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cbr600 wrote: What BC did you use? What's your calculated velocity at 100 yards and 1000 yards?

Looks like the BC of a typical 22 long rifle would likely be between .150 and .200, but I don't yet know how to incorporate BC into the formulae. Still researching...

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.

cbr600 wrote:What BC did you use?

I assume you mean bullet caliiber. For this example, lacking the facts, I used 1300 fps initial velocity.

What's your calculated velocity at 100 yards and 1000 yards?

I did not calculate velocity.

HP calculator formulae:
range = initial velocity sqared / gravity acceleration x sin(2 x angle)
distance =initial velocity x cos(angle) x seconds in flight
height = initial height + initial velocity x sin(angle) x seconds in flight - 1//2 x gravity acceleration x seconds in flight squared

Using the range formula, I set the range to 5280 ft and solved for the angle. The result was less than 3 degrees. I then used 3 degrees in the other formulae.

I can recalculate this once we know the initial velocity of the round that was actually used and the berm distance and berm height and the actual to the victim’s location.

I know I'm late for the party, but I couldn't resist this challenge:

CrimsonSoul wrote:... the shooter would have had to be aiming extremely high in order to make it that far ...

According to my HP 50g Graphing Calculator and the included formulas for projectiles, I compute the following:
The initial angle would only be +3 degrees and range would be 5124 feet when the bullet once again arrived at 5ft above ground 3.9 seconds later.
assumption: bullet leave barrel at 1300 fps from 5ft above ground (shoulder height)

here is some more interesting data.

At ~150 yds and .35 secs the bullet would be 25 ft above ground level
At ~300 yds and .7 seconds the bullet would be 40 ft above above ground level

I can recompute the data if someone can provide the actual berm distance from shooting position and height of the berms.

Also, I can provide the actual formulas that I used, but I won't bore you with that.

Lonest4r, perhaps you could double check my figures.

Has anyone heard any more on this?

Paul