Math question re bullet drop

[SheepDog]

Using the standard data and a 150 grain fmj bullet at 2850 muzzle velocity the difference in drop between 450 and 451 yards is .28 inches.
The difference in bullet trajectory is .23 inches. If sighted in at 200 yards the trajectory of the bullet is 33.40 below point of aim.
If you change atmospheric conditions it will vary.

 

[Toby Bradshaw]

PS. Open to and welcome any corrections.

OK.

This estimate would be correct if the bullet had no downward component of its velocity vector at 450 yards. But the bullet has been accelerating at 1g (ignoring drag for the moment) since it reached the top of its trajectory (typically several hundred yards before).

 

[SheepDog]

The acceleration of gravity increases over time you have to calculate the entire time the bullet is in flight and calculate the drop at both time cycles to get a credible answer. I just ran it through an exterior ballistic program using the default settings.

The bullet has been falling at 1 g since it left the barrel not since it hit the peak of its trajectory.

 

[Toby Bradshaw]

The bullet has been falling at 1 g since it left the barrel not since it hit the peak of its trajectory.

Nope. According to that (faulty) logic, a bullet fired straight up and another fired horizontally will hit the ground at the same time.

 

[dickn52]

Interesting question, but from a practical standpoint, why would you need this info since there is nothing out there that ranges to a 1 yard increment. Every laser detector I've ever used at a +/- 1-3 yards built into it.

 

[SheepDog]

Nope. According to that (faulty) logic, a bullet fired straight up and another fired horizontally will hit the ground at the same time.

Toby,
The bullet in the vertical shot is accelerating at -1 g while it is traveling up too. It has farther to fall. To simplify things the vertical bullet is decelerating until it reaches its peak height and then it continues to accelerate toward the ground from the height of peak altitude.

Gravity doesn't care what direction you are traveling, it just pulls at 1 g from the time you start to the time you stop. The vertical bullet falls from a greater height but gravity is working on it as soon as it leaves the barrel just like a horizontal shot. The horizontal shot has less distance to drop.

If gravity didn't affect the vertical bullet it would just continue to go in the vertical direction and never fall. Gravity (along with air resistance) stops the vertical climb.

 

[M-61]

Interesting question, but from a practical standpoint, why would you need this info since there is nothing out there that ranges to a 1 yard increment. Every laser detector I've ever used at a +/- 1-3 yards built into it.

To prove whether a bullet can enter and pass thru a 1½ "dia. tube, one foot long, without touching the inside of the tube from 450 yards.
From sheepdog's post #21 it looks like there is room to spare. Bit more than ¼" in one yard of drop if I'm following it correctly

 

[SheepDog]

I'm not THAT good.
There is a show for myth busters! They once disproved the arrow splitting arrow theory and then proved it could be done. So it has to do with the uncertainty principal. The arrow is in both places at the same time and it depends on when you look at it as to whether it splits the other arrow or not...

 

[Toby Bradshaw]

Toby,
The bullet in the vertical shot is accelerating at -1 g while it is traveling up too.

Sure, the bullet experiences a downward force of 1g all the time after leaving the muzzle, but the bullet doesn't start "falling" until its velocity (not acceleration) vector goes negative (assuming that "up" is positive).

 

[SheepDog]

From a pure physics point of view it is accelerating toward the ground which slows its vertical velocity. There is a force acting upon it from the time it loses its support in the barrel. That force is accelerating it toward the ground.

If you fire a bullet at a 45 degree angle the bullet falls from the line of exit from the time it leaves the barrel. To a person standing at the side the bullet is moving up away from the ground but it falls from its support all the time. The same is true regardless of the angle. It all depends on your perspective. The force of gravity is included in all ballistic calculations, even vertical calculations.

 

[Toby Bradshaw]

It all depends on your perspective.

So from your perspective is a bullet that is accelerating downward, but traveling upward, falling or rising?

