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This case study models the airframe of a NASA HL-20 lifting body, a low-cost complement to the Space Shuttle orbiter. The HL-20 is unpowered, but the model includes both airframe and controller.

For most flight control designs, the airframe, or plant model,
needs to be modeled, simulated, and analyzed. Ideally, this airframe
should be modeled quickly, reusing blocks or model structure to reduce
validation time and leave more time available for control design.
In this study, the Aerospace Blockset™ software efficiently models
portions of the HL-20 airframe. The remaining portions, including
calculation of the aerodynamic coefficients, are modeled with the Simulink^{®} software.
This case study examines the HL-20 airframe model and touches on how
the aerodynamic data are used in the model.

The HL-20, also known as the Personnel Launch System (PLS),
is a lifting body reentry vehicle designed to complement the Space
Shuttle orbiter. It was developed originally as a low-cost solution
for getting to and from low Earth orbit. It can carry up to 10 people
and a limited cargo_{ }[1].

The HL-20 lifting body can be placed in orbit either by launching it vertically with booster rockets or by transporting it in the payload bay of the Space Shuttle orbiter. The HL-20 lifting body deorbits using a small onboard propulsion system. Its reentry profile is nose first, horizontal, and unpowered.

**Top-Front View of the HL-20 Lifting Body (Photo:
NASA Langley)**

The HL-20 design has a number of benefits:

Rapid turnaround between landing and launch reduces operating costs.

The HL-20 has exceptional flight safety.

It can land conventionally on aircraft runways.

Potential uses for the HL-20 include

Orbital rescue of stranded astronauts

International Space Station crew exchanges

Observation missions

Satellite servicing missions

Although the HL-20 program is not currently active, the aerodynamic data from HL-20 tests are being used in current NASA projects [2].

You can open the HL-20 airframe and controller model by entering `aeroblk_HL20`

at
the MATLAB^{®} command line.

Preliminary aerodynamic data for the HL-20 lifting body are taken from NASA document TM4302 [1].

The airframe model incorporates several key assumptions and limitations:

The airframe is assumed to be rigid and have constant mass, center of gravity, and inertia, since the model represents only the unpowered reentry portion of a mission.

HL-20 is assumed to be a laterally symmetric vehicle.

Compressibility (Mach) effects are assumed to be negligible.

Control effectiveness is assumed to vary nonlinearly with angle of attack and linearly with angle of deflection. Control effectiveness is not dependent on sideslip angle.

The nonlinear six-degrees-of-freedom aerodynamic model is a representation of an early version of the HL-20. Therefore, the model is not intended for realistic performance simulation of later versions of the HL-20.

The typical airframe model consists of a number of components, such as

Equations of motion

Environmental models

Calculation of aerodynamic coefficients, forces, and moments

The airframe subsystem of the HL-20 model contains five subsystems, which model the typical airframe components:

The 6DOF (Euler Angles) subsystem contains the six-degrees-of-freedom equations of motion for the airframe. In the 6DOF (Euler Angles) subsystem, the body attitude is propagated in time using an Euler angle representation. This subsystem is one of the equations of motion blocks from the Aerospace Blockset library. A quaternion representation is also available. See the 6DOF (Euler Angles) and 6DOF (Quaternion) block reference pages for more information on these blocks.

The Environmental Models subsystem contains the following subsystems and blocks:

The WGS84 Gravity Model block implements the mathematical representation of the geocentric equipotential ellipsoid of the World Geodetic System (WGS84).

See the WGS84 Gravity Model block reference page for more information on this block.

The COESA Atmosphere Model block implements the mathematical representation of the 1976 Committee on Extension to the Standard Atmosphere (COESA) standard lower atmospheric values for absolute temperature, pressure, density, and speed of sound, given the input geopotential altitude.

See the COESA Atmosphere Model block reference page for more information on this block.

The Wind Models subsystem contains the following blocks:

The Wind Shear Model block adds wind shear to the model.

See the Wind Shear Model block reference page for more information on this block.

The Discrete Wind Gust Model block implements a wind gust of the standard “1 - cosine” shape.

See the Discrete Wind Gust Model block reference page for more information on this block.

The Dryden Wind Turbulence Model (Continuous) block uses the Dryden spectral representation to add turbulence to the aerospace model by passing band-limited white noise through appropriate forming filters.

