Step 6: Speed testing

Picture of Speed testing
Cannon 3 004.JPG

Since I earlier made rash claims about shooting ping pong balls at supersonic speed, I need to describe how these speeds were measured.

I made a "ballistic pendulum"; a device once used to measure  muzzle velocity of rifle bullets, but now mainly used in physics classes to demonstrate the principles of conservation of momentum and energy. The projectile is shot into a block, and is retained inside the block. The block + projectile then swing due to the momentum of the projectile. The vertical height gain of the block is measured, and when multiplied by the mass of the block + projectile, represents potential energy increase. Using the following equation gives the velocity of the projectile:

Velocity = (m+M)/m (√2gh)

m = mass of projectile, in kilograms (ping pong ball mass = 2.4 g = 0.0024 kg)
M+m = mass of projectile, in kilograms (1.32 kg)
g = acceleration of gravity, 9.81
h = vertical height gain, meters, less height gain from air only tests. (2.5 cm = 0.025 m)

The numbers in parentheses are the average values from my tests.

“A ballistic pendulum is a device for measuring a [projectile's] momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity. Although the ballistic pendulum is considered obsolete, it remained in use for a significant length of time and led to great advances in the science of ballistics. The ballistic pendulum is still found in physics classrooms today, because of its simplicity and usefulness in demonstrating properties of momentum and energy.” (From Wikipedia).

Photos below show the ballistic pendulum I made (along with a view of my screwdrivers and chisels).
The lines on the panel in the background are to measure height, in centimeters.
The laser pointer shows height of the block. In the photos, the first shows height before firing, the second shows maximum height just after firing. A video camera records the action.
The last photo shows the ping pong ball caught in the block.

In addition to momentum from the ball, there is momentum transferred to the block from the air exiting the cannon. I made some test runs using air only and subtracted this average height (0.03 cm) from the tests with ping pong balls.

Light_Lab2 years ago
I like this Instructible a lot, so elegant in it's simplicity. I can suggest a few things from my experience with vacuum apparatus. With regard to the quality of the vacuum you are possibly worrying too much; the driving force for this is the pressure differential between atmospheric and the ~vacuum. There is not much difference between 14.9999 PSI and 14.9psi or for that matter 14.8psi. I wonder how well a modified electric tyre pump would work.
When I was doing ballistic research ~40 years ago we did extensive work with ballistic pendulums in comparison to a recently developed ballistic chronograph. We made ~ 100 pendulums of different designs and tested numerous firearms from air rifles up to high velocity hunting rifles. We found a very poor correlation between the pendulums and the highly accurate chronograph.
The reason was well known: the incomplete transfer of kinetic energy from the projectile to the pendulum. Using your device as an example: if the ping pong ball was not complete and round after the collision then part of the energy has gone to destroy the ball. We tried all sorts of bullet catchers: ballistic gels, cotton battens, sand, water sawdust etc with out much success. The interesting thing is that the pendulums always gave velocities lower than reality in our results!
Your device is an example of a pressure wave device; just like an organ pipe the air pressure is not distributed evenly along it's length at any time during firing. Yes, as some have pointed out, the air can't enter the tube faster than the speed of sound but we are not dealing with the speed of sound at atmospheric pressure.
The ball has inertia so the incoming air momentarily compresses behind the ball and then re-expands like a spring as the ball moves. All pressure wave devices from a two stroke engine exhaust, though pneumatic hammers to organ pipes are tuned for best performance. I believe that  the length of the tube and the position of the ball have a 'sweet spot' where best performance will be obtained.
It would be very interesting to use clear tubing, apply a smoke source near the inlet end and video it with a high speed camera.
Thanks for submitting. 
Bill WW (author)  Light_Lab2 years ago
Thank you for your comprehensive analysis, Light_Lab.

You said "The ball has inertia so the incoming air momentarily compresses behind the ball and then re-expands like a spring as the ball moves." Great observation, I had been wondering about that!
I plan to go to a local industrial supply store to get transparent PVC pipe; I know it is available. And will also look for high speed video camera.

