Hello all!
Now, I understand that
it has been a few months since I last posted, but I have been preparing for my
CEng interview (awaiting result) and a few other bits, so I haven’t had the
time. Now that is all over and winter is drawing in, I’ll have more time indoors
to geek-out and design it.
So, what have I been
doing since the last post? I’ve estimated the size of the sail to figure out
the possible force from the wind on the mast to figure out the keel bulb size
through moments to calculate the correct size for the carbon fiber mast to be
strong enough.
Approximate Size of
the Sail
Okay, so I estimated the size of the sail to be triangular
at 2.5m tall to 1m long across the bottom, giving us an area of:
S = 0.5 x 2.5 x 1 = 1.25m^2
(NB: Although I have
carried this value forward in my calculation below, it is wrong. As the sail
will only be a maximum of 1.7m tall, the area of the sail will only be
0.85m^2.)
Wind Force on the
sail
The
full expression of the force is:
F = 0.5 x rho x S x C x V^2
with
- F : aerodynamic force, expressed in Newtons
- rho : air density (varies with the temperature and the pressure) ;
- S : typical surface. For the sail, it is the sail area in m²
- C : aerodynamic coefficient, which is dimensionless. It is the sum of two percentages: the percentage of recovered energy on the leeward side + the percentage of the recovered energy on the windward side.[28] For this reason, the aerodynamic coefficient can be greater than 1, depending on the angle of upwind sailing.
- V: Speed is the speed of the wind relative to the sail (Apparent wind) in m/s.
ρ = 1.423 @ 25 degC
S = 0.5 x 2.5 x 1 = 1.25m^2
C = 1
V = 70mph = 31.2928 m/s (Assuming strongest possible winds
in Atlantic).
F = 0.5 x 1.423 x 1.25 x 1 x 31.2928^2 = 871 N
Okay, this is a lot of force. I’ll see how the rest of the
calculation comes out before I over-react.
Moments on vessel
Through a simple
calculation of the area and thickness of the keel, I estimated it to be 4kg (it’s
going to be 5mm thick aluminium sheet). Taking this and scaling up the size of
the keel bulb to be around 6kg, I got the following figure for the moments:
Weight (kg)
|
Dist (mm)
|
Moment
|
|
Keel
|
4
|
362.5
|
1450
|
Bulb
|
6
|
725
|
4350
|
Total
|
-
|
-
|
5800
|
So, to balance this,
the mast needs to be able to handle a certain amount of force at a distance of
1.7m. When this force is exceeded, the vessel will topple over. This is a good
thing as it will protect the sail. I’d better say now that I’m designing this
boat to be tumbled over and over in a storm, then self-right. IT is all part of
the master plan.
So, the moments on the
mast should be:
Weight
(kg)
|
Dist
(mm)
|
Moment
|
|
Mast
|
3.41
|
1700
|
5800
|
So, at the moment, a force
of 34.1N @ 1.7m will topple of vessel over? This is a far cry from the 871N
that I could see in the Atlantic. This is good because it will protect itself,
but bad because it will only take a light wind to topple it over...? I’m
thinking a rework of the calculation is required here...
The wind to push it
over in this configuration could be:
34.1 = 0.5 x 1.423 x
1.25 x 1 x 31.2928^2
Therefore v =
SQRT(34.1/(0.5 x 1.423 x 1.25 x 1)) = 6.192m/s = 13.85mph
This value seems
incredibly small.......
I’ll continue this
tomorrow. I’ve written up part of the mast calculation and I’ll rework the
calculations to make sense of it.
