Methods Of Calculating Flotation
Flotation regulations for recreational boats.
How to calculate flotation amounts.
One of the more important tasks a builder must perform for a small boat
is determining weight and persons capacity, calculating how much
flotation is needed and making a label for the boat. Also attaching a
Hull Identification Number (HIN) is required.
Back Yard Boat Builders (Home Built):
HINs
For back yard boat builders in the US, who are building a boat for
themselves, an HIN can be obtained from the state office that registers
boats. When registering the boat tell them it is a home built
boat. They will have you fill out a form declaring that you built the
boat, and assign an HIN.
In Canada this number is available from the Canadian Office of
Boating Safety:
Canadian
Office of Boating Safety Regulations
Calculations:
Methods of Calculating Capacity:
Many
people consider calculating capacities and flotation as some mysterious
scientific process beyond the capabilities of the average boat builder.
This is definitely not true. Anyone with a basic education can do it.
If you can add and subtract, multiply and divide, you can
calculate boat capacities and flotation.
For a boat like the FL 12 it is even simpler because the shapes
are all squares, rectangles and triangles. You need to be able to find
area and volume.
Area
of any rectangle is the length times width.
Area
of a square is one side times itself (or length times width but in this
case the length equals the width)
The
area of a triangle equals the base of the triangle (the bottom width)
times the height, divided by two.
Volume
involves one more dimension, the thickness or depth. So the volume of a
box is the length of the box times the width times the depth.
The
same applies to a triangular shapes.
Any
boat like the FL12 that has a flat bottom, or even a vee bottom can be
divided up into these shapes and the volume of each shape is found.
Then the volumes are added up.
The total volume times the weight of water (62.4 pounds per cubic
foot) equals the displacement.
As
shown in the below illustration the volume of this shape is relatively
simple to calculate by simplifying the shape and taking each piece at a
time.
Length
W1 + W2 divided by 2 is the average width, W, of the front side of the
box.
(W1
+ W2)/2 times height b gives the area of the front of the box,
Find
the area of the back face using the same method.
Then
add the two areas together and divide by two to get the average area.
Multiply the average area by the width of the box (length e) to
get the volume of the box.
By
doing this for each section of the boat, and then adding up the volumes,
you get the total volume of the boat.
Displacement
is the weight of the water that is moved out of the way when you make a
hole in the water by putting a boat in it. Displacement divided by five
is the maximum weight capacity. If
you subtract the weight of the outboard motor, battery, and a portable
fuel tank, you get maximum persons capacity.
That weight plus 32 and divided by 141 equals the number of
person.
Of
course the simplest way to do this is put weight in the boat. Add weights until water is about to come in. The total weight
is the displacement weight. Divide the total by five, and that gives you
maximum weight capacity. Subtract the weight of the outboard motor,
battery, and a portable fuel tank and you have persons weight. Add 32 to persons weight and divide by 141 to get
persons.
An
easy way to find persons capacity is to put weight on one side of the
boat as far outboard as possible. Add
weight until the boat heels to the point where water comes in.
Divide that weight by 0.6 (or multiply by 1.6667) and that is the
maximum persons Weight.
Add
the engine weight, battery, and a portable fuel tank, to the Maximum
Persons Weight and multiply by five and you have the Maximum Weight
Capacity.
For
the FL 12 I divided the boat into 10 equal sections. Each section forms
a box. Then I measured the
dimensions of each box to get the volume.
Starting
at the bow. The bow section, shown here as Box A, forms a triangular
shaped box. Box A is 10” by 18 ½” by 21 ½”
10”
= 0.8333 ft
18
½ “ = 1.54 ft
21
½ = 1.79 ft
The
formula is 0.8333 X 1.54 / 2 = 0.642
Then
multiply 1.79 X 0.642 / 2 = 0.5746
= volume of Box 1
Box
B is a little more complicated because one side is large than the other
side. That is the rear side
is bigger than the front side.
The
front side is 21 ½ by 18 ¼ by 11 ½.
It is not a rectangle, but since two sides are the same length we
can treat it the same as a rectangle by using the average of the length
of the two unequal sides.
21
+ 11 ½ = 32 ½ 32 ½ / 2 = 16 ¼ = 1.354 front area
the
rear side = 28 ¾ by 22 by 18 ½
28
¾ + 22 = 50 ¾ 50 ¾ / 2 = 25 3/8 = 2.115 rear area
Station 
Volume 
bow 
0.2535 
01 
1.3940 
12 
2.6700 
23 
3.5800 
34 
4.3570 
45 
4.7700 
56 
4.8370 
67 
4.7990 
78 
4.5380 
89 
4.1670 
910 
3.6400 
10T 
1.7483 
Total Vol 
40.7538 


