Mast Stiffness

Is there a standard measure for mast stiffness? If not can we make one? I noticed on Lester’s site that he cantelevered 1 meter off his workbench and hung 300 grams on the end and measured the deflection. I think a standard would make any dicussion about masts easier.

Thanks
Don
Vancouver Island

Might have a lot of different “standards” especially when it comes to mast length. The 2 Meter multihull has a 9 foot mast - so the same deflection (inches/weight) in a longer mast would “appear” to be stiffer than a shorter mast. Perhaps a mast suspended horizontally at top and bottom with weight in middle might make comparison easier - providing the “span distance” is also included.

If we were to just measure the top meter or so of the mast wouldn’t that at least give use a minimum stiffness. It would be nice to be able to say “I have a mast of “X” stiffness” and have everone know where you’re coming from.

Thanks
Don
Vancouver Island

I would think it wouldn’t - since the bend is taking place over the entire length of the mast.

Also, there would be different bend characteristics if you add spreaders, or shrouds - depending how high up and where they are placed.

Just my opinion - let’s see what others are thinking.

[ I use tapered cross country ski poles which are extremely stiff - just an FYI ]

In the windsurfing industry, there is a standard measurement technique where you support the mast at both ends (between two chairs or something like that) and hang a weight from the middle. The DIN measurement was then the weight divide by the deflection.

Some corrections were made for mast height and un-even curvature. So you might have a 500 cm mast with 7.4 DIN and flex top curvature…

Mainly this was used by the sail makers when specifying the right mast to use with a given sail. So the length that was needed by the sail was fixed and there were only two types of curvature - flex top, and constant curve…

You might want to copy that…

  • Will

Will Gorgen

The effect of taper/no taper and the bend curve of the mast are essential for the sailmaker. I provide my sailmaker a full scale bend curve of the mast determined by setting the rig up like it will be used and tensioning it. Big differences between traditional rigs and newer square heads in the amount of taper required with some forms of square head not needing any taper at all.
I think if a number of rigs could be measured in sailing trim and the bend recorded using a straight edge off the back side of the mast you could experiment using weight with the mast setup on two supports at the ends to recreate the bend curve taken off the actual boat. Then to test subsequent mast sections you would know exactly how much weight where recreates the proper mast curve(for that boat) and if a tested section didn’t bend properly you’d know not to use it.Data would have to be established for each class but every owner would then be able to test a prospective mast section . By using the actual rig behaviour as a guide for how much and where to place the weight and by putting mast supports at the ends of the masts as a “standard” technique bend characteristics of any tube could be checked against a “master”.

Doug Lord
–High Technology Sailing/Racing

Greg - I think your idea will work, but if there is “some number” we all want to use for reference, it has to have a standard weight, and then the amount of deflection, and the distance between supports would need to be included. Do you think we could get that Dan Sherman guy to come up with some mathematical formula to allow a “number” that has meaning over the entire range of materials, and mast lengths?

Your lay-over the scale and push down until it touches the surface might work, if all our scales were same height from table. Also, a longer mast would touch the table at each end sooner than a short section - or at least with a difference in pressure needed to make the bend.

I would think that a fixed (agreed upon) weight and then the distance deflected and the length of the mast could result in “some” arbitrary number that would show flex. Doesn’t need to have much meaning - just that it is done always teh same way, with the same weight. Of course, then when you throw in the tapered masts, it is yet another factor in the equation. Obviously if I deflect my mast that tapers from 1/2 inch to 3/16 inch, it certainly can’t be compared to a short mast of straight wall form.

DAN SHERMAN - are you out there ? You seem to be the “physics guy” in the audience. What say you?

I’ve been out in the garage trying a bunch of stuff without any firm results. I thought that if you to measure the deflection for the whole mast and then divide or multiply by the length you might reach a constant but I couldn’t get it to work yet. I looks like if you double the length the deflection goes up ten times-or it seemed like that with the quick measuring I did.

Dick
I don’t think it matters what method is used to measure the deflection as long as everyone uses the same method and that it is easy to do. The weight could be a can of Campbell’s Tomato Soup-something everone has. I think that if we could come up with a deflection-per-foot or something then tapered mast would be O.K. because it would be an average. You would just take into consideration that the bend wouldn’t be even like a straight mast.

