A Formular for wind pressure and other sailing related calculations

[DaKea90]

Hey guys, 

In octobre I've started studying civil engineering and looking at a ship, I thought "Isn't a ship just a house with long sticks on top that has to withstand the forces of Walter and move?" 

 

I asked a teacher, who tries to teach is the basics of structural engineering. He turned out to be interested in ships, too, and showed me some basic stuff I can already calculate concerning a boat/ship an calm sea. 

 

One thing that he did not know, was how to calculate the wind pressure. With this I mean the force the wind of a certain speed puts on a piece of cloth (a sail) of a certain dimension. 

 

Is there a book/ebook/epaper, that revolves around this and/or related topics? Questions like "what high a force can a rope of a certain dimension withstand before it starte to fail?" or "How big is the braking force a sail provides?" are also left to be answered. 

[wefalck]

These Saxons ask complex questions   Perhaps one should devonvolute them a bit:

 

I gather you already learned that air is a compressible 'fluid', which makes things more complicated and simple static calculations may not be sufficient. A sail is a complex shape, it was not only the outside dimensions, but is curved in two dimensions. I gather there is a formula to calculate the resistance of a hemisphere in laminar flow, but here you are dealing with a surface that has one or more linear edge (where it is attached to e.g. the spar) and three other edges that follow more or less the shape of a catena - that is assuming that the wind hits the sail perpendicular to the main axis, which in fact is rarely the case. Well, I assume that there must be some some sort of engineering handbook for designers of sails for competitive sailing boats ... on the other hand I think a lot of these questions are resolved in wind-tunnel experiments or some high-end fluid dynamics modelling for compressible and turbulent fluids. Turbulence behind the sail (see Karmann) is an important aspect.

 

The breaking strength of rope obviously depends on the material and the way how it is made. For wire-rope one may be able to calculate this from the properties of the individual wires, as these can be manufactured to specified properties. It is different for natural fibres, the strength of which is only roughly known and varies from source to source. These properties are usually determined/verified experimentally. There should be some rough estimates in late 19th/early 20th century rigging textbooks, when materials testing was developed.

 

The third question can only be answered, when you know the exact geometry of the sail. I could imagine that for a given shape this could be answered with modern computational fluid dynamics that take into consideration both, the compressibility of the air and a highly turbulent flow (not many packages can do this, I believe). Otherwise, wind-tunnel experiments still would be the answer.

 

However, as wind-tunnel experiments are expensive, it may be quite possible that the serious competitive yacht-designers now have computational tools that can do the above simulations. Perhaps you should look into this direction.

 

In any case, with simple static calculations you will not get very far and you wouldn't even know, whether you are on the safe side with your results ...

[Jaager]

Would not the core calculation be: F = mVV? 

The surface area that the force acted on would be an absolute bear to determine.  It would also probably be dynamic, with the effective sail area adapting and changing with differences in force.  I can imagine that the complexity exceeds any practical utility for a formula in predicting a wind speed vs vessel speed.   Reverse calculations should work.  Measure the two speeds and the necessary force can be cranked out.

One factor that I keep overlooking is that a slight incremental change in wind speed can have a significant effect on vessel speed. Why the frantic and continuous changes in sail area and sail angle was necessary when wind speed was above a critical value.  And also why a sudden and unfortunate change in wind direction could roll a vessel with a poor design past the point where it could right itself.

[wefalck]

For a ship at sea there are an awful lot more variables to consider: the constant rolling, heeling and pitching changes the aspect the sail presents to the wind, the wind itself changes direction not only in the horizontal, but also in the vertical, the wind speed constantly changes slightly, due to the ship's movement and the movement of the waves the wetted surface constantly changes, the length of the waves and hence their interaction with the ship-generated waves constantly changes, etc. etc. Some of these variables can be simulated numerically and generated randomly, but that requires a huge amount of computer-power. In principle it is easier for the water part, because water is not compressible. This is why in many cases experiments in wind-tunnels and/or wave-troughs etc. with scale-models are still needed.

[Lieste]

There have been a number of simulations attempted along those lines - Among these are the old "HMS Surprise" applet, a set of notes, plans and a spreadsheet on HMS Southampton (1757), from iirc Richard Braithwaite, and an 'admittedly hacked together' simulation of a 5th rate 'Lively' ish ship in "Painted Ocean", which is still available to download and play with on Twitch.io (the others seem to have fallen by the wayside along the way).

