dimensions, equations and why they are needed.

Firstly here are some dimensions taken from the YSR-10 racing yacht.

Boat
LOA
34,2 ft
LWL
32,8 ft
Width
10,5 ft
Displacement
ex 1400 kg
Draft
9,8 ft
Draft keel lifted
5,9 ft
Sail
Sail Area Main
43 m2
Sail Area Jib
28 m2
Sail Area Code 0
52 m2
Sail Area Genacker
130 m2
Mast Height over DWL
15,50 m

Now that some dimensions are know we can use these to calculate the force on the mast due to the wind.

Force on mast = mass flow rate X time X acceleration due to gravity

Force on mast = ρvAtg

Where:
· Ρ = density of air
· V=velocity of air
· A=area of sail
· T=time
· g=acceleration due to gravity

NB: this equation gives the total amount of force acting on the sail over a period of time, therefore to find the force acting on the mast at a given point in time. Time is negligable.

Next we can calculate the bending moment and deflection using the following formulas:

Bending moment equation = (ρvAtg z^4)/24 assuming that the force on the mast is uniformly distributed.

Therefore the deflection equation

V= (ρvAtgz^4)/24(230x10^9)(9.54x10^-5)

Assuming:
· the mast has an internal diameter of 100mm with a wall thickness of 22% of the internal wall.
· The mast is made from carbon fibre with a young’s modulus of 230Gpa
· The mast has a constant diameter and does not taper.

Reasons for the equations:

1. It is important to know how much force the mast can take before breaking, this can be calculated using the first equation and the elongation percentage of the carbon fibre.

2. The bending moment can be used to find the maximum slope of the mast and thus find the spot on the mast where strain is highest and where the guages should be placed.

3. Deflection equation can be used to calibrate software and strain guages.