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psehorne wrote:

jimlongley wrote: It looks like you are missing a factor or two. Remember that air resistance is significant (BC is Ballistic coefficient BTW) it appears that your formulae would only apply in a vacuum.

The path of a projectile fired in our atmosphere does not describe the perfect arc your program predicts, because the projectile has significantly less velocity at the terminal end.

Here's a quick test: Calculate the maximum range and see what the incident angle would be. If it's anywhere near 45 degrees then it's wrong for a projectile in air.

You are correct. Do you (or anyone following this) know how to incorporate air resisrance into the formulea? In the meantime I will do some research.

Once we have complete formulae, it will be a simple matter to plug in various data to run different scenarios, and eventually plug in the actual initial velocity and BC of the round used. For now it will suffice to use characteristics of a representatice round (22lr or 223 for example).

It is important to know berm height and distance from the shooting station in order to determine the feasibility of a round leaving the shooting range being the culprit.

The actual solution incorporating air resistance is a differential equation of the third order. I would have to dig out my textbook for this particular type of question, but I am really busy with other classes at this point. It is best to do such a problem in Mathematica or Matlab because it has the tools you would need built into the software. If I get any time to work the problem out I will let you know, but I have two tests coming up this week and will therefore probably be very busy.

Excaliber wrote:

ScottDLS wrote:

glock27 wrote: ...
i watch mythbusters they did a terminal velocity test on dropping a penny from "empire state building" all in scale of course. but a pennies maximum speed is something like 62 miles per hour. a .22 would weigh less than a penny and have less terminal velocity
....

Oh...please tell me you are joking. I believe it was Galileo c.1634 that proved that all objects regardless of weight, fall at the same rate of acceleration (absent wind resistance). Newton then described the physics in much more detail somewhat later. So, drop an anvil and a coyote from a plane and both will fall at the same speed unless coyote spreads out to have a bigger surface area than the anvil.

A .22 would have less wind resistance than a penny and so have a terminal velocity somewhat higher, but I would volunteer to catch it in my hand at 1 mile.

What you're both missing is the difference between drop speed and forward speed, and the role of mass. All are in play. The forward speed is imparted by the expanding gas produced by the burning powder charge, and the drop speed is that imparted to the bullet by gravity. The forward speed is what makes the .22 dangerous instead of merely an annoyance.

That's also why you might not mind catching a penny dropped from the empire state building in a sturdy hat, but you wouldn't want to catch that same coin from a supersonic fighter in flight because the penny would also carry the fighter's forward velocity.

The anvil's mass is what makes that much more dangerous than a coyote when dropped straight down. The formula for terminal energy is mass x velocity squared. If you add a lot of mass, it bumps this number up substantially.

Correspondingly, if you take two items of the same mass and impart lots more speed to one than the other, the faster one will deliver significantly more energy to the target, all other things being equal.

Excaliber is correct in many ways, however, I am a mechanical engineering student with significant experience in Newtonian mechanics and agree that this problem is about bullet energy. There are two basic types of energy. Kinetic energy, which is the energy of objects in motion, and potential energy, which can be in various subtypes (chemical, elastic, gravitational). When the round is sitting in the chamber, it has an abundance of chemical potential energy, which is rapidly converted into kinetic energy (KE=0.5mv^2) as the bullet accelerates down the barrel. Now that the bullet has left the barrel, it is subject only to gravity and resistance from the fluid it is travel traveling through.

Some of that potential energy was also converted to rotational energy, which makes the bullet fly straight, but also reduced the shape factor that produces "air resistance." As long as we can reasonably make the assumption that the bullet is still spinning along an axis parallel to the direction of travel we can also assume a high terminal velocity. When that bullet leaves the gun and travels at an angle from the ground, an amount of energy that was formerly kinetic, builds up as gravitational potential (GPE=mgh) . As the bullet descends, that energy is once again transferred back into kinetic energy, less the amount lost to air resistance. Like I said before, if that bullet maintains its rotation the losses will be small. As that bullet is coming down, it accelerates at a constant 9.8 m/s^2 downward, which means the farther past the apex of the trajectory it goes the greater the angle at which it will be coming down. So for long shots that strike a target after the apex of the shot they will have to be at steeper angles.

When that shot hits, its energy is NOT either going to be the dropping energy or the forward energy that hits you, but a vector sum of the two combined. Since those two energies are merely converted, the magnitude of the energy imparted on the target will be the same.

I hope this helps!
SIDENOTE: if you are interrested, spheres actually make for terrible ballistic objects because of the low pressure wake that trails them in flight.

This story worries me because I frequently go to GPSR and would hate to see something like this force the range to close or move. I formerly shot at the Backwoods T.R.A.P.S. until the subdivision that was being built across the street forced them out. If you are building houses near an outdoor gun range you know that issues will eventually arise with homeowners, whether it be noise or the possibility of a stray shot someday leaving that range. I wouldn't buy a house next to a loud busy highway and then complain that they should move the highway, it would be my own fault for being a lousy consumer. What is this comment in the story about neighbors hearing popping sounds at night? Perhaps they mean evening?