I have several Aussie friends near Townsville, got my master's degree from James Cook University.
Even though Townsville is in Queensland and I live much further South in Victoria, I have many friends and contacts that went to James Cook. Even the daughter and nephew of our Pastor went there. I think a lot of young people like to go there because of the proximity to the Gold Coast.
Usually transparent PVC is flexible tubing (plasticized) you might have to go for acrylic (perspex) or polycarbonate tubing and it could be expensive.
Another variable is the weight of the ball; a syringe with a fine needle might enable water to be injected into the ball to enable the weight to be varied. (Bryron asks that too.) I imagine the hole could be sealed with super glue or tape. More weight, more inertia, this would effect both the compression wave and the initial acceleration. I would expect that over a limited range of weight increase the velocity would be approximately the same; but the peak barrel kinetic energy would increase proportionally. This should have a marked effect on muzzle velocity as there must be a considerable loss of energy as the lighter ball bursts through the second membrane, and is no longer accelerating into a vacuum but now into a cushion of air.
Casio makes a series of low cost high speed cameras that go up to 1000 FPS (at reduced resolution):
You can also use a high speed camera to get an estimate of the muzzle velocity.
I noticed you mentioned, "academic papers give the theoretical maximum of the vacuum cannon as Vm = √(P/ρ), where P = pressure; ρ = gas density."
Any chance you can give a link to those papers? I would very much like to read them.
Bill WW (author)  Light_Lab2 years ago
Thanks for your ideas and comments.

I may experiment with the higher mass ping pong balls, will first find a way to measure speed and/or take high speed photos. Thank you for your link to Casio.

My professor of astronomy at James Cook was Wayne Orchiston.

Here is one paper:

And here is the other:

thanatos3702 years ago
Have you ever considered using a denser projectile, like a golf ball? I'm interested to see what that would do, both to a target and to your speed measurements. . .
Bill WW (author)  thanatos3702 years ago
Thanks for your comment.

Have had that suggestion, golf balls, potatoes, etc.
A golf ball has a diameter of 42.7 mm,too large to fit into the 1 1/2" sch 40 pipe (ID = 40.9 mm).
So, perhaps fortunately, can't try this without different pipe.
MrPTrog2 years ago
My local gun range/gunsmith has a chronograph that would end this debate over speed. I'm sure one close to you does too.
I'm curious about range. I'm sure the ball bleeds off most of its speed quickly. How far have you shot one?
Bill WW (author)  MrPTrog2 years ago
Thank you, MrP -

Good idea, the shooting range chronograph. Looked it up online, there seem to be many available. Will be giving it some thought.
Regarding range. So far I have only shot it in my shop, limited to a few feet. I plan to set it up in the garage, pointing out the door, and test range. Of course my wife thinks I'm nuts. I will do this when she is gone somewhere.
The light ball slows down quickly, I'm sure. The kinetic energy will be converted to heat energy from air friction, so I will see if the ball warm up.
flatboat2 years ago
An added note on the speed of sound of the propellant limiting projectile velocity: light gas guns use helium to accelerate projectiles to 7 km/s when labs try to understand space debris and meteoroid impacts. The helium accelerates projectiles much faster than normal propellants. The speed of sound is roughly proportional to square root of compressible modulus divided by density. Most gasses have about the same modulus but the low density of helium raises the speed of sound and thereby projectile velocity. A normal explosive is used with a piston to get the helium to a high pressure.
Bill WW (author)  flatboat2 years ago
Excelent point, flatboat, thank you..

The academic papers give the theoretical maximum of the vacuum cannon as Vm = √(P/ρ), where P = pressure; ρ = gas density. So with a less dense gas like helium, max speed would icrease greatly!
flatboat2 years ago
Great instructible! But I have to comment on velocity measurement. The air accelerating the ball in the tube cannot push the ball faster than the speed air can flow into the tube. The speed of sound limits the applied pressure and therefore the maximum speed of the projectile. How can the ballistic pendulum and your correction be in error? My theory ( unverified) is that as the ping pong ball enters the tube it accelerates air out the back like a rocket. The ballistic pendulum works by absorbing the momentum of the ping pong ball and having no rebound effects that could double the energy. Could a screen on catcher end of pendulum change the result? Otherwise I have to go with your calibration not catching air pressure from the gun as previously suggested. Great work and this presents a challenging thought problem on how to reconcile ballistics limitations in the gun with the pendulum measurements. Thank you!
madenairy2 years ago
any chance of doing an instructable on making / calibrating a ballistics pendulum?
Bill WW (author)  madenairy2 years ago
Yes, but it is mostly described in the speed testing step.

You might want to check out this site:
Great indestructible.

You built a vacuum canon that was within the means of someone of most people and it worked as promised.

I really don't get though why some are obsessed with you perfectly measuring the speed. You didn't promise to build one that would meet the specs for something being built for Fermi.and then prove its worth by send ping pong balls along at exactly X speed.

