Math help with Ballistics

kinematics equations are idealizations but they should work for the maximum height of a bullet because of the nature of projectile motion (things fall at the same speed regardless of their mass)
the only thing that might affect it that I can think of is air friction but bullets have very little surface area so it's negligible

Thanks a lot, I appreciate it

>It's parabolic so the math isn't that hard.
It isn't and this is entirely why the problem exists.

>who is Paddock?
Las Vegas shooter who gunned down a bunch of people at a concert then offed himself. Reportedly he left a piece of paper on the table next to him with ballistics calculations. How do you not know this?

A bullet is a projectile. Just use the kinematic equations and add wind reeistance. I assume you are a nutter trying to pull a JFK.

Air resistance _IS_ significant for bullets.
If you're allowed to neglect that, the bullet's initial upwards velocity is muzzle velocity times the sine of the gun's angle from the ground. Every second it rises it's losing 32.2 ft/sec (9.82 mtrs/sec) to gravity. After time, T, it comes to a halt at maximum altitude and begins to drop back. The average velocity during the climb is half the initial vertical velocity. Multiply by T to get the height.

All this assumes the bullet follows a parabola. Which is not really true but which is a good approximation if the range is only a small fraction of the Earth's circumference. The _actual_ trajectory is an ellipse with one foci at the center of the Earth. Just like the Moon or any satellite orbiting the Earth. Except that most of the bullet's trajectory lies within solid rock and that part is only of theoretical interest.

Can't think of any reason a madman would want to know maximum ordinate, so it's safe to explain these things to you. In addition, the material you found on rockets applies to bullets too. Only the part of the trajectory traveled under acceleration is very short; just the length of the gun barrel. All that does is simplify the calculations.

Doesn't the spin of the bullet significantly impact its trajectory in ways that make naive applications of basic kinematics inaccurate? Maybe I was falsely under that impression.

Why is physics and engineering in general so fucking easy?

I appreciate the info. I understand the initial concept, I'll have to work the math out. But yeah, the fella had mentioned Kinematics which sounded plausible and to an extent can be for other applications. But while reviewing some of the Kinematic formulas, I had noticed that the empirical data input for external factors what minimal. I know that just to make 1500yd shot, I've had to account for: (Ambient Air Temp using an Anemometer, Barometric Pressure which I suppose is the same as elevation and Atmospheric Pressure, my Angle Cosine or the angle of fire, Relative Humidity, Ammo Temp, Barrel Temperature, I've had to account for the Spin Drift which comes from the rifling within the Barrel itself, the distance to target objective, "danger space", and then Coriolis). What lot's of people forget is that once the bullet exits the crown of the muzzle, it's now considered to be in "free flight", and the wind acts as a force against the bullet along with gravity. "This stuff aint easy", so in SOTIC they give tid bits of what is necessary and what is not necessary, regarding long distance precision shooting. The reason the maximum is relevant to me, is that it lets me know how far above my (line of fire) I need to be concerned with (foliage, trees, maybe firing to the opposite end of a tunnel, and it helps me to visualize weather the bullet will drop and "yaw" or fall nearly vertically on top of the target objectives head).

The stuff about the spin of the bullet, the air temperature, pressure, humidity, etc. is all related to air resistance. I suspect those "corrections" are derived empirically, based on actual firing data.

Barrel temperature and rifling only affect muzzle velocity.

I don't think Coriolis force is important for handguns and rifles. Cannon, yes. (The was a notorious sea battle once where the British Royal Navy kept missing because they were fighting in the southern hemisphere and no one had thought to issue new correction tables.)

Couldn't tell from original question what degree of precision you were looking for.

I want to illustrate, so here is an example: INTEL -
Target Objective (TO) is a Mobile Launcher carrying a Soviet Era Missile.

Distance to TO: 1736yds
Angle of Fire: 2.2* Downward
Altitude: 5341 (Above Sea Level)
Ambient Temp: 73*F
Humidity: 02.00 %
Projectile Muzzle Velocity: 3178fps
Ammo Type: .50 M2 (AP SB)
Ballistic Coefficient: 1.083 BC
Sectional Density: 0.544 lbs/in>2
Muzzle Velocity Variation: 34fps AVG

Still have to account for Coriolis, Spin Drift, Wind. So yeah, lots of external factors

Yeah, anything related to Internal Ballistics I think effects the Muzzle Velocity of the Projectile like you said. Basically anything internal affects the speed. Transitional Ballistics I suppose has minimal effect on the projectile as well. It's the External and Terminal Ballistics I'm fascinated with. Transitional is not too terribly important. But yeah, SOTIC started with a Green Beret looking over old Artillary field data, and Coriolis information. For the standard Sniper, I suppose Coriolis is negligible, but when shooting out to 1600yds or more, you pushing mile, and it definitely can throw your point of impact off by a lot.

The Coriolis effect and all those other things deflect the bullet laterally so the only factors affecting the height of the bullet are the initial vertical velocity, gravity and air resistance right??

