Transverse gas guns, i.e., the electrothermal ramjet, the ram accelerator, the vortex gun, and the ice gun, can accelerate large projectiles to a much higher velocity than the conventional gas guns. The flow of propellant in the transverse gas gun is transverse to the projectile movement. To understand the concept of the transverse gas gun imagine a glider plane hovering over a thermal vent. Suppose that the plane has the lift-to-drag ratio of 20 and the air rises at the rate of 1 m/s. The plane can maintain its altitude flying forward with a velocity of 20 m/s. Transverse gas gun projectile has the lift-to-drag ratio of about 5, so it can theoretically attain velocity 25 times greater than speed of sound in the propellant.
Conventional gunpowder artillery is impracticable above 2 km/s.
Electromagnetic guns (coilgun and railgun) are heavy and expensive due to the high cost of the electric power supply and switches. Refer to the January issue of IEEE Transactions on Magnetics in odd number years, from 1989 to 1999, for the proceedings of the Symposium on Electromagnetic Launch Technology.
AERODYNAMIC DRAG
When a rocket, a projectile, or any other object moves through the atmosphere, it generates force of friction called aerodynamic drag. Drag of a cannonball equals:F = Cd*S*V2*A/2
- where:
- Cd = 0.2 = coefficient of drag of a fast moving smooth sphere
- S = 1.3 kg/m^3 = density of dry air at sea level
- V = velocity of the cannonball
- A = Π*D2/4 = cross section area of the cannonball, D = its diameter
The coefficient of drag Cd depends on the Reynolds number:
Re = V*D*S/N
- where:
- V = velocity of the cannonball
- D = diameter of the cannonball
- S = 1.3 kg/m^3 = density of dry air at sea level
- N = 2*10^-5 Nsm^-2 = viscosity of dry air at sea level at 60 degrees Celsius
Large, fast moving objects such as rocket launchers and large gun projectiles have Reynolds number greater than 10^6. Sharp nose cone reduces the coefficient of drag. Detailed description of the coefficient of drag is presented in: Stuart Winston Churchill, Viscous Flow: The Practical Use of Theory (Fluid Flow), Butterworth-Heinemann, October 1, 1988.
HYDROGEN INJECTION
A one-ton projectile flying through dense atmosphere experiences deceleration of about 50 g due to aerodynamic drag. Injecting hydrogen from the nose cone of the projectile into the adjacent air reduces the aerodynamic drag, noise, temperature of the nose cone and its ablation. Steel does not corrode in warm hydrogen, so it is a perfect material for the entire projectile. Scramjet experiments have proved that hydrogen mixes poorly with air at orbital velocity. This is bad news for scramjets but good news for the guns, because a small amount of hydrogen will suffice to reduce projectile drag by at least one order of magnitude. The projectile flying through the atmosphere will experience deceleration on the order of several g; too small to harm fragile cargo or people. Hydrogen injection makes it possible to launch cheap, reusable gun projectiles at a grazing angle to the Earth surface. The apogee rocket motors are light-weight because the projectiles are launched at a small angle. Hydrogen injection reduces the aerodynamic drag in four ways:
- The initial velocity of injected hydrogen is the same as the projectile velocity. Air is pushed aside.
- Density of hydrogen is 14 times smaller than density of air.
- The speed of sound in hot hydrogen is so high that hydrogen expands before impinging on the nose cone, thereby reducing its density and drag. It also generates forward thrust by contracting on the tail cone.
- Some of the hydrogen burns, thus increasing pressure on the tail cone. (This beneficial effect is so small that it can be ignored.)
Hydrogen injection
Suspending the gun on balloons, or erecting it on a steep mountain slope further reduces the aerodynamic drag. The best mountain slopes near the equator are on the south side of Pegunungan Maoke mountain range on the island of New Guinea. The slopes are steeper than 10 angle degrees and longer than 10 kilometers. Most of the area is accessible only by helicopter and uninhabited, so no one will be disturbed by the noise.
