Game Development Reference
In-Depth Information
resistance is known at a certain velocity, the effective power required can be computed. If the
coefficient of propulsive efficiency is known, it can be compared against the maximum power
output of the engine to determine whether the engine can provide this level of power.
When the propeller rotates through the water, it generates a thrust. The thrust power,
P
T
,
is equal to the thrust force,
F
T
, multiplied by the speed of advance of the propeller.
PFv Fv w
=
=
(1
−
)
(9.14)
T
T
a
T
b
f
The effective power and thrust power are related by the coefficient of
hull efficiency
,
h
H
.
P
=
h
P
(9.15)
eff
H
T
Combining Equations (9.13), (9.14), and (9.15) results in an equation for the thrust produced
by the boat engine as a function of the engine power, boat velocity, wake fraction, and the coef-
ficients of propulsive and hull efficiency.
h
P
pe
F
=
(9.16)
(
)
T
h
v
1
−
w
Hb
f
The key to using Equation (9.16), however, is that you need values for the two efficiency
coefficients,
h
p
and
h
H
, and for the wake fraction,
w
f
.
Drag
A boat traveling through the water will experience drag forces that will resist the motion of the
boat. Boats are a bit different from the projectiles and cars we have previously explored because
part of the boat is below water and part of the boat is above water. A boat will therefore experi-
ence both hydrodynamic drag due to interactions with the water and aerodynamic drag on the
boat structures that are exposed to the air.
The good news is that the same equation that was used for aerodynamic drag can also be
applied to hydrodynamic drag, namely that the hydrodynamic drag force,
F
HD
, is equal to the
product of the square of the boat velocity,
v
b
, the fluid density,
r
, a characteristic area,
A
, and a
coefficient,
C
R
, known as the
coefficient of resistance
.
1
2
2
F
=
C
r
v A
(9.17)
HD
R
b
The area,
A
, in Equation (9.17) is the wetted area of the boat, meaning the surface of the
hull that is in contact with the water. Many different phenomena contribute to the total hydro-
dynamic drag experienced by a boat. The three major components are skin friction drag, wave
drag, and form drag. The overall coefficient of resistance can be written as the sum of these
three components.
CCCC
=++
(9.18)
R
f
w
Form
Let's look at the three main components of hydrodynamic drag in a bit more detail starting
with skin friction drag.
