Mast Stiffness

Rcsailing.net General Discussion
21

<blockquote id=“quote”><font size=“1” face=“Verdana, Arial, Helvetica” id=“quote”>quote:<hr height=“1” noshade id=“quote”>Originally posted by wgorgen

Question, what did the bend of the mast look like? With a tapered section, it might have bent more toward the top than it did toward the bottom so that your bend would be unsymmetric? I’m not sure with only one inch of bend over 63 inches that you would be able to see any sort of unsymmetric-ness in the bend, but maybe…
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Will - I used an old belt to spread the weight over about 1 1/4 inches of mast section in the center. I specifically looked at the mast versus the stretched string and didn’t see enough of a difference to warrant a closer look. I measured what appeared to be the maximum deflection, and it occured right in the middle where the weight was hanging. It would be possible to subject the mast to a specific location bend/stress, but where would one place the weight? I went to the middle, since a mast without spreaders would probably bend there if one were to really clamp on the backstay tension. Somewhere there were calculations for identifying the location and amount of wind to generate “X” lbs. of force on the mast, but couldn’t find it right away to verify.

On the other hand, the guys using fishing pole rods, with thin, bendy tips would see a lot less force needed and a bend further up the mast. This is why I wonder how useful any kind of data will be from doing these measurements.

I have a double section mast for my F-48 that is just shy of 8 feet tall (does need trimming) and my guess is that I might see close to 2 or more inches in bend if I tried the same experiment. But on that one, I was already planning a set of diamond wires and spreaders to enable the mast to be stiffer than without. That’s the mast that currently has a set of “M” Class sails attached, but I’m not sure I would go with such high aspect ratios unless the winds are really light!

Back to a practical use of test info.

What if someone took my mast section for a slightly smaller boat. If you cut off the length from the small tip - or from the larger I.D. bottom, it might change the entire mast bend completely? I think I need to find the calculation info that I mentioned above. Somewhere, the owner needs to determine the amount of sail area he will be carrying, the strength of the wind in which he will sail, and use those “pounds” (kgs.) to select the appropriate mast and mast bend characteristics. Once that is done, then the sailmaker can tailor the luff curve to fit the mast bend.

Doesn’t make much sense to have a luff curve of 3/8 inch, because then you have to search for a mast section that will bend to that curve - but in what air?

After fooling a bit with this test and measurement, I can see where trying to pick a mast section based on deflection, might just add more confusion to the process, rather than to just grab any piece and ask sailmaker to make a sail to fit the bend.

DON - Test was done very carefully, as the case was raised on a container. The belt looped through the handle, and tightened just to begin to deflect the mast. Then the support was removed while case was held, and gradually the case was lowered to transfer weight to mast.

Since the mast was engineered as a professional cross-country racing ski pole, my guess is that in compression it was rated for perhaps 150 - 180 lbs. before it would deflect. For this reason, I felt safe with a 20 lb. right angle load to the mast - but still did it slowly. I had also thought about using a gallon can of paint, but it “felt” too light and I didn’t think it would deflect the mast tube enough to allow me to measure deflection.

I can now see that perhaps the test needs to be done with several weights that correspond to the amount of pressure that is imparted by a specific sail area in a specific wind. If we do that, we are now moving from home testing to that which must be done in a lab under better control situations.

I reckon my test and measurement to be akin to sticking my fingers on a “hot” electrical wire. “Yup ! There sure as hell is current there - but don’t make me touch it again to try to tell the voltage!” In my case, “Yup - the mast bends 1 inch at 20 lbs. over a 63 inch length. So now what?”