UMBRELLA PROJECTILE
If a terrestrial gun accelerates the projectile to a velocity lower than the escape velocity (11.2 km/s), its trajectory must be circularized by other means to prevent it from deorbiting (plunging back into the atmosphere). Orbital devices can be used for this purpose, but they are too massive to be used in the short term. A better solution is to use an apogee rocket motor ignited by a simple delay fuse, and spin the projectile like a gyro to avoid the expensive rocket control electronics.
Closed umbrella projectile
Open umbrella projectile
The minimum velocity increase during apogee motor burn (reproduced from Pearson's article)
BIBLIOGRAPHY
A. E. Seigel, "The Theory of High Speed Guns," AGARDograph 91, May 1965.
A. E. Seigel, R. Piacesi, and D. N. Bixler, "Wall Friction, Heat Transfer and Real-Gas Propellant Effects in High-Speed Guns," Fourth Hypervelocity Techniques Symposium, Arnold Air Force Station, TN, November 1965, pp. 352-378.
A. E. Seigel, "Theory of High-Muzzle-Velocity Guns," in "Interior Ballistics of Guns" eds. H. Krier and M. Summerfield, Vol. 66, AIAA Progress in Astronautics and Aeronautics, 1979, pp. 135-175, ISBN 0-915928-32-9.
Harry Fair, "Hypervelocity Then and Now," International Journal of Impact Engineering, Vol. 5, 1987, pp. 1-11.
Alexander C. Charters, "Development of the High-Velocity Gas-Dynamics Gun," International Journal of Impact Engineering, Vol. 5, 1987, pp. 181-203.
William F. Weldon, "Development of Hypervelocity Electromagnetic Launchers," International Journal of Impact Engineering, 1987, pp. 671-679.
Harold E. Gilreath, Robert M. Fristrom, and Sannu Molder, "The Distributed-Injection Ballistic Launcher," Johns Hopkins APL Technical Digest, Vol. 9, No. 3, July-September 1988, pp. 299-309.
Ludwig Stiefel, (editor) Gun Propulsion Technology, AIAA, 1988, ISBN 0-930403-20-7.
Gerald V. Bull and C. H. Murphy, Paris Kanonen -- The Paris Guns (Wilhelmsgeschuetze) and Project HARP, Verlag Mittler, Bonn, 1988.
Harry D. Fair, Phil Coose, Carolyn P. Meinel, and Derek A. Tidman, "Electromagnetic Earth-to-Space Launch," IEEE Transactions on Magnetics, Vol. 25, No. 1, January 1989, pp. 9-16.
Lewis A. Glenn, "Design Limitations on Ultra-High Velocity Projectile Launchers," International Journal of Impact Engineering, Vol. 10, 1990, pp. 185-196.
M. R. Palmer and R. X. Lenard, "A Revolution in Space Access Through Spinoffs of SDI Technology," IEEE Transactions on Magnetics, Vol. 27, No. 1, January 1991, pp. 11-20.
I.I. Glass and J. P. Sislian, Nonstationary Flows and Shock Waves, Clarendon Press, Oxford, 1994.
Robert Frisbee, John Anderson, Jurgen Mueller, and T. Pivirotto, "Evaluation of Gun Launch Concepts," AIAA Paper AIAA 94-2925, 30th AIAA/SAE/ASME/ASEE Joint Propulsion Conference, Indianapolis IN, June 27-29, 1994.
Alexander C. Charters, "The Early Years of Aerodynamics Ranges, Light-Gas Guns, and High-Velocity Impact," International Journal of Impact Engineering, Vol. 17, 1995, pp. 151-182.
John A. Morgan, "A Brief History of Cannon Launch," AIAA 97-3138, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, July 6-9, 1997, Seattle, WA.
Andrew J. Higgins, "A Comparison of Distributed Injection Hypervelocity Accelerators," AIAA-97-2897, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, July 6-9, 1997, Seattle, WA.
Gun research at McGill University.
The following guns can be used as a means of Earth-to-orbit transportation: