Game Development Reference
In-Depth Information
The
wing aspect ratio
is defined as the ratio of the square of the wing span,
s
, divided by
the wing reference area,
A
.
s
2
A
=
(10.23)
R
A
The wing reference area in Equation (10.23) is the wetted area of the wing, the same value
that is used in the lift and drag equations. In looking at Equation (10.22), the induced drag coef-
ficient is inversely proportional to aspect ratio. A long, slender wing will have a greater aspect
ratio, and therefore less induced drag, than will a short, stubby wing.
Total Drag Equation Revisited
The total drag experienced by an airplane can be divided into parasitic and induced drag compo-
nents that are a function of the parasitic and induced drag coefficients. As you learned in the
previous section, the induced drag coefficient is a function of the lift coefficient. An updated
version of the total drag equation is shown in Equation (10.24).
⎛
C
2
⎞
1
1
(
)
2
2
FF F
=+=
C C vA
+
r
=
C
+
L
r
vA
(10.24)
⎜
⎟
D
p
i
p
i
p
2
2
p
Ae
⎝
⎠
R
To use Equation (10.24) requires the parasitic drag coefficient,
C
Dp
, as well as the lift coef-
ficient,
C
L
. In some situations, the lift coefficient can be related to other quantities. For example,
when an airplane is traveling in straight-and-level flight, the lift generated by the airplane is
equal to the weight of the airplane.
1
2
2
LW
==
C vA
r
(10.25)
L
In Equation (10.25), the weight of the airplane,
W
, is simply equal to the mass of the airplane
multiplied by the gravitational acceleration. When Equation (10.25) is incorporated into
Equation (10.24), the total drag equation for straight-and-level flight becomes the following:
1
2
W
2
FF F
=+=
C vA
evs
r
2
+
(10.26)
D
D p
,
D i
,
D p
,
22
2
pr
Let's use Equation (10.26) to compute the straight-and-level flight drag profiles for the
Cessna 172 Skyhawk. The airplane has a wingspan of 11.0
m
, an airplane efficiency factor of
0.77, and a reference wing area of 16.2
m
2
. The weight of the airplane will be assumed to be
10675
N
(2400
lb
). The coefficient of parasite drag will be assumed to be 0.035. The density will
be taken to be 1.2
kg/m
3
. The calculations will be performed from the stall speed of 25.5
m/s
up
to the maximum velocity the airplane can achieve, which is 62.6
m/s
.
The total drag profile for the Skyhawk is shown in Figure 10-19. Also shown on the curve
are the parasitic and induced drag profiles. It is apparent from Equation (10.26) that parasitic
drag is a function of velocity squared, whereas induced drag is an inverse function of velocity
squared. The maximum induced drag will therefore occur at the lowest velocity, and the maximum
parasitic drag occurs at the highest velocity. The minimum total drag occurs somewhere in the
middle, at a velocity of 37.5
m/s
.
