Practical Boat Owner – August 2019

David Harding/Sailing Scenes

Yacht design

➜

The square–cube law

This law can be stated as follows:

When an object undergoes a

proportional increase in size, its new

surface area is proportional to the square

of the multiplier and its new volume is

proportional to the cube of the multiplier.

Let ́s first look at a simple object, a cube

with sides 1m long.

The volume of this cube is 1m x1m

x1m = 1m^3. And the total area is 6m^2

(six sides each 1m x 1m). The ratio of

volume/area for this cube is 1/6 =

0.17

Now let’s double the size and make

a cube with the side length 2m. The

volume is now 2m x 2m x 2m = 8m^3.

And the area is 24m^2 (six sides each

2m x 2m).

The ratio of volume/ area for this

bigger cube is 8/24 = 0.33.

An even bigger cube, say 10m

long, will have a ratio volume/area

that is 1.67

This is a fundamental law that effects

how everything is constructed, even

yourself. If you haven't given this much

thought before, you are in good company.

When Jonathan Swift wrote A voyage to

Brobdingnag, where Gulliver visits the

giants who are more than ten times bigger

than he is, Swift missed this aspect of size

totally.

If someone were to create a giant ten

times the size of a human, the giant would

have a lot of problems. Moving around

would be one – and is directly linked to

the ratio Volume/area. Being ten times

bigger than Gulliver, the volume, and

thereby also the weight, will be 10 x 10 x

10 = 1,000 times more. While his feet will

have an area of only 10 x 10 = 100 times

more.

This makes ten times more weight on

each square unit of his soles: when

walking on soft ground his feet will simply

sink into the soil.

Every part of the giant’s construction

can be analysed in the same way, and

A

B

C

1m 2m 10m

1m

2m

10m

10m

2m

1m

The square-cube law

Volume

Area

Ratio:

A B C

1m

6m

0.17

3

2

~~

8m

24m

0.33

3

2

~~

1000m

600m

1.67

3

2

Volume ~~

Area

How to make

a model yacht

that sails

If you want to make a model of
your favourite yacht that looks
exactly proportionate to the
original, and will sail properly,
here is a tip: make the model as
light as possible and fit a bulb to
a narrow, deep fin, like the keel
on a Volvo Ocean racer. This fin
can be made detachable and fit
into a slot in the keel of the
model when sailing. This way
you will have a true looking
model of your yacht that also
makes up for the lack of righting
moment you get when you
shrink a sailing boat design.

reveals numerous problems. The giant

would probably be very bored, since his

braincell count will have increased one

thousand times while his input stimuli will

have only increased by one hundred.

Since sight, feel and taste – most of our

senses in fact – are related to area and not

volume (as the brain is) – the result will be

a lot of redundant braincells!

Now, back to boats. Theoretically you

can’t shrink a boat and expect it to work as

the original. Some things will be much too

big and others will be much too small.

Look at a cruise ship or a car carrier. Why

doesn’t the wind blow them right over, and

why do they have such small anchors?

The answer is the ratio of volume to area.

When things get that big the volume (and

weight) gets so much bigger compared to

the area for the wind to catch that the

effect of the wind is much smaller than on

a yacht.

Size and strength

The laws of size also dictate how strong a

construction is and tell us that it is much

easier to make a small boat strong than a

big one.

Many times when I have walked along a

rocky seashore I have found lightbulbs

washed up among the rocks by the waves

without breaking. Why don’t they break?

Because they are small! If a lightbulb was

the size of a yacht it would crack with the

first touch of a rock.

If we analyse what happens when a big

wave hits a boat, we see that the hitting

force is proportional to the area of the

boat. If you double the size (length) of the

boat, the area and force gets four times

bigger.

That is bad! But even worse is that the

weight of the (double-size) boat is now

eight times bigger. When a wave hits a

boat, the boat must have the ability to

instantly accelerate away from the hitting

force. Unfortunately the ability to

accelerate decreases proportionally to the

weight of the boat.

Small boats are more like shuttlecocks.

No matter how hard you hit it, it won’t

break; it just bounces.