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# Antenna Launcher Modelling

This article will discuss some aspects of mathematically simulating the Tennis Ball Antenna Launcher performance, some results, and finally some software that you can use to do your own calculations.

## Antenna Launching

To Launch an Antenna we first Launch a light line over or into a tall tree using a Compressed Air propelled Tennis Ball. The Tennis Ball was selected for safety and simplicity and has been found to be more effective than Archery or Slingshots. Next we pull a light line such as nylon mason twine that either supports the end of a wire or we pull a heavier line for supporting beam type antennas. Two supports are generally used with the antenna in between.

## Brief History

We have employed Archery gear to launch antenna lines for many years. We have tried slingshots, both commercial and homemade. This is about a much more powerful technique, while at the same time more controllable and safer. It does not require a lot of strength, or a large investment.

Eric, WD6CMU and I had been discussing ways of improving our Antenna Installation system for Portable Operations including Field Day. Archery and Slingshots are often illegal in the backyard, and we wanted a system that could be used near home as well as far afield. Launching a Tennis Ball seemed the way to go, as the projectile has a great deal of safety built-in.

After Eric, WD6CMU built a Pneumatic Tennis Ball Launcher based on information he found on the net he then measured the velocity performance over a range of pressures (see his website link below). Armed with this data, and basic Physics, I attacked the work of simulating the system mathematically in a computer model. Using the data I was able to calibrate the model, and judge its correctness over the range of pressures.

This is primarily about the software that models, or calculates the effects of the system variables. It allows many more experiments to be performed with little cost or effort. It shows performance and predicts behavior of the system. It allows us to build a better system.

## Pneumatic Launcher Modelling

Initially I tried computing the acceleration on the Tennis Ball using the pressure times volume = pressure times volume relationship. I note that many of the programs I found on the net do just that. Comparing with Eric's measured data we find that isn't even close to reality. It turns out that a portion of the airflow in the valve becomes supersonic at modest pressures and this limits the flow rate. This requires an interesting formula to compute the airflow. Thanks to John Bercovitz for help with this - The formulae are well developed, the important ingredient being the valve flow capacity (also called conductance), or Cv. After adding that equation to the basic physics for pressure, acceleration, etc. I was able to get a model that fit Eric's data pretty well. You can see Eric's data on his web page for the G2 Launcher.

Then I played with it. A lot. Tried different chamber sizes, numbers of valves, and barrel lengths.

I noticed that a lot of folks worry about the Ratio of the chamber to the barrel volumes. I found that this ratio doesn't make much difference unless you have a really good valve. And with Tennis Balls, you often don't have a good valve. The problem is that a moving 2.4" diameter Tennis Ball sweeps a large volume quickly, and the generally much smaller valve cannot flow enough air to 'keep up' very well. As the Ball accelerates it takes a great volume of air to keep the pressure (behind it) up, and the Valve is generally the limit. A 3/4 inch electrically operated sprinkler valve is poor. Two 1" sprinkler valves modified for Pneumatic Actuation are fairly adequate. One 1" sprinkler U-valve does work, though it requires more pressure and will not reach the high performance of the dual valve. Note that even with the dual valves much of the chamber pressure doesn't make it into the bore while the tennis ball is still there. Look at the exit bore pressure and exit chamber pressure. Note also that often (especially with longer barrels) the bore pressure is negative at exit! The momentum of the tennis ball is starting to draw a slight vacuum!! Note that any exit bore pressure less than about 2 psi indicates the ball is slowing down - the bore is too long. Note that the bore drag is about 10 pounds (measured) and the ball area about 5 square inches, so it takes about 2 psi to balance out the bore drag. But we are getting ahead of ourselves. Let's look at some modelling results.

## Examples

Eric asked me to put in some graphs to make this more understandable. There are many parameters, so I'll have to make some assumptions to make this practical. These calculations are based on the "Field Day Special" Launcher. The launcher is described in the Performance Data section of this web. It is a basic over/under design with 2.5" barrel, 3" chamber, and the valve is a 1" Rainbird operated Pneumatically. The configuration puts the valve in the barrel section and leaves 2" or more of barrel protruding to mount the reel that holds the line being launched. The default configuration is 24" bore and barrel, though other configurations are considered variations on the model.

The following graphs are computed using the modelling software. Differences from measurements will be discussed.

The first graph is for the 24" barrel and 24" chamber version of this Launcher, which is what we built a couple of in 2003 for Field Day. We don't have performance measurements yet, but they did work well. Rich WA6FXP built one, and he indicated that at 20 psi the ball barely launched, but at 40 psi it hit the far fence in his back yard pretty hard. These heights are for a slightly weighted 4 oz Tennis Ball. So, let's take a look at Pressure versus Height for different values of Valve Conductance (Cv):

### Launch Peak Height versus Pressure for various System Conductances (Cv)

Valve vs System Cv - The valve isn't the only element that determines the system flow. Other piping, elbows, etc matter as well. So the Cv that we are looking at is affected by the system design. Also the rate at which the valve opens affects the Cv. The same valve operated electrically vs pneumatically can have dramatically different performance. The electric solenoids have small apertures and release pressure slowly. The pneumatically upgraded valves have large apertures and the air operating the valve is exhausted quickly. The slowness of the electrical valves is intentional by the manufacturer - to protect plumbing from shock in the sprinkler system.

