Game Development Reference
In-Depth Information
match significant features of the curve. For example, in Figure 10-13 the maximum propeller
efficiency value of approximately 0.83 occurs at an advance ratio value of about 0.65. The slope
of the curve at this point will be zero. Using this information, the values of the constants to
match Figure 10-13 can be obtained.
3
h
=
1.83
J
−
1.32
J
(10.9)
p
The results of the curve fit are shown in Figure 10-14. Equation (10.9) does a good job of
matching the original data up to and a little beyond the peak efficiency coefficient value at
J
= 0.65. The curve fit loses accuracy at high advance ratio values, but propellers are generally
not intended to reach such high advance ratio values anyway, so for simulation purposes,
Equation (10.9) is sufficient.
Figure 10-14.
Original and curve fit values of propeller efficiency
Now that a curve fit expression for the propeller efficiency coefficient is available, a general
expression for the propeller thrust as a function of the advance ratio or velocity can be obtained.
The starting point is the equation relating thrust, propeller power, and engine power.
hh
==
PP
P
pe
pe
F
T
=
(10.10)
T
v
v
Jnd
Using the general form of the curve fit relation shown in Equation (10.8), the propeller
efficiency in Equation (10.10) can be written in terms of the advance ratio,
J
.
P
P
(
)
(
)
F
=
e
aJ
+
bJ
3
=
e
a
+
bJ
2
(10.11)
T
Jnd
nd