Plus, it's hard to find accurate data regarding some of the Ammo. Everyone wants to publish Ballistic Coefficient data based off the G1 Form Factor, which I couldn't tell you why they do that, the G7 is far more accurate and applicable to the shape of the projectiles nowadays. Most of the time.

2nd order effect. Shoot East or West (with or against the Earth's spin) makes a difference. Why rockets are aimed East and fired from as near equator as possible.
Shooting North or South, Coriolis would introduce an East/West component, so there'd be SOME tiny effect.

Um... Yes and No. In a perfect setting (indoors) yes, the only thing that would effect the vertical height of the projectile would be the speed at which it exits the muzzle, and of course barrel temp etc. However, outside, it's not that easy. For example, I have shot from what was essentially one cliff to another (where a dummy target was), and the heat from the depression I shot across actually effected the point of impact, which I was genuinely surprised at. Density Altitude also effect the point of impact, the less dense or more dense the air is around, the easier or harder it is for the bullet to travel along it's trajectory, humidity also affects the vertical height as well. As humidity goes up, so does the point of impact. That's why I said, it's very hard to find a solid formula ANYWHERE where I can plug in the known data, to get the Maximum Ordinate (MO) of the bullet.

Um... Yes and No. In a perfect setting (indoors) yes, the only thing that would effect the vertical height of the projectile would be the speed at which it exits the muzzle, and of course barrel temp etc. However, outside, it's not that easy. For example, I have shot from what was essentially one cliff to another (where a dummy target was), and the heat from the depression I shot across actually effected the point of impact, which I was genuinely surprised at. Density Altitude also effect the point of impact, the less dense or more dense the air is around, the easier or harder it is for the bullet to travel along it's trajectory, humidity also affects the vertical height as well. As humidity goes up, so does the point of impact. That's why I said, it's very hard to find a solid formula ANYWHERE where I can plug in the known data, to get the Maximum Ordinate (MO) of the bullet.

You are correct, shooting East or West only has a minimal Coriolis Effect vertically, and as you mentioned it would be pretty small depending on how far you were shooting. North or South shooting (as in aiming north or south) you'll get that lateral dispersion you mentioned. The thing about rockets and propulsion, is that there is a constant force pushing and or accelerating the projectile, where as a bullet essentially beings to fall towards the earth the moment it's in free flight. And, once in free flight everything external effects the trajectory.

Because stuff in real life is surprisingly mathematically clean

Rockets are also "falling: the instant they clear the pad. It's just that the "gun barrel" is reallllly long and can be adjusted so long as fuel remains.
Don't forget that exterior ballistics begin at the muzzle. Add in _your_ height and whatever you're standing on.
I know. We're getting silly now.

forget the coriolis effect and the elliptic path someone mentioned, if you're just shooting a gun this pretty much doesn't matter, however air resistance absolutely must be accounted for

That's just different flavors of air resistance.

To the average person it isn't. Also those equations only deal with mechanics with constant acceleration. They are useless with rockets.

To elaborate, temperature, pressure, and humidity all act through changing the density (mass / volume) of the air. This in turn affects the drag on the projectile.

The equations handle variable accelerations quite well. In fact, you HAVE to use them for rockets.
Rockets keep losing mass. Unless you throttle the motors (or pre-program the grain of a solid booster) the acceleration keeps going up.

Try searching on dtic.mil
dtic.mil/dtic/tr/fulltext/u2/830264.pdf

You're probably that N. Korea guy.

If I was the North Korean guy I'd be scared.

Correct. Unfortunately there seems to be WAYYY too many external factors for there to be some sort of formula to figure all this jazz out. As you correctly stated many external/ environmental factors effect the overall (Air Density) of the "Air" which in turn can deviate the point of impact.

All things being equal, what sort of math are we looking at getting into to determine this. I just wanted to know for myself. It seems one must be part Meteorologist, Part Mathematician, Part Physicist, and Artillery to determine this stuff lol.

dude are you trolling? this is a problem from the first month of physics I in lower division

Dude, are you lying? I took Physics 1 and 2, and at no point during the entire two semesters did we once ever even SLIGHTLY touch on the topic of Firearm or Rifle Ballistics. NOT ONCE. So what are you talking about? Are you trying really hard to appear or sound like some "intellectual edge lord" that's just too smart to be bothered with the mere Propulsion discussion? Is it just too below your genius level IQ?

It's not a simple problem when you take air resistance into account!

time to max height=v*sin(theta)/g.
range=(v^2)sin(2*theta)/g
height at any time=(v^2)(sin^2(theta))/2g

And what are you talking about? There is no Physics 1 "lower division" LOL! Not unless you go to a Community College or some Autist School. It's Physics 1 then 2, then on to something more complex. Where did you get this Physics 1 "lower division" lol? Guy, if your gonna lie, or try lying to prop yourself up on some sort of holier than thou social brownie point pedastol, there are other boards on here where you can bullshit random anons as much as you want. But please don't push that nonsense here, we were having a serious discussion.

