IEEE - Aerospace and Electronic Systems - April 2023 - 31

de Celis and Cadarso
Table 1.
Thrust Profile Versus Time
Time (s)
Thrust (N)
Time (s)
0.35
Thrust (N) 968.96
Time (s)
0.7
Thrust (N) 1222.92
Time (s)
1.05
Thrust (N) 1258.42
Time (s)
1.4
Thrust (N) 1102.91
Time (s)
1.75
Thrust (N)
Time (s)
Thrust (N)
48.32
2.1
22.91
0.05
0.4
1027.19
0.75
1237.72
1.1
1250.73
1.45
1053.97
1.8
28.6
2.15
27.77
0.1
0.45
1076.42
0.8
1248.95
1.15
1239.23
1.5
995.28
1.85
27.63
2.2
5.21
0.15
0.5
1117.78
0.85
1256.92
1.2
1223.4
1.55
925.54
1.9
22.22
2.25
0.01
0.2
0.55
1152.28
0.9
1261.83
1.25
1202.65
1.6
843.32
1.95
28.05
2.3
0.25
820.47
0.6
1180.8
0.95
1263.76
1.3
1176.23
1.65
758.82
2
22.91
2.35
0.3
900.51
0.65
1204.13
1
1262.67
1.35
1143.31
1.7
354.7
2.05
27.77
2.4
Table 2.
Rocket Parameters
Parameter Initial mass Propellant mass
Value
7.00 kg
1.50 kg
XCG0
Caliber
Ix0
Iy0
0.45 m 0.065 m 0.01 kg m2
0.25 kg m2
controlled force and corresponding moment in a perpendicular
plane to the rocket section.
Table 1 shows the thrust profile, whereas Table 2 provide
the mass statistics for the rocket and Figure 2 the aerodynamic
parameters. Note that, Ix0 and Iy0 are the inertia
moments at launch, XCG0 is the position of the center of
gravity at launch (measured from the tip along the xb-axis),
CD0
ðMÞ and CDa2
ðMÞ are linear and square drag force
coefficients, respectively, a is the attack angle, CLa ðMÞ
and CLa3 ðMÞ are the linear and cubic lift force coefficients,
respectively, CmfðMÞ is the coefficient for Magnus force,
CNqðMÞ is the coefficient for pitch damping force, CMa
and CMa3 ðMÞ are linear and cubic overturning moment
coefficients, respectively, CMq ðMÞ is the coefficient for
ðMÞ
pitch damping moment, CmmðMÞ is the coefficient for Magnus
moment, CspinðMÞ is the coefficient for spin damping
moment, andCNdðMÞ is the coefficient for canard force.
All of these parameters' values are based on either
experimental observations or computational fluid
APRIL 2023
dynamics calculations and wind tunnel testing. Cubic
spline interpolation is used to maintain the continuity
and derivability of aerodynamic profiles and thrust
with respect to Mach number and time, respectively.
MODELFOR THEFLIGHTDYNAMICS
Two axes systems are defined to develop the flight dynamics
model: body axes and Earth axes. The body axes are
defined by subindex b. xb, which points forward to the
rocket axis, is perpendicular to zb, which points down.
Both of them are embedded in the rocket's plane of symmetry.
A clockwise trihedron is formed by yb. The origin
of the body axes is the center ofmass of the rocket. Subindex
e defines Earth axes, often known as north-east-down
axes. xe points north, ye points east, and ze is perpendicular
to xe and ye, and points nadir. Figure 3 shows these
definitions. To obtain flight dynamics and actuation
IEEE A&E SYSTEMS MAGAZINE
31
IEEE - Aerospace and Electronic Systems - April 2023

Table of Contents for the Digital Edition of IEEE - Aerospace and Electronic Systems - April 2023
