Basic Canoe Design
Before considering the pontoon and bridge design here is the basic canoe design. I have uploaded a spreadsheet with all the following calculations.
Basic Canoe Measurements
Canoe Basic Metrics | |||
Length Overall (LOA) | 3.930 | m | |
Beam Overall (BOA) | 0.650 | m | |
Length Water Line (LWL) | 3.600 | m | |
Beam Water Line (BWL) | 0.550 | m | Actually the bottom width |
Depth Water Line (DWL) | 0.075 | m | |
Rocker | 0.025 | m | |
Amidships Deadrise | 0.000 | Degrees | Flat bottom |
Amidships Freeboard | 0.200 | m | |
Forward Freeboard | 0.325 | m | |
Rear Freeboard | 0.325 | m |
Note: Bold numbers are inputs.
Design Pressure
Now some basic calculations but most importantly the design pressure:
Basic Calculations | |||
Mid-Section Area | 0.041 | m^2 | |
Plan Water Line Area | 1.320 | m^2 | |
Displacement Volume | 0.088 | m^3 | |
Displacement Weight | 90.200 | kg | |
Prismatic Coefficient (cp) | 0.593 | ||
Displacement Length Ratio (DLR) | 42.080 | ||
Hull Speed | 4.605 | kt | |
Design G Force | 3.500 | g | Light duty |
Design Pressure | 2.346 | KN |
To calculate the design pressure I have assumed the canoe is loaded 3.5 time the rated displacement of 90 kg.
Bottom Plywood Thickness
Bottom Plank Design | |||
Design Pressure (P) | 2.35 | kPa | |
Span (L) | 550 | mm | BWL |
Allowable Stress (S) | 14000 | kPa | F14 Plywood |
Plank Thickness (t) | 5.03 | mm | t^2=P*L^2/2/S, ~fixed sides |
Design Plank Thickness (t) | 6.00 | mm | |
Modulus of Elasticity (E) | 8400000 | kPa | Factored 80% for wet condition |
Moment of Inertia (I) | 18000 | mm^4 | |
Deflection (d) | 3.70 | mm | d=P*L^4/384EI (2% max) |
Deflection Ratio | 148.74 | ||
Maximum Concentrated Load | 0.50 | kN | =S*t*t |
Here I calculate 5 mm but the nearest larger plywood thickness is 6 mm. Although this is okay for water pressure it is too thin for an adult to stand on. The middle section of the bottom of the canoe needs to be reinforced.
Bottom Reinforcement
Upon reflection it would have been easier just to double up the plywood in the middle of the canoe or that fibre-glass both sides with 4 oz/sq_yd fibre-glass cloth. The calculations assume a "T" section across the hull (beam-ward) with plywood strips (see image). It is also assumed that two "T" sections share the load as they are quite close together:
Hull Centre Reinforcement | |||
T-Section Modulus | |||
Maximum Rib Spacing (Flange Width) | 256 | mm | Fw<36t+w |
Design Rib Spacing | 150 | mm | |
Plank Thickness (Flange Thickness) | 6 | mm | |
Rib Thickness (Web Height) | 6 | mm | |
Rib Width (Web Thickness) | 40 | mm | |
A | 1776 | mm^2 | |
cy | 3.8 | mm | From top of T |
cx | 0.0 | mm | From centre line of T |
Ixx | 10474 | mm^4 | |
Iyy | 8420608 | mm^4 | |
Design Point Load | 1.00 | kN | ~100kg |
Span | 550 | mm | |
Allowable Stress | 14000 | kPa | F14 Plywood |
Bending Moment | 69 | Nm | |
Section Modulus | 2749 | mm^3 | |
Working Stress (per rib) | 25013 | kN | |
Distribute Load (over two ribs) | 12506 | kN | |
Safety Factor | 112% |
Here is an image of the reinforcement:
If you look carefully you can see the filled wire holes below the single strip of 4 oz/sq_yd fibre-glass tape.
Side Plank Calculations
If the side plank is the same thickness as the bottom plank then no calculations are necessary but here they are anyway:
Side Plank Design | |||
Design Pressure (P) | 2.35 | kPa | |
Span (L) | 275 | mm | |
Allowable Stress (S) | 14000 | kPa | F14 Plywood |
Plank Thickness (t) | 2.5 | mm | t^2=P*L^2/2/S, ~fixed sides |
Design Plank Thickness (t) | 6.0 | mm | Okay |
Hog and Sag Calculations
So put 3.5 big guys in the canoe and get two even bigger guys to lift the canoe up by the ends. Is it strong enough (not actually required)?
First the Load Calculation:
Hull Section Modulus | Triangular Load & Free Ends | ||
Design Pressure | 2.35 | kPa | |
Width | 550 | mm | BWL |
Length | 3600 | mm | LWL |
Allowable Stress | 14000 | kPa | F14 Plywood |
Required Section Modulus | 99547 | mm^3 | SM=PsL^2/12/S |
Now the Strength Calculation (assuming a channel section):
Channel Model | |||
Chine Width (web) | 550 | mm | BWL |
Side Height (flange) | 275 | mm | |
Deck Width (lip) | 50 | mm | |
Thickness (t) | 6 | mm | |
cy (from bottom) | 86 | mm | |
I | 75400372 | mm^4 | |
Rg | 102 | mm | Radius of gyration |
Slenderness Ratio | 35 | ||
Z | 398812 | mm^3 | |
Safety Factor | 401% | Assumes no significant keel or stringers |
Yes, a 401% safety factor is okay.
Fibre-Glass Tap Join
You will be lucky to find anything on the Internet calculating the fibre-glass joint strength other than rules of thumb. Here are some actual calculations:
Plywood Fibre Glass Joins | |||
Spw | 14000 | Pa | |
b | 1 | m | |
h | 6.00 | mm | |
M | 84000 | Nm | M=Spw*b*h^2/6 |
Sfg | 120000000 | Pa | |
t | 0.12 | mm | t~((6*M*h/Sfg/b+h^3)^(1/3)-h)/2 |
F/G Weight | 1.87 | oz/sq_yd | Each side of plywood |
F/G Overlap (each side of join) | 18 | mm | =3*h [JS = 15%*(1+L/h)] |
Scarf Joins
You will find rule of thumb of beween 8 to 1 all the way up to 12 to 1 for scarf joins:
(source: www.amateurboatbuilding.com/articles/howto/joining_ply/scarf1.gif)
This tells you the fibre-glass tape should span 8 times the plywood thickness:
(source: www.amateurboatbuilding.com/articles/howto/joining_ply/plyjnt5.gif)
However, I found a paper that suggests that 6 times is enough (www.wfdt.teilar.gr/research.files/2005_05.pdf).
AlanX
Discussions
Become a Hackaday.io Member
Create an account to leave a comment. Already have an account? Log In.