Calculating Sheet Loads

When you size your running rigging, you need to make sure it can withstand the loads you will place on it. These loads will come from the force of the wind exerted on the sails. It is best to size your running rigging for the worst imaginable situation: The sails sheeted in tight to a gust of wind on the beam. This will place all of the sail area under load, which will transmit the highest amount of force to your running and standing rigging. 

First we need to understand a few points: 

What is the force exerted on the sails?
How is that force transmitted to the running rigging?
How strong does my running rigging need to be?

The force of wind on the sails is equal to:

Wind Pressure per Square Foot = (0.00256) x (Wind Speed in mph)^2

It is important to note that the wind speed is squared. This means that as the speed of the wind increases, the force it exerts on the sail also increases; but at a much higher rate! 

At 5 mph, the pressure would only be 0.064 pounds per square foot.
At 10 mph, the pressure would rise to 0.256 pounds per square foot.

This may sound insignificant, but on a large mainsail of say 500 square feet, these numbers would translate into:

5 mph = 32 pounds of wind pressure
10 mph = 128 pounds of wind pressure

Just doubling the wind speed quadrupled the wind pressure. This force gets transferred to the sheets and halyards that have to hold the sail in place.

While the actual formula for calculating the force of the wind is actually much more complicated taking in many more variables. For our purposes of properly sizing the rigging, we can trim the formula down to just these variables.


The simple way

Harken provides online calculators on their website that can help provide an easy idea for sizing the sheet loads on their website.

For the Mainsheet: http://www.harken.com/MainsheetLoading/
For the Headsail: http://www.harken.com/content.aspx?id=9096

Samson also provides a formula to calculate the amount of force on the clew:

(windspeed in mph)^2 x 0.004 x (sail area in square feet) = Sheet Load at Clew in pounds

New England Ropes also provides a nifty tool on their website where you answer a few questions and it will tell you what line and what size to use

http://www.neropes.com/InteractiveLineSelector/Sailing_Type.html


The not so simple way

The sheets serve to hold the sail against the wind and keep it from turning into a giant flag flapping in the breeze. 

Headsail sheets need to withstand the full load of the sails clew alone, as the single sheet is run to the winch. The mainsheet has the advantage of being in a purchase system, spreading the load over various lines, greatly reducing the loads on the mainsheet line itself.

 

When wind exerts force on the sail, the sail in turn wants to move. The job of the sheet is to resist that movement and keep the sail in its position. This force is shared between the tack, head and clew. If the sail were not attached, it would simply blow away; but by being secured, it exerts a force which serves to pull the vessel along. 

Loads.jpg

The luff is maintained tight by the tack and head pulling to resist deformation of the sail. The tension for the luff is provided by the halyard pulling on the head. The leech and foot are both held in tension by the clew. 

Adjusting the jib sheet angle shifts where its force is applied. When the jib car is forward, the jib sheet acts more on the leech. When the jib car is aft, the jib sheet acts more on the foot.

For our example, we will look at a 400 square foot jib under winds of 25mph. 

Our wind pressure would be:

Wind Pressure per Square Foot = (0.00256) x (Wind Speed in mph)^2
0.00256 x 25^2 = 1.6 pounds per square foot x 400 square feet = 640 pounds of force on the sail

While the force on the sail is 640 pounds, the force on the sheets and halyards will be much higher because they need to hold that force at various angles. 

The formula for calculating the jib sheet loads is:

Sail Area in square feet x Wind Speed^2 in mph x 0.00431 = Sheet Load in Pounds

Our Jib sheet load would be = 400 x 25^2 x 0.00431 = 1077.5 pounds

To select the proper jib sheet size, we would want to take into account two points:

Tensile strength
Comfort in your hands

For tensile strength, you would need a line that can withstand 1077.5 pounds as a minimum.

For safety reasons, factor in an additional 20% for safety margin and that gives us a minimum value of 1,293 pounds
For a higher safety margin, use 50%, which gives a minimum value of 1,616.25 pounds

When looking at lines, this translates into actual products that we can use on our boat safely.

Most stretch

Most stretch

Less stretch

Less stretch

Minimal stretch

Minimal stretch

With a 50% safety margin, you could use:

1/4" New England Ropes Three Strand
1/4" New England Ropes Sta-Set
1/4" (6mm) New England Ropes VPC

 

With a 20% safety margin, you could use:

1/4" New England Ropes Three Strand
3/16" New England Ropes Sta-Set
1/4" (6mm) New England Ropes VPC


In my hands, 1/4" is tiny and is hard for me to hold onto for an extended period of time. For comfort reasons, I like to keep my lines bigger than 3/8"; 1/2" being very comfortable. 

A line of this size will be incredibly strong, 9,500 pounds of strength in VPC! That lines breaking strength would "in theory" be able to hold the sail in winds of 74mph

400 x 0.00431 x 74.23^2 = 9499.4 lbs
I would have reefed that sail long before then!

This is where sizing the sheets based on comfort comes into play. First calculate the minimum size of line for your sheets, then choose a comfortable size in your hands making sure that the comfortable line size is strong enough to support your running rigging's requirements. This will lead you to selecting a capable and comfortable line.

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