Hello all!
I’m not doing very well
with these updates, am I? Anyway, a few updates:
- I am now a chartered engineer! For. The. Win!
- I have finally finished doing the brushless DC motor for a STEM project, so I can get back on it!
Since the last post, I’ve
checked my calculations for the items I posted in the last update, which I will
go on to discuss now.
Approximate Size of
the Sail
As I noted in my last post, I had the size of the sail
written incorrectly. This should be:
S = 0.5 x 1.7 x 1 = 0.85m^2
Wind Force on the
sail
With the new sail size, this becomes:
ρ = 1.423 @ 25 degC
S = 0.5 x 1.7 x 1 = 0.85m^2
C = 1
V = 70mph = 31.2928 m/s (Assuming strongest possible winds
in Atlantic).
F = 0.5 x 1.423 x 0.85 x 1 x 31.2928^2 = 592 N
Although I don’t think I actually need this calculation for
the sail sizes, it’ll be nice to know for later on.
Moments on vessel
As detailed before, the
moments on the boat created by the keel will remain at 5800. I may look to
reduce the thickness of the keel at a later date as it seems quite…well…thick.
However, I have played with a 3mm thick piece of aluminium that is 1m long and
it just flexes more than I would like to see. I think I need to get “hands on”
to confirm this decision now.
So, to balance this,
the mast needs to be able to handle a certain amount of force at a certain
distance. Although last time I performed the calculation at 1.7m, I have
realised that this is not sensible as the centre of the force on the sail will
be a lot lower down.
I think the centre line
of a triangular sail that is 1.7m high by 1m long is 850mm, but to double check
it:
Line height
|
850
|
mm
|
Length of line
|
500.09
|
mm
|
Area above line
|
2.125E+05
|
mm^2
|
Area below line
|
2.130E+05
|
mm^2
|
Within calculation
error, this is close enough. The force centre of the sail is at 850mm high.
So, with the moments from
the keel remaining at 5800, the balancing force on the mast should be:
Force
(N)
|
Dist
(mm)
|
Moment
|
|
Mast
|
68.24
|
850
|
5800
|
Following on from the
last post, I have looked at the wind speed that would topple the vessel with
the force calculated above. I then completed a simple calculation at how the
angle of the wind to the vessel would effect it:
Possible Speed to topple boat
|
10.62
|
m/s
|
@ 90 deg to boat direction
|
23.76
|
mph
|
@ 60 deg to boat direction
|
27.44
|
mph
|
@ 30 deg to boat direction
|
47.52
|
mph
|
@ 15 deg to boat direction
|
91.80
|
mph
|
@ 5 deg to boat direction
|
272.62
|
mph
|
Then I added another
assumption. My vessel is rarely going to be bolt upright, it’s more likely that
the boat will be travelling along with at least a 30 degree lean (heel?). So,
with that assumption in place, the numbers are changed as thus:
@ 90 deg to boat direction
|
47.52
|
mph
|
@ 60 deg to boat direction
|
54.87
|
mph
|
@ 30 deg to boat direction
|
109.75
|
mph
|
@ 15 deg to boat direction
|
424.03
|
mph
|
@ 5 deg to boat direction
|
4865.17
|
mph
|
So, this makes a lot
more sense. I have looked up the average wind speed in the Atlantic, which is
(give or take) at 40mph.
So conceivably, if I
have my calculations correct, this should be the perfect mass of keel bulb and
sail size to keep sailing happily at normal, perpendicular wind speeds in the
Atlantic.
Before someone points
this out to me, I haven’t taken into consideration the weight of the mast or
the weight of the sail which will change these calculations, but then the
weight of the batteries that will sit under the waterline may counteract some
of that. If during testing, the vessel heels over too much, I’ll review the
design to improve it.
Size of the mast
Doing the calculations
for this has been a pain as there still isn’t a lot out there. I asked for
assistance from some of my Mechie friends, but they weren’t sure either as it
is quite a new material. Anyway, I managed to find an online tool that gives me
the deflection (bend) and the stress on a tube of a certain size (http://easycalculation.com/mechanical/deflection-round-tube-beams.php).
I found the material properties on another site (http://www.performance-composites.com/carbonfibre/mechanicalproperties_2.asp)
and then I reworked my calculation as shown below:
Carbon
Fibre Tube Inner Diameter
|
Carbon
Fibre Tube Thickness
|
Force
at 850mm
|
Deflection
(Bend dist)
|
Bending
Stress
|
||||
mm
|
Inches
|
mm
|
Inches
|
N
|
Pounds
|
Inches
|
mm
|
psi
|
14
|
0.55
|
1.35
|
0.05
|
68.24
|
15.34
|
2.745
|
69.723
|
54622
|
18
|
0.71
|
1.4
|
0.06
|
68.24
|
15.34
|
1.087
|
27.6098
|
27922
|
19
|
0.75
|
1.4
|
0.06
|
68.24
|
15.34
|
0.9097
|
23.10638
|
24680
|
22.2
|
0.87
|
1.4
|
0.06
|
68.24
|
15.34
|
0.563
|
14.3002
|
17734
|
26.5
|
1.04
|
1.4
|
0.06
|
68.24
|
15.34
|
0.319
|
8.1026
|
11991
|
28.5
|
1.12
|
1.4
|
0.06
|
68.24
|
15.34
|
0.252
|
6.4008
|
10210
|
32
|
1.26
|
1.4
|
0.06
|
68.24
|
15.34
|
0.174
|
4.4196
|
7922
|
35
|
1.38
|
1.4
|
0.06
|
68.24
|
15.34
|
0.131
|
3.3274
|
6522
|
When I preliminarily
did this a while back, I worked out that the 22.2mm wide tube would do the
trick, but that the 26.5mm tube would be better as it is over-spec’d slightly.
Putting the results of the calculation here shows them all laid out. I might
even go bigger than this.
To be 100% honest with
you, I’m now quite tired, so I won’t make a decision tonight and come back to
this next time. Now that I finally have more time, I’m hoping this will be next
weekend.
Next Steps
- I think I need to work into my design the displacement to make sure I know how much load this design will take before it will no longer float.
- Keel bulb size and shape.
- Keel thickness review.
To be continued.........
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