Forces in fittings

Hello,

I would like to calculate the forces and tensions into sheets and halyards in order to dimension fittings (cleats, clutches, winches ...).
Is there any formula I could use ?

I only know this formula : F = pressure in sail = 1/2.ρ.S.V^2.C
ρ = density of air (1.29 kg/m3)
S = Sail area (m2)
V = Wind Velocity (m/s)
C = aerodynamic coef. (about 0.9)

Can I assume the tension into the halyard is F/2 ?

Thank you very much.

 

the pressure distribution over a sail is a complex subject, and distrubution varies with various trim configurations and headings. I do not think it is reasonable to attempt to working out with basic aero equations because of this complexity, this is true of the halyard tension as well as the load at all of the attachments and sheets, etc. I say this as an engineer that has a number of years doing computational fluid-mechanics and aerodynamics professionally.

However, I have seen used by rigging designers, and I used it myself for my own deign dingy rigs, a value of about 1 lb per square foot of sail area to calculate rigging stress, with a 1.5 saftey factor. Use the centroid of each sail and simple rig geometry to determine loads and tensions in the rig. It has worked pretty well, the stangnation pressuer in normal air to give 1 lb/sf is about 22 knots if I remember, and usually you would reef before than, so it should give conservative values without making the rig overly strong (and heavy).

Most of the yacht design procedures just use design tables for various size and rig type, rather than calculating loads. this has worked reliably well for conventional rigs, how ever if you are building something unconventional than you are on your own.

Good luck. What are you designing?

 

Sheet load of Genoa

SL = SA x V2 x 0.02104

SA- sail area in meters^2
V- wind speed in knots


Mainsheet load
ML=(E^2 x P^2 x .02104 x V^2) / (SqrRoot(P^2+E^2)+ (E-X))

E-foot length in meters
P-Luff length in meters
V-wind speed in knots
E-distance from aft end of the boom to mainsheet attachment point in meters


While I think Petros is correct, for gear selection you just need to approximate the maximum load on a piece of hardware, not identify the current load at any given point making the job much easier.

 

those equations are approximations at best, but will get you close enough. They are likely derided from observations rather than scientific analysis. Thanks for posting them stumble, they could be useful.

should not that first equation have V^2 and not V2 in the second value? forces in a fluid is usual a function of a square of the velocity, just like you have in the second equation.

 

The formulae in the Stumble's post #3 have been created by Roger Marshall, a prolific yacht designer and author of a number of books on yacht design and boat building. He is a NA at Roger Marshall Yacht Designs (not actually sure if he is still actively designing boats) and former consultant at Sparkman & Stephens. Those formulae are valid scantling tools and are being used even by producers of rigging accessories like Harken.

An important note about them: the calculated loads are in kg.

Regarding the formula for the mainsheet load, some renown riggers claim (and some write it in their books - like Danilo Fabbroni, a former designer at Harken and now owner of F&V Rigging) that it gives an overestimated value of mainsheet load (which isn't necessarily bad from the safety point of view) and that it can be safely substituted by the formula for Genoa sail, multiplied by 1.5:

ML = SA x V^2 x 0.02104 x 1.5 [kg]

Cheers

 

Thanks for the catch Petros. Yes it should have been V^2.

One of these days I would love to see get a load cell and actually take some measurements, but I can't figure out what I would do with them except just have some random data points.


One of the things I find fascinating is that a lot of people seem to massively overestimate the loads a boat sees.

 

It depends on your boat, but:

If you have a block and tackle mainsheet, no winches, say an 8:1 purchase. Then you can only pull in 8 x your body weight, so say 600kgs. That has to be the max load on the mainsheet or you cannot release it - the boats way of saying "reef"

Richard Woods of Woods Designs

www.sailingcatamarans.com

 

What is the safety factor used when specifying hardware. Is this factor the same with no stretch rope ?

