NASA Technical Reports Server (NTRS) 19980008580: Design and Calibration of the X-33 Flush Airdata Sensing (FADS) System

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by  NASA Technical Reports Server (NTRS)

/,,v- o _
NAS A/TM- 1998-206540
Design and Calibration of the X-33 Flush
Airdata Sensing (FADS) System
Stephen A. Whitmore, Brent R. Cobleigh, and Edward A. Haering
Dryden Flight Research Center
Edwards, California
January 1998
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NASA/TM- 1998-206540
Design and Calibration of the X-33 Flush
Airdata Sensing (FADS) System
Stephen A. Whitmore, Brent R. Cobleigh, and Edward A. Haering
Dryden Flight Research Center
Edwards, California
National Aeronautics and
Space Administration
Dryden Flight Research Center
Edwards, California 93523-0273
January 1998
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DESIGN AND CALIBRATION OF THE X-33 FLUSH AIRDATA
SENSING (FADS) SYSTEM
Stephen A. Whitmore,* Brent R. Cobleigh,* and
Edward A. Haering, Jr.*
NASA Dryden Flight Research Center
Edwards, California
Abstract A/D analog-to-digital conversion
A' first angle of sideslip triples algorithm
This paper presents the design of the X-33 Flush coefficient
Airdata Sensing (FADS) system. The X-33 FADS uses a
matrix of pressure orifices on the vehicle nose to A0(Moo) zero'th order angle of attack
estimate airdata parameters. The system isdesigned with calibration coefficient
dual-redundant measurement hardware, which produces
At(Moo) first order angle of attack calibration
two independent measurement paths. Airdata parameters
coefficient
that correspond to the measurement path with the
minimum fiterror are selected as the output values. This A2(Moo) second order angle of attack
method enables a single sensor failure to occur with calibration coefficient
minimal degrading of the system performance. The
A3(Moo) third order angle of attack calibration
paper shows the X-33 FADS architecture, derives the
coefficient
estimating algorithms, and demonstrates a mathematical
analysis of the FADS system stability. Preliminary b flush airdata sensing geometry
aerodynamic calibrations are also presented here. The dummy variable
calibration parameters, the position error coefficient (_),
B second angle of sideslip triples
and flow correction terms for the angle of attack (5_),
algorithm coefficient
and angle of sideslip 0513)are derived from wind tunnel
data. Statistical accuracy of the calibration is evaluated B' first angle of sideslip triples algorithm
by comparing the wind tunnel reference conditions to the dummy variable
airdata parameters estimated. This comparison is
accomplished by applying the calibrated FADS B0(M oo) zero'th order angle of sideslip
calibration coefficient
algorithm to the sensed wind tunnel pressures. When the
resulting accuracy estimates are compared to accuracy Bt(M_ ) tirst order angle of sideslip calibration
requirements for the X-33 airdata, the FADS system coefficient
meets these requirements.
B2(Moo ) second order angle of sideslip
Nomenclature calibration coefficient
B3(M,_ ) third order angle of sideslip calibration
a flush airdata sensing geometry
coefficient
coefficient
CTE coefficient of thermal expansion
A angle of attack triples algorithm
coefficient C" second angle of sideslip triples
algorithm dummy variable
*VehicleAerodynamicsGroupLeader,AerodynamicsBranch.
+AerospaceEngineer,AerodynamicsBranch. DFRC Dryden Flight Research Center
_.AerospaceEngineer,AerodynamicsBranch.
Copyright © 1998by the American Instituteof Aeronauticsand ESP electronically scanned pressure
Astronautics,Inc.No copyrightisassertedintheUnitedStatesunder module
Title 17,U.S.Code.TheU.S.Governmenthasaroyalty-freelicenseto
exerciseallrights underthecopyrightclaimedhereinforGovernmental f[Mo,, ]subsonic subsonic Mach number function
purposes.Allotherrights are reserved by thecopyrightowner.
