Goal

Provide flight dynamic aero, propulsion, and mass properties models for a conceptual, probably unfeasible, two-stage-to-orbit launch vehicle in order to generate flight simulation verification time history data.

Acronyms

Acronyms

ANL

Aircraft nose left

ANR

Aircraft nose right

ANU

Aircraft nose up

RWD

Right wing down

SRB

Solid rocket booster

n.d.

no dimensions

Assumptions and Limitations

The various models are specified in accordance with AIAA S-119 [S119], also known as DAVE-ML. See http://daveml.org for more information.

Origin of data

The vehicle represented by these subsystem models arose from the fertile mind of Dr. Eric Queen of NASA’s Langley Research Center in Hampton, Virginia after a plea from the author to provide an extraordinarily simple two-stage rocket that could be used to exercise and compare simulation frameworks within and outside the Agency. A note on one slide of the original document indicates the aero data is based on "V2 at Mach 3"; another slide indicates the rockets are modeled after the Shuttle solid rocket boosters (SRB). No attribution of any other data appears necessary.

The vehicle is envisioned to be two 3 m diameter solid rocket boosters stacked; the first stage is 25 m long with a dry mass of 35,000 kg and 180,000 kg of propellant. The second stage is 10 m long with a dry mass of 15,000 kg carrying 80,000 kg of propellant, for a total booster length of 35 m. It is carrying a 4,000 kg payload to orbit.

The vehicle is stable but unguided. Don’t try this at home.

Scope of effort

A representative but unclassified and open-source flight vehicle model is provided for use in generating or comparing launch vehicle trajectories in atmospheric and exo-atmospheric flight, in a non-proprietary format that is both human- and text-readable.

The S-119 format is designed for unambiguous representation of flight dynamic models in an archivable format.

To this end, separate system models of a two-stage-to-orbit rocket-powered launch vehicle are provided in the following files:

twostage_aero.dml, Rev A, dated 2014-03-27

Simple aerodynamics model

twostage_prop.dml, dated 2013-08-10

Simple propulsion model

twostage_inertia.dml, dated 2012-08-09

Mass properties model

Components

Each component model is described in detail below.

twostage_aero.dml

Each of these models is based on data given in [Queen13] by Dr. Eric Queen.

Table 1. Input Signals - twostage_aero.dml
Name Units Sign Description [nominal value]

angleOfAttack

deg

+ANU

Angle of attack

angleOfSideslip

deg

+ANL

Angle of sideslip

Table 2. Output Signals - twostage_aero.dml
Name Units Sign Description

longitudinalReferenceLength

m

const.

Longitudinal reference length [3 m]

lateralReferenceLength

m

const.

Lateral reference length [3 m]

referenceArea

m^2

const.

Reference area [7 m]

liftCoefficient

n.d.

+up

Total coefficient of force normal to flight path

sideforceCoefficient

n.d.

+right

Total coefficient of force along the body Y-axis

dragCoefficient

n.d.

+down

Total coefficient of force parallel to the flight path

rollingMomentCoefficient

n.d.

+RWD

Total coefficient of moment around the body X-axis (rolling moment)

pitchingMomentCoefficient

n.d.

+ANU

Total coefficient of moment around the body Y-axis (pitching moment)

yawingMomentCoefficient

n.d.

+ANR

Total coefficient of moment around the body Z-axis (yawing moment)

twostage_prop.dml

The first stage is modeled as having 17,000,000 N thrust with an Isp of 360 sec. The second stage has 5,000,000 N thrust with an Isp of 390 sec. Both stages should burn until prop is depleted.

It is an error to have both stages burning simultaneously.

Table 3. Input Signals - twostage_prop.dml
Name Units Sign Description

stage1firing_flag

n.d.

0-1

Indicates if the first stage is firing

stage2firing_flag

n.d.

0-1

Indicates if the second stage is firing

Table 4. Output Signals - twostage_prop.dml
Name Units Sign Description

bodyThrustForce_X

N

+fwd

Steady-state thrust of engine for given inputs in body X axis

bodyThrustForce_Y

N

+right

Steady-state thrust of engine for given inputs in body Y axis (always 0)

bodyThrustForce_Z

N

+down

Steady-state thrust of engine for given inputs in body Z axis (always 0)

bodyThrustMoment_Roll

N-m

+RWD

Steady-state moment of engine for given inputs about the body X axis (always 0)

bodyThrustMoment_Pitch

N-m

+RWD

Steady-state moment of engine for given inputs about the body Y axis (always 0)

bodyThrustMoment_Roll

N-m

+RWD

Steady-state moment of engine for given inputs about the body Z axis (always 0)

massDot

kg/s

+incr

Propellant consumption rate

twostage_inertia.dml

This model linearly interpolates mass properties, including center of mass location, during flight. Inputs are total fuel consumed in stages 1 and 2 and if the vehicle has staged (dropped the first stage). Outputs are mass properties, fuel fraction consumed in both stages, and the location of the moment reference center (which moves when the vehicle stages).

Table 5. Input Signals - twostage_inertia.dml
Name Units Sign Description

rocketHasStaged

n.d.

