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Reentry Air Data System for a Sub-orbital
Spacecraft Based on X-34 DesignJoel Ellsworth
Utah State University
4130 Old Main Hill
Logan, Utah 84322
Stephen A. Whitmore
Utah State University
4130 Old Main Hill
Logan, Utah 84322
Background
Several companies have been formulated during the past decade
with the intention of developing a sup-orbital space tourism
market. These companies include Okalahoma City based
Rocketplane-Kistler, Roswell New Mexico based Virgin Galactic,
and San Diego based SpaceDev among others.
Most designs are intended to glide back to earth after using a
rocket engine to boost themselves out of the atmosphere.
Knowledge of the wind-relative vehicle state parameters -
dynamic pressure, Mach number, angle-of-attack and -sideslip,
and surface winds - are especially critical for the landing phase
for energy management and runway alignment.
Why use the X-34 as a Baseline Vehicle?
The X-34 was chosen for this study because it incorporates many of the features needed by a commercial suborbital tourist spaceflight system.
The X-34 aerodynamic database was developed using public dollars and is available in the public domain.
For this design study a typical X-34trajectory was used to generate simulated nosecap surface pressure values based on wind-tunnel derived calibration models.
1heat
le
qR
∝&
High temperatures and dynamic
pressures associated with
attached shockwaves (reentry
conditions) will destroy
traditional pitot probes and
directional vanes.
Heating is related to leading
edge curvature
Why Develop a New System?
Solution:
Flow Model:
The FADS algorithm uses the
pressures measured by a matrix
(at least five) of flush mounted
pressure ports to produce a full
air data state.
Flow model is a blend of
Modified-Newtonian Flow and
Potential Flow over a sphere.Potential flow for a sphere
(M <<1)
Modified Newtonian flow
(M>>1)
( )( )
( )( )
2 2
2
5cos sin
4
cos
p pCp
qc
p pCp
qc
θθ θ θ
θθ θ
∞
∞
−= = −
−= =
( ) 2 2
2 cos sinp qc pθ θ ε θ ∞ = + +
FADS flow model for a spherical nosecap
X-34 Trajectory and Simulation Results
The X-34 trajectory was used to generate surface pressures on the
nosecap of the vehicle, which were then corrupted with random
noise, pneumatic lag, sensor resolution, and sensor latency before
being passed to the FADS algorithm Results are shown with and
without the inertial filtering algorithm active.
Simulation results without inertial
filtering active.
(s)
(s) (s)
(s)
Simulation results with inertial
filtering active.
(s)
(s)
(s)
(s)
FADS Solution Algorithm:
The parameter αind can be de-coupled from βind
by using only pressures triples aligned along a
vertical meridian. The result is a quadratic
expression in terms of tan αind.
2 2 2 2 2 2 2sin sin sin tan cos cos cos
2 cos sin cos cos sin cos cos sin cos tan 0
ik j ji k kj i ind ik j ji k kj i
ik j j j ji k k k kj i i i ind
φ φ φ α φ φ φ
φ φ λ φ φ λ φ φ λ α
Γ + Γ + Γ + Γ + Γ + Γ +
Γ + Γ + Γ =
Once we know Angle of Attack, we can
calculate Angle of Sideslip using any
combination of ports exclusive of sets with all
ports on the vertical meridian.
By taking strategic differences of three surface sensor readings
("triples") the parameters qc2, p
∞, and ε, are eliminated.
Γ ik cos2 θ j + Γ ji cos2 θk + Γkj cos2 θi = 0 Γ ik = pi − pk , Γ ji = p j − pi , Γ kj = pk − p jwhere
2' tan 2 ' tan ' 0ind ind
A B Cβ β+ + =
( )
( )
( )
( ) ( ) ( ) ( )
( ) ( ) ( )
2 2 2
2 2 2
'
'
'
cos cos sin sin cos
sin sin
ik j ji k kj i
ik j j ji k k kj i i
ik j ji k kj i
ind indijk ijk ijk ijk
ijk ijk ijk
A b b b
B a b a b a b
C a a a
a
b
α λ α λ φ
λ φ
= Γ + Γ + Γ
= Γ + Γ + Γ
= Γ + Γ + Γ
= +
=
where
Altitude is found by table look-up of freestream pressure, p∞ .
Mach number is found through the ratio of dynamic compressible
pressure, qc2, and free stream pressure.
2
1
1 1 1 1
2 2 2 21 2 1 2
0 0 1 0 0
0 0 1 0 0
0 0 0 01 1 1 1 1 1
0 0 1 0 0
c n n
n n n n
q q p
q q q p
p
q q p
−
∞
Θ ΘΘ Θ Θ Θ Θ Θ =
Θ
L L
M ML L
M O M M M O ML L
L L
2 2cos sini i iθ ε θΘ = +where
2
1 1 1
2
1 1 1
2
2
1 1 1
n n n
i i i i i i
i i i
n n n
i i i i i ic i i i
n n n
i i i i i
i i i
q q p q
q q p qq
pq q q
= = =
= = =
∞
= = =
− Θ Θ
− Θ Θ =
Θ − Θ
∑ ∑ ∑
∑ ∑ ∑
∑ ∑ ∑
This can be simplified to
Subsonic Mach number
2
1
21 1
1
cq
Mp
γ
γ
γ
−
∞
∞
= + − −
Supersonic Mach number
2
12
1
12
1
21
2 1
1 1
c
Mq
p
M
γγ
γ
γ
γ γ
γ γ
−
∞
∞ −
∞
+ = −
−− + +
Noise reduction is accomplished through the use of an inertial
filtering algorithm that combines the unbiased FADS data with
the biased INS data to give a high fidelity airdata state with a
minimum of system noise. Although all states are filtered, the
sideslip filter is presented here.
After adding an altitude scheduled weighting factor, Awght, to
further reduce noise at high altitudes, and applying a bi-linear
transform to convert to the time domain we have
( ) ( )( )
( )1 1 11
1 tan tan 1 tan12 2 2
1 tan 1 tan 1 tan 1 tan2 2 2 2
k k k k k k
wght wght
k k inert inert FADS FADS inert inert
t t tA A
t t t t
τ τ τβ β β β β β β β
τ τ τ τ
− − −−
∆ ∆ ∆ − −
= + − + − + −
∆ ∆ ∆ ∆ + + + +
1
inertial FADSs
s
τ β ββ
τ
+=
+In the Laplace domain, sideslip is given by
Place matrix of pressure sensors
flush with surface behind a
detached shockwave.
Matrix of ports allows for
determination of the full airdata
state, as well as the potential for
fail-operational capability and
full redundancy.
This requires a flow model
simple enough to invert in real-
time, yet accurate enough to
still provide useful data.
The effect of the filter can be seen in the figures at the far left.