See the Dryden Wind Turbulence Model (Continuous) block reference page for more information on this block.

The environmental models implement mathematical representations within standard references, such as U.S. Standard Atmosphere, 1976.

**Environmental Models in HL-20 Airframe Model**

**Wind Models in HL-20 Airframe Model**

The Alpha, Beta, Mach subsystem calculates additional parameters needed for the aerodynamic coefficient computation and lookup. These additional parameters include

Mach number

Incidence angles ()

Airspeed

Dynamic pressure

The Alpha, Beta, Mach subsystem corrects the body velocity for wind velocity and corrects the body rates for wind angular acceleration.

**Additional Computed Parameters for HL-20 Airframe
Model (Alpha, Beta, Mach Subsystem)**

The Aerodynamic Coefficients subsystem contains aerodynamic data and equations for calculating the six aerodynamic coefficients, which are implemented as in reference [1]. The six aerodynamic coefficients follow.

C_{x} | Axial-force coefficient |

C_{y} | Side-force coefficient |

C_{z} | Normal-force coefficient |

C_{l} | Rolling-moment coefficient |

C_{m} | Pitching-moment coefficient |

C_{n} | Yawing-moment coefficient |

Ground and landing gear effects are not included in this model.

The contribution of each of these coefficients is calculated in the subsystems (body rate, actuator increment, and datum), and then summed and passed to the Forces and Moments subsystem.

**Aerodynamic Coefficients in HL-20 Airframe
Model**

The aerodynamic data was gathered from wind tunnel tests, mainly on scaled models of a preliminary subsonic aerodynamic model of the HL-20. The data was curve fitted, and most of the aerodynamic coefficients are described by polynomial functions of angle of attack and sideslip angle. In-depth details about the aerodynamic data and the data reduction can be found in reference [1].

The polynomial functions contained in the `aeroblk_init_hl20.m`

file
are used to calculate lookup tables used by the model's preload function.
Lookup tables substitute for polynomial functions. Depending on the
order and implementation of the function, using lookup tables can
be more efficient than recalculating values at each time step with
functions. To further improve efficiency, most tables are implemented
as PreLook-up Index Search and Interpolation (n-D) using PreLook-up
blocks. These blocks improve performance most when the model has a
number of tables with identical breakpoints. These blocks reduce the
number of times the model has to search for a breakpoint in a given
time step. Once the tables are populated by the preload function,
the aerodynamic coefficient can be computed.

The equations for calculating the six aerodynamic coefficients are divided among three subsystems:

Summing the Datum Coefficients, Body Rate Damping, and Actuator Increments subsystem outputs generates the six aerodynamic coefficients used to calculate the airframe forces and moments [1].

**Datum Coefficients Subsystem. **The Datum Coefficients subsystem calculates coefficients for
the basic configuration without control surface deflection. These
datum coefficients depend only on the incidence angles of the body.

**Body Rate Damping Subsystem. **Dynamic motion derivatives are computed in the Body Rate Damping
subsystem.

**Actuator Increment Subsystem. **Lookup tables determine the incremental changes to the coefficients
due to the control surface deflections in the Actuator Increment subsystem.
Available control surfaces include symmetric wing flaps (elevator),
differential wing flaps (ailerons), positive body flaps, negative
body flaps, differential body flaps, and an all-movable rudder.

**Forces and Moments Subsystem. **The Forces and Moments subsystem calculates the body forces
and body moments acting on the airframe about the center of gravity.
These forces and moments depend on the aerodynamic coefficients, thrust,
dynamic pressure, and reference airframe parameters.

These subsystems that you have examined complete the HL-20 airframe.
The next step in the flight control design process is to analyze,
trim, and linearize the HL-20 airframe so that a flight control system
can be designed for it. You can see an example of an auto-land flight
control for the HL-20 airframe in the `aeroblk_HL20`

example.

[1] Jackson, E. B., and C. L. Cruz, “Preliminary Subsonic Aerodynamic Model for Simulation Studies of the HL-20 Lifting Body,” NASA TM4302 (August 1992)..

[2] Morring, F., Jr., “ISS `Lifeboat' Study Includes
ELVs,” *Aviation Week & Space Technology* (May 20,
2002).