That olny works in vacuum, not in real world.

Did you account for Drag? Did you account for spin drift considering gyroscopic stability is what's keeping the bullet from yawing? How fast is your bullet spinning, what's your rifle twist? If your shooting or aiming north or south at a distance of 1700yds have you accounted for the drop in point of impact due to Coriolis oh great physics professor/ Nobel laureate?

Times Mu, fucking retard.

what kind of school did you go to?

pic related, page 11 of my physics notes, so right in the middle of week 3. notice a), the exact thing OP was asking for

You wanted a semester#1 physics#1 question answered, I answered it in a physics#1 way.

If by Mu you mean drag, it doesn't work like that. The magnitude and direction of drag varies throughout the bullet’s flight.

Correct, you are 100% correct. That's how I know this guy is full of it. At no point in time do they teach ballistics in a physics class LOL. Not unless you want to move on to Applied Mechanical Engineering, and or Propulsion or Aeronautical Engineering. All that I learned in Physics were formulas that accounting for things in an imaginary world, or a vacumn like you indicated. This fella has apparently forgotten that once a bullet exit the muzzle and moves from internal to transitional and external ballistics and on in to "free flight": gravity affects it, wind effects it, Coriolis DOES affect it at certain distances, Spin Drift, all of which I'm sure they taught in his super awesome sophisticated extra advanced Physics class lol

The bullet's flight isn't an integral. Mu is, and it accounts for climate gradients during travel.

Your trying to make what we are discussing sound non-chalant, easy, a waste of your time. I suppose you are doing this in order to feel better about yourself, more intelligent, more mathematically proficient, I can't say exactly. But Ballistics is extremely difficult, physics or no physics class. And none of it occurs in a vacuum, it all occurs in an environment with imperfect meteorological conditions that vary depending on where you are, how high you are, and how far you are shooting, along with a myriad of other input variables. Maybe your excited because your finishing up your physics class or something and think you know it all already, I can't say, but the way you think it works is you (apply a formula from physics class) and that will dictate what your Maximum Ordinate will be, that's not the case. And that's not how it works. Perhaps in a perfect world, or a vacuum yeah, but back here in reality land, it doesn't. BTW, what happens to your trajectory if it starts raining, or snowing, at the same time it's windy?

wow this bro is mad

...

It's not a formula because most problems involving drag don't have analytic solutions. Find the equation for coefficient of drag of the bullet shape based on Reynolds number, then include the drag force in your differential equation and then solve numerically.

You gave an example of firing through a tunnel and wondering if the bullet would hit the roof,
Do the calculations ASSUMING you're shooting through a vacuum.
The actual maximum height (in air) will be lower.
If you're OK in a vacuum, you're OK in reality.

People have been trying to help you, but this thread has already run far too long!

With the same initial velocity, you have to aim higher when shooting through air than through a vacuum. Are you sure the maximum height is lower through air?

I gave you the bare bones mechanics of ballistic motion. The rest is going to be fudge, by definition.

You are a faggot.

How am I a faggot? You have to aim higher when shooting through air.

Think about it.
Air immediately starts to reduce muzzle velocity as soon as the bullet leaves the barrel.
So the bullet doesn't climb as high and drops to the ground at a shorter distance than it would if fired in vacuum.
Same effect as using a smaller powder charge and leaving everything else the same.

Consider the limiting case; aiming straight up.

Yes, obviously, which is why you have to compensate by aiming higher in order to hit the same target.

>aim straight up
>"hurrr compensate by aiming higher"
idiot

...

Wrong.
Anyone can draw a diagram.
Please explain the source of the "lift" which causes the trajectories to diverge as shown.
Bullets don't have wings. Air just increases drag.

Body lift applies to bullets. Wings are more efficient but not necessary given a high enough speed.

There is no lift. In air you have to point the gun higher angle to compensate for drag.

...

>aim STRAIGHT up
>draws a picture of slanted lines
idiot

why the fuck does the blue line have more initial speed? is the gun suddenly much better when fired in air?

the gun is NOT pointing in same direction in air and vacuum!

IT HAS MORE INITIAL SPEED.

THIS is how same speed different angle looks like

Red is vacuum, NO DRAG, Blue is air, DRAG!

are you retarded? it goes even slower in air. if it looks like it has more initial speed in air, it does

You are the retarded one!

In case everyone has forgotten, the OP wanted to know how high the bullet went.
Like, if he was firing through a tunnel, would it hit the ceiling.
I told him to figure the vacuum trajectory.
If it didn't hit, the air trajectory would be even lower -- IF everything else remained the same!

Stop introducing BS about changing the gun angle and muzzle velocity!!!!
That's not what was asked!
His statement of the problem fixed those quantities!

I'm sure he wants to hit the target! He asked how high the bullet goes IN THE REAL WORLD where the is drag and other factors. YOU told him about alternative reality where bullets fly in vacuum!

shut the fuck up. the vacuum height is a good upper bound for the real height.