Game Development Reference
In-Depth Information
Equation (10.11) can also be expressed in terms of the airplane velocity.
⎛
2
⎞
P
v
F
=
e
a
+
b
(10.12)
⎜
⎟
T
22
nd
n d
⎝
⎠
Equation (10.12) is what we will use when we create a flight simulator a little later in the
chapter. It states that the thrust generated by the propeller at any time is a function of the
engine power, airplane velocity, propeller turnover rate, and propeller diameter.
Altitude Effects
One of the complications in computing the thrust of a propeller engine is that the engine thrust
is a function of altitude. The power generated by the engine, and therefore the thrust generated
by the propeller, decreases as the altitude increases. The power decrease is largely a function of
atmospheric density and is represented by a
power drop-off factor
,
Φ
.
s
−
Φ=
C
C
(10.13)
1
−
The
C
parameter in Equation (10.13) is an altitude-independent mechanical power loss
factor. It is normally assigned a constant value of 0.12.
2
The
s
parameter is the ratio of the
current atmospheric density to sea-level density.
r
s
=
(10.14)
r
o
Atmospheric density is a function of altitude and is also a function of the air pressure and
temperature. For altitudes below 11
km
, the pressure and temperature can be found by equations
that are a function of the altitude,
h
, and the sea-level values of pressure and temperature.
3
T
=
288.15
−
0.0065
h
(10.15)
5.25
h
⎛
⎞
p
=
101325 1
−
0.0065
288.15
(10.16)
⎜
⎟
⎝
⎠
The temperature in Equation (10.15) is in
K
, and the pressure in Equation (10.16) is in
N/m
2
. The altitude in both equations is in
m
. Once the pressure and temperature are known for
a given altitude, the density can be computed.
p
T
r
=
0.00348
(10.17)
To incorporate altitude effects into the airplane thrust model, the power drop-off factor is
simply added to the thrust equation.
⎛
2
⎞
Φ
P
v
F
=
e
a
+
b
(10.18)
⎜
⎟
T
nd
n d
22
⎝
⎠