 

[SheepDog]

If I was the bullet? I would be rising but accelerating toward the ground with one vector while screaming to the sky with my remaining velocity.
Gravity will eventually win.
The only acceleration on the bullet is toward the ground. That is the only vector that is showing growth.

 

[Toby Bradshaw]

Gravity will eventually win.

Not if you're going fast enough.

The only acceleration on the bullet is toward the ground. That is the only vector that is showing growth.

But "rising" and "falling" are determined by the velocity vector, not the acceleration vector. So, back to the original problem, to calculate the downward velocity of the bullet (neglecting drag), you start the clock at the peak of the trajectory (v(down)=0), not at the muzzle.

 

[SheepDog]

No Toby, if you ignore the time of flight to the peak of trajectory in any shot other than vertical your calculations will be off. Gravity is an acceleration. for each second it accelerates in the direction of the earth at 32,17 feet per second squared.
It will accelerate to 32.17 feet per second in the first second and attain a speed of 16.085 fps while in the second second it will accelerate to 64.34 fps and attain a speed of 48.22 feet per second. At the point a bullet in flight reaches its maximum height above the line of sight it has already fallen away from its angle of departure. Gravity makes the bullet fall from its departure angle as soon as it leaves the barrel. Gravity is affecting its flight from the time it leaves the barrel.

For instance; shooting up hill or down hill reduces the time that gravity has to affect the bullet (gravity works at 90 degrees to horizontal) and the bullet will hit higher when fired up or down at an angle than if it was fired horizontally. Firing down hill adds to the bullets velocity (gravity assist) and shooting down hill will impact slightly higher than firing up hill at the same angle because firing up hill gravity helps to slow the bullet slightly. If what you were saying was right then shooting uphill would shoot higher than shooting horizontal and shooting downhill would shoot lower. It just doesn't work that way in real life.

 

[Toby Bradshaw]

When the bullet's velocity vector (up or down) is zero relative to the surface of the earth, it doesn't matter what has happened to it in the past to get it there. The bullet begins to fall. Its downward velocity vector component (ignoring drag) from the peak of trajectory onward is simply a function of time^2.

 

[SheepDog]

Tony,
Gravity has already affected the path of the bullet.
If I sight my 3006 in at 175 yards it reaches its high point in its trajectory at 110 yards.
The bullet has already dropped 2.8 inches from the line of departure. It has spent this part of its flight rising from the ground.
It now begins to "drop" as perceived in relation to the ground but the acceleration of that drop continues to grow with time. It does not suddenly begin to accelerate at this time. Its downward speed is determined by the total time of travel.

 

[carlsbad]

Stephen Hawking could, the rest of us not so much.
I am sure there is a formula to do what you are after though.

Speak for yourself. It's not nuclear physics, although I AM a nuclear physicist. A Hornady 155 Amax with 2750 fps muzzle velocity will drop .265" from 450 to 451 yards assuming sea level, 59 deg F, 78% relative humidity, and barometric pressure of 29.52 in Hg.

--Jerry

 

[carlsbad]

And because I am a physicist, my kids have banned me from watching Mythbusters with them (or practically any scientific show such as Scorpion) as I point out the (many) flaws in their assumptions, technique, and results.

--Jerry

 

[Toby Bradshaw]

Tony,
Its downward speed is determined by the total time of travel.

Nope. Let's say that you're shooting a bullet at 3000 ft/sec. Point your rifle straight down with the muzzle 3 feet from the ground and pull the trigger. Time to impact ~ 0.001 sec, impact velocity ~ muzzle velocity. Point your rifle straight up and pull the trigger. Time to impact (ignoring drag) ~ 3 min, impact velocity ~ muzzle velocity. The difference in time of travel is >5 orders of magnitude yet the speed at impact with the ground is the same.

 

[Toby Bradshaw]

P.S. Since I gave the correct answer to the OP's question 33 posts ago, it's not clear why this thread continues.