lt-basic.htm Tri-Mode ARLA

Amateur Rocket Launch Assist (ARLA)

Launch Tube Basics


Launch Tube Principle

Launch tubes operate on the same principle as the ancient blow gun. A projectile is inserted into the tube, a gas (air or other) is forced into one end of the tube and the projectile shoots out the other end.

Kinematics For velocities well below the Speed of Sound (SOS for the gas being used), there are simple relationships between the gas pressure, tube diameter, projectile mass, length, acceleration, exit velocity, and travel time. For example, if you double the pressure, the acceleration doubles and the exit velocity increases by 1.414. If you double the mass of the projectile then the acceleration drops by half. The following are the equations associated with this.

Basic Equations of Motion
 Velocity when acceleration and time are known.

      v = at  

   ex v = (32.2 ft/sec.sec)x(1 sec)

      v = 32.2 ft/sec

 Velocity when acceleration and distance are known.

      v = sqrt(2as)

   ex v = sqrt([2]x[32.2 ft/sec.sec]x[100 ft])

      v = 80 fps

 Distance when acceleration and time are known.

      s = at.t/2

   ex s = (32.2ft/sec.sec)x(2 sec)x(2 sec)/2

      s = 64.4 ft

 Distance when velocity and acceleration are known.

      s = v.v/2a

   ex s = (1000 ft/sec)x(1000 ft/sec)
          ---------------------------
              (2)x(322 ft/sec.sec)

      s = 1553 ft

 Time when velocity and acceleration are known.

      t = v/a

            2000 ft/sec
   ex t = --------------
          322 ft/sec.sec

      t = 6.21 sec

 Area of a 6 in diameter tube.

      A = Pir.r = PiD.D/4

          (3.414)x(6 in)x(6 in)
   ex A = ---------------------
                   4

      A = 28.3 in.in

 Volume of a 6 in Diameter Tube, 30 ft long.

      V = Al (Area x length)

   ex V = (28.3 in.in) x (30 ft) x (12 in/ft)

      V = 10,188 in.in.in

   and

                  10,188 in.in.in
      V = --------------------------------
          (12 in/ft).(12 in/ft).(12 in/ft)

      V = 5.90 ft.ft.ft

 Force created by gas pressure.

      f = pA

   ex f = (100 lbf/in.in) x (10 in.in)

      f = 1,000 lbf

 Acceleration in Gravities (g).

      G = f/m

   ex G = 100 lbf/10 lbm

      G = 10 g

 Acceleration in fps.s

      a = G x 32.2 fps.s/G

   ex a = (10 g) x (32.2 ft/s.s.G)

      a = 322 fps.s

 Symbols.

A = Cross Sectional Area of a Tube (square inches = in.in)
a = Acceleration (feet per second squared = ft/sec/sec)
f = Force (pounds force = lbf)
G = Acceleration (g)
l = length (inches or ft)
m = Mass (pounds mass = lbm)
p = Gas Pressure (pounds force per square inch = lbf/in.in = psi)
Pi = 3.414
r = Radius of a Tube (inches = in)
s = Distance (feet = ft)
t = Time (seconds)
V = Volume (cubic inches or cubic feet)
v = Velocity (feet per second = ft/sec)
     Table tx

     Tube         Cross         Gas        Force
   Diameter     Sectional    Pressure     Created
   (inches)    Area (in.in)    (psi)       (lbf)
   ------------------------------------------------
      1           0.78           50           39.2
      1           0.78          100           78.5
      1           0.78          200          157
      4           12.6          100        1,257
      6           28.3          100        2,830
     12          113           100       11,300

Gasses

The purpose of the gas is to provide a force to accelerate the projectile to the desired velocity. This force is due to the gas pressure and can be estimated from the above calculations up to about 90 percent of the SOS for the gas in the tube. Above that speed the efficiency drops off sharply and shock waves in the tube make design and construction difficult. The following discussions are based on not exceeding Mach 0.9 for the gas in use.

Speed of Sound (SOS) in a gas

The following paragraphs describe the major factors affecting the SOS in a gas.

Temperature The SOS in a gas is directly related to the square of the temperature (above absolute zero) and has the equation:

SOS = sqrt(GRT/M)

  G = Ratio of Specific Heats
  R = Gas Constant (8.314 J/Mol.K)
  T = Absolute Temperature
  M = Molecular Mass

In short, the hotter the gas the higher the SOS. Air has an SOS at 72 degrees Fahrenheit (F) of about 1,000 fps. But at 1,700 F the SOS is about 2,280 fps.

