**Sources/Resources:**

*Introduction to Electrodynamics*by David J. Griffiths- http://web.mit.edu/mouser/www/railgun/physics.html
- http://www.dtic.mil/dtic/tr/fulltext/u2/a345008.pdf
- https://physics.le.ac.uk/journals/index.php/pst/article/viewFile/468/275
- http://www.instructables.com/id/Rail-Gun-Linear-Accelerator/
- Vassar College Lab Technicians

**Materials:**

- LaTeX and Mathematica Software
- Pen and Paper for derivations
- Gas Reservoirs
- Gas Valves
- Steel Tube
- Pneumatic Pipes
- 10 400 Volts 450 uF Capacitors
- Solid Aluminum Bar
- Acrylic

**General Project Plan:**

The first and most important part of our project is to use Mathematica to model the magnetic fields, current, capacitance, and eventually forces/equations of motion of a generic rail gun. This will require a great deal of derivation using principles from Griffith’s book, and a working knowledge of Mathematica. We have found several resources online that will help us through the derivation process.

The rail gun will essentially be made of four components: a power supply, two rails, and a sliding bridge with a projectile attached. This bridge will complete the circuit. The current will create a magnetic field and push the projectile/bridge forward. This motion generates a number of interesting properties which we hope to model on Mathematica.

We will build a rail gun using materials both from the lab and that we acquire independently. After doing so, we will take a video of the rail gun using Vassar’s high speed camera. We then will use video analysis software like LoggerPro to analyze our results and compare them to known existing value and the values that we calculate.

**Estimated Time Line:**

Week 1 (4/6-4/12): Acquire working knowledge of Mathematica and begin hand derivations of relevant equations and concepts. Make list of materials required for assembly of railgun.

Some basic equations we will work with are:

Biot Savart-

(1)

Ampere’s Law-

(2)

Ohm’s Law-

(3)

Resistance-

(4)

I will apply these equations to our specific case and find how they change with time specific to the parameters.

Week 2 (4/13-4/19): Finish my models of current and resistance as functions of time. Begin to plot them on Mathematica. Attain all materials for assembly of rail gun

Week 3 (4/20-4/26): Finish modeling current, resistance, and capacitance on Mathematica. Combine my results with John’s results to model equations of motion. Finish assembly of rail gun

Week 4 (4/27-5/3): Test rail gun and compare results to our experiment. If time permits, factor different mediums/materials into the Mathematica models.

**Collaborator:**

I will be working with John Loree. He will use mathematica to model the induced magnetic field and forces upon the railgun. Together, we will build the railgun.

Jenny MagnesIt will be good to publish a building plan for your railgun. For the projectile to be accelerated there must be a force. What equation does that correspond to?