disp 

lb 
2543.0371 
Then
divide the displacement weight by five to get the maximum weight
capacity. Subtract the
weight of the outboard motor for persons weight.
Get the weight of the motor from USCG Table 4 or ABYC S10. To
get the number of people add 32 to the persons weight and divide by
141.
But
I wanted to see how this compares to doing it by using Simpson's Formula
to see how accurate it is.
By
using both methods the results were very close to each other, and the
number of persons was the same.
Weights are in pounds 
Simpsons 

Blocks 

Boat Weight 
100 

100 
Max Disp Boat Weight 
2445.30 

2443.04 
Max Weight Capacity 
733.59 

732.91 
Max Persons Capacity 
637.73 

637.12 
Max Persons 
4.75 

4.75 




This
method is not limited to flat bottom boats.
Boats with more complex shapes can use the same method. The following illustrates a vee bottom boat.
Each
block can be split into triangles, rectangles and squares.
The areas and volumes are simple to calculate. Curves to the shape can be considered as straight lines if
you break it into smaller blocks.
Flotation
Calculations:
Once you
know the capacities calculating flotation is next.
You need to
find the amount of flotation to float three things;
The boat itself:
The persons:
The engine (if there is one.):
Wood Boats:
Example: The boat is plywood. The boat weighs 100 lbs. Plywood
is buoyant so the amount needed is negative, that is the plywood provides
some flotation. Flotation foam at 2 lbs per cubic foot supports 60.4
lbs.
Boat Weight
(Wh) X a factor for plywood (0.81) divided by 60.4 = Cubic feet = 1.34
The outboard
motor: a 2HP motor weighs 30 lbs according to
Table33
CFR 183.75 and
S30. Submerged it weighs 27 lb. For a 2 HP motor there is no battery or fuel tank weight.
Engine
Weight (27) divided by 60.4 = 0.44701 (0.45) Cu Ft
The people. People don't weigh as much in water
as they do in air. Plus that it is assumed that with flotation, part of
the persons body will be out of the water so the factor is 2/15.
But in the USCG Guidelines they use 1/4, or 0.25. This gives you a
safety factor of about two for the amount of flotation for persons
weight.
Persons
weight (627.72 x 0.25) divided by 60.4 equals 2.639611
Total Flotation = 0.45 + 2.639611  1.34106 =
1.74855 (1.8) Cu Ft
Round this to 1.75, 1.8 or even two.
Boats not made of Wood:
If the boat is made of fiberglass the the
calculation for flotation for the boat has to include weight of the
Fiberglass, which is not buoyant like wood.
Boat Weight
(Wh) X a factor for Fiberglass (0.33), divided by 60.4 = Cubic feet
of Flotation
If the boat weighs 100 lb and is all fiberglass;
Flotation for the boat = (100 x 0.33)/60.4 =
0.546 (0.6) Cubic Ft.
Manually propelled Boats:
However, if this is a manually propelled boat,
i.e. no motor, Engine weight is zero. engine weight is taken out of the
equation.
Boat Weight
(Wh) X a factor for plywood (0.81) divided by 60.4 = Cubic feet = 1.34
Persons
weight (627.72 x 0.25) divided by 60.4 equals 2.639611
Total Flotation = 2.639611  1.34106 =
1.29855 (1.3) Cu Ft
Air Chambers for Flotation:
Suppose the boat uses air chambers for
flotation? Then you would divide by 62.4 rather than 60.4 because in
these calculations air has no weight and supports 62.4 lb per cubic foot
in fresh water.
Where to put the Flotation.
Place the flotation for the engine in the back
of the boat on the inner side of the transom.
Split it in two and put half in the starboard quarter and the other in
the port quarter. This supports and balances the engine weight.
Divide the persons flotation up and put it under the seats so that it
will stabilize the boat when it is swamped.
Revised 03/17/2019 © newboatbuilders.com 2010 All rights reserved
