rotated round vs rotated eliptical mast section

My rough calculations suggest that an non structural eliptical fairing 55' by 10" by 20" tapering to 10" by 5" with a constant thickness of 1/16", should weigh about 100 lbs if Kevlar epoxy, or 154 lbs if s-glass. A structural internal carbon fiber epoxy tube 10" in diameter at the base and 5" in diameter at the head 1/4" thick at the base tapering in thickness to 1\16" should weigh about 164 lbs.
My question. assuming that my numbers are remotely in the ball park ( I left school at 14), is the added weight of more efficient section shape of the rotated elliptical mast worth it in terms of performance as opposed to omitting the fairing and simply rotating the structural tube , adding the saved weight as ballast as low as possible? Any help would be appreciated.

 

Assuming you have done the basic strength numbers correctly, my concern would be the posbility of buckling at the base of the mast with such a thin wall thickness to diameter ratio. Have you done an Euler buckling analysis? I don't have the data to do this.

 

No I have not . Wish I could but I don't know how . As I said I have a very limited education. At any rate I was thinking of free standing masts and consequently wasn't considering compression loads. I took the dimensions from my current aluminium masts that are free standing and adjusted the figures as well as I could for the specific gravities of the suggested materials. I guess I didn't phrase my question clearly. What I would like to know is, all things considered, is the extra weight ,the complication of calculating the bending characteristics and the extra work and expense of making a rotating tapered elliptical mast rather than a simple rotating tapered tube worth it. The figures I provided are no where near exact and I only used them to get a general idea of what kind of weight savings might be expected.

 

The formula for the Euler buckling force for a circular column is
F = n.(pi squared).E.(rA/L)squared
Where:
E = elastic modulus
r = radius
A = cross-sectional area of material
L = effective length

The value of n is:
0.5 for one end fixed, one end free (the self-supporting mast case)
1 For both ends held by ball joints
2 for 1 end fixed, the other held by a ball joint stayed (mast)
4 For both ends fixed

even without the compressive force of the standing rigging buckling would still apply, but I don't know the formula. Perhaps one of the MA's will provide it. Buckling has to do with flexing of the material rather than failure due to stress, although of course the buckling results in failure as it rapidly progresses. That is why it contains a term for material stiffness rather than strength.

 

Unless one is seriously into racing, and after every tenth then I cannot see the need for the additional complexity.... To cruise, (my objective), one should consider ease of handling (simple layout with minimal tweaking adjustments) and robust construction that can be readily repaired / replaced.... That does not mean you are restricted to slow bath-tub performance.... I anticipate a good turn of speed in favourable weather, (3 to 15 knots wind in calm seas), when compared to other cruising yachts of similar loa, but still be able to make way carefully, in a strong wind warning situation...

11 tenths racing or more, - then the limiting factor is the budget / sponsorship / rules constraints... Good sailing... - only in that arena would I contemplate rotating mast or carbon mast, as for cruising there appears no real advantage...

 

Your modulus of elasticity will vary widely from the round to the elliptical section. These are things you can't guess at, without understanding some basic engineering principles.

 

masali I am inclined to agree with you but I am open to argument. The rig I have now(cat ketch wrap around sails) is about as simple and self regulating as you can get. Its also near failsafe. In 30 years the only thing that has failed was a swedge on the mizzen topping rig .It happened as I was reefing and as a result the the boom narrowly missed my head when it fell. I think it is ironic that the closest I have come to catastrophe is because of a simple part on the nearest thing I have to standing rigging. Par I am not an engineer and I am making assumptions. I am assuming that a carbon fiber epoxy mast of the same dimensions and scant lings as my aluminium ones that have endured for thirty years would be stiffer lighter and more resistant to buckling under load. I am also assuming that the weights I proposed are some where in the ball park as when I modeled my own mast in my 3d program it gave me a volume in cubic ft. which I then multiplied by 63 and then 2.7 (I think close enough to the specific gravity of aluminium) . The result was within 10% of the actual weight of my mast. I then repeated the calculations for the carbon tube substituting a specific gravity figure of 1.54 and then for the elliptical fairing using specific gravity figures of 1.3 Kevlar and then 2 s-glass . I didn't worry about the bending characteristics of the elliptical fairing as my thinking was that being much more elastic than the carbon fiber tube it would just go along for the ride. Recognizing that the figures presented are aproxamations and that I am not trying to engineer a mast (I will leave that to the professionals)I think that they never the less indicate that significant weight savings are realized utilizing a round sectioned tube and forgoing the fairing . What I am trying to get is some incite into is weather or not the aerodynamic efficiency of a rotating elliptical section justifies the extra weight and complexity .

 

Your luff round will be dramatically affected if switching from round to elliptical section. I don't see how a sail maker could compensate for the elliptical sections "odd" variations is bend. This bend on free standing sticks, accounts for much of the usefulness (efficiency) of the sail plan in specific wind strengths.

Efficiency up wind may be measurable with an elliptical section, but it would be fractions of a knot and likely only relative if racing against other round sectioned cat ketches of the same design. Frankly, given the information, I'd happily compete against you, if I had a round section cat ketch on the same model boat. This assumes I could get better sail shape over changing wind direction and strength with the round spar (assumed).

 

Par I believe you are right and that the differences between elliptical and round sections or for that matter rotating masts are negligible on cruising boats . It seems to me that aspect ratio has a greater impact on windward performance. I look at the Wylie Cats with their super light non rotating thin round sectioned flexible masts and think ,thats the way to go . On the other hand Eric Sponberg makes a convincing argument that elliptical rotating is the way to go and the boats built with his masts seem to validate him convincingly. I would like to know the weight difference of a mast of the Wylie cat variety and that of Sponberg's type if the same length, and designed for the same righting moment.

 

I have also been thinking about elliptical mast sections. It seems to me that the principal force component on a mast is parallel to the sail. Such a force would be across the major axis of an elliptical mast if it is able to rotate freely. If this argument is correct then the change from a round mast to an elliptical (or foil-shaped) mast should surely be implemented by reducing the minor axis (thickness) not increasing the major axis (fore-aft depth).