02/11/2007, 06:17 AM
Finally wee learn something useful in physics. Ballistics. CSIs use this method, its not that hard and pretty accurate, and you don't really need anything special. This will work for guns, paintball markers, airsoft or anything of any power with a few adjustments (and of course safety precautions). DO NOT TRY THIS AT HOME.
So, this is what you'll need if you were doing this at home. Remember the airsoft I used was very weak so you might want to make your pendulum heavier:
- Some kind of stand, a screwdriver taped to a table would work for instance
- Some cylinder roughly the size of the inside of a straw or smaller
- Some straws, 2 or 3. The kind that you can bend near the top
- Some power tape, as means of catching the bb in
- Something to shoot something with
- A camera, any webcam will do if it can do about 15fps or more
- Photoshop or similar
- A ruler
- A calculator (google will do)
- A knife or scissors
The steps:
Take one straw and bend the top 90 degrees. Slide the small part over the screwdriver so it hangs loosely. Take it off again.
Take a second straw, but cut off the twisting part so you only have one straight tube. Tape it to the other straw to make it longer. Doesn't need to be watertight, just straight.
Take around 20cm of powertape, and make an inside out circle. Then, folding it in half, make a sort of tube with the inside roughly the size of the bullet you want to catch in it. Then use the rest to tape it to the straight end of the straw such that when you aim the gun inside the tape tube the pendulum swings:
![[Image: schlg5.jpg]](http://img339.imageshack.us/img339/1158/schlg5.jpg)
Wee use tape because wee want to have the bullet inside the pendulum when it moves so all the energy is transferred.
Position your camera and hang up the pendulum, press record, aim, shoot. Make sure the pendulum is stable and shoot again a few times. Stop recording.
If you pendulum barely moves, your shot is too weak or your pendulum is way too heavy. If it spins around and around, its too light. Make it out of cardboard or something. It won't work if the pendulum goes over the top and back down. Preferably it should stay below 90 degrees movement. Position your camera so that only the moving part of the pendulum is in sight to maximize accuracy.
Take your movie, and look for the shot where the pendulum goes the highest. Make your media player almost as full screen as possible. Move to the frame (hint: use the arrow keys) where the pendulum is about to start moving, and take a screenshot. Then move forward to the frame where the pendulum is at its maximum (this is easy to recognise. the pendulum stops for an instant at the top, so it should be the only sharp frame, after which it begins to fall again). Take a second screenshot.
Open both files in photoshop and put the second one as a layer over the first one, and make it 50% opaque so you can see both. Now select a point that is clearly visible on both pictures. The best point is the center of gravity of the pendulum (this is the point where if you balance it on your finger and it stays, this is where your finger is). Then draw two straight lines as seen below. Also, pick two points on the pendulum that are easily recognizable on the real thing.
![[Image: pendulumtw1.jpg]](http://img256.imageshack.us/img256/7551/pendulumtw1.jpg)
Measure the two points that are recognizable on the real pendulum and compare them to the real one to find the scale of your image. If the distance irl is 5cm and on the screen is 10cm, you multiply every distance on the screen by (5 / 10) to get the real distance.
Now you can measure the height between the two lines you made (on my screen the top and bottom horizontal lines). This is the height that the center of gravity moves during the flight of the pendulum. Convert it using your scale to a real value and convert it to meters.
You now have a value for h in meters. Write it down.
Next, weigh the pendulum with the bullet inside. This should be fairly accurate so use a good scale. Then weigh the pendulum without the bullet. The difference is the weight of the bullet (or if its known, like .20g for a common airsoft bb, use that). Convert all three values to KG and write them down.
Now, using the law of energy conservation (KE = GPE from when the pendulum hangs still to when it is in mid-air) and the law of momentum conservation (the momentum of the bullet is equal to the momentum of the leaving pendulum), this formula can be deducted:
The speed of the bullet = ( √ 2 * height * 9.81 * Mass of pendulum+bullet ) / ( Mass of bullet )
i.e.![[Image: formulatw6.png]](http://img254.imageshack.us/img254/115/formulatw6.png)
Simply fill this in and out rolls a number (in my case 28, which is pathetic) in meters per second (speed). In order to compare this to specs that are often mentioned with airsoft, fps and Joule, use these formulae:
M/s to fps:
fps = 3.281 * m/s
M/s to Joule:
Joule = .5 * mass of bullet in kg * (m/s)2
So, for 28, that is a mere 91 fps (i used .20s but the gun needs .12s, thatll explain a lot) and about 0.13 J.
