This page is to show a method of finding the optimum length of a launch tube to match a tank/valve/pressure combination for launching shirts.



Theory
In theory a tank and valve has a finite ability to produce an air flow. The flow is limited by several parameters. This includes the volume of the tank, operating pressure, valve opening time, and flow restriction when open. To try to model the perfect length is pretty much impossible for the average high school student and many college grads from engineering. As a technician, I took a different approach. The cut and try method can easily waste a lot of supplies and money. There had to be a better way. If there was an easy way to clock a shirt through the entire in barrel launch, parameters such as a terminal velocity being reached prior to reaching the muzzle, loss of speed due to depletion of air supply, or slow acceleration from a slow valve could all be seen and adjustments made.

Taking something I know and apply it to the task may provide a solution.

When a magnet passes the end of a coil of wire, the magnetic flux lines cross the conductor and induce a voltage. When a magnet passes through a coil of wire, a voltage is generated as flux lines cross the wire as the magnet approaches and the opposite polarity voltage is generated as the magnet leaves out the other side. In the middle the voltage crosses zero in a rapid change from magnet entering to magnet leaving. Nice, we have an easily identifiable marker of when the magnet crosses the center of the coil. Voltage is created only when moving flux lines cross the conductors.

Testing

To test the feasibility, a simple test was performed. A loop of wire was quickly tossed together larger than our largest barrel, a 4 inch foam ball launch tube. We wanted to see if a small magnet is easily detected falling through the coil. With the use of an oscillioscope, a small neodymium magnet was dropped through the coil. It was sucess at first try. We captured a trace with a classic s curve as expected.
magnetic_pickup_test1.JPG
Initial magnet coil test. Edge of coil and small magnet used


Encouraged by the initial test, the test was expanded to try a multiple coil pickup to time coil crossings. For this a short piece of 2 inch pipe was used and several coils were placed evenly spaced and connected in series with all the coils turning in the same direction. They were all wound in the same direction so the voltage pulses would all be the same polarity for easy measurement. Again a drop test was performed with great results. A nice effect was seen as a bonus. We tested the coil / pipe standing on end on the carpet. The last coil was on the carpet, so the exit was blocked. We saw a distorted wave form as the magnet struck carpet and bounced, and got another trace as the magnet fell to the floor again. We have the bounce time.

Another shot was done without the bounce to expand the display for easy measurements. The horizontal axis for each square is 25 ms. You can measure the time between each center of the s curve to find the times for travel every few inches of distance. This is a shot of acceleration by gravity. Using gravity acceleration and working backwards a good student can calculate how high above the first coil the magnet started from and what coil spacing was used for this shot.. I needed good motion on the first coil to trigger the scope. I believe gravity accelerates objects at about 32 ft/sec squared before wind resistance becomes a factor. Arlington was given this type of print to calculate speed and acceleration of various barrel and pressure combinations.
web_4_coil_drop.jpg
4 coil test drop


The ability for the student team to perform measurements without a scope was considered and a solution was found. Use audio recording software that permits expansion to the sample level and take the times of the crossings. An open source program called Audacity was tested and found to work well in place of an oscilloscope.. My laptop has a dead light in the screen, so for my testing, it's simply easier to use the scope and printer instead of lugging a desktop and monitor out to the test site. Audacity is free and can be downloaded in either Windows or Linux versions. I am using the Linux version on Ubuntu Studio. Here is the test with a sound card and Audacity showing the magnet bounced off the carpet. The time line is above the traces. The last downward next to the 4 coil blips is the magnet returning back up after the bounce. the last blip on the right is the magnet falling back through the last coil. the wiggle after that is the magnet again returning back up on the second bounce. Not shown is the last fall through the coil. Using the time between the two bounce coil crossings, you can find the "air" hang time and find the height of the bounce. Check with your physics teacher if you need help figuring this. A hint is given in the wiggle in the line directly between these traces. The magnet bounced high enough to be detected by the coil above the bottom coil. At slow speed, it may have even passed through it. The distortion to the classic s curve is from the AC coupling provided by the microphone amplifier. The frequency response is not flat down to 0 Hertz. Later traces using a microphone mixer to pre-amplify the signal exhibit this distortion.