22

I contacted Lester and he said he would put it on his “to do” list. So we at least will get a user friendly way of determining the E*I. As for a practical use for this info- all I really had in mind was a way of comparing stiffness over the internet. If I am Joe Blow from West Fencepost Alberta and I have a piece of material that I want to use for a mast, with this number I will know that it could be a free-standing mast, it’s going to need baby stays and diamond stays or it should be used to prop open the privy door. As for your query about shortening your tapered mast if you shorten the distance between supports and then slide the mast one way the measure the deflection and then slide it the other way and then measure again you should find that the bottom section is stiffer than the top. Unless they put more material in the top than in the bottom. I don’t think this information would be of much use when you are ordering sails-especially with a tapered mast. It also occured to me that this number could be used to compare fins. There is lots of talk about how stiff so-and-so’s fin is. This could clear the grey areas. Maybe- We’ll see.

Thanks
Don
Vancouver Island

23

Dick,

Remember that the Length of the mast (between the supports) is also in the equation. So as a mast of constant EI section gets longer it deflects more under the same weight. Therefore, this formula to calculate EI is only really used to compare mast sections. Deciding what section stiffness is needed for a given mast is up to the designer.

As an extreme example: No one would consider a 1" diameter carbon tube to be suitable to use for a mast for a Hobie 18, would they? But this same 1" dia carbon tube would be severely overstiff for a footy class boat.

As a designer, you can take the equation I have supplied and use it in reverse. If you want to achieve a certain mast bend (say 3/8") and you know about how much backstay tension you want to apply to achieve that bend (say 2 lbs) then you can use the equation to determine what sort of E*I you need to achieve that kind of bend under that sort of loading…

Actually, given the reaction loading at the forestay and the moment induced by those loads on a fractional rig, there are some different equations you will want to use. You would need to use some geometry to break down the backstay tension into the compression load and the bending load. Similarly, you would break down the forestay load into the compression and bending loads there.

Are you ready for this? Here goes…

To make the equation easier to write, the value of k is defined as follows:

k = (P/(E*I))^0.5, where P is the total compressive load at the base of the mast. For those who never studied, the ^0.5 power is simply the square root function…

Now, for the case where the mast base is supported by partners the mast deflection at the forestay “da” is given by:

da = (F/(kP))*[(sin k(l-a)/cos kl) - k(l-a)]

where a is the height of the forestay, l is the total height of the mast, F is the bending load of the forestay (the component of the forestay load that pulls straight forward.

Now, my guess is that this is probably way to cumbersome of an equation to use in daily life… Suffice it to say that the E*I we have been talking about changes the deflection for a given amount of loading.

Basically, the EI number allows for simple comparison. If the number is twice as big for a given mast section compared to some other mast section then the section is twice as stiff. If you are working with a mast that is way too flexible then you might want to search through the list looking for a mast section with higher EI.

Another thing you can do with this equation is look at the I portion of the E*I. THe I is the sectional moment of inertia. For a tube, I is given as:

I = (Pi/4)*(Ro^4 - Ri^4)

where Ro is the outer radius (1/2 of the outer diameter), Ri is the inner radius and Pi is of course that number we all learned about in school 3.14159…

So if you want to increase the stiffness of the mast for the same material, you can look at this equation and figure out how much on an increase in either outer diameter or wall thickness you will need…

In order to really work with all this information, Dick, you will need to have studied college level structural statics and beam theory. There is no way I can cover 2 semesters of college level material in one post or even an entire thread. And once you have those basics, figuring out how to apply these equation to a design problem takes years of experience.

So it is sufficent for our purposes to simply record values of E*I. We can use this to compare the stiffness of different mast sections to aid in choosing the right section. But it will still involve some trial and error to get things just right. The only thing this database will do is help you make a somewhat more informed choice of what to try next if your current mast is too flexible or too stiff…

  • Will

Will Gorgen

24

Will -

had a bunch of similar stuff “several” years ago when studing architecture (now it is given to structual engineers to calculate) - and understand what you are saying - which in a way is similar to what I’m trying to say - but here is the point that comes up taken to the next step… "SO WHAT?

How does “Joe Average” find a mast section that will give him the number he has calculated - or desires?

