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Programming with M-files: Analyzing Railgun Data Using For Loops

Module by: Darryl Morrell

Summary: 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.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Note:

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 aa of the projectile (in units of ms2 m s 2 ) is a function of the current cc through the projectile (in units of kAmp). This function is given by the equation

a=0.0036c2sgnc a 0.0036 c 2 sgn c (1)
where sgnc sgn c is 1 if c>0 c 0 and -1 if c<0 c 0 .

Exercise 1

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 Figure 1.
Figure 1: Plot of railgun current versus time.
Figure 1 (CurPlot.png)

Exercise 2

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

References

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

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