Game Development Reference
In-Depth Information
There are four forces that we will consider to act upon the boat. You are already well
acquainted with the force due to gravity. It pulls the boat downward. In order for the boat to
float on the water, another force must be there to counteract the force of gravity. This force is
referred to as the
buoyancy
of the boat. We will look at buoyancy in more detail in the next
section, but for now it suffices to say that if the buoyancy force is large enough to counteract
the gravitational force, the boat will float.
The two forces that act in the horizontal direction are thrust and drag. In a powerboat,
propellers that are connected to the boat's engine provide the thrust. This chapter will cover
the different types of boat engines and how to determine the power and thrust that they provide
later in this chapter. Drag forces resist the forward motion of the boat. You will learn more
about boat drag a bit later in this chapter as well.
There are additional forces that might be included but won't be discussed in detail in this
chapter. For example, there may be a current in the water that would affect the boat in a way
similar to the way wind affects the trajectory of a projectile. Some types of boats, in particular
sailboats, are greatly affected by the direction and magnitude of the wind.
Buoyancy
You know from your own experience that some things float and some things don't. You also
know that the force of gravity will pull any object on a body of water downwards to the bottom
of the body of water. For an object to float, there must be another force that balances the grav-
itational pull. This force is referred to as the buoyancy force.
Buoyancy has been studied for a very long time. Archimedes discovered the principles of
buoyancy over 2200 years ago. Archimedes, who lived in Syracuse, Sicily, is considered the
greatest mathematician and scientist of the ancient world. Along with the field of hydrostatics
(of which buoyancy is a part), Archimedes also discovered how pulleys and levers could be
used to lift heavy objects.
■
Tidbit
Archimedes allegedly discovered the principles of buoyancy while he was taking a bath. When the
idea came to him, he jumped out of the bath and ran through the streets yelling “Eureka!,” which means
“I have found it!” Hopefully, he wrapped a towel around himself first.
To understand buoyancy, consider what happens when a rock is dropped into a pail of
water and sinks to the bottom. The water that used to be in the space now occupied by the rock
has been pushed away, or displaced, by the rock. The volume of water displaced is equal to the
volume of the rock.
Archimedes discovered that the weight of an object submerged in water is less than the
weight of the object in air. In other words, the net force on the submerged object is lower,
which means a force must be acting on the body that opposes the force of gravity. This force is
due to the buoyancy of an object. Archimedes also discovered that the reduction in weight of a
submerged or floating object is equal to the weight of the water displaced by the object. The
buoyancy force,
F
B
, is therefore equal to the weight of the displaced water, which is equal to the
density of the water,
r
w
, multiplied by the volume of the displaced water,
V
w
, and the gravita-
tional constant,
g
.