Thanks
Don
Vancouver Island

Don,

For the same mast section and the same weight applied, the deflection will go like the cube of the length. So if you double the length the deflection will go up by a factor of 8 (your guess at a factor of 10 is not far off)

The formula for a cantelevered beam is:

deflection = (Weight * Length^3)/((3 * E * I)

where E is the modulus of elasticity and I is the section moment of inertia. In this case, the load is appled at the far end and the deflection is also measured at the far end (away from the cantelevered clamp)

If you load it in the middle of a simply supported beam (two ends on chairs) you have

deflection = (Weight * Length^3)/(48 * E * I)

This opens up the door for another way to measure the stiffness of the mast. That is to measure the EI value. In fact, If you look at the SailsEtc catalog, they tell you the stiffness of their sections in exactly these terms. Measuring the EI allows you to compare masts of different length pretty effectively. The downside is that it is not an easy number to understand nor an easy number to give to your sailmaker. Plus it does not tell you anything about taper unless you describe the E*I as a function of mast length…

Sometimes it is painful to be an engineer…

  • Will

Will Gorgen

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

This opens up the door for another way to measure the stiffness of the mast. That is to measure the E*I value.

Sometimes it is painful to be an engineer…

  • Will

Will Gorgen
<hr height=“1” noshade id=“quote”></blockquote id=“quote”></font id=“quote”>

Is there a simple-do-it-in-my-garage-method of measuring this E*I ?

Thanks
Don
Vancouver Island

Don,

You can take the equations I gave in my earlier post and turn them around.

So if you use the simply supported beam method (mast held between two chairs and a weight applied mid-way between them), then you get:

EI = (WL^3)/(48*d)

Where W is the weight applied, L is the lenght between the chairs and d is the deflection (measured at the point where the weight is applied). If you use english units, W is in pounds, L and d are in inches. The units of EI are poundsinch^2. This is a weird unit, but it makes sense since modulus (E) is in pounds per square inch (psi) and the sectional moment of inertia (I) is in inch^4.

If you are using those silly canadian metric units, then the weight needs to be in Newtons and the length in meters. Then EI would be in Nm^2.

You can do a similar test with the cantelevered beam equation, but I would not recommend this as it is nearly impossible to get a rigid enough clamp to not effect your deflections. With the simply supported method, chairs are rigid enough to use as the supports…

  • Will

Will Gorgen

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

Don,

You can take the equations I gave in my earlier post and turn them around.

So if you use the simply supported beam method (mast held between two chairs and a weight applied mid-way between them), then you get:

EI = (WL^3)/(48*d)

Where W is the weight applied, L is the lenght between the chairs and d is the deflection (measured at the point where the weight is applied). If you use english units, W is in pounds, L and d are in inches. The units of EI are poundsinch^2. This is a weird unit, but it makes sense since modulus (E) is in pounds per square inch (psi) and the sectional moment of inertia (I) is in inch^4.

If you are using those silly canadian metric units, then the weight needs to be in Newtons and the length in meters. Then EI would be in Nm^2.

You can do a similar test with the cantelevered beam equation, but I would not recommend this as it is nearly impossible to get a rigid enough clamp to not effect your deflections. With the simply supported method, chairs are rigid enough to use as the supports…

  • Will

Will Gorgen
<hr height=“1” noshade id=“quote”></blockquote id=“quote”></font id=“quote”>

So if some clever person would write up a little script that we could all download we could just plug in weight(we all have or should have scales)and distance between chairs (I hope we all have chairs) and we would have a number that would work for all lengths of masts and maybe even booms?

Thanks
Don
Vancouver Island
EDIT Wouldn’t the constants in your formula have to be different for the silly metric system (I’m old enough to remember the old way)

I’m here Doug.

I didn’t say anything because Will has got it spot on, atleast how i learned it. Here is a link to a bunch of deflections.
http://www.aviasport.net/catalog/carbon/

The 3 point bend test was used to get the deflection, and from what i have seen it seems to be the status quo in the composite tubing industry.

-Dan

My idea was to create a database based on mast bend information gleaned from the top boat or close thereto in any class and translate that to a set of instructions that would tell a prospective “mast tester” how much and where to put the weight on a prospective mast tube. That way a skipper would have exact information about the bend characteristics(how much and where) for a tube that would be exactly similar to one used at the top of a class.

Doug Lord
–High Technology Sailing/Racing

I think we may be close. Will Dan or Will please respond. Will this formula result in a single number that would describe the stiffness of a mast? I was thinking that if it would that I would e-mail Lester Gilbert and ask him to make one of his famous downloads and put it on his site. I think his site is the best place to go for this kind of stuff. You don’t happen to be reading this do you Lester?