SoundCard1.png
Magnet drop with sound card capture in Audacity


Audacity has the ability to zoom in to get fine measurements. The crossings at the ends of the highlighted area can be zoomed in for very precise measurements.
SoundCard3.png
Audacity software




4 coils on a tube for test drops.
web_4_coil_drop_tube.jpg
4 coil test setup


Here is a sound file of a magnet dropped in the 4 inch launch tube. It includes the magnet bouncing off the carpet and bouncing back up through the last coil, hitting the next coil up and falling again to the carpet with another bounce. The bounce does not have a classic s curve on the way back up because after the bounce, the magnet picked up a spin and rotated on the way up.
The wiki is hiding the uploaded MP3 file behind an embedded player. Use the envelope at the top of the main page to email Technician and ask for the MP3 files. Send your school or home email address to send them to. Open it in Audacity or other sound editing software to see the waveform and get the coil crossing times. This is what our raw data looks like for some launches. Arlington was sent some MP3 files to measure instead of printouts. Can you measure the time it took for the magnet to go the last foot before hitting the carpet. How long was it airborne on the first bounce? What is the time to cross between all the coils. How far above the first coil was the magnet when it was released?





Implementation

Since we were designing the launcher to compete in the 4 inch foam ball competition, we sized the tank to supply the air needed for a good launch. With a 700 cubic inch supply, math for a 1:1 volume ratio tank to launch tube would mean a 4 foot tube would be ideal, but is it the best?

It's time to find out. A longer tube was constructed to measure and trim if needed. To provide the volume at the velocity needed in the 4 inch tube through our 2 inch valve, we noted we needed the valve to supply air at 4X the rate of our launch as the area of a 4 inch tube is 4X that of the 2 inch valve restriction. With the restriction in mind we expected to see a terminal velocity rapidly achieved, and then maybe a drop as the supply pressure drops. The intent is to trim the tube at the max velocity point where the acceleration diminishes.

Test site as used for testing foam ball launcher
web_4_inch_test_site.JPG
Test setup

Coil Detail
web_4_inch_coil_detail.JPG
Coil detail and foam ball

Test equipment desk includes scope, printer, and audio mixer to pre amplify the coil signal. The wimpy single coil trace is from a very low pressure test shot.
web_4_inch_test_equipment_detail.JPG
The essentials - Scope, Printer, Mixer, Paper, Pens, Safety glasses


Results
I assumed the higher velocity would provide lots of voltage from the high speed. To save wire the coils were drastically reduced in the number of turns. As a result the initial tests failed to trigger the scope and produce a graph. Grr.. Knowing the signal was there, but too low in amplitude, I knew I needed to either re-wind the coils, or amplify the signal. I had a disk jockey style mixer floating around so I grabbed it and used it to pre-amp the coil by feeding it into the microphone jack. It worked like a charm. After tuning the launch tube to length for a 60 PSI shot, the trace shows acceleration the entire length of the launch tube with a noticeable drop in acceleration along the length. The exit point is now at the peak speed. Taking the time to cross the last two coils shows a speed of 454 FPS. A field test shot produced a launch of over 300 feet with a foam ball.

Here is a video of the 4 inch foam ball launch at Arlington.

