Game Development Reference
In-Depth Information
the boat forwards or backwards. Let's take a little time now to understand how a boat propeller
works.
When the propeller rotates, as shown in Figure 9-6, the underside of each propeller blade
pushes the water next to it down and back, similar to the hand motion of a swimmer doing the
backstroke. Because the propeller blades are pushing on the water, the pressure on the rearward-
facing side of the propeller blade is greater than the pressure on the forward-facing side of the
blade. This pressure difference generates a thrust that pushes the propeller, and therefore the
boat, forward. This effect is similar to that seen with airplane wings where the pressure differ-
ence between the top and bottom surfaces of the wing generates lift.
Figure 9-6.
Side view of a typical boat propeller pushing water away from it. (Photo courtesy of
Piranha Propellers, www.piranha.com)
There are two important numbers that are used to characterize boat propellers. These
numbers are usually listed after the propeller name. For example, you might see the numbers
“20×24.” The first number is the diameter of the propeller, usually in inches. The second number
is called the
pitch
of the propeller and represents the theoretical distance, again usually in inches,
that the propeller will move relative to the water around it for every revolution of the propeller.
The theoretical forward velocity of the propeller,
v
T
, is equal to the pitch of the propeller,
, multiplied by the propeller turnover rate,
n
(in revolutions per second).
P
T
v n
=
(9.5)
Unfortunately, the theoretical velocity is never achieved because some losses will occur
due to propeller blade bending, air bubbles in the water, and other causes. The actual distance
traveled per propeller revolution to be less than the pitch of the propeller. The actual forward
velocity of the propeller relative to the water around it, also known as the
speed of advance
, is
less than the theoretical maximum velocity by a quantity,
s
r
, known as the
real slip ratio
.
(
)
(
)
v
=−
1
s
v
=−
1
s
Pn
(9.6)
a
r
T
r
The real slip ratio is a dimensionless quantity with a value between 0 and 1. We've been
careful to note that the speed of advance is the forward velocity of the propeller relative to the
water around it. In general, this will not be the same as the velocity of the boat. When a boat
moves forward in the water, the water just behind the boat will acquire a forward motion in the
same direction as the ship. The forward moving water is known as the
wake
of the boat. The
wake velocity
,
v
w
, is equal to the difference between the velocity of the boat,
v
b
, and the speed
of advance,
v
a
.
vvv
=−
(9.7)
wb
a