If you would like more detailed explanation about the steps or the calculations post. If you have any use for this, digg it :D
Also, if in a few months this article saves ur donkey in an exam, rep me :P
![[Image: digg.gif]](http://www.gbhfusion.com/content/images/icons/digg.gif)
So, this is what you'll need if you were doing this at home. Remember the airsoft I used was very weak so you might want to make your pendulum heavier:
- Some kind of stand, a screwdriver taped to a table would work for instance
- Some cylinder roughly the size of the inside of a straw or smaller
- Some straws, 2 or 3. The kind that you can bend near the top
- Some power tape, as means of catching the bb in
- Something to shoot something with
- A camera, any webcam will do if it can do about 15fps or more
- Photoshop or similar
- A ruler
- A calculator (google will do)
- A knife or scissors
The steps:
Take one straw and bend the top 90 degrees. Slide the small part over the screwdriver so it hangs loosely. Take it off again.
Take a second straw, but cut off the twisting part so you only have one straight tube. Tape it to the other straw to make it longer. Doesn't need to be watertight, just straight.
Take around 20cm of powertape, and make an inside out circle. Then, folding it in half, make a sort of tube with the inside roughly the size of the bullet you want to catch in it. Then use the rest to tape it to the straight end of the straw such that when you aim the gun inside the tape tube the pendulum swings:
Wee use tape because wee want to have the bullet inside the pendulum when it moves so all the energy is transferred.
Position your camera and hang up the pendulum, press record, aim, shoot. Make sure the pendulum is stable and shoot again a few times. Stop recording.
If you pendulum barely moves, your shot is too weak or your pendulum is way too heavy. If it spins around and around, its too light. Make it out of cardboard or something. It won't work if the pendulum goes over the top and back down. Preferably it should stay below 90 degrees movement. Position your camera so that only the moving part of the pendulum is in sight to maximize accuracy.
Take your movie, and look for the shot where the pendulum goes the highest. Make your media player almost as full screen as possible. Move to the frame (hint: use the arrow keys) where the pendulum is about to start moving, and take a screenshot. Then move forward to the frame where the pendulum is at its maximum (this is easy to recognise. the pendulum stops for an instant at the top, so it should be the only sharp frame, after which it begins to fall again). Take a second screenshot.
Open both files in photoshop and put the second one as a layer over the first one, and make it 50% opaque so you can see both. Now select a point that is clearly visible on both pictures. The best point is the center of gravity of the pendulum (this is the point where if you balance it on your finger and it stays, this is where your finger is). Then draw two straight lines as seen below. Also, pick two points on the pendulum that are easily recognizable on the real thing.
Measure the two points that are recognizable on the real pendulum and compare them to the real one to find the scale of your image. If the distance irl is 5cm and on the screen is 10cm, you multiply every distance on the screen by (5 / 10) to get the real distance.
Now you can measure the height between the two lines you made (on my screen the top and bottom horizontal lines). This is the height that the center of gravity moves during the flight of the pendulum. Convert it using your scale to a real value and convert it to meters.
You now have a value for h in meters. Write it down.
Next, weigh the pendulum with the bullet inside. This should be fairly accurate so use a good scale. Then weigh the pendulum without the bullet. The difference is the weight of the bullet (or if its known, like .20g for a common airsoft bb, use that). Convert all three values to KG and write them down.
Now, using the law of energy conservation (KE = GPE from when the pendulum hangs still to when it is in mid-air) and the law of momentum conservation (the momentum of the bullet is equal to the momentum of the leaving pendulum), this formula can be deducted:
The speed of the bullet = ( √ 2 * height * 9.81 * Mass of pendulum+bullet ) / ( Mass of bullet )
i.e.
Simply fill this in and out rolls a number (in my case 28, which is pathetic) in meters per second (speed). In order to compare this to specs that are often mentioned with airsoft, fps and Joule, use these formulae:
M/s to fps:
fps = 3.281 * m/s
M/s to Joule:
Joule = .5 * mass of bullet in kg * (m/s)2
So, for 28, that is a mere 91 fps (i used .20s but the gun needs .12s, thatll explain a lot) and about 0.13 J.
If you would like more detailed explanation about the steps or the calculations post. If you have any use for this, digg it :D
Also, if in a few months this article saves ur donkey in an exam, rep me :P