AAE 450 Spring 2008

Stephan Shurn31 January 2008

PropulsionRail Gun Feasability

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

AAE 450 Spring 2008

Electricity Cost Calculation

Propulsion

Velocity (m/s) 2000 2000 2000 2000 2000 5000 5000 5000 5000 5000D - Length of Rails (m) 100 500 1000 1500 2000 100 500 1000 1500 2000mass (kg) 100 100 100 100 100 100 100 100 100 100Force (N) 2000000 400000 200000 133333.3 100000 12500000 2500000 1250000 833333 625000I Current (A) 200000 40000 20000 13333.33 10000 1250000 250000 125000 83333 62500Length between/of rails (m) 1 1 1 1 1 1 1 1 1 1B (tesla) 10 10 10 10 10 10 10 10 10 10u (Henry/m) 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06accel (m/s2) 20000 4000 2000 1333.333 1000 125000 25000 12500 8333 6250accel. (g's) 2,038 407 203 135 101 12742 2548 1274 849 637Voltage 20000 20000 20000 20000 20000 50000 50000 50000 50000 50000Kilo-Watts 4,000,000 800,000 400,000 266,666 200,000 62,500,000 12,500,000 6,250,000 4,166,666 3,125,000Cost ($) 220,800 44,160 22,080 14,720 11,040 3,450,000 690,000 345,000 230,000 172,500

Future Work Group code testing Work with group members on other parameters

AAE 450 Spring 2008

Backup

Propulsion

AAE 450 Spring 2008

Electricity Cost Calculation

Propulsion

Velocity (m/s) 2000 2000 2000 2000 2000 5000 5000 5000 5000 5000D - Length of Rails (m) 100 500 1000 1500 2000 100 500 1000 1500 2000mass (kg) 100 100 100 100 100 100 100 100 100 100Force (N) 2000000 400000 200000 133333 100000 12500000 2500000 1250000 833333 625000I Current (A) 400000 80000 40000 26666 20000 2500000 500000 250000 166666 125000Length between/of rails (m) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5B (tesla) 10 10 10 10 10 10 10 10 10 10u (Henry/m) 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06 1.26E-06accel (m/s2) 20000 4000 2000 1333.333 1000 125000 25000 12500 8333. 6250accel. (g's) 2038 407 203 135 101 12742 2548 1274 849 637Voltage 10,000 10,000 10,000 10,000 10,000 25,000 25,000 25,000 25,000 25,000Kilo-Watts 4,000,000 800,000 400,000 266,666 200,000 62,500,000 12,500,000 6,250,000 4,166,666 3,125,000Cost ($) 220,800 44,160 22,080 14,720 11,040 3,450,000 690,000 345,000 230,000 172,500

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

Calculations Current Needed

I = (v2*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

Definition of VariablesV = 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/s2)

AAE 450 Spring 2008

AAE 450 Spring 2008

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]