Round ball ballistics.

[credns]

Due to gravitational pull if I were to shoot an elongated bullet up hill I would have to aim UNDER my target to hit the mark. On an elongated bullet the bullet surface exposed to gravity changes when shooting uphill vs. parallel to the Earth's surface.

If I were to shoot a round ball uphill at that same mark where would I aim? The gravitational pull on the surface of the round ball exposed to gravity doesn't change whether shooting uphill or parallel to the earth's surface.

[roundball]

Hold is "under" for both up and down angles compared to straight & level.
There would be different amounts of "hold under" based upon the degree of the angle, distance to the target, and differences in projectiles being compared.
The effects of gravity work on the weight of the round ball, not its shape.

[smylee grouch]

One of my favorite places to shoot has a gong that is 300 ft. away, down hill, but actual yardage that gravity acts on it is only 50 yds.  Its a 12 inch square gong and not too hard to hit but many shooters will shoot just over the top most of the time.      Smylee

[Dphariss]

One of my favorite places to shoot has a gong that is 300 ft. away, down hill, but actual yardage that gravity acts on it is only 50 yds.  Its a 12 inch square gong and not too hard to hit but many shooters will shoot just over the top most of the time.      Smylee

Sounds like they need to zero their rifles for a longer point blank or shoot a higher velocity load.
 
Dan

[Dphariss]

Due to gravitational pull if I were to shoot an elongated bullet up hill I would have to aim UNDER my target to hit the mark. On an elongated bullet the bullet surface exposed to gravity changes when shooting uphill vs. parallel to the Earth's surface.

If I were to shoot a round ball uphill at that same mark where would I aim? The gravitational pull on the surface of the round ball