The design process is the hardest part of creating the pneumatic launching system. The first step is designing the launch tube. You can choose any diameter you would like. In this example I will chose the diameter of 3 inches. You then must find the cross sectional area of the launch tube. To find this you must use the formula: A= Pi r2. · A= (3.14)(1.5) 2 · A= 7.068583471 in2 The answer will be in inches squared. The next procedure will be to find the accelerating force of the target psi on the launch vehicle. The target psi in this example will be 75. The equation for this is: F= pA, where “F” is the force in pounds per foot (lb/ft), “p” is the target pressure, and “A” is the cross sectional area of the launch tube. · F= (75)(7.068583471) · F= 530.1437603 lb/ft The next step is to find the maximum acceleration of the launch vehicle in the launch tube. You will find this with the equations: G=F/m and a=G (32.2 ft/sec.). The first equation will give you the force of the acceleration on the launch vehicle in “G”s, or force in gravities. The “m” in this equation stands for the mass of the launch vehicle in pounds. In this example I will use the actual weight of the launch vehicle used in my experimentation. The weight of my launch vehicle is 1 lb. The second equation will give you the acceleration of the launch vehicle in feet per second. In this equation you just have to plug in the answer to the first equation in for the “G” and solve to get the maximum acceleration. · G= F/m · G=(530.1437603)/(1) · G=530.1437603 · a=(530.1437603)(32.2) · a=17070.62908 ft/sec The next step in the designing process is to find the length of the launch tube. To do this you must use the simple equation: s=v2 /2a. The “s” stands for the length of the tube in feet, the “v” stands for the target velocity, my target velocity will be 500 feet per second, and the “a” stands for the acceleration that was found in the equations above. · s=v2 /2a · s=(5002)/2(17070.62908) · s=7.322518661 feet The next equation tells you how long the travel time of the launch vehicle will be while it is still in the tube. This equation is relatively simple, it is: t=v/a. The “t” is the travel time, the “v” is the target velocity, and the “a” is the acceleration in feet per second. The shorter the time the faster the launch vehicle will be going. · t=v/a · t=(500)/(17070.62908) · t=0.029 sec. This next part is the most complicated part of the design process. This next equation is important to find out the volume of the pressure chamber for gas storage, you will need to launch the launch vehicle to the predicted specifications above. Assuming that the starting psi is 100(P1), and the average pressure is 75 psi, then the ending pressure needs to be no less than 50 psi(P2). · P1- initial pressure (only the pressure chamber has pressure) · V1-initial volume (only the pressure chamber) · P2- final pressure (the pressure chamber and the launch tube) · V2- final volume (the pressure chamber and the launch tube, Vl+ Vlt) These pressures are theoretical. I chose them because they are easily obtained using an air compressor. Using the gas laws: · P1V1 = P2V2 = P2 (V1 + Vlt) = P2V1 + P2Vlt We know by the following formula that the volume of the launch tube is: · Vlt = Al = (PiD2)(s)(l2 in/ft)/4 · Vlt = ((3.14)(32)(7.322518661)(12))/4 · Vlt = 621.1180124 in3 From the gas law formula you can find the volume of the pressure chamber: · P1V1 = P2V1 + P2Vlt · Vlt = (P2)(Vlt)/(P1-P2) · Vlt = (50)(621.1180124)/(100-50) · Vlt = 621.1180124 in3 If you use 4 inch pvc pipe for the pressure chamber then the cross sectional area will be: · A= Pi r2 · A= (3.14)(2)(2) · A= 12.56637061 inches squared And the length is: · l = Vlt/A · l = (621.1180124)/( 12.56637061) · l = 49.42700098 in. = 4.118916748 ft. Now that the design parameters are finished you are now able to construct the pneumatic launching system. All of the parts may be constructed out of pvc piping which can be found at the hardware store, the air valve can be found at the auto parts store and the main valve may also be found at the hardware store. The construction is very simple but takes a long time. All the pieces must be pre-cut and fitted prior to gluing. After the pieces are fitted together let it sit for about thirty minutes before pressurizing.
