Ask an Expert: Measuring Force

 Posts: 2
 Joined: Mon Sep 24, 2007 6:51 am
Measuring Force
I'm building a linear magnetic accelerator ("Gauss Rifle") and would like to measure the force at which the ball is shot out. I can't figure an easy way to do this. Can you help?
Mike
Interesting topic and a good question. What grade are you in and how much math do you know?
If you are familiar with Newton's 2nd Law of Motion, the force equals mass times acceleration. So, if you know the mass of your ball (in kilograms) and the acceleration of the ball, you can determine the force on the ball.
Measuring the mass of your ball is quite straightforward: put it on a triple beam balance or electronic balance, etc. (whatever you happen to have) and record its mass in kilograms.
The acceleration is a little bit more difficult. Acceleration is, roughly, a quantity describing how quickly the velocity (you can think of velocity as speed in this case) is changing. Acceleration is measured at a particular time. So, we need to determine at what time you want to measure the acceleration (and thus force) of your ball. I would suggest measuring the acceleration as the ball leaves the barrel of the accelerator.
Now, we must consider that the velocity of the ball is constantly changing (speeding up, in this case), so we need a way to determine acceleration at a given time.
Once you have told me how much math you know, we can talk about how to figure out the acceleration, and therefore the force, of your ball as it leaves the accelerator.
If you are familiar with Newton's 2nd Law of Motion, the force equals mass times acceleration. So, if you know the mass of your ball (in kilograms) and the acceleration of the ball, you can determine the force on the ball.
Measuring the mass of your ball is quite straightforward: put it on a triple beam balance or electronic balance, etc. (whatever you happen to have) and record its mass in kilograms.
The acceleration is a little bit more difficult. Acceleration is, roughly, a quantity describing how quickly the velocity (you can think of velocity as speed in this case) is changing. Acceleration is measured at a particular time. So, we need to determine at what time you want to measure the acceleration (and thus force) of your ball. I would suggest measuring the acceleration as the ball leaves the barrel of the accelerator.
Now, we must consider that the velocity of the ball is constantly changing (speeding up, in this case), so we need a way to determine acceleration at a given time.
Once you have told me how much math you know, we can talk about how to figure out the acceleration, and therefore the force, of your ball as it leaves the accelerator.
All the best,
Terik
Terik

 Former Expert
 Posts: 1297
 Joined: Mon Oct 16, 2006 11:47 am
Historically, ballistics calculations have used muzzle velocity and kinetic energy instead of force.
Getting accurate direct acceleration measurements is extremely difficult in practice because measuring time precisely is difficult. Simple accurate ballistics measurements for projectiles have historically been done in reverse by determining how far the projectile (ball) goes when launched at some upward angle. Using 45 degrees up from horizontal simplifies the calculations and maximizes the range which minimizes the effect of measurement errors, so 45 degress is often the angle of choice.
See http://hyperphysics.phyastr.gsu.edu/hbase/traj.html and go down to General Ballistic Trajectory and then to Range of Trajectory.
For 45 degrees, R * g = Vo * Vo (where g = 32ft/sec/sec, R is range in ft, and Vo is muzzle velocity in ft/sec using the English units system).
Muzzel kinetic energy is 1/2 * m * Vo * Vo.
Getting accurate direct acceleration measurements is extremely difficult in practice because measuring time precisely is difficult. Simple accurate ballistics measurements for projectiles have historically been done in reverse by determining how far the projectile (ball) goes when launched at some upward angle. Using 45 degrees up from horizontal simplifies the calculations and maximizes the range which minimizes the effect of measurement errors, so 45 degress is often the angle of choice.
See http://hyperphysics.phyastr.gsu.edu/hbase/traj.html and go down to General Ballistic Trajectory and then to Range of Trajectory.
For 45 degrees, R * g = Vo * Vo (where g = 32ft/sec/sec, R is range in ft, and Vo is muzzle velocity in ft/sec using the English units system).
Muzzel kinetic energy is 1/2 * m * Vo * Vo.
Craig

 Posts: 2
 Joined: Mon Sep 24, 2007 6:51 am
Measuring force
I'm working with my dad and he has had through differential equations  though it was a long time ago he says. He promised to help me with any math but he wants me to figure out as much of this project as i can on my own.
I had thought that I could shoot the ball at a hanging clay target with a marker attached and use the marker to record how far the pendulum was displaced . Knowing the weight of the pendulum and how far it was displaced, I could ratio the equations and get a relative force but this till doesn't get me an accelaeration. I shot one last night and it's really fast!
I had thought that I could shoot the ball at a hanging clay target with a marker attached and use the marker to record how far the pendulum was displaced . Knowing the weight of the pendulum and how far it was displaced, I could ratio the equations and get a relative force but this till doesn't get me an accelaeration. I shot one last night and it's really fast!
Mike
mikekilough,
Craig's idea about measuring kinetic energy and velocity are much less complicated than the way that I was thinking about, so I would suggest using the method he suggests (it also requires a bit less messy math).
Read the article Craig posted and let us know if you have any questions.
Craig's idea about measuring kinetic energy and velocity are much less complicated than the way that I was thinking about, so I would suggest using the method he suggests (it also requires a bit less messy math).
Read the article Craig posted and let us know if you have any questions.
All the best,
Terik
Terik

