Detailed Sail Mast Design: Analysis, Materials, and Life Cycle - MD I

This presentation provides a detailed design of a sailboat's main sail mast, addressing the requirements of a mechanical design project. It begins with modeling assumptions and system considerations, including the application of the Euler-Bernoulli beam theory for structural analysis. The presentation covers force analysis, including peak equivalent static pressure and the log decrement of damping, essential for understanding wind loads and mast behavior. It includes formulas for wind pressure and Bernoulli's principle. Material selection is discussed, comparing wood, aluminum, and carbon fiber, along with their properties and life cycle considerations. Shear force and bending moment diagrams are presented to analyze the strength of the boat and the mast's ability to withstand various forces. The design incorporates detailed calculations, material properties, and considerations for mast construction, installation, inspection, and safety factors, providing a comprehensive overview of the sail mast design process.

NAME
PRESENTATION

EULER-METHOD BERNOULLI BEAM THEORY FORMULA
W=∂^2/ ∂^2x*{ [EI* (∂^2*u/ ∂^2*x)]}
Where W is distribution of the load along the beam
E is elasticity modulus of the materials
I is amount of inertia of the cross-section of the beam
u is deflection of the beam
MODELLING ASSUMPTIONS
 Masts is modelled as a cross-section beam which is constant
Geometric measurements which is not given shall be estimated
Compressive forces leading to additional stresses in buckling will be
considered indirectly
We consider shrouds as points of load

SAIL MASTS SYSTEM DRAFT
Given that the size of the sail boat is 45ft, mast size 100ft and sail area
400ft^2 we can therefore formulate factors of consideration in the sail
masts design as follows;
i. Center of gravity
ii. weight
iii. Aerodynamics efficiency
iv. Flexibility of masts
We will adopt the Euler-Bernoulli beam theory as the design method.
This method is appropriate because it combines the Hooke’s law of
elasticity and the calculus methods in order find the deflection of the
sail masts or rather maximum loads that could be applied in the beam.
The formula takes into consideration the deflection of the beam (u),
distribution of the load along the beam (w), the elasticity modulus of the

(CONT…)SAIL MASTS SYSTEM DESIGN
• The Sails most supporting structures are the masts and booms and therefore
he choice of the materials to be used is of great importance. For the
purposes of the masts design of this sailboat, we will utilize wood, aluminum
and carbon fiber.
• The masts and booms should be wooden to be supported by the standing
rigging with a sailboat shroud at the two sides and the forestay be attached
to the bow.
• The aluminum is going to be extruded to form a hollow spars, purchase the
extruded section and fabricate into a masts using the design specification.
• The shrouds and the stays are to be attached internally by use of captive T-
bar and in-mast terminal to cut down the windage created by the external
tangs and toggles

(CONT…)SAIL MASTS SYSTEM DESIGN
• The spinnaker pole track is positioned on the leading edge of the
yachts masts with the boom and gooseneck on the trailing edge.
• The masthead must also be mounted with wind instruments, the
tricolor navigation light and the VHF aerial.
• The foot of the masts is then incorporated with a number of pulley
blocks that disperses the halyards and controls via the blocks and
rope stoppers
• We will then mount the Deck stepped masts on an inverted T-shaped
fitting. The keel-stepped masts are also shocked tightly at deck level
with wedges, and a neoprene gaiter at the deck level to prevent
water from getting into the hull

FORCE ANALYSIS
TRANSDUCER: We use the method to pick up the pitching moments and the
aerodynamic forces acting on the masts.
PRESSURE SENSING: this will be used to monitor the behavior of the masts wake at
the chords distances from the TE, and to determine its velocity profile
• Peak equivalent static pressure: This is the force which multiplies with the wind
area to calculate the force on the masts.
• EqH = ßδqHe
• where ß is high masts response factor which takes into account the way wind loads
are effective on high mast light poles
• Δ is the high size mast reduction factor. This takes into account high masts small diameter relative to the
size of the peak gust
• High masts reference pressure EqH: This is calculated based on the effective
wind speed
• EqH=0.613v^2e

FORCE ANALYSIS
We can also be able to find the log decrement of damping. This can
be achieved through adding the log decrement of Aerodynamic damping
to the log decrement of structural damping.
μa=(þa∑RWTV/2no ∑mr)
Where
þa is the density of air kg/m^3
RWT is the Sum of the wind resistance calculated as the product
projected area and the force coefficient
Vt m/s is the hourly mean wind at the top of the masts
No Hz is the high masts natural frequency

FORCE ANALYSIS
Wind pressure is given by the equation p=0.00256*v^2 where V is the
speed of wind in miles per hour (mph) and the unit for the wind pressure
is pounds per square feet (psf).
Edmund Bernoulli will be used to determine the force against fluids
P =I/2*ÞV^2 + Þh =c
Where
• P is the fluid pressure (N/M^2)
• Þ is the fluid density (KG/M^3)
• V is the gravitational acceleration N/M^2
• H is height

FORCE ANALYSIS(CONT…)
WIND & SAILS
We are concerned with making the boat move forward and not sideways
and therefore , it is going to be accomplished by the keel which is
underneath the sail boat. Therefore, for the sail boat to move forward,
the sailing must involves the wind and the sails, and the water and the
keel

FORCE ANALYSIS(CONT…)
Vw is the wind velocity relative to the sail boat. Fsails is broken into lift(it acts
perpendicular to the wind direction Vw) and the drag ( it acts parallel to the
direction of wind Vw) hence it generates as much force.
There are two forces which must cancel
for the sailboat to
move at a constant velocity
These are the resultant force acting on the
boat due to wind
pushing on the sails and the resultant
force acting on the
boat due to movement through the water

SHEAR FORCE AND BENDING MOMENTS
We are concerned with the strength of the boat to withstand the rough
weather of the sea and also capability of not capsizing incase of rough
storm
Shear force distribution is a mathematical integration of the load
distribution along the length of the beam, while the Bending Moment
distribution is the mathematical integration of Shear force distribution
along the length of the beam. These two forces are important in
analyzing the strength of the sail boat
The masks performs one of the key roles in sails boat as it transfer power
generated by winds and sails into yacht.
The masts should e able to withstand the ever changing forces that
include the shear force, the torsion, bend and compression. The choice
of the masts therefore must be driven by reliability and the performance.

SHEAR FORCE
Finding the shear force is done at different locations indicated in the drawing
below (usually the stations) along the length of the vessel.