Section 2.2 - Guns and Accelerators

This section covers Guns and Accelerators. Although the details are quite varied, what they share is a larger fixed installation which provides acceleration to a smaller projectile or cargo. The construction of a large fixed device is justified if you use it many times and the maintenance per use is moderate.

Note: This section is continued at Guns and Accelerators 2 due to page size.

A. Mechanical Accelerators

As the name indicates, this group uses direct force from the device structure.

9 Leveraged Catapult

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Type:

Description: A leveraged catapult uses a relatively large or heavy driver to accelerate a smaller payload at several gravities by mechanical means. Such devices date back to the Medieval period, but this is an updated version using modern materials. Devices such as a multiple sheave pulley or a gear train convert a large force moving slowly to a small force moving fast, and transmit the force along a cable. The mechanical advantage produces more than one gravity of acceleration. This concept may be one of the simplest to implement on a small scale. Despite the seeming simplicity of the concept, velocities of several km/s are possible, which would greatly reduce the size of a rocket needed to provide the balance of the velocity to orbit. The performance of this concept reaches a limit due to the weight, drag, and heating of the cable attached to the payload and the magnitude of the driving force, which is divided by the leverage ratio to yield the force on the payload.

Status:

Variations:

• 9a Drop Weight - A falling mass is connected to a vehicle by a high strength cable running over a multiple-sheave pulley, cable reels with different diameters, or connected with a gearing ratio. Two types of natural locations with large height difference are possibilities - river gorges and mountain peaks. Locations such as the Grand Canyon and the Columbia River gorge have lots of vertical relief for the drop weight. At these locations the weight can consist of a large fabric bag filled with water from the river at the bottom. The bag can be emptied before hitting bottom. This reduces the weight that has to be stopped by a braking system. For mountain peak locations, the drop weight runs down a set of rails and is stopped by running into a body of water or running up an opposing hillside plus possibly wheel braking. The mountain location may be preferred because of the greater launch altitude. This example assumes a mountain with a solid weight sliding on rails:

We assume that a 15,000 kg cryogenic rocket using RL-10 engines is being thrown. An acceleration of 60 m/s^2 is tolerable by humans for the 20 seconds required to reach 1200 m/s assuming the human is in good health and properly supported. The linear path traversed would be 12,000 m (7.5 miles) at constant acceleration. The tow cable pulls with 900 kN (202,000 lb) of force on the rocket. High strength carbon fiber is available with tensile strengths of up to 6.9 GPa (1,000 ksi). Allowing for a factor of safety and a braided overwrap surrounding the fiber bundle (to protect the carbon fibers from abrasion), we assume a working stress of 3.45 GPa (500 ksi). The cross sectional area required is then 0.00026 m^2, or a circular cable 0.0182 m (0.72 inch) in diameter.

With a density of 1840 kg/m^3, the cable mass is 0.48 kg/m. For a 12,000 m long cable, the mass would be 5,760 kg without allowing for taper. Since the cable has to be accelerated also, the leading end, closer to the drive mechanism, has to be able to apply sufficient force to accelerate the rocket and all the cable in between the rocket and leading end. To a first approximation, the leading end must be 40% larger in cross section than the trailing end to account for the acceleration of the cable itself. The mean weight of the cable is then 0.576 kg/m, giving a cable mass of 7,000 kg. Something has to be done with the cable after it finishes the job of accelerating the vehicle. It can be taken care of by looping the cable back from the drive mechanism to the starting point (where the vehicle is at the start). At the completion of a launch, the loop of cable is moving at 1200 m/s, and is gradually allowed to come to a stop. Some method will be required to reduce hoop stress on the cable as it makes turns around a pulley at high velocity.