There are also some papers which cover approaches to the problem and some of these might ease 're-inventing the wheel' - for example a paper entitled "Application of simulation technology to the performance evaluation of HMS Victory as an exemplar of the ships at the battle of Trafalagar", from the University of Southampton (Jan 2006) is downloadable online, and at a first glance might serve as a point of entry at least. (Though I haven't been able to look over it and crunch numbers/play with dynamic behaviour to see if the model holds water).

[Roger Pellett]

There is a huge difference between science, academic engineering, and practical engineering.  For example, science describes  the behavior of materials under tensile loads, academic engineering might teach advanced analysis methods for determining the strength of wires twisted together and the practical engineer who will understand the theory describing the strength of wire rope, selects the actual wire rope to be used from a manufacture’s catalog. 

 

The amount of high end analysis performed also depends on the application. A Naval Architect designing a mass produced day sailer can avoid expensive engineering analysis by over designing, as the slight loss in performance is less likely to be as important as the final cost of the boat.  On the other hand, when designing an America’s Cup Yacht, budgets usually include state-of-the-art engineering analysis as performance is all important.

 

Loading on sails is completely dependent on rig.  The square rig is intended for downwind or reaching performance so loading is mostly direct impingement of wind on the sail cloth.  The sail fails when the fabric tears; The sail blows out.  Modern sailboat rigs are designed for optimal upwind performance.  In this case the sail acts as an airfoil and eventually the sail cloth stretches to the point where the sail loses its shape and must be replaced.  That’s why sails on new high performance racing yachts are often black.  The cloth fibers are Kevlar.

 

Roger

[Lieste]

Sailing on the wind, and on a reach is done with the sails lifting, even on square rig. It is *only* when going downwind that sails can only be employed in a stalled drag mode, and sailing speed suffers from the combination of running with the wind, and the lower sail efficiency in this mode.

Upwind sailing performance is limited by the bracing angle of the sails, rather than a failure of the sails to lift when the angle of attack is appropriate.

[Matt D]

I think what you’re asking for is the maximum theoretical force.  That would simply be the dynamic pressure times the cross sectional area.  Dynamic pressure is the pressure of air in the direction of flow, which is 1/2 rho x V^2, where rho is air density and V is velocity.  It’s not possible for the force to be higher than that.  The ratio between the actual force and the maximum theoretical force is the drag coefficient.  This is an application of Burnoulli’s principle.

[bridgman]

Strelok:

Depending on how deep you would want to get into sailing theory and application you might look at "Aero-hydrodynamics of Sailing" by 

C. A. Marchaj, 1980,700 pages. His examples used are contemporary sailing craft, but the concepts would apply to ahy wind driven craft and there numerous  variations discussed.

Bridgman Bob

[DaKea90]

Thank you all for your quick and very informative responses. 

 

It seems to me, that I underestimated the complexity of aero-hydrodynamics a tiny bit 😅 

I thought, there is some kind of a diagram or list that says "windspeed of x km/h produces a pressure of y N/m^2 on the sail" so I can make a rough estimate about how big a force is acting on the point of the yard, which is diverted by the mast itself and the standing rig into the hull. Mast and rig take the pressure relative to their tolerances. 

 

At my current level of skills, I just want to look at the parts of the ship as separate pieces and only in calm sea without waves and a steady amount of wind. 

 

@bridgman

Your book recommendation looked promising, but it is outside my financial possibilities, unfortunately. 

[Lieste]

5 hours ago, Matt D said:

I think what you’re asking for is the maximum theoretical force.  That would simply be the dynamic pressure times the cross sectional area.  Dynamic pressure is the pressure of air in the direction of flow, which is 1/2 rho x V^2, where rho is air density and V is velocity.  It’s not possible for the force to be higher than that.  The ratio between the actual force and the maximum theoretical force is the drag coefficient.  This is an application of Burnoulli’s principle.

It can be higher than that. The aero forces are the vector sum of lifting and drag forces.

Depending on the form, lift can significantly exceed a Cl of 1.0, and drag, - form, skin and vortex can be a significant fraction of lift for the relatively low aspect ratio of a square rig. When stalled and either not lifting well, or acting as a parachute drag becomes the dominant factor, with relatively low lift forces.

A backed sail is constrained against the mast, so will not fill to the same form, but otherwise behaves similarly to a filling sail.

The overall effect is complex, with the lift from one mast altering the flow over those both up and downstream from it, as well as reducing wake energy for following masts.