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f[M _]supersonie supersonic Mach number function 5[3 angle of sideslip correction term, deg
FADS flush airdata sensing F pressure difference for triples
algorithm, lb/ft 2
FailOp fail-operational (airplane operates as if
there were no failures) 7 ratio of specific heats
M estimation algorithm geometry matrix e position error calibration parameter
MAAF Michael Army Air Field, Tooele, Utah e M variation of ¢ with Mach number at
ae, _e = O°
MAFB Malmstrom Air Force Base, Great
Falls, Montana ¢al first order coefficient, fit of ¢ with
angle of attack
MSE mean square error
M_ free stream Mach number ea2 second order coefficient, fit of E with
angle of attack
NASA National Aeronautics and Space
Administration EI_1 first order coefficient, fit of E with
angle of sideslip
P port pressure, lb/ft 2
_1_2 second order coefficient, fit of _ with
P_ free stream static pressure, lb/fl 2 angle of sideslip
q weights on measured pressures 2. cone angle of FADS port, deg
qc impact pressure, lb/ft 2 ¢ clock angle of FADS port, deg
9_ pressure weighting matrix O local flow incidence angle, deg
RCC reinforced carbon-carbon (r standard deviation
RLV Reusable Launch Vehicle u? dummy variable used in angle of
sideslip root analysis
RMS root mean square
2
X chi-squared distribution
TPS thermal protection system
,) ,)
f_ FADS geometry term, cos'0 + _:sin'0
UPWT Unitary P/an Wind Tunnel, Langley
Research Center, Hampton, Virginia S__0perscripts, Subscripts, and Mathematica] Operators
x state vector
i port index
X2 mean square fiterror, (lb/ft2) 2
j port index
angle of attack, generic, deg
(j) iteration index
_e local angle of attack sensed by FADS, k port index
deg
^ FADS estimate
free stream angle of attack, deg
a fr_e
Det[.] matrix determinant
angle of sideslip, generic, deg
[.]-I matrix inverse
local angle of sideslip sensed by
FADS, deg [.IT matrix transpose
_ true free stream angle of sideslip, deg V [.Ix gradient with respect to vector x
b[.]
quadratic solution 1for angle of 3x partial derivative with respect to x
sideslip, deg
Introduction
f_2 quadratic solution 2 for angle of
sideslip, deg The primary goal of the Single-Stage-to-Orbit
5(/ angle of attack correction term, deg Technology program is to radically reduce the cost of
access to space, and the X-33 advanced technology
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demonstrator is the centerpiece of this effort. The X-33 performance and cost of a Flush Airdata Sensing (FADS)
design is a 53-percent scale model of the Lockheed system to a set of deployable probes similar to that
Martin VentureStar rM*Reusable Launch Vehicle (RLV) system installed on the space shuttle. This study
and is based on a lifting-body design which features two concluded that a FADS system was more economical
linear aerospike rocket engines. The autonomous-flight by a factor of approximately two. Two issues
X-33 will launch from Edwards Air Force Base at made the probe-based system prohibitively expensive:
Edwards, California and land at one of two sites: 1) integration onto the X-33 airframe, and 2) system
Michael Army Air Field (MAAF) in Tooele, Utah, or calibration. The FADS system requires no deployment
Malmstrom Air Force Base (MAFB) in Great Falls, mechanisms and can be integrated directly onto the
Montana. The vehicle is designed to achieve a peak vehicle nosecap with no movable parts. Because the
altitude near 300,000 ft and speeds of greater than Mach FADS system does not probe the flowfield, but instead
12. After atmospheric re-entry, the X-33 returns to Earth uses the natural contours of the forebody, the flow field is
much cleaner and is easier to calibrate. An additional
with an unpowered horizontal landing. A comparison of
the X-33 and VentureStar vehicles is presented in advantage of the FADS system is that it offers the
TM
figure 1. potential to sense airdata on ascent, an option not
available to the probe-based system. Based on the results
Because the X-33 is to perform an unpowered landing, of this study, Lockheed Martin Skunkworks, Palmdale,
knowledge of the dynamic pressure, angle of attack, and California, selected the FADS system in favor of the
surface winds is critical, so that the terminal area energy deployable probes.