The return portion of the cable has to be able to accelerate the part of the cable past the drive mechanism at 6 g's. Given a 7000 kg lead section, we get a mass of 3200 kg. Thus the total mass accelerated at 6 g's is 25,200 kg, and the total accelerating force is 1.512 MN. Given a 45 degree slope on a mountain, we assume that the drop weight accelerates down at 3 m/s^2. Thus the gear ratio is 20:1, and the force of the drop weight on the drive system must be 30.24 MN. Since a free-falling weight on this slope would accelerate at 7 m/s, there is a 4 N/kg retarding force due to the drive system. Therefore the drop weight must be 7,560 tons. If it is a 4 meter square block of steel (about the cross section of a railroad car), it will weigh 124.8 tons per meter, and hence must be 60.6 meters long. The rails must be 12,000 m/20 long, or 600 meters long.

• 9b Locomotive Driver - A set of railroad locomotives provides the motive force, which is multiplied by a gear mechanism to a higher speed. Example: launching a 20,000 lb

vehicle at 3 g's to 1100 m/s. This requires a 20 km straight run of track. The rail cars needed would include:

1 tank car for vehicle fuel

1 special purpose car to carry the glider

2-3 cars with tow rope guides to keep the tow rope off the ground.

1 pulley system car

30 locomotives in tandem.

We assume the locomotive top speed is about 27 m/s, therefore a 40:1 gear ratio will provide the desired speed at the vehicle. Locomotive traction averages 80,000 lb/engine, or 2000 lb per engine when reduced through the gear ratio. The gear-down mechanism and launch cable drum are mounted on a flatbed rail car. This car can be anchored to a foundation on either side of the railroad track to hold it in place when the combined pull of the locomotives is exerted. The starting traction of 30 locomotives is 1800 tons. Since the couplings between engines are probably not designed for this load, a set of steel cables on both sides of the locomotives are used to transmit the traction force from each engine to the gear mechanism. The vehicle is attached to the anchored rail car by a high-strength cable which is 20 km long. At 3 g's it takes this distance to accelerate to the desired speed.

Two or three rail cars are spaced out along the 20 km with towers with a pulley wheel on top, to guide the cable and keep it off the ground during the initial acceleration. The vehicle has glider type wings attached that will generate lift as it gains speed, so the vehicle will climb once it reaches 100 m/s or so. When the vehicle reaches the desired speed, the cable is released and the vehicle continues to climb under the glider's lift. Eventually the glider drops the vehicle, which proceeds under rocket power. Although 30 locomotives is a lot, you only have to lease them long enough to do a launch, after which they can return to normal railroad use.

A small prototype would consist of a single Locomotive driver. 1250 lb rocket @ 4 g peak. Final velocity = 700 m/s. Accel time = 17.5 sec distance = 0.5at2 = 6.1 km. Engine traction = 80,000 lb average @ 25:1 gear ratio.

• 9c Jet Driver - This is similar to the locomotive case, but the gear ratio is lower since the jet can reach a higher speed on a take-off run. Example: an F-15 can tow 40,000 lb rope tension if near empty. @10:1 gear ratio can accelerate 1000 lb object @ 4 g's. Aircraft top speed on deck = 300 m/s. Object top speed in theory would be 3000 m/s. In practice would be limited by aerodynamics and cable heating (perhaps to 1500 m/s? limit is not well understood)

References:

10 Rotary Sling

Alternate names: Centrifuge Catapult

Type:

Description: In principle, this is a sling or bolo scaled up and using aerospace materials. Rotating cables can reach a significant fraction of orbit velocity on Earth, or all of orbit velocity on smaller bodies. A drive arm is driven in rotation by methods such as an electric motor, or a jet mounted on its tip. In larger versions a cable with the payload attached to the end is played out gradually as the system comes up to speed. The drive arm leads the cable slightly so the cable and payload see a torque that continues to accelerate them. When the desired payload velocity is reached, the payload releases and flies off. The cable is then retracted and the drive arm slows down. When it stops, another payload is attached. In smaller versions the cargo can be connected directly to the drive arm without a cable.

In a vacuum, such as on the Lunar surface, this is theoretically a very efficient system, as the sling can be driven by an electric motor and the mechanical losses can be held to a low value. Some method of recovering the energy of the arm and cable (such as by transferring it to a second system by using the motor as a generator), can lead to efficiencies over 60% in theory.

