Programming with M-files: Analyzing Railgun Data Using For Loops 1.3 2006/09/29 18:19:14 GMT-5 2006/10/05 12:39:09.383 GMT-5 Darryl Morrell morrell@asu.edu Darryl Morrell morrell@asu.edu Engineering modeling for loop MathScript MATLAB Octave This is an example of using m-files to solve a simple engineering data analysis problem in which velocity and position of a railgun projectile are computed from acceleration data; the acceleration data is computed from the current driving the railgun. This example requires an understanding of the relationships between acceleration and velocity of an object moving in a straight line. A clear discussion of this relationship can be found in Acceleration; the Wikipedia article Motion Graphs and Derivatives also has an explanation of this relationship, as well as a discussion of average and instantaneous velocity and acceleration and the role derivatives play. Also, in this example, we will compute approximate integrals using the trapezoidal rule; The Wikipedia article Trapezium rule has an explanation of the trapezoidal rule.

Velocity Analysis of an Experimental Rail Gun A railgun is a device that uses electrical energy to accelerate a projectile; information about railguns can be found at the Wikipedia article Railgun. The paper Effect of Railgun Electrodynamics on Projectile Launch Dynamics shows the current profile of a railgun launch. The acelleration a of the projectile (in units of m s 2 ) is a function of the current c through the projectile (in units of kAmp). This function is given by the equation a 0.0036 c 2 sgn c where sgn c is 1 if c 0 and -1 if c 0 . Get the data Download the current data set in the file Current.txt onto your computer (right click on this link). The file is formatted as two columns: the first column is time in mili-seconds, and the second column is current in kA. The following sequence of commands will load the data, create a vector t of time values, create a vector c of current values, and plot the current as a function of time. load Current.txt -ascii t = Current(:,1); c = Current(:,2); plot(t,c) xlabel('time (msec)') ylabel('current (kA)') The plot should be similar to that in .

Plot of railgun current versus time.

Compute the projectile velocity as a function of time. Note that velocity is the integral of acceleration.

Alexander E. Zielinski; Paul Weinacht Effect of Railgun Electrodynamics on Projectile Launch Dynamics IEEE Transactions on Magnetics 1999 35 1 118-123