lt-examp.htm
The following are two example systems chosen to describe how the basics are applied and to provide starting points for the amateur rocketeer. None of these have been built and therefore cannot be used as a blueprint. This means that the amateur rocketeer will have to use some ingenuity and a little trial and error to make their launch tube work properly. However, it also means that this is a place "Where No One Has Gone Before."
To my knowledge, none of what is described here has been ever built. All of technology described herein is available in the open literature, and in fact, in textbooks. This means that none of it is classified or subject to limited distribution. However, once it has been built, debugged, and successfully operated some of the details may come under federal restrictions.
Adding 400 fps to an amateur rocket can significantly improve it's performance. It can be built as a large scale compressed air potato gun using garage air, PVC tubing, and available valves.
Basic AssumptionsBecause 400 fps is well below the speed of sound for the gas we're working with there will be no need to pre-heat the air in the launch tube ahead of the launch vehicle.
Cross Sectional Area of a 4 inch Diameter TubeA = PiD.D/4 or Pi.r.r A = (3.414)x(2 in)x(2 in) A = 12.57 in.inAccelerating Force of 100 psi on the Launch Vehicle
f = pA f = (100 lbf/in.in)x(12.57 in.in) f = 1,257 lbf Note: f(max) = 1,570 lbfLaunch Vehicle Acceleration
G = f/m G = 1,256 lbf/15 lbm = 83.73 g a = (G)x(32.2 ft/sec.sec.g) a = (83.73 g)x(32.2 ft/sec.sec.g) a = 2,696 ft/sec.sec
This is nearly 84 g (105 g max). Check to make sure your rocket can take this. Also, consider using a sabot.
Tube Lengths = v.v/2a (400 ft/sec)x(400 ft/sec) s = ------------------------- (2)x(2,696 ft/sec.sec) s = 29.7 ft
This means that the tube needs to be three 10 ft long, 4 inch diameter PVC tubes.
Note: A 4 inch nominal diameter PVC tube is 4.5 inches outside diameter (OD) and the ID may be slightly less than 4 inches. See the appendix on Launch Tubes for more details.
Launch Vehicle Travel Time in the Tubet = v/a 400 ft/sec t = ---------------- 2,696 ft/sec.sec t = 0.15 secondsGas Storage Requirements
Assuming the starting pressure is 125 psi (P1) and the average pressure is 100 psi then the ending pressure needs to be no less than 75 psi (P2).
From the textbook gas laws
P1.V1 = P2.V2 = P2.(V1 + Vlt) = P2.V1 + P2.Vlt
We know by the following formula that the volume of the launch tube is
Vlt = Al = (PiD.D/4)x(l) (3.14)x(4 in)x(4 in)x(30 ft)x(12 in/ft) Vlt = --------------------------------------- 4 Vlt = 4,522 in.in.in
From the gas law formula we find the volume of the tank (V1)
P1.V1 = P2.V1 + P2.Vlt V1 = (P2.Vlt)/(P1-P2) (75 lb/in.in).(4,522 in.in.in) Vlt = ------------------------------ (125 lb/in.in - 75 lb.in.in) Vlt = 6,783
If we use 6 inch diameter PVC for the gas storage tank then the cross sectional area is
A = PiD.D/4 A = 28.3 in.in
and the length is
l = V/A = 6,783 in.in.in/28.3 in.in l = 240 in or 20 ft
Making both of them the same length makes construction and stiffening simple. It also allows the use of a little lower pressure or gaining higher velocity. Sufficient volume could also be obtained by using two 4 inch tubes.
Next you need a valve to go between the gas storage tank and the launch tube. You need a valve that is at least the same size as the launch tube or you will choke off the air flow.
Next you need to provide a way to pack the rocket into the launch tube. If the rocket fits nicely (no fins sticking out) into the tube then all you need is a pusher plate. You may want to build up in speeds with dummy rockets to make sure the pusher plate holds up. Otherwise, you might drive several hours to the launch site only to have the pusher plate shred before the rocket leaves the tube.
If the rocket fits loosely in the tube then you may need to form a sabot around it with some stiff foam packaging, styrofoam, or other suitable materials.
Next you need a way to keep the PVC standing straight up. If there is a convenient telephone pole, tree, or building handy then the launch tube and gas storage tank could be attached to those. Other means are guy wires or truss frames. There is a type of antenna tower available for amateur radio and television antennas that telescopes up.
This is a Mach 2 exit velocity launch tube, serious stuff. If not for air friction the projectile would coast to over 60,000 ft even without the rocket firing. This is twice the altitude of commercial aircraft. If the rocket adds another 1,500 fps then the rocket could coast to over 190,000 ft or 36 miles. A rocket that adds 3,000 fps would coast to over 388,000 ft or almost 74 miles. If a ramjet stage is added to take the rocket to 100,000 ft altitude and 5,000 fps followed by an additional 3,000 fps from the rocket the rocket would peak out at over 200 miles. This is where the Space Shuttle flies.
Basic AssumptionsFor this we'll use the following parameters.
f = pA = p(PiD.D/4)
(180 lbf/in.in)x(3.14)x(8 in)x(8 in) f = ------------------------------------ 4 f = 9,050 lbfLaunch Vehicle Acceleration
G = 9,050 lbf/45 lbm = 201 g a = (201 g)x(32.2 ft/sec.sec.g) a = 6,480 ft/sec.secTube Length
s = v.v/2a (2,000 ft/sec)x(2,000 ft/sec) s = ----------------------------- (2)x(6,480 ft/sec.sec) s = 310 ftLaunch Vehicle Travel Time in the Tube
t = v/a t = (2,000 ft/sec)/(6,480 ft/sec.sec) t = 0.31 sec
This is tall but manageable. This would be a good candidate for launching from the ocean. Once loaded, the breech end of the launch tube could be sunk in 290 ft of water leaving 20 feet sticking out. The water around the tube would help keep the expanding gas from cooling too much. The ocean bottom (hopefully bedrock) will take up the recoil.
Gas Storage RequirementsNext we need to know how much gas to purchase.
We know by the following formula that the volume of the launch tube is
Vt = Al = (PiD.D/4)x(l) (3.14)x(8 in)x(8 in)x(310 ft) Vt = ----------------------------- = 15,600 in.in.ft 4 (15,600 in.in.ft) Vt = --------------------- (12 in/ft)x(12 in/ft) Vt = 108 ft.ft.ftTank Volume (V1)
P1.V1 = P2.V1 + P2.Vt V1 = (P2.Vt)/(P1-P2) (180 lb/in.in).(108 ft.ft.ft) V1 = ------------------------------- (2,400 lb/in.in - 180 lb/in.in) V1 = 8.8 ft.ft.ft
Converting this to scf
P1.V1 = P2.V2 V2 = (P1.V1)/(P2) (2,400 lb/in.in)x(8.8 ft.ft.ft) V2 = ------------------------------- (14.7 lb/in.in) V2 = 1,440 scf
This means that more than one 1,100 scf bottle will be needed. In fact, in order to keep the gas flowing at high enough velocity we would need two 1,100 scf bottles. This will probably cost a few hundred dollars but probably less than 10% of the cost of building the launcher.
This Page Last Updated 26 Nov 98