On bodies with an atmosphere, such as the Earth, the system is hindered by air drag. One method of reducing drag is to attach an aerodynamic shape to the cable material, so as to lower drag compared to a circular cable. Another is to mount the drive arm on the top of a large tower, so the cable is not moving in dense gas. A third is to generate lift along the cable or at the payload raising its altitude. The rapidly moving part of the cable near the payload then has less drag.

A counterweight is desirable in situations where the unbalanced load of the cargo would put too much stress on the pivot and supporting structure. The counterweight gets released at the same time as the cargo. Due to gyroscopic effects, the rotating cable will attempt to keep its axis of rotation fixed. When attached to a rotating body such as the Earth, the location and mounting of the cable will have to take that into account.

Design Example:

This example is for a terrestrial sling with a tip velocity of 1800 m/s, or about 24% of Earth orbital velocity, and a cargo of 10,000 kg including propulsion for going to orbit:

- Assume tip acceleration is 10 gravities (100 m/s²) for non-living cargo.

- Then r = 32,400 meters.

- For a 10,000 kg projectile at end, cable tension is 1 MN. If carbon fiber is used with a 3400 MPa design stress, then cable area is 1/3400 m2, or about 3 cm².

- Cable mass is 0.6 kg/meter, adds 60 N/meter at tip. The implied scale length is 16.67 km. Acceleration falls linearly with radius, so effective radius is 16.2 km for load purposes, and cable mass ratio is 2.8:1. Therefore cable mass is 18,000 kg.

- To spin up in 1 hour, we need an average accelerating force of 0.5 m/s², or 5000 N.

- Drag counteracts the accelerating force. Assume the cable is shaped to be 1 cm tall by 3 cm deep. Since drag is proportional to velocity squared, and velocity goes linear with radius, drag over the entire length will be 1/3 that at the tip. At the tip drag is 0.5 Cd rho A v². Cd = 0.04 for shaped airfoil. rho = 1.225 kg/m3 at sea level. A = 0.01 m2. v = 1800 m/s. Then tip drag = 2381 N/m, or 1/3 x 32,400 m x 2381 N/m = 25.72 MN at sea level.

- If we assume our drive motor can produce a peak of 4 times the average accelerating force, then peak drag can be at most 15,000 N. The motor is then driven to maintain a surplus of 5000 N force above drag. Since sea level drag is 1715 too high, we want to go to an altitude where density is that factor lower, or 7.14 x 10^-4 kg/m³. This density is at 53 km altitude. The cable will drape in a curve due to the combination of radial and gravity forces, so the tower height will need to be approx 60 km.

Status: Slings and bolos are ancient devices. So far as is known, a modern one for space transport has not been built

Variations:

• 10a Jet Driven Sling - A jet engine is mounted to the rotating arm in order to get high starting torque. The launch velocity is increased by the ratio of cargo radius to jet radius from the pivot point.
• 10b Two Stage Sling - A second rotating cable or arm is mounted on the first one to reduce mass ratio of the entire system. This adds complexity, so is only an advantage where the mass ratio of a single stage version becomes too extreme.

References:

B. Artillery

Guns have been in use in the West since about 1300 AD. A "space gun" is merely one large enough, and with a high enough muzzle velocity, to be useful for space transport purposes. It also needs to point sufficiently above the horizon for the projectile not to hit the terrain, and lower the amount of air to travel through. The earliest illustration of using a cannon to reach orbit is from Isaac Newton's Principia Mathematica, where he was illustrating the concepts of gravity and orbits. Thus the idea is as old as orbit mechanics. In the 20th century rockets were developed for ballistic missiles and then placing payloads into orbit. They were able to reach higher velocities with lower maximum acceleration and infrastructure at the time. Even though guns have a much longer heritage, and both artillery and rockets are both still used by military forces, they were bypassed in the early part of the Space Age.