Maybe if you had included "approx" in your speed measurements you would have avoided a couple of the questions. LOL
mdeminico2 years ago
Cool instructible. I'm not entirely sure though that your "calibration" test with air only is equivalent to the force being imparted by the ping pong ball plus the air. I believe air exiting the cannon will behave differently in the presence of the ping pong ball than it will without the ball. The ball will create a vacuum to some degree to pull the exiting air right along with it, somewhat focusing the air.
Very Nice atm gun. We have a similar cannon here at Cal Poly Pomona. We got to film it last year in high speed. You can check it out at http://www.youtube.com/watch?v=5h3Ak10GsXk. We made a can holder to hold three cans in a row. We found that mylar balloons to be great to cover the ends of the tube. We have never measured the speed but have heard that it averages around 300 m/s. I wonder if you could measure the speed by measuring the sound? Maybe having a oscilloscope capture the sound of the air rushing by then the ball? On our video you can see there is a compression of the can before the ball even hits it but just seconds... so almost supersonic.
perfo2 years ago

Great ideas. Even though I'm well aware of the effects and problems with sudden release of a vacuum I'd never thought about using it like this, so thanks. Out of interest a standard fridge or freezer compressor will pull a pretty decent vacuum if you connect up the intake side of it. They may not last fantastically long but are normally get hold able for nothing and can be made to last if you want to fiddle with lubricators etc. As for the ballistics pendulum I'm not expert but I would be concerned about a couple of things. One is tolerance how accurate can you measure the height movement? What difference in results do you get when considering this? I would think there would also be a constant somewhere which relates to the ration of masses involved as I guess this sets your sensitivity of the set up. For example imagine a super light object travelling at speed A this may not give you any noticeable deflection on the pendulum and even if you double the speed it still may not show anything. In my mind there will have to be some correlation between the inertia to get the pendulum going and the speed in which the energy can be dissipated. As in the super light above it would hit the pendulum and give off all its energy in heat and noise before the pendulum had time to move. Still like I said I'm only thinking aloud and see this point as a pretty small one compared to walloping coke cans. What differences would a different tube size shape make? If the tube is infinitely long would the ball reach a max speed? In an absolute vacuum it would of course. Is it the pull of the vacuum that causes the accelerating or the push of the atmosphere? What about a bulb type shape on the far end? Would that increase the speed? As I said you've raised a lot of interest in me. I'll be following you next one if you try a positive pressure reservoir to see how it goes.. Thanks.

Bill WW (author)  perfo2 years ago
Wow, Perfo, you raised some good questions.

"How accurate can you measure the height movement?"
I marked the scale behind the pendulum with lines 1 cm apart, made sure they (the lines) were level with the bench. The laser projects a fairly sharp beam, and I estimate the distance between lines. I could be off by a mm or so.
"What differences would a different tube size shape make? If the tube is infinitely long would the ball reach a max speed?"
If you only consider atmospheric force on the ball, a infinitely long tube would result in an infinite speed - theoretically. But the atmospheric pressure (force) has to accelerate the mass of air entering the tube, as well as the ball. So there is a terminal velocity. The physics profs calculate ths as: Theoretical maximum (per academic papers) = √(P/ρ) = √(101325/1.2) = 290 m/s
"Is it the pull of the vacuum that causes the accelerating or the push of the atmosphere? "
You look at this as the push of atmosphere. But wit vacuum on the other side there is NOTHING holding it bacK!
perfo Bill WW2 years ago
If you were off by say +/- 1mm giving you a total of 2mm error what difference would that make to your speed calcs ?
Also the vacuum isn't a pure vacuum so it will have resistance albeit pretty small.
clide2 years ago
You probably need to subtract the momentum from the air and not just the height.

You would end up with something like Velocity = [(m+M)(√2gh)-M(√2gha)]/m
Where ha is the height with just the air.

There also may be other factors that effect the energy transfer from the air to the pendulum differently when you don't have a projectile.  While that pendulum will get you in the ballpark I'm not sure I would trust the precision all that much with this type of setup. The mass of air in the full tube is almost the same as the mass of your projectile, so it will play a significant role.
Bill WW (author)  clide2 years ago
Great observation, I went too quickly over that part of my testing.

Will look at your equation (have to think for a while to ket the gears moving in my head!)

Thank you very much, love your website!

diggerevans2 years ago
fantastic instructable ,well done my friend
Bill WW (author)  diggerevans2 years ago
Thanks; I spent several weeks on this one!