 Former Expert
 Posts: 1297
 Joined: Mon Oct 16, 2006 11:47 am
Glad that you have already discovered the pendulum momentem exchange method as well through your research. It is another commonly used measurement technique for determining the kinetic energy of a projectile. The accuracy of the pendulum method depends a lot on appropriately sizing the mass of the pendulum target.
Craig

 Former Expert
 Posts: 123
 Joined: Mon Aug 29, 2005 10:02 am
Hi Mike!
This sounds like an excellent project  I wish I could see what you've been able to build for myself!
I have a couple of questions for you, to add to the great posts already supplied by the other experts:
Did you determine the mass of your projectile and what size (diameter) is it?
As Craig already mentioned, historically, an angle of elevation of 45 degrees was typically used in order to maximize the range of a projectile. However, this was due to the fact that the effect of wind resistance was extremely small on very large objects  such as those typically hurled in ancient warfare. The greatest factor affecting 'flight' was gravity. Now, as the mass of the object becomes smaller and smaller, the effect of wind resistance increases dramatically  though, of course, gravity is *always* there, trying to pull the bullet down to earth. Consequently, current maximum range calculations actually have an angle of elevation much closer to 30 degrees than the traditional 45 degree angle. (Of course, if the projectile were to be launched in a vacuum  which has no air  the angle of elevation returns to 45 degrees.) In addition, a rotational spin is also typically added to projectiles, which provides gyroscopic stability. (In fact, the shape of the projectile also affects the maximum range, too.) This is actually a fascinating subject, so there is plenty of material available if you're interested!
Anyway, to go back to your question about measuring velocity. Muzzle velocities are usually measured by means of a chronograph  a device which has a specified distance between the first and last screen. As the projectile passes over the first screen, an electronic stopwatch is started; as the projectile passes over the final screen, the stopwatch is stopped. Since the projectile has traveled a known distance (the distance between the screens) in a known time (the time on the stopwatch), the velocity of the projectile can be measured. Chronographs are relatively inexpensive, but there may be a way for you to carry out a similar type of calculation using other means  any ideas? It won't be as accurate, but it may help answer your question.
Once you have an estimated, average velocity (you will need to do quite a few testfires), you can then calculate the kinetic energy of your projectile.
Please post back with your thoughts, and if you have any questions, please just let us know.
Good luck!
Geoff.
This sounds like an excellent project  I wish I could see what you've been able to build for myself!
I have a couple of questions for you, to add to the great posts already supplied by the other experts:
Did you determine the mass of your projectile and what size (diameter) is it?
As Craig already mentioned, historically, an angle of elevation of 45 degrees was typically used in order to maximize the range of a projectile. However, this was due to the fact that the effect of wind resistance was extremely small on very large objects  such as those typically hurled in ancient warfare. The greatest factor affecting 'flight' was gravity. Now, as the mass of the object becomes smaller and smaller, the effect of wind resistance increases dramatically  though, of course, gravity is *always* there, trying to pull the bullet down to earth. Consequently, current maximum range calculations actually have an angle of elevation much closer to 30 degrees than the traditional 45 degree angle. (Of course, if the projectile were to be launched in a vacuum  which has no air  the angle of elevation returns to 45 degrees.) In addition, a rotational spin is also typically added to projectiles, which provides gyroscopic stability. (In fact, the shape of the projectile also affects the maximum range, too.) This is actually a fascinating subject, so there is plenty of material available if you're interested!
Anyway, to go back to your question about measuring velocity. Muzzle velocities are usually measured by means of a chronograph  a device which has a specified distance between the first and last screen. As the projectile passes over the first screen, an electronic stopwatch is started; as the projectile passes over the final screen, the stopwatch is stopped. Since the projectile has traveled a known distance (the distance between the screens) in a known time (the time on the stopwatch), the velocity of the projectile can be measured. Chronographs are relatively inexpensive, but there may be a way for you to carry out a similar type of calculation using other means  any ideas? It won't be as accurate, but it may help answer your question.
Once you have an estimated, average velocity (you will need to do quite a few testfires), you can then calculate the kinetic energy of your projectile.
Please post back with your thoughts, and if you have any questions, please just let us know.
Good luck!
Geoff.
Geoff Bruton
Firearm & Toolmark Section
Ventura County Sheriff's Department
Forensic Sciences Laboratory
Firearm & Toolmark Section
Ventura County Sheriff's Department
Forensic Sciences Laboratory
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