. This could be graphed as a low amplitude reasonably high frequency sine wave, graphing actual wind velocity against time. When already fully powered up what then happens when we are on the upper section of the sine wave of wind strength? What needs to happen is that the upper sail twists off very momentarily flattening the upper sail section, and lowering both drag and drive in the upper third, which means that no noticable additional heeling occurs, and the boat accelerates. Possibly a second or two later the sine wave has moved to a point less than the mean wind strength. The mast starts to straighten out in the upper section rapidly, (and this is the entire crux of high speed reflex response), and the sail powers up in the upper third again and the sailor feels almost no change in the heeling force but boat speed barely drops as the rig is suddenly generating more power due to less twist and slightly more camber in the upper third of the sail. This needs to happen very quickly and in harmony with a fairly constant hiking force, i.e righting moment exerted by the sailor, who does not need to rapidly move his body further or less further to windward. I hope that this descriptive but non-mathematical explanation sort of clears up the mystery for you now.

I understand these concepts, and did before this thread. So perhaps I am up to speed on them? Is that all you have to offer? Sorry for the somewhat pointed diction, but since you seem to have no trouble trouncing on me, I'll give a little pissyness right back at ya.

The rate of deflection and how it relates to the boat speed is way more complicated than that dude. And it will be variable depending on a whole host of factors on a particular boat in given conditions. My original comment that weight aloft, mast dimensions, and static stiffness will have orders of magnitude more impact in the average boat speed still stands. I think I'm at least as up to speed on this as you are, buckwheat, at least from the subjective, very basic conceptual stuff you've offered up so far.

I also understand that none of these lesser effects are readily quantifiable as you say. They are often interpreted by the sailor and designer without strict controls, as that is the only reasonable way to address the issues without monstrous budgets. The pseudo engineering of deflection v. load on the fiberspar web site to a trained engineer is a big "so what". Yes 2+2=4. Been done before.

[frosh]

Hi Water Addict, lets call a truce on this issue. I concede you probably know your stuff pretty well, it's just that the message you convey is that so why is reflex response very important at all? You probably know a lot more about static and dynamic loads on rigs on larger yachts than me, and I have no wish to prove otherwise. After all, isn't boating your profession? For me it's a passion only, and I am really only into sailboards and high performance small dinghies and multis. I really have no wish to trounce anyone; OK?
Regards, Sam