Where would the bullet land?

[druski85]

Ah, but does it blend? 

Some how Airborn brought back this proof in my head. Learned it in High School.

http://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html

HiTech

Haha, I was proud of myself for getting that one, but failed miserably at the other classic fallacies.   

[BuckP]

So Hitech, what figures do you use for atmospheric drag in the game?  How is it scaled through altitude (linear, logarithmic, etc.)?  Is this information even something we are privy to?  This question has come up before within our squad actually, when trying to answer some questions (as seen on the white board pic I posted up with the equation answering the OP's question).  I'm not being a jerk here, just asking because I work with mathematics.  Oh, and no, I don't plan to go through and check every aspect of the game, lol.

[hitech]

So Hitech, what figures do you use for atmospheric drag in the game?  How is it scaled through altitude (linear, logarithmic, etc.)?  Is this information even something we are privy to?  This question has come up before within our squad actually, when trying to answer some questions (as seen on the white board pic I posted up with the equation answering the OP's question).  I'm not being a jerk here, just asking because I work with mathematics.  Oh, and no, I don't plan to go through and check every aspect of the game, lol.

Standard atmospheric  density tables.

I've posted them before so try a search in this topic. Both speed of sound and density.

HiTech

[jeep00]

42

Bob

[moot]

if
a=b
then
a²-ab = 0
and that's trouble waiting to happen

[Mystery]

Just a guess, but there are standard external ballistics calculators around (i.e. Sierra and some freeware) that can do this calc.

The only "tricks" are to input atmospheric density at the firing point, and to use the true airspeed as a full value 0 degree wind.

Hitech - how did you account for changing atmospheric density as the projectile drops?

Just curious

[Mystery]

what about a HVAR rocket? how fast does it travel, when will it hit the ground at 45k and will it take a nose dive or go at a little bit of a slope?

At first glance this is trickier because the rocket is powered during a portion of its flight. But if you know the rocket's c/d, frontal area, terminal speed at the point of motor burnout and how much it has already dropped from the launching altitude at that point...it can be calculated. I'll do a little digging but I'm not optimistic about finding c/d's and frontal areas for HVARs.

In general terms though, I believe it will be in a nose dive since air resistance (Vo, c/d and frontal area) will overcome forward momentum.

[hitech]

Just a guess, but there are standard external ballistics calculators around (i.e. Sierra and some freeware) that can do this calc.

The only "tricks" are to input atmospheric density at the firing point, and to use the true airspeed as a full value 0 degree wind.

Hitech - how did you account for changing atmospheric density as the projectile drops?

Just curious

Simple, I ran a computer simulator that does it.

HiTech

[BaDkaRmA158Th]

Unrelated kinda, but i wish the cannon rounds that had "timer-fuses" to detonate the round before ground fall would work as they should.

Case in point, the 37mm cannon round for our p-39's had a fuse, would be a nice addition.

[augustk]

The real question is if the bullet in question falls in a forest, does it make a sound?   

[HPriller]

Interesting thread, Hitech is quite correct on his mention of the effects of drag.  In most cases at the altitudes mentioned the bullet would destabilize long before hitting the ground.  The resultant tumbling would have two major effects.  The forward momentum of the bullet would pretty much be lost entirely and it would start to fall more or less straight down, and any wind might even push it in a completely different direction.   Second, the terminal velocity of the bullet would be greatly reduced.  As mentioned earlier in this thread, mythbusters did an episode with experiments related to this and their bullet (a 9mm I believe) topped out around 160mph when falling straight down if I recall correctly.  They even concluded that a bullet tumbling in such a fashion wouldn't impart lethal force on impact.  To answer the initial question as to whether or not the plane passes the bullet before it hits the ground, it does.  There is a catch to this as the size of the round gets larger it will take longer for the drag forces to slow the round sufficiently to destabilize it, hence large caliber artillery being capable of firing several miles accurately.

[230G]

Just a guess, but there are standard external ballistics calculators around (i.e. Sierra and some freeware) that can do this calc.

  Interesting.....all this talk about ballistics, drag, calculus, etc. and after almost four pages someone finally mentions a ballistics calculator. There are quite a few on-line, but most of them are limited in their range.

  One of the factors that I was surprised no one mentioned is the ballistic coefficient (BC). This, in laymans terms, is a measure of a projectiles ability to overcome air resistance in flight and can vary greatly depending on the shape of the projectile. As an extreme example, a .50 cal. round lead ball would have a BC of around .120 (going from memory) while the US M33 Ball projectile a BC of .670. This equates to a HUGE difference in trajectory. BC is also affected by altitude and temperature(changes in air density) as well as the decreasing velocity of the projectile.
 
  A few have mentioned the destabilization of the bullet and I wonder about this. I wonder to what extent bullets destabilize. I shoot rifles competitively and have had the long range shooters tell me that it's quite important that the bullet remain supersonic all the way to the target. This due to the fact that a projectile will destabilize slightly when making the transition from trans to subsonic...not however to the point of tumbling. I wonder if a projectile will eventually begin to tumble. I have my doubts....especially in the case of a long, aerodynamic projectile such as those used in the 50 BMG cartridge.

   230G/35Whelen

[Golfer]

I got my initial information where I was doing my calculations using several ballistics calculators against one another.  They don't go out so far as to calculate 8 miles of bullet drop, lateral distance covered taking into account fired from an aircraft moving at 450knots and decelerating until falling darn near straight down..

You won't see sierra, winchester or any other of the popular calculators used for long range shooting because they don't work for this calculation.  Frankly asking about it is a waste of time, which is exactly why I posed the question here.

And I had my answer weeks ago.

[230G]

 

And I had my answer weeks ago.

  Oh?   I read through all the posts and I didn't see what I thought was a definitive answer. And please don't think that statement means that I have the answer.
  I do remember learning this in high school physics: If you fire a projectile from a gun X number of feet from the ground and at exactly the same instance drop an identical projectile from the same height, they both hit the ground at the same time. Ms. Nash, my cat-eye glasses wearing physics teacher, demonstrated this with a little contraption and two steel balls.
  230G   

[Golfer]

Yeah.  That's a good and popular schoolhouse example of gravity and the time for the bullet to hit the ground from X really isn't in question.  I was curious about distance traveled from the bullet which is decelerating compared to the airplane which is flying at a constant speed and where they would be when the bullet hit the ground.

Hitech's numbers seem good enough for me.