# Crude simulation for free standing mast - sail - luff curve ?

Discussion in 'Hydrodynamics and Aerodynamics' started by jmf11, Aug 6, 2021.

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### jmf11Junior Member

Hello,

I want to design a small sail for a small land yacht and a aluminum free standing mast (tubes of different sections set together). As a A-Cat and wind surf sailor, I know that mast - sail combination is of primary importance. Free standing mast are very flexible. Mast and sail influence each others a lot. Luff curve will depend in my understanding of that interaction.

I understand that classic practice is generations of trials and errors converging to optimal solutions. But here it is more of a one-off serie... so no good template at hand.

Are there some open source options to have a crude modeling of the mast-sail combo, find the static equilibrium and derive a luff curve that make sense ? FEM and CFD needed ? Some better way to proceed ?

I'm sort of bugged on that question, and would be happy to learn if there are options to address that for hobbyist in an elegant way.

Help / explanations welcomed

JMF

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### BlueknarrSenior Member

Flex the master with a tension line.
Measure the distance between the mast and the tension line at frequent intervals.
The luff curve should be slightly less than the max mast bend.

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### jmf11Junior Member

Maybe could work, my my readings describe a different picture for the type of sail-mast combination I consider. This is described here Making a sail – sailrepair.co.uk https://sailrepair.co.uk/making-a-sail/ <= the picture with the sail and mast curve that cross each other around the middle: more sail curve than mast curve low down and reverse up.

I have a paper about RSX Olympic windsurf board, and it is the same (see attached picture).

I also attach a picture of my land yacht moidel, that demonstrate the issue I have to solve.

Or do you mean that I could use measure the mast bend, use it as an input in Sailcut (Sailcut CAD | Sailcut http://www.sailcut.com/) to derive panel shape, and that the resulting luff curve could look like the one on the wensite and the RSX?

However, as I'm curious about simulation and progress in that area, I would be interested in sail-mast combination simulation ;-)

JMF

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### AJBJunior Member

JMF,
To understand this in a practical way, you need to separate the elements... try this as an adaption of a normal development process.

1. Use just three horizontal sections to control the shape and the luff curve; one at the hounds and one more above and below; equidistant between that section and the head, and that section and the tack... So - "upper, hounds, lower'..
2. Estimate what the mid -range flying depth you need, probably around 11% upper and 15 % lower, so perhaps 13.5 % "hounds".
3. Estimate average mast bend to establish chord lengths at the three heights; and calculate the horizontal broad seams necessary to achieve the flown depths. Start at the hounds and add the increment for the lower. Use zero for the upper broad seam, excluding stretch compensation, which might require around 2 - 3 mm added, depending on your material, batten stiffness, roach etc.
4. Deflect the spar to your expected midrange load and measure at the three heights.
5. For 2d cutting, calculate the material absorbed by the broad seams as luff curve.
6. Add the deflections from step 4 to the absorbed amounts from step 5 to arrive at 'total luff curve'.
7. Adjust the curve for twist and progressive flattening, possibly around + 8 mm at "lower" and -3 mm at "upper'.
8. Pray a bit and test fly!

AJ

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### gonzoSenior Member

You are asking for the software sail and mast manufacturers spend millions developing. I doubt anyone will give it away for free. The luff shape is only one of the parameters. They all interact, therefore a sail/mast combination needs to take into account all the forces, including righting moment.

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### TANSLSenior Member

I am not very sure that to calculate a free standing mast you have to take into account the righting moment. In any case, a moment cannot be included among the acting forces.

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### jmf11Junior Member

Yes, I agree that it is a bit of a dream to consider open source software to do what professional companies spend lot of k\$ to buy. However, I had a lot of surprises with quite good tools available today for free, that we would have dreamed of few years ago. CAD programs (FreeCAD), PCB design programs (KiCAD), Aero simulations like XFLR5, OPENFOAM, SU2... Sure there is in most cases a trade-off with usability and maintenance. But in some case it works quite well!

Mast sails combination looks quite complex to me. I wanted to check if it could me more easy than I thought. Seems it is not ;-)

In a pragmùatic move, I will head to AJB process, helped by freeware Sailcut (Sailcut CAD | Sailcut http://www.sailcut.com), which seems to automate part of the proposed calculations (but not design choices).

And in my case, I call freestanding, an unstayed mast, as on my land yacht above. In my understanding there is in that case a righting moment. At least a max force at which the landd yacht capsizes (I have experienced it).

JMF

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### gonzoSenior Member

The righting moment will determine how much the mast will bend.

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### jmf11Junior Member

And I imagine that the bending curve will, for parts depend:
- Righting moment (lateral bending),
- sheeting - downhauling (fore-aft bending),
- sail pressure distribution (how the pressure distributes along the height of the mast). Maybe second order displqcements ?

And all those bendings impact the sail shape, which in turn impacts the mast bending. I think that for planes, they call it aero-elasticity. Is it correct ?

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### AJBJunior Member

JMF
You got it ... one of the reasons that the trial and error method remains (for these very flexible rigs) is that the modelling is very complex, and well informed trial and error can progress quickly.

Usually, it proves difficult to reverse engineer the trial and error result in the model!

The span-wise distortion and elasticity is certainly difficult.

AJ

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### jmf11Junior Member

Agree, and I reckon that this is overkill for a small land yacht not aimed at competition

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### SkyakSenior Member

Just a suggestion -to my eye these pictures indicate you would benefit most from a strain analysis of your mast. It looks like a two piece pipe that is overstressed at the joint (possibly not a tight fit?). You could just WAG a reasonable load distribution, set it to sum up to the max righting moment of you in the cart and do the beam calculation for each tube. Then go back and look at the strain on the joint. You can even do some actual measurements with some weights and a laser to verify. Once you fix the mast and know it's deflection properties, the cut should be just a targeted leach tension.

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### jmf11Junior Member

The mast is a 5 pieces mast (not good for mechanical perspecive, but good for transportation). I finally played with the FEM module of FreeCAD (based on MIT code Calculix). I simulated my mast with the different reinforcements. And it gives the elements below. It does shon a not constant curve, but no obvious kink. Sheeting in the real sail+mast at home, without lateral wind pressure looks also OK. But during real sailing with lateral pressure, the sails shape is not good at all, with very open leech from very low as in the upper picture.

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### SkyakSenior Member

Dollars to donuts the kink is on a joint. Do some calculation of that joint. What are the actual dimensions of each pipe in that joint? I don't think the pictured FEA caught the stress and strain from the fit between pipes. I don't see any indication of hoop stress on the top lip of each section. How well do your section fit?

Also, what did your FEA load look like? Does the force/deflection agree with what you have? It's only good the sail unloaded -maybe we can relate to leach tension.

Last edited: Aug 11, 2021

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### SkyakSenior Member

I just thought of another significant factor. The pre-stressed curve needs to be accounted for. The load distribution from wind is not planar.

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