Manufacturers specify Cv for air valves. They don't generally specify it for sprinkler valves. In any case I have not found their values to agree closely with my modelling calculations. They measure Cv at a small pressure drop with a moderately low flow. We launch Tennis Balls with a very high turbulent flow. So it is really a different operating regime.

So what values of Cv are to be expected for our Launchers? First, a couple of comments about my experience with Cv and fitting to measured data. The Cv value isn't quite constant. It changes slightly with pressure and chamber size. Perhaps due to the springs in the valves, or the turbulence, or variation in bore friction, or the model's inaccuracies. So don't assume that your Launcher will have a Cv that is totally constant, or that performance will lie exactly along one of these lines. Smaller chambers generally yield lower Cv values. So do lower initial launch pressures. Typical behavior is for the Cv to increase by a point or so from low to high pressures.

The graphs show Cv for 4,6,8,12,16 and 20 Gallons per Minute per PSI pressure drop. (Sorry, but those are the 'standard' units for Cv). How do these numbers relate to our measurements? A good 1" electric sprinkler valve is around 4 on this scale. The same valve modified for pneumatic actuation is around 6. Two in parallel is around 12. And I'm guessing that a good piston or diaphram valve is more like 20 or more, but that's just a guess.

The Cv of a valve is roughly related to the cross sectional area of the open valve. So you might expect a 3/4" valve to have about half the Cv of a 1" valve. Two valves in parallel have about twice the Cv of a single one.

Now what happens if we change the size of our launcher. We will continue to use the Field Day special with a single 1" valve. I assumed a Cv of 6 for this exercise. We've measured values of about 5 to 7 for this case. I varied the 'overall length' of the launcher which changes both bore and chamber length to see what happened. The 'chamber' to 'bore' ratio would stay roughly constant. I also show the 24"/24" model, and a set of values that would maximally fit within the overall length.

This graph shows variants starting at 14" chamber and 11" bore and go out to 30" chamber and 27" bore. Note that the performance at the low end is about the same for all models. As the pressure is raised the longer bore becomes an asset instead of a liability, and the increased chamber volume helps as well.

It is interesting to note that the performance doesn't really change all that much for these different sized launchers. Unfortunately this doesn't quite match reality as we've measured it. There are other effects which tend to make the smaller launchers underperform somewhat more than is indicated here. My theory is that the lesser flow fails to open the spring-loaded valves as far, so the effective system Cv drops somewhat for small pressure chamber volumes.

So we have shown that the system conductance, dominated by the valve, extremely important to performance. It has a much larger effect than increasing both the bore length and chamber capacity.

But -- how much performance is adequate? One important thing to keep in mind is the application of the Launcher. Antenna setups do not require a lot of performance. Eric's big launcher can do the job at 25 psi or so, and is capable of 100 psi. The electric U-valve model has plenty of performance for antenna launching at about 60 psi. The pneumatic version works adequately at 40 psi. In terms of height, 150 is generally adequate and 200 feet might be required for the occasional longer range launch.

## Internal Ballistics

The modelling software works by computing the amount of air that passes through the valve every 100 microseconds, subtracting the from the pressure chamber and adding it to the bore. The force on the Tennis Ball is computed, the net acceleration, velocity, and new position. New pressures are computed for the bore and chamber. This is repeated until the ball leaves the bore. This allows us to see what is happening in some detail. The next graph is for a 40 pound launch in the FD Special 24" bore 24" chamber Cv=6 valve as before:

Time in milliseconds is on the horizontal axis. The dark blue line shows velocity which rises quickly, nearly flattens out, and then drops very slightly. The light blue line shows chamber pressure which drops from the initial 40 psi gradually down to 30 psi at muzzle exit. The yellow line shows bore pressure which rises to a peak of about 25 psi and then drops to about 1 psi at exit. The pink line shows bore position which starts at 1.2 inches (half the ball diameter) down the bore and progresses to 24 inches at exit. The exit velocity produced a height of 143 feet, very typical for antenna launching applications. This is with a 4 oz tennis ball.

It is evident from this graph that the valve is not flowing enough air to really utilize the chamber and barrel in this launcher. Essentially full velocity has been reached at 12 inches down the bore, and only about 5 psi of the 40 psi in the chamber were applied to the ball in the 150 milliseconds it took to get that far. At that point the bore pressure had fallen off to about 7 psi and acceleration after that was negligible. In fact, the ball slightly decelerated just before exiting the bore.

