Dr. Gregg Abate, an AFRL exchange engineer, developed a new method for determining aeroballistic parameters from projectile flight data. Assigned to the Fraunhofer Institute for High-Speed Dynamics (commonly known as the Ernst-Mach Institute), Freiburg, Germany, Dr. Abate was a participant in the AFRL-managed Engineer and Scientist Exchange Program, a Department of Defense effort to promote international cooperation in military research, development, and acquisition through the exchange of defense engineers and scientists.

To perform traditional aeroballistic data analysis, scientists use free-flight spark ranges. Using these facilities, they measure the position and attitude of a projectile as a function of time and derive resultant aeroballistic parameters by matching integrated equations of motion to the measured data. As a result of recent advances in both the area of radar technology and that of onboard sensors, in particular, analysts can now directly measure linear and angular accelerations, velocities, and/or positions of a projectile in free flight. Despite these advances, however, accurate determination of aeroballistic parameters still requires analysts to model aerodynamic coefficients and stability derivatives in order to match the integrated equations of motion with an observed trajectory.

Dr. Abate's new method employs instantaneous position, motion state, physical properties, and environmental conditions to determine aeroballistic parameters. His novel approach subsequently evolved into a fully developed software analysis package called AeroSolve (see figure). AeroSolve runs in the Microsoft® Windows® operating environment and is accessible via a graphical user interface. AeroSolve segments measured flight data into user-defined Mach number ranges in which aeroballistic parameters are assumed to vary slowly. This approach avoids both the problem associated with extreme nonlinearity of aeroballistic parameters at Mach 1 and that related to trajectory matching with extremely long trajectories.

Test engineers using the new approach acquire experimental flight data from two different sources: (1) a radar-based system that measures the projectile's velocity in the earth-fixed frame of reference, and (2) an onboard instrumentation suite that measures the projectile's Euler angles (excluding roll) and roll rate in the bodyfixed reference frame. Test engineers process the radar-based data to extract the projectile's position and acceleration, whereas they use the data acquired on board to determine the projectile's angular rates (pitch and yaw) and angular accelerations. Not only do the radar-based and onboard data sources reflect different spatial reference frames, they operate at different sampling rates as well. Therefore, test engineers must convert the collected data into a common time frame. The result of this conversion is a listing of position, velocity, acceleration, Euler angles, body rates, and body angular accelerations at discrete time increments over the duration of the flight.

In addition to collecting flight data through radar-based and onboard sources, analysts using the new testing procedures measure atmospheric data just prior to the experimental firing. The atmospheric data they collect consists of pressure, temperature, and wind speed and direction as a function of altitude. Based on the projectile's position, the analysts can interpolate the atmospheric data to calculate local conditions of Mach number, air density, and wind speed and direction. Analysts also record the projectile's physical properties (mass, moments of inertia, and diameter) immediately before initiating the experiment; they then integrate this information with the acquired flight data for all points along the trajectory.

Since past research has revealed that aeroballistic parameters vary nonlinearly with angle of attack and Mach number, the new process parses flight data by Mach number, at trajectory locations where aeroballistic parameters are assumed to be nearly constant in Mach number. For each grouping, the analysis accommodates nonlinearity with angle of attack and small variations in Mach number. Test engineers then analyze each Mach number group individually. Using the equations of motion, they determine the aerodynamic forces and moments for each instantaneous state of motion within each parsed group. Employing a multidimensional, least-squares data-fitting methodology called Chi square, the analysts next fit the force and moment coefficients to the aerodynamic parameters to obtain the aerodynamic coefficients and stability derivatives. They repeat this sequence of activities for each of three distinct projectile motions: drag/swerve, roll, and pitch/yaw.

The AeroSolve analysis software allows the test engineer to specify which aerodynamic parameters to include or exclude from the modeling process and which dynamic model (earth- or bodyfixed) to employ. The engineer can also filter the experimental data by Mach number, angle of attack, and/or signal-to-noise ratio. Another AeroSolve system feature allows the engineer to simultaneously analyze multiple projectile tests to increase the density of data and enable a statistical averaging of data obtained from repeated tests with identical nominal firing conditions. In addition, the engineer has a variety of choices for plotting the experimental data or rapidly processing it via automatic analysis routines.

To validate the AeroSolve software package, Dr. Abate's team used synthetic data generated by a six-degrees-of-freedom trajectory simulation. With this data serving as input values, AeroSolve was able to successfully determine the aeroballistic coefficients used to create the simulation. To test the stability of the AeroSolve solution methods, the scientists deliberately corrupted the synthetic data by introducing modest levels of Gaussian error. AeroSolve was able to calculate the aeroballistic parameters from the corrupt data, albeit with greater levels of parameter uncertainty.

*Dr. Gregg Abate, of the Air Force Research Laboratory's Munitions Directorate, wrote this article. For more information, contact TECH CONNECT at (800) 203-6451 or place a request at http://www.afrl.af.mil/techconn/index.htm. Reference document MN-H-05-03.*

##### Air Force Research Laboratory Technology Horizons Magazine

This article first appeared in the October, 2005 issue of *Air Force Research Laboratory Technology Horizons* Magazine.

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