As a pleasant surprise, the optimum length was not 4 feet, but 5-1/2 feet. The trace also shows that after the first coil is crossed, the acceleration is already starting to drop, which is good. It shows the valve is not still opening. After the first crossing, it is wide open. Using a french curve and using the peaks of the traces, the expected zero speed point can be found. The first coil is detecting a voltage at this time, indicating the valve is in motion. The starting time of the motion prior to the acceleration curve crossing zero, shows the valve opening time. It looks to be under 1 ms. This is the ideal launch tube length for this pressure, valve, tank, and load. Muzzle exit is at peak speed.

web_60_PSI_Foam_ball.jpg
60 PSI foam ball launch from 4 inch tube after trimming. There is almost no speed increase in the last foot


The circle on the ball is there to show me where in the ball the magnet is located so it is launched with the poles on axis of the launch tube.. A sideways magnet won't be detected. A slit was cut in the side of the ball and the magnet was shoved into the middle. The slit was filled with bathroom caulk and squeezed back out and let dry. A pocket compass was used to find the orientation of the magnet and the pole was indicated on the ball with an ink pen. The ball is loaded with the circle mark facing forward. I'll plan on bringing the ball to the game for examination. The ball is tough and is intact even after cracking my bucket.

Bucket_Sandbags_Foam_Ball.jpg
bucket, foam ball and magnet pole mark


Next on the list of to-do was to work on our shirt launch tube. Which is better with our tank, a 2.5 inch tube or a 3 inch? Maybe a 4 inch. The 4 inch tube was already wired up and ready to go, so a series of shots was taken at various pressures with a tightly rolled shirt with a shop towel over the end as a sabot. The added mass was apparent as the launch speeds were much lower than with a foam ball. A 3 inch and 2.5 tube were tested and the results compared. Both easily beat the 4 inch by a long shot because the 2 inch valve was too restrictive to provide the flow needed to fill the 4 inch tube. Terminal velocity was reached very early. The 1:1 volume ratio for 2.5 and 3 inch tube is over 10 feet. Knowing the longer tube worked well with the foam ball, a 10 footer was tested with the shirt. We found head loss in the smaller diameter pipe produced a terminal speed for the shirt with little to no acceleration in the last 4 feet. It is time for the saw. This terminal velocity was not expected at less then a 1:1 tank to tube volume ratio, but it is clear to see the lack of acceleration in the last few feet in this graph.. Other teams were reporting little gains in longer launch tubes. Our graphs confirm it. This photo is of the last of the coils. This 10 footer has 11 coils. The first is used to detect initial motion. From this graph, it is clear we are not getting the mega acceleration expected from our air supply and a 10 foot acceleration tube. The 3 inch tube did much better. From this we trimmed a 3 inch tube and moved on to flight tumble problems. This shirt is traveling a lot slower than the foam ball in the 4 inch tube.


websize_50_PSI_T_Shirt_2.5_inch-a.jpg
Expanded end section of 10 foot 2.5 inch tube shows little acceleration in the last 4 feet. The last coil was in the opposite direction as an identifier


After changing to 3 inch and trimming, we got a lot better speed at the same pressure. For comparison, here is the 50 PSI graph for a 3 inch tube showing acceleration all the way to the muzzle.
web_50_PSI_3_inch.jpg
3 inch 50 PSI t shirt launch. Exit is over 300 FPS.




We have a full set of graphs from 10 PSI to 60 PSI every 10 PSI for the 2.5, 3, and 4 inch tubes.

Grab a free copy of audacity, a magnet from a broken i Pod headphone, some wire, a laptop, and post your launcher's results. We used 1 foot spacing for easy math. The inverse of the time is FPS. In the trace above, the time between the last two pulses is 3.2ms as indicated by the on screen cursors. This is an average of 312.5 FPS between the coils. Not all graphs were supplied to the school with cursor marks.

This is a recording of the tank and valve at 50 PSI to show the time it takes to dump the tank contents. The high speed video on the photos page and this sound with Audacity were used to figure out the tank can deplete a full charge in under 20 ms.


The wiki is hiding the uploaded MP3 file behind an embedded player. Use the envelope at the top of the main page to email Technician and ask for the MP3 files. Send your school or home email address to send them to.

Data by Technician. Analysis by Arlington team and Technician.