management (TAEM) can ensure that the target runway
be reached under a wide variety of atmospheric The DFRC FADS design builds on work which
conditions. Direct feedback of angle of attack and angle originated in the early 1960's with the X-15 program, 1
of sideslip are also required for gust load alleviation on continued at NASA Langley, 2' 3 and Dryden Flight
the vehicle airframe during the ascent of the flight. Thus, Research Centers 4' 5 in the 1970's and 1980's, and
it was determined early in the X-33 program that the full recently concluded flight testing of an onboard real-time
airdata state, including Mach number, angle of attack, system in the early 1990's. 6' 7 The FADS concept, in
angle of sideslip, dynamic pressure, airspeed and which airdata are inferred from nonintrusive surface
altitude, would be a flight-critical requirement for both pressure measurements, does not require probing of the
the RLV and the X-33. local flow field to compute airdata parameters. This
innovation allows the extreme hypersonic heating
To achieve the TAEM and ascent airdata requirements
caused by the small radius of a flow-sensing probe to be
the airdata system must be operational between
avoided, which extends the useful range of the airdata
Mach 0.20 and Mach 4.0 and meet the following I-G
measurement system to the hypersonic flow regime. This
accuracy requirements.
paper describes the X-33 FADS system design, develops
1. Mach Number: +5.0 percent accuracy for the aerodynamic model which relates the airdata
2.5 < Moo <4.0, +2.50 percent accuracy for parameters to the measured pressures, and derives the
0.6 < M_o < 2.5, +0.015 absolute error between computational algorithms used to compute the airdata
Mo_ = 0.20 and Moo = 0.60, from the pressure measurements. Wind tunnel
2. Angle of attack: +1.5 ° absolute accuracy for first calibration and validation of the FADS system is also
three flights, +0.50 °thereafter, presented.
3. Angle of sideslip: +0.5 ° absolute accuracy for all F10sh Airdata Sensing Aerodynamic Model
flights.
The fundamental concept of the FADS system is that
4. Geopotential altitude: +200 ft absolute accuracy
airdata parameters can be estimated from flush surface
for0.2 < Mo_<4.0.
pressure measurements. To perform this estimation, the
5. Dynamic Pressure: +15 lb/ft2for 0.2 < Moo <4.0. airdata states must be related to the surface pressures by
an aerodynamic model that captures the salient features
To determine the best means of meeting the airdata
of the flow, and isvalid over a large Mach number range.
requirements, NASA Dryden Flight Research Center
To be useful, the model must be simple enough to be
(DFRC) performed a feasibility study to compare the
inverted inreal-time so that the airdata parameters can be
extracted. To solve the problem of describing a complex
*LockheedMartin, Inc.,MountainView,California flow scenario with a simple model, the FADS
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aerodynammicodewlasderiveadsaspliceoftheclosed-
used for the vehicle thermal protection system (TPS) and
formpotentiafllowsolutiofnorablunbtody8,applicable
isin the stagnation region. The nosecap is hemispherical
atlowsubsoniscpeedsa;ndthemodifiedNewtonian with a radius of 47.58 in. and extends longitudinally aft
flowmode9l,applicablaethypersoniscpeeds.
Both from the nose tip 20.8 in. Aft of the RCC nosecap an
potential flow and modified Newtonian flow describe the RCC skirt is used to protect the windward side of the
measured pressure coefficient in terms of the local vehicle, and a honeycomb metallic TPS is used for the
surface incidence angle. To blend the two solutions over leeward sides.
a large range of Mach numbers, a calibration parameter
(e) was allowed for. This parameter must be empirically Measurement Location_
calibrated to allow for the effects of flow compression,
The number of measurements in the X-33 pressure
body shape, and other systematic effects such as shock
matrix was selected as a compromise between the need
wave compression or Prandtl-Meyer expansion on the
to accurately measure the flow conditions at the nose and
forebody. The resulting model is6
the cost of locating ports on the vehicle. Since there are
pi = qc[COs2(Oi)+Esin2(Oi)]+P_o (1) four airdata states and a calibration parameter to be
estimated, at least five independent pressure
measurements must be available to derive the entire
In equation 1, 0i is the flow incidence angle between
airdata state. Using five sensors to estimate the airdata is
the surface normal at the i'th port and the velocity vector.
equivalent to a higher order spline fit and results in an
The incidence angle is related to the local (or effective)
estimating algorithm which is sensitive to noise in the
angle of attack, (ore) and angle of sideslip, (13e) by6
measured pressures. Providing an additional sixth
sensing location mitigates the noise sensitivity, increases
cos(0i) = cos(Ote)COS(_e)COS(_i)
redundancy options, and results in a system which gives
+ sin(fJe)Sin(Oi)sin(_,i) (2) overall superior performance.
