1. AAE 450 Spring 2008 Stephan Shurn 31 January 2008 Propulsion Rail Gun Feasability

2. AAE 450 Spring 2008 Rail Guns  Multiple variables – barrel length, Rail distance, muzzle velocity  Assuming no drag or friction losses, 100kg projectile  High electricity cost, high energy inputs  High start-up and development costs  Needed extra rocket boost, esp. with low muzzle velocity  High g-loads Propulsion

3. AAE 450 Spring 2008 Electricity Cost Calculation Propulsion Velocity (m/s)2000 5000 D - Length of Rails (m)100500100015002000100500100015002000 mass (kg)100 Force (N)2000000400000200000133333.31000001250000025000001250000833333625000 I Current (A)200000400002000013333.331000012500002500001250008333362500 Length between/of rails (m)1111111111 B (tesla)10 u (Henry/m)1.26E-06 accel (m/s2)20000400020001333.3331000125000250001250083336250 accel. (g's)2,0384072031351011274225481274849637 Voltage20000 50000 Kilo-Watts4,000,000800,000400,000266,666200,00062,500,00012,500,0006,250,0004,166,6663,125,000 Cost ($)220,80044,16022,08014,72011,0403,450,000690,000345,000230,000172,500 Future Work  Group code testing  Work with group members on other parameters

4. AAE 450 Spring 2008 Backup Propulsion

5. AAE 450 Spring 2008 Electricity Cost Calculation Propulsion Velocity (m/s)2000 5000 D - Length of Rails (m)100500100015002000100500100015002000 mass (kg)100 Force (N)20000004000002000001333331000001250000025000001250000833333625000 I Current (A)400000800004000026666200002500000500000250000166666125000 Length between/of rails (m)0.5 B (tesla)10 u (Henry/m)1.26E-06 accel (m/s2)20000400020001333.333100012500025000125008333.6250 accel. (g's)20384072031351011274225481274849637 Voltage10,000 25,000 Kilo-Watts4,000,000800,000400,000266,666200,00062,500,00012,500,0006,250,0004,166,6663,125,000 Cost ($)220,80044,16022,08014,72011,0403,450,000690,000345,000230,000172,500

6. Calculation Assumptions  Elec. Run for 1 hr.  No Drag or friction losses within rail gun  Price of elec. - $0.0556 / kW*hr (New Mexico Industrial average for 2007)  100 kg projectile mass  Electromagnetic Field of 10 Tesla AAE 450 Spring 2008

7. Calculations  Current Needed I = (v 2 *m)/(2*D*L*B)  Voltage V = v*B*L  Wattage Watts = V*I  Cost Cost = ($0.0556/kW*hr)*(Watts)*(1 hr)  Acceleration A = F/(m*9.80665) AAE 450 Spring 2008

8. Definition of Variables V = Voltage (Volts) I = Current (amperes) v = Muzzle Velocity (m/s) m = projectile mass (kg) D = Length of Rails (m) L = Distance between rails (m) B = Magnetic Field Strength (Teslas) a = Acceleration (m/s 2 ) AAE 450 Spring 2008

9. Sources Propulsion  Energy Information Administraion, “Average Retail Price of Electricity to Ultimate Customers by End-Use Sector, by State”, December 13, 2007, [http://www.eia.doe.gov/cneaf/electricity/epm/table5_6_b.html Accessed 29 January 20008.]  “Jengel and Fatro’s Rail Gun Page,” April 24, 2002, [http://home.insightbb.com/~jmengel4/rail/rail-intro.html Accessed 22 January 2008]  Yavuzkurt, Savas, “Thermal Sensor Design for Electromagnetic Gun Rails,” [http://www.mne.psu.edu/me415/spring07/BAE2/ Accessed 23 January 2008]