11 Solid Propellant Charge

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Description: This method uses an explosive charge which vaporizes behind a projectile in a barrel. The high gas pressure generated this way accelerates the projectile to high velocity. Conventional artillery reaches speeds of around 1000 m/s. Velocities much higher than this are difficult to reach because the barrel mass becomes extreme at higher pressures, and the temperature and molecular weight of the resulting gas limits the internal speed of sound, which in turn limits muzzle velocity.

Status: Artillery has a long history and extensive use. The High Altitude Research Probe project attached two naval gun barrels in series and used relatively light shells to reach higher muzzle velocities than conventional artillery.

Variations:

References:

• Newton, Isaac, Principia Mathematica.
• Verne, Jules, From the Earth to the Moon.

12 Liquid Propellant Charge

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Description: This is similar to conventional solid propellant artillery except liquid propellants are metered into the chamber, then ignited. Liquid propellants have been studied because they produce lighter molecular weight combustion products, which leads to higher muzzle velocities, and because bulk liquids can be stored more compactly than shells, and require less handling equipment to load. Metering the propellant flow into the barrel lowers the peak pressure relative to a detonation, leading to lighter barrels.

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13 Gaseous Charge

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Description: A mixture of fuel and oxidizer is introduced into a chamber, and then ignited. This is similar to how automobile engines function. This method covers projectiles directly driven by the resulting high temperature gas. Indirect drive guns are covered under Light Gas Guns on the next page. The igniter is a separate device in the basic concept. An alternate version called a Scramjet Gun uses the projectile itself as a traveling igniter. It must be moving supersonic to keep the ignition front from getting ahead of it, so it needs a gas injector at the start to get it moving fast enough.

Status: Research prototypes. Methane/air mix was used as the driver for the Livermore 2 stage gas gun. The combustion drives a 1 ton piston, which in turn compresses hydrogen working gas. Research on the scramjet gun was being performed at the University of Washington under Prof. Adam Bruckner. Research gun was located in the basement of a building there.

Variations:

• 13a Scramjet Gun (Ram Accelerator) - Fuel/oxidizer mixture present in barrel is burned as projectile travels up barrel. If projectile shape resembles two cones base to base, as in an inside-out scramjet, the gas is compressed between the projectile body and barrel wall. The combustion occurs behind the point of peak compression, and produces more pressure on the aft body than the compression on the fore-body. This pressure difference provides a net force accelerating the projectile.

One attraction of this concept is that a high acceleration launch can occur without the need for the projectile to use on-board propellants. If the projectile has a inlet/nozzle shape (hollow in the middle) it might continue accelerating in the atmosphere by injecting fuel into the air-only incoming flow, extending the performance beyond what a gun alone can do. Another attraction of this concept is the simplicity of the launcher, which is a simple tube capable of withstanding the internal pressure generated during combustion.

References:

• A. Hertzberg, A.P. Bruckner, and D.W. Bogdanoff, "The Ram Accelerator: A New Chemical Method of Accelerating Projectiles to Ultrahigh Velocities" , AIAA Journal, Vol. 26, No. 2, February, 1988. (The original scramjet gun paper)
• P. Kaloupis and A.P. Bruckner, "The Ram Accelerator: A Chemically Driven Mass Launcher" , AIAA Paper 88-2968, AIAA/ASME/SAE/ASEE 24th Joint Propulsion Conference, July 11-13, 1988, Boston, MA. (Applications to surface-to-orbit launching)
• Breck W. Henderson, "Ram Accelerator Demonstrates Potential for Hypervelocity Research, Light Launch," , Aviation Week & Space Technology, September 30, 1991, pp. 50-51.
• J.W. Humphreys and T.H. Sobota, "Beyond Rockets: the Scramaccelerator" , Aerospace America , Vol. 29, June, 1991, pp. 18-21.

14 Rocket Fed Gun

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Type:

Description: A rocket engine is mounted at the chamber end of a gun to produce hot gas to accelerate projectile. In a conventional gun, all the gas is formed at once as the charge goes off. In this concept the gas is produced by a rocket type engine and fills the barrel with gas as the projectile runs down it. Compared to a conventional gun, the peak pressure is lower, so the barrel is lighter.

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NOTE: Guns and Accelerators is continued on the next page.