 

That is absolutely correct, Richard. Apart that, imo, it is not the max. body weight that one should consider for the calculations of the necessary purchase. It should be done, imo, by using the max. pulling force of a single arm - which should be around 30 kg (unless your last name is Schwarzenegger ).
The Marshall's formula given by Stumble for the main sail sheet load is to be preferred to the simplified version given by myself, because the former one takes into account the point of attachment of the mainsheet (X), which is absolutely fundamental for a correct calculation.


By the way, on the Harken site one can find the on-line calculators for genoa and mainsail sheet and system loads. It can be found here:
http://www.harken.com/Calculators/
The calculators use the Marshall formulae seen above and give some more correction factors to be used in particular cases.


All the formulae are valid for displacement monohulls. Hence if you are calculating for a fast cat or ULDB, they are not valid because they tend to overpredict the actual loads. for the same reason, they can be applied for a first guess when performing a conservative scantling - since the actual loads on cats and ULDBs will be certainly lower.

The formulae are also not valid for very heavy displacement boats, like motorsailers, for which the calculated loads will be underpredicted.

Cheers

 

It will depend on the hardware detail you are considering, as well as on the boat type. Typically, the factors of safety (FOS) for blocks and sheets, based on maximum loads calculated with Marshall formulae (which are pretty conservative) are:
- 1.5 for performance yachts
- 2.0 for average cruising yachts.
- 2.5 for heavy displacement yachts.
Placing the design in the right category will vary case by case, depending also on how much importance is given to an eventual failure of a given piece of hardware. In an ideal world, in which we would know exactly the maximum loads acting on each part of the boat, every single part of it would be designed with the same FOS. In reality it is not so, and the FOS will depend on what piece is being considered, where is it mounted, what task it will perform and how much would it's failure cost (in terms of money or even lives).

If the boat type is designed to class (or ISO) rules, then the FOS will be given by the class rule. For example, GL prescribes a FOS of 3.3 for rigging, based on the ultimate stress of materials or breaking load of wire ropes. For chainplates, it is 1.6 times the breaking load of the attached wire rope. And wire ropes in general have a minimum breaking load equal to 5 times the design load.... As you can see, different pieces of equipment have different FOS requirements.

In case of blocks, travellers etc. and relative supporting structures, one also has to consider that loads will vary in function of sheet angle (or wrap angle). See the attached drawing which shows the relationship between the sheet angle, block reaction force angle and block load/sheet load factor.

Cheers

 

Interesting. Thanks.

Also of note is that ive never had a line fail, it has always been the hardware or its fasteners. Naturally, angle of load effects the hardware not the line.

 

Fibre and wire ropes already have a hefty built-in safety factor of 5. So, a rope designed for a 1 t load has a minimum breaking load of 5 t.
A typical block or traveller is designed with a FOS of 2 or 3. So, a block designed for 1 t load will break under just 2 t.
It is important for the boat designer or rigger to know these facts, or else it becomes pretty easy to choose an undersized piece of hardware.

 

Hello,

Thank you very much all, it really help me for my work.
Just mind in the Stumble equation, it seems there is a mistake if I compare to the equation given on the Harken website.

Mainsheet load
ML=(E^2 x P^2 x .02104 x V^2) / (SqrRoot(P^2+E^2) x (E-X))

E-foot length in meters
P-Luff length in meters
V-wind speed in knots
X-distance from aft end of the boom to mainsheet attachment point in meters

 

This is the formula (metric):



as visible in the Harken website: http://www.harken.com/content.aspx?id=9094

Yes, there is an error in Stumble's transcript, but also in yours. The X which you have indicated with red color is the multiplication operator, not the distance.

Cheers

 

Hi,

You' re right, my reply may be confusing. There was actually 2 mistakes. The + should be a x (multiply) and the X (not E) is the distance from aft end of the boom to mainsheet attachement point.
The picture of the formula explains at the best and avoids mistake.

Anyway, thanks to all for explanation and the provenance of the formulae.