Chamber to Bore Ratio is often discussed, but as can be seen by this modelling, this isn't a very good indicator of performance. Note that after the first 12 inches of bore in this example, making the bore longer has little impact on performance, but it would change the ratio numbers significantly. Note also that increasing the chamber capacity beyond the example will only provide a small improvement - as during the acceleration phase only 5 psi was dropped in pressure. There's not a lot of improvement available there. Depending on the conductance of the valves, most of the chamber pressure may never make it into the bore. When the system is valve limited, increasing the chamber size helps only moderately.

Eric's G2 Launcher has more bore length and more chamber capacity than is required for antenna launching. The goal is to carry a tennis ball with light line over the tree. His system easily sailed over 100 foot trees at 25 psi with lots of room to spare. Operating at such low pressure does promote safety - the stress on the PVC is very low. It also makes the Launcher large and heavy.

## The Bottom Line

For Antenna Launching only very moderate performance is required. Even a very small launcher with a 1" valve can reach this level of performance. Building the launcher larger allows operation at lower pressures. The point of diminishing returns (according to this modelling computation) is reached at about 22 inches of chamber and 19 inches of barrel with the Field Day Special design (Over/under with 1" valve on the barrel side of the U). This configuration should reach 150 feet at slightly less than 45 psi, and 200 feet around 55 psi.

## Running the Pneumatic Launcher Modelling Software

"Compressed Air Launcher Modeler, Interactive" - calmi.py

Now let's get to the good part. You can run this program with different values and see how well the system will work at different pressures, with different weight projectiles, and with different valves and barrel lengths.

This program computes the performance of a system consisting of an air pressure storage chamber, a valve, and a barrel for accelerating a projectile. It has been compared to data from actual measurements and found to be fairly accurate - far more than other simpler programs that were tried from the internet. It requires that you know (or estimate) the pressure chamber inside diameter and length, the barrel length and diameter, the projectile weight, the bore friction, and the valve flow capacity (or meausured velocity). If you have measured velocity you can compute the flow capacity. If you don't know the flow capacity, estimate it and try a few different values to get an idea of how the performance might be.

This program has a very simple user interface. It has two basic functions - one is to compute Cv values given the physical characteristics of the launcher and a measured velocity. The other is to produce a table of various information at a number of different pressures. The information includes velocity, barrel time, exit bore pressure, exit supply chamber pressure, approximate straight-up launch height and total time of flight.

The sytem flow capacity (Cv) is dominated by the valve. We have fitted Cv data from Eric's second prototype launcher, and the 1" Rainbird straight-line valves seem to have Cv values in the 5-6 gpm / psi range (improving slightly as the pressure goes up). Eric modified his valves for pneumatic actuation, which improves their flow rate over the stock electrical triggering. Using two valves in parallel yields nearly twice the Cv. Commercial air valves will have Cv ratings in the specifications, but these are 'best case' values and should be derated some before using in this program. The best procedure is to measure the velocity at every ten or twenty psi pressure and then compute Cv for your actual system. If you don't know the Cv precisely then compute system performance for a range of Cv values in the neighborhood and see how it affects system performance. Small changes in Cv make small changes in performance, so you still get a good idea of whether chamber capacity and barrel length make sense for the system.

To use the program, download it, saving to a file. Decompress by double-clicking on the zipfile (requires a zip decompressor program installed such as WinZip).

Download and install Python (links below). The Python interpreter is required to run the software.

Double-click on the calmi.py program file to run it. If there is an error it will disappear too quickly to read the message. In this case run a command window, cd to the directory where the program is, and run it by typing the program name. This will allow viewing the message(s) after the program quits.

Calmi Program Menu described

```-1  exit  quit the program
0   vel   compute the velocity from physical parameters
1   Cv    compute the flow (Cv) from physical parameters and measured velocity
2   Key   display the variable and column name descriptions
3   U37   compute the data for the U37A launcher
4   DV54  compute the data for the DV54 launcher
5   QE20  compute the data for the QE20 launcher
6   EgCv  compute example Cv values derived from DV54 measurements
```

## Safety

Putting compressed gasses into PVC pipe is not an approved use. If the PVC fails it can create PVC shrapnel that the compressed gas can accelerate to high velocities. If you choose to experiment with compressed air in PVC make sure to use eye protection and maintain adequate safety margins. Only use Pressure Rated new materials and fittings and the recommended fresh primer and glue. Follow all glueing procedures (especially surface preparation and drying times) and proof test at about 25% higher than planned operating pressures with extra protection (such as wrapping it in a heavy blanket) in case of failure.

Another thought - I plan to stay away from combustion type launchers. Compressed air is very predictable, and the pressures will only go down when the valve is opened. Combustion produces unknown pressure peaks, and igniting stuff in the National Forest seems like a poor idea anyway...

Another launcher modelling tool is available called the Gas Gun Design Tool. This graphical program has a very nice user interface. It is written in visual basic and the author does not release source code. It is available direct from their website (see link below).