0-1

If non-zero, indicates first stage is missing.

stage1fuelConsumed

kg

 — 

Amount of fuel burned in first stage

stage2fuelConsumed

kg

 — 

Amount of fuel burned in second stage

Table 6. Output Signals - twostage_inertia.dml
Name Units Sign Description

stage1FuelRemainingFrac

frac

0-1

Fraction of fuel remaining in first stage

stage2FuelRemainingFrac

frac

0-1

Fraction of fuel remaining in second stage

bodyMomentOfInertia_Roll

kg-m^2

>0

Rolling moment of inertia about the body X axis

bodyMomentOfInertia_Pitch

kg-m^2

>0

Pitching moment of inertia about the body Y axis

bodyMomentOfInertia_Yaw

kg-m^2

>0

Yawing moment of inertia about the body Z axis

bodyProductOfInertia_ZX

kg-m^2

0

Cross-product of inertia in the body X-Z plane (no sign reversal)

bodyProductOfInertia_XY

kg-m^2

0

Cross-product of inertia in the body X-Y plane (no sign reversal)

bodyProductOfInertia_YZ

kg-m^2

0

Cross-product of inertia in the body Y-Z plane (no sign reversal)

totalMass

kg

>0

Total mass of the vehicle

vrsPositionOfMrc

m

+aft

Longitudinal location of the moment reference center (+aft from nose)

bodyPositionOfCmWrtMrc_X

m

+fwd

Longitudinal location of the center of mass relative to moment reference point

bodyPositionOfCmWrtMrc_Y

m

+right

Lateral location of the center of mass relative to moment reference point

bodyPositionOfCmWrtMrc_Z

m

+down

Vertical location of the center of mass relative to moment reference point

Implementation

Interpretation of models

The AIAA S-119 standard is an XML-based encoding scheme that provides both human- and machine-readable algorithm and data table specifications in an unambiguous way, suitable for exchange over distance and, for archival purposes, time. While specifying models in this fashion may initially present a challenge to the implementer, investment in automated scripts or parsers should greatly simplify future exchange of models. The nature of XML should make these models understandable even without reference to the formal grammar definition document (available from http://daveml.org).

The grammar is simple enough that equivalent source code can be implemented by hand in most cases. If preferred, several parsers are available, some open and some by request. See the Tools section of http://daveml.org for a current list.

These parsers are intended either for use at run-time (an interpreting parser) or at compile-time (a translating parser that emits C, Simulink®, FORTRAN or other programming source code). A parser that can do both is also available.

S-119 models may also contain their own self-verification check-cases that will help ensure proper implementation of the model by the chosen parser. At present, the aero (F16_aero.dml) and propulsion (F16_prop.dml) models contain verification checkcase definitions and data.

Variable names used by these various models, where appropriate, reflect the suggested naming convention described in [S119].

Hooking up the models

Inputs from the simulation framework are normal flight conditions: angle-of-attack, angle-of-sideslip, and dynamic pressure. These are used to obtain aerodynamic coefficients of forces and moments about the current moment reference center, which changes when the vehicle stages.

The specified initial conditions (see below) are assumed for the flight conditions, and the first stage is ignited (by passing the appropriate flag to the propulsion model). The resulting thrust acts along the body X axis and begins to accelerate the vehicle. The amount of fuel consumed by each stage must be calculated by external logic; the mass of fuel consumed is provided to the inertia model, which provides the current mass properties including the offset between the center of mass and the moment reference center.

This moment arm is used to transfer the aero forces and moments from the reference center to the current center of mass using an external cross-product operation of the two vector quantities; thus the actual moments and aerodynamic forces can be summed with the thrust value from the propulsion model and accelerations can be calculated at the center of mass.

The simulation framework integrates the accelerations twice to arrive at new flight conditions, and the simulation loop starts over.

Some internal logic is required to turn off the first stage when it is depleted (remaining fuel fraction reaches 0), then the vehicle is allowed to coast for 96.79 seconds before the first vehicle is dropped (or staged) and the second stage is ignited. The second stage continues to burn until fuel depletion.

At this point the vehicle should be in an elliptical orbit with a perigee greater than 125 km for a circular, rotating, earth (although an ellipsoidal/WGS-84 earth should work as well).

The simulation framework is responsible for the appropriate atmospheric model, integrating both the equations of motion and the fuel consumed values, providing the moment transfer to the center of mass, and the simple switching logic for coasting and staging upon depletion of stage 1.

Initial conditions

The rocket should be launched from sea level at the equator heading Eastward with an initial pitch attitude of 55.220 degrees (measured from horizontal). The initial velocity should be close to zero; for comparisons sake and to avoid singularities involving division by zero, use 0.1 ft/s as the initial velocity along the X-body axis.

For simplicity’s sake, the center-of-mass of the vehicle should start at sea level (which would physically place the lower part of the rocket below sea level [Madden1403]).

Initial angular rates should be zero with respect to the launch site. The vehicle should pitch over along the flight path in response to the effect of gravity as it accelerates away from the launch site (the so-called gravity turn).

Atmosphere model

For comparsion, the full US Standard Atmosphere, 1976, should be used [NOAA1976]. Many simulations that support the 1976 atmosphere do not include the portion in the troposphere, which is a separate set of tables or equations. The lack of atmospheric data above 86 km if the troposphere data is not available will cause slight differences in linear and rotational accelerations.

Change history

Table 7. Revisions to this file

2013-08-09

v1

Original version

2014-03-30

v2

Tightened scenario specifications, added

References

  • [S119] Anon.: "Flight Dynamics Model Exchange Standard." American National Standard ANSI/AIAA S-119-2011, American Institute of Aeronautics and Astronautic, Washington, DC, March 2011. Available from http://arc.aiaa.org/doi/book/10.2514/4.867965 (as of May 2013)

  • [Queen13] Queen, Eric M.: "Two-Stage to Orbit Test Case," found in a Microsoft PowerPoint slide presentation, twosgatetoorbit.pptx dated 2013-07-15.

  • [Madden1403] Madden, Michael M.: "Firming Up the Scenario Definition for Atmospheric Case #17 (Two Stage Rocket)," e-mail to the author dated 2014-03-28, with a follow-up correction.

  • [NOAA1976] National Oceanic and Atmospheric Administration, "U.S. Standard Atmosphere, 1976." NOAA—S/T 76-1562, Washington, DC 1976.