+ sin(O_e)COS(_3e)COS(d_i)sin(_,i)
Figure 3shows the FADS measurement locations. Five
measurement locations are on the nosecap, and a sixth
In equation 2, the cone angle (_.) is the total angle the measurement location is on the carbon-carbon skirt. The
normal to the surface makes with respect to the
layout along meridian lines allows the calculations for
longitudinal axis of the nosecap. The clock angle (qb) is
angle of attack to be decoupled from the calculations for
the clockwise angle looking aft around the axis of
angle of sideslip using the triples algorithm, the real-time
symmetry starting at the bottom of the fuselage. These
airdata algorithm for the X-33. The mathematical
coordinate angles are depicted in figure 2. The remaining
properties of the triples algorithm will be discussed in
parameters in equation 1are impact pressure (qc) and the
detail inthe Flush Airdata Sensing Estimation Algorithm
free stream static pressure (P_). Using these four basic
section, and the algorithm equations are derived in the
parameters (o_e, _e' qc, and P_) most other airdata
appendix. The system layout is designed to give good
quantities of interest may be directly calculated.
sensitivity for local angles of attack varying from -20 ° to
In addition to the calibration for e, the local flow 45°, and angles of sideslip of up to +20 °. The nominal
incidence angles (o_e and _e) must be related by clock and cone angles of the X-33 FADS ports are
tabulated inTable 1.
calibrations to the true free stream flow angles. These
flow-angle calibrations account for such additional
systematic effects as bow shock flow deflection and Table 1. X-33 FADS ports, clock and
body-induced upwash and sidewash. For the X-33 a cone angles.
preliminary set of calibrations is derived using wind
Port no. _bi,deg Xi' deg
tunnel data. The wind tunnel tests and the results of the
calibrations are discussed in detail in the Calibration of 1 180 20
the Aerodynamic Model section.
2 270 20
The X-33 Flush Airdata Sensing Pressure M_tri_ 3 0 0
Since the simple model of equation 1is derived from 4 90 20
potential and Newtonian flow around a blunt body, it is
5 0 20
most valid near the vehicle stagnation point. Thus, the
most desirable location for the FADS pressure matrix is 6 0 45
the reinforced carbon-carbon (RCC) nosecap which is
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American Institute of Aeronautics and Astronautics
pneumatic Layout data flow path II as the set of computations which uses
the six lower and inboard pressures, then the FailOp
Each X-33 flight-critical measurement subsystem capability of the system will always be ensured by
must have a fail-operational (FailOp) capability. That is, selecting the computational path with the minimum
the subsystem can tolerate one failure anywhere in the mean square fit error. The mean square fit error is
system software or hardware and still produce a usable computed as
result. The FADS design exploits the built-in redundancy
of the pressure port matrix to achieve FailOp capability 6
with dual redundant system hardware. This dual qitrr ,,(mieasured) -tq.^ctCOrS 2^Ui.(O^_e, _e)
redundancy is achieved at each surface measurement i=l
location by installing a plug with two surface ports.
X2 + _;sin20i(_e ,_e)] +Pool 2
= 6 (3)
Figure 4 shows an exploded view of the plug design.
To survive the peak stagnation temperature of _.. qi
approximately 2000 ° F, the FADS plugs are fabricated i--I
from C-103 niobium alloy, t0 The C-103 alloy has a
where, the ^ designates a quantity estimated by the
melting point in excess of 4000 ° F and a maximum
FADS algorithm. This redundancy management scheme
working temperature of approximately 2500°F. An
additional advantage of using niobium alloy for the selects the system with the best overall fit consistency,
and allows for a soft sensor failure (one which is not
surface plug is that the alloy has a coefficient of thermal
expansion (CTE) which is very close to the CTE of detected by the hardware diagnostics) to occur without
carbon-carbon. I1 This match of the thermal expansion degrading the performance of the system.
properties ensures that hot gas leakage around the plug is
unlikely to occur. The relatively close match of the two If the mean square error (MSE) of the output flow path
materials expansion coefficients also ensures that undue is normalized by an expected population variance (that
thermal stresses are not imparted to the RCC nosecap is, by the expected range of fiterror that is allowable for
when high heating loads are applied. The plug design a system with no failures) then the MSE becomes
was derived from an adaptation of the Space Shuttle distributed as Z2and is a good indicator of the absolute
Entry Airdata System 3which used niobium inserts with system health. This chi-squared approach was developed
excellent success. and successfully employed by Whitmore, et a112"J3 on
previous flight tests. Expected values for the fit error
On each plug the two surface ports are connected to
ranges are still to be determined from additional wind
the pneumatic tubing using a high-temperature titanium
tunnel tests.