<blockquote id=“quote”><font size=“1” face=“Verdana, Arial, Helvetica” id=“quote”>quote:<hr height=“1” noshade id=“quote”>Basically, the EI number allows for simple comparison. If the number is twice as big for a given mast section compared to some other mast section then the section is twice as stiff. If you are working with a mast that is way too flexible then you might want to search through the list looking for a mast section with higher EI.<hr height=“1” noshade id=“quote”></blockquote id=“quote”></font id=“quote”>

I don’t disagree with anything said - I’m simply asking if you have a number (any number 6-12-14-or ???) how does one translate that into a section of mast from a supplier to get to that comparison number? Will carbon tube suppliers furnish that spec number? I doubt it. So here we are back to “Joe Average” - he has a fillament wound tube in one hand, and a pultruded tube in the other. Both are straight sections (to make it easier) of .375 diameter. Where (or how) does he make a decision as to which to choose? I am imagining a guy with forty tubes of same size from different manufacturers all having a different deflection characteristic. Perhaps he still doesn’t get the bend he desires. What is the next step here that I am missing? If you read the original post, Don was looking for a magic (standard) number to indicate how stiff a mast is. As we both have noted - that number is based on diameter, on length, on method of fabrication, and on actually having and testing a section to confirm what he bought equals the desired “stiffness”.

“Rockwell” is a hardness number that indicates how “hard” a metal surface is. But - it is dependant on how the hardness was created, the type of steel, and it can be influenced by oil or water quence - so the same pieces of steel could have two different hardness “numbers”.

I am trying to figure out that with whatever number is calculated, it doesn’t help with the decision as to what to buy and from whom -

25

<blockquote id=“quote”><font size=“1” face=“Verdana, Arial, Helvetica” id=“quote”>quote:<hr height=“1” noshade id=“quote”>
I am trying to figure out that with whatever number is calculated, it doesn’t help with the decision as to what to buy and from whom -
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You’re right Dick. For the present time this number will only be used to compare what we already have. I suppose a friendly supplier might let you test his wares. And who knows-maybe down the road suppliers might put the E*I on thier masts. The information should be easily available for them. We’ll wait and see, I quess.

Thanks
Don
Vancouver Island

26

Dick,

Right now the database is not populated, but when it is, I would think that we would want to include information like manufacturer and model information. So, if I buy a tube from Hang 'em High and measure it and enter that into the database, then someone else who decides he might need a section of similar properties knows where to order it from.

As folks out there measure their masts sections from the major suppliers (SailsEtc, Sterne, Hang 'em High, Walrus, etc) then we will all be able to access that information so that we can pick a section that makes sense for our applications.

If I have an aluminum section from SailsEtc and I measure the EI and come up with a number of 12. Then that gives me a starting point for my next mast. I know that I need to be very careful with my rig tensions because this mast is pretty flexible and needs to be held straight. If I find a carbon tube in the database that has an EI of 15, I know that it will be a little stiffer, but not much. If I find another that is 20 then I know that I am going to be a little less than twice as stiff. If I find one at 100, then I know that is going to be very stiff. I probably don’t want it to be any more than twice as stiff, so I would not choose the section with an EI of 100, but rather would probably choose the one that is 20.

That is how I see the database working.

If you want to try and select your next mast from an engineering evaluation, then you are going to have to dig into those old textbooks and probably solve some fairly heavy duty equations, but if you already have a good starting poijt, then this database will help you improve your design. It will not replace the idea of asking other people what they have done for similar sized boats, but it will add to your ability to use that information. If someone says that their .6" diameter tube was not quite stiff enough and you find that tube on the database and find another tube that is stiffer, then you have a pretty good idea that the stiff tube will be better for your application.

  • Will

Will Gorgen

27

Yeah! that!

Thanks
Don
Vancouver Island

28

Will - OK - I was down the road waiting for you to catch up. [B)]

So who’s going to develop a spreadsheet that does the calculations, and where can it be posted to allow the rest of us to post our findings and data?

29

You missed a post. Lester has said he will do it.

Thanks
Don
Vancouver Island