Thanks
Don
Vancouver Island

Don -

here are your first set of numbers, to which you can proceed to determine a comparison for mast stiffness. This was a very NON-SCIENTIFIC test, but is one that can be easily recreated at home. How you intend to compare - is up to you, but here are the specifications and first figures:

<u>MAST: </u>The mast tested is for my 1 Meter multihull. It is a carbon tube that is tapered and of wrapped construction. Originally designed/manufactured as a X-C Ski pole, it is extremely stiff (to my thinking). The mast is 63 inches long overall. 1 inch at each end was supported for this horizontal test. The mast is tapered (as noted) and OD at the base is 5/8 inch and OD at the top is 3/8 inch.

<u>WEIGHT: </u>used was a 24 pack of full Pepsi pop cans. I suppose you can use Coke, Mountain Dew, or even a case of beer. (but not sure about the “lite” beers [:D] -but what the heck - Pepsi was all I had on hand at the time.) Weight was suspended from the middle of the mast section at about 31 1/2 inches. According to a “bathroom scale” the case of Pepsi weighs 20 lbs. Not sure how accurate it is - but it <u>IS</u> a home test.

<u>MEASUREMENT: </u>of deflection was done as follows…
a) The mast was taped at each end to the supporting surface to prevent the mast section from rolling.

b) A 1/8" nylon string was stretched and taped to the top of the mast at each end. This allowed the mast to bend in the middle, while the the string remained tight. Measurement was taken between the string and the top of the mast to determine amount of deflection.

<u>THE RESULT: </u>A maximum deflection at midpoint of 1 inch.

<center>RECAP of SPECS:</center>
MAST: 63 inches in length, with 61 inches unsupported. Tapered from 5/8 inch to 3/8 inch over length.
WEIGHT: 20 lbs. suspended from middle of mast.
RESULT: 1 inch of deflection measured at middle of unsuspended portion of mast.

Would like to see other’s findings.

Don,

Yes, if you apply the formula I posted, you will get one number for the E*I of the mast section.

As far as turning it into a database or a script, this would be easily accomplished in an excel spreadsheet: Have one column for the distance between the supports, one column for the weight and one column for the deflection and then calculate the E*I in the final column.

If you wanted to you could also add some columns for description of the mast (material, diameter, wall thickness, length, manufacturer, taper, etc). Then you could easily sort the results (say sorting by mast diameter or sorting by length or whatever) to help identify the “ideal” mast for some application.

Lester’s site seems like a perfect home for this spreadsheet, although lester may not want to deal with the headache of updating the sheet with everyone’s test results on an ongoing basis. But maybe he is clever enough to develop a way to automatically update the sheet with a HTML form that you can fill out with your test data…

Dick,

As to your test, it sounds like you did everything right. Strictly speaking the string that you use to create your “straight line” that you measure deflection from should be taped to the mast at the supports. If you have any overhang past the supports, these will deflect upward and if the string was attached to the overhang that could skew the results. But it sounds like your overhangs were small enough to be well within the measurement error of your eyeball and ruler method…

  • Will

Will Gorgen

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

Dick,

As to your test, it sounds like you did everything right. Strictly speaking the string that you use to create your “straight line” that you measure deflection from should be taped to the mast at the supports. <hr height=“1” noshade id=“quote”></blockquote id=“quote”></font id=“quote”>

Clarification:

a) Supports were flat top surfaces at same height - not a single point.
b) Tape to prevent rolling of mast section was done at each end - from surface - over mast - back to surface.
c) String was taped on top of the other tape, so was actually attached at each end of mast. It was not taped to the other end of the mast until the weight was applied, At that point it was stretched tight to allow measurement (ruller) from string to mast. Since mast was supported by 1 inch of surface at each end, at 20 lbs. it is possible that these “ends” moved upward as the center of the unsupported mast moved down, but with the “Critical Eyeball Method” - nothing was discovered that would need to be measured. (i.e. - no “positive” (upward) movement at each end of mast.

Sorry not be clear on that. [personal view - VERY concerned about the 3/8 diameter tip taking that much load, but mast held the weight! Strong stuff - that carbon !]

Dick,

I think you’re test results are fine… For the sake of accuracy, I might have tried taping the string to the level surfaces rather than to the top of the mast and then measured from the string to the bottom of the mast. But the difference would have probably been so small that you would not have been able to measure it…

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…

  • Will

Will Gorgen

Why don’you just measure it before and after you hang the weight on? I admire your bravery- 20lbs. is an awfully large first try!!

Thanks
Don
Vancouver Island