alloy braze. The individual surface ports are plumbed to
the measurement sensors using approximately 8-12 ft of The Flush Airdata Sensing Estimating Algorithm
pneumatic tubing with an approximate inside diameter
of 0.21 in. The pneumatic response of this arrangement The aerodynamic model of equations ! and 2 is
was analyzed extensively along the X-33 flight inherently nonlinear in terms of the state parameters and
trajectory. Based on these analyses, it was determined can not be directly inverted. A nonlinear regression
that the pneumatic latencies in the system would not method inwhich the equations are recursively linearized
introduce significant errors into the airdata estimates. and inverted using iterative least squares has been
developed and successfully flight tested. 14 Problems
Computational Architecture and Redundancy with the stability of the algorithm were encountered,
Management. however, and the algorithm required special software
patches to maintain stability. Because the FADS isto be
A schematic of the computational architecture and
used for closed-loop flight control on the X-33, the
redundancy management scheme for the X-33 FADS is
presented in figure 5. The design of the X-33 FADS nonlinear regression algorithm was determined to be too
system provides a total of twelve surface pressure risky and was abandoned.
measurements; however, the pressures from the dual
A new solution algorithm was developed for the X-33
redundant pressure ports are always analyzed
independently. Defining data flow path I as the set of FADS. A better solution algorithm is offered by taking
computations which use the grouping of the six upper strategic combinations of three sensor readings that will
and outboard pressure measurements on each plug, and decouple the flow angularity states from the static and
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impact pressure states and the aerodynamic calibration. clock and cone angles corresponding to these triples
Detailed derivations of the FADS estimator equations are combinations are presented in Table 2.
presented in the appendix. For completeness, portions
Table 2.Angle of attack triples, clock and cone angles.
necessary to explain the flow of the algorithm are
restated here. _i, Z'i, _j, _'j, _*, Z'k,
Triple no. deg deg deg deg deg deg
Angle of Attack Triples Estimator
1 0 0 0 20 180 2O
By strategically taking the differences of three surface 2 0 0 0 20 0 45
pressures (referred to in this paper as "triples") the
pressure related states (qc, Poo, and e) are eliminated 3 0 0 180 20 0 45
from equation 1.The resulting pressure equation is 4 0 20 180 20 0 45
2 2
Fikcos20j + Fjicos Ok+ Fkjcos 0i = 0 (4a)
The output angle of attack estimate is determined as
where the mean of the values computed using the four
individual triples. This averaging procedure provides a
measure of noise rejection for the estimator. Clearly, if
Fik = (Pi - Pk), Fji = (Pj - Pi), Fkj = (Pie - Pj) (4b)
one of the ports along the vertical meridian is deemed
unusable and isweighted out of the algorithm, then only
and Pi,Pj, and Pkare the pressures used in the data triple.
In equation 4 the local angle of attack can be decoupled one valid triple remains for computing the angle of
attack.
from the local angle of sideslip using only pressures
aligned along a vertical meridian where q) = 0° or 180°.
Angle of Sideslip Estimator
In this geometry arrangement, terms related to angle of
sideslip fall out of equation 4. For lotI< 45° the solution Once the local angle of attack has been estimated, then
for ot is the angle of sideslip may be evaluated using any
combination of the available ports, other than the
' EAt
obvious set in which all three ports lie on the vertical
t_ = _tan-J (5a)
meridian. The result, derived in the appendix, is a
quadratic equation in tan 13.
where
A'tan213 + 2B'tan13+ C = 0 (6a)
A = Fitsin2_.j + Fjisin2_._ + Utjsin2_.i
where
B = Fikcost_jsin_.jcosX j
(5b)
+ FjicosCPk sin_._:cosL_
+ FkjCOS_isin_.icos_. i A' = Fitbj_"+Fji b/ + Fk)bi 2}
When Iotl > 45° the correct solution is given by the
(6b)
complement of equation 5(a) B' = {Fikajb j + Fjiakb k+ Fkjaibi}
ot= _(r_-tan-I[ AI) (5c)
C' = {Fikaj2+ Fjiak 2+ Fkjai 2}
For the X-33 there are four possible independent
and
combinations of ot-triples on the vertical meridian. The
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