PFR - Aerospace Engineering Sciences Senior Design Projects ...

Project Final Report – CUDBF April 30 th , 2009
ASEN 4028: Aerospace Senior Projects
The s-plane is a visual representation of the roots of the system to characterize the behavior of
the system. Poles in the right half of the plane are unstable where as poles in the left half of the s-
plane indicates stability.
As seen in Figure 37 and Table 7, the real roots are located on the negative real axis. These roots
are stable and have time constants of 6.04 s -1 and 0.17 s -1 . The short period is slightly unstable.
The period of the short period roots were analyzed to determine if this is a concern. The period
for both short period roots is 31.60 seconds. Since the period for natural instability in the short
period mode is as slow as 31.60 seconds, this indicates that the pilot has 31 seconds to input
control surface response to the system. As a result, this is not an issue.
The analysis in the s-plane for the airplane with four rockets is shown in Figure 38:
0.15
0.1
Longitudinal Stability Modes for Four Rockets on the Airplane
Real Roots
Short Period
0.05
Imaginary
0
-0.05
-0.1
-0.15
-0.2
-8 -7 -6 -5 -4 -3 -2 -1 0 1
Real
Figure 38: Longitudinal Stability Modes for Four Rockets on the Airplane
The natural frequency and period of each of the roots in the longitudinal case for the scenario
with four rockets on the airplane are summarized in Table 8:
66