Conversely, as the gas temperature drops so does its SOS. This can be significant if a compressed gas is used. As the compressed gas is released and expands it cools. The higher the pressure drop the colder the gas gets. For some applications this means that the gas must be heated to maintain the proper SOS.

Thermal Coefficients The temperature rise (or fall) of a gas with a given heat input (or loss) is determined by its two thermal coefficients, constant pressure (Cp) and constant volume (Cv). The lower the coefficients the less heat is needed to raise the temperature. Helium has low coefficients and therefore takes less heat to raise its temperature.

Molecular weight The lower the molecular weight the higher the SOS. Nitrogen has an SOS (at 72 F) of about 1100 fps while helium has an SOS of 3,400 fps. Hydrogen is even lighter than helium and has a higher SOS, but can be very dangerous to use.

Safety

Packaging, Handling, Shipping, and Transportation (PHS&T)

These design factors don't affect the exit velocity of the projectile but are critical to operations.

Combustion of gasses

For higher performances it may be desireable to heat the gas through combustion. This has two advantages. First it raises the temperature (and SOS) almost instantaneously and second it reduces the amount of gas to be transported and stored (hot gas takes up more volume than cold gas).

Common Gasses

Some common gasses. Appendix A has more detail but here are brief descriptions of some recommended gasses to start with.

Launch Tube construction

Building a compressed air potato gun can be very simple. Many of these are described on the World Wide Web (WWW). One claims to have achieved 450 miles per hour (mph - 670 fps) exit velocity with garage air and about a six foot tube. Another claimed to achieve 450 mph with one projectile and a sonic boom with a very light weight projectile from a 10 ft tube using CO2. Most of these compressed air potato guns use PVC pipes and garden sprinkler valves, cost under $40, and take only a few hours to build. This would be a good starting point for the amateur rocketeer but hitting 2,000 fps will require a little more effort.

Materials

There are many materials available to the amateur rocketeer.

For low pressures (0-125 psi) and temperatures (below 100 F) PVC plumbing is probably a good choice (though steel would be much safer). It is easily available, low cost, and simple to assemble. PVC tubes are available in up to 1.2 inch thick wall, 12 inch diameter, 40 ft lengths. Farmers often use aluminum irrigation pipes in 20 and 40 ft lengths in diameters from 2 inch to over 24 inches. Stock steel pipes are available in sizes to 24 inch diameter and 40 ft lengths. This author has seen a fabricated pipe 12 ft in diameter, 2 inch thick walls, and 40 ft long being transported along the freeway. The driver said he had hauled up to 150 ft long pipes like that.

When selecting materials the amateur rocketeer needs to consider the gas to be used (temperature, corrosiveness, etc), transportation to the launch site, field assembly, and cost, among many other things.

Gas Storage

The simplest gas storage for air is probably the home garage air compressor tank. They're low cost, readily available, and usually come with the compressor. Unfortunately, most have a relatively small volume and a small hose adaptor which won't allow a high enough flow rate. The most common compressed air potato gun gas storage concept is also suitable for many other gasses. For gas storage this uses a pipe the same length but of larger diameter than the launch tube (if not larger then the pressure will drop to half by the time the projectile exits the tube. Alternatives include a pipe of the same diameter but much longer or several pipes the same size all feeding into one.

Gas Valves For most amateur rocket use the travel time of the projectile in the tube will be less than 1 second. In order to get the highest exit velocity the pressure needs to rise much less than this. Compressed air potato guns achieve this with garden sprinkler valves which are available up to about 2 inch diameters. Ball valves and butterfly valves are available in almost all sizes and can be very fast acting. Many of these are electrically operated allowing the launch director to be a safe distance away.

Gas Management

A low pressure compressed air launch tube would require little in the way of gas management. But to achieve the high speeds it requires some effort.

Gas Storage

Siting

For most amateur rockets the launch tube will need to be transported to a distant site, assembled, used, disassembled, and transported home. This can be done by making it modular and designing in quick fasteners and connectors.

Also, remember that for every action there is an equal and opposite reaction. If the force accelerating the projectile is 4,000 lbf then the tube will recoil with 4,000 lbf. In short, you need to provide a very sturdy mount for your launch tube.



This Page Last Updated 9 Dec 98