lt-basic.htm
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 MotionVelocity 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
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.
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.
These design factors don't affect the exit velocity of the projectile but are critical to operations.
Packaging. Most gasses of interest can be purchased from a local welding supply house at pressures up to 2,400 psi and in tanks (bottles) up to 1,100 standard cubic ft (scf, the volume when expanded to sea level pressure at room temperature). Much larger volumes can be obtained through special order. Some gasses, such as steam, refrigerants, and propane can be stored as liquids then heated to gasses at the temperature needed.
Handling. Some gasses are easier to handle than others. Air can be compressed as needed with very simple handling. Water is very safe to handle, until it is converted to steam. Steam has great potential for scalding and, at higher temperatures, reduces the strength of the plumbing and tubing materials. When selecting a gas you need to recognize how you intend to handle it at all times and design the launch tube and operating procedures accordingly.
Storage. This refers to storage of the gas any time you are not using it. Some gasses may require vented buildings while others may require special permits.
Transportation. If you are using low pressure air and launching from your back yard then transportation is probably not a concern. Most high performance rockets require a trip to an authorized launch field or a dry lakebed. This could mean Department of Transportation (DOT) permits, special vehicles, or special containers. Know your gas, the laws, and local regulations.
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).
Some common gasses. Appendix A has more detail but here are brief descriptions of some recommended gasses to start with.
Air: Air is safe (except for high pressures and temperatures), very low cost, easy to PHS&T, and convenient. Under most conditions it should be useful up to 900 fps without heating. It can be heated by passing it through a chamber of hot metal pieces. Or it can be mixed with a fuel (such as propane) and combusted directly.
Steam is generated from water, which is very safe, compact, cheap, and etc. Converting water to steam, however, requires extra equipment, a heat source, materials that can withstand the temperature, and special safety precautions. Steam has about the same speed of sound as air at elevated temperatures.
Steam can be generated by heating the water in a pressure vessel then piping it directly to the launch tube. However, at a vapor pressure of 200 psi the temperature of the steam is only 380 F with an SOS of about 1230 fps. As the water evaporates and the steam expands it will cool, further reducing the SOS. An alternative is to heat up a rock or scrap metal bed inside a pressure vessel and injecting water directly. The water will evaporate and superheat the steam but requires additional equipment.
Steam can also be generated by directly combusting hydrogen and oxygen. This creates very high temperature (7,000 F) steam. For very short travel times (1-2 seconds) this may not have an adverse affect on the launch tube materials. For longer times it can easily melt any metal. This temperature can be reduced by injecting water (or lower temperature steam), air, or other gasses.
Nitrogen
Nitrogen is a low cost, inert gas which can be easily obtained at a local welding supply house. It's commonly transported and used throughout the world. It's also available as a cryogenic liquid making it easily transported in bulk. It's SOS is similar to that of air (air being 70 percent nitrogen). It can be conductively heated as easily as air and has none of the oxidizing problems of air.
Nitrogen can't be combusted directly, as air or hydrogen can. However, it can be mixed with combustion gasses (such as oxygen and hydrogen) to lower the overall gas temperature from 7,000 F to the more useable 1,700 F.
Nitrogen can be passed through a hot particle bed to heat it and, because it is inert, it will not cause corrosion or oxidation of the plumbing.
Helium
Helium is a very light gas, is inert, and is generally available for low to moderate cost. One local welding supply house sells it in K-bottles (110 scf) for $135 ($30 for refill). They also sell it in 1,100 scf bottles.
Helium is very safe to handle and has an SOS of over 3,000 fps at room temperature. This means that, even considering the temperature drop due to expansion, it should still have an SOS of 2,000 fps under most conditions. When heated to about 1,700 F the SOS is 6,000 fps, far more than most amateur rocketeers need. For small numbers of launches per year helium is probably the ideal gas.
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.
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.
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.
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
To achieve supersonic exit velocities cold air will not work.
If air is used for velocities greater than 900 fps then it must be heated. Further, the entire tube ahead of the projectile must be either evacuated or the air inside it must be heated. Otherwise the SOS of this air will not be high enough for it to get out of the way of the projectile causing many design and performance problems. Evacuating the tube can be difficult but an alternative is to shunt some of the initial hot air around the projectile for a few seconds to preheat the tube.
If other gasses are used then there may be an economic need to recover the gas. For example, if helium is used then the tube ahead of the projectile should be filled with helium. This can be kept in place by using a very thin sheet of plastic over the exit end of the tube. Once the projectile passes through, though, all of the gas will be either lost or contaminated with air. An alternative is to use light weight tavern doors that will swing open with the pressure pulse ahead of the projectile. This could then be automatically closed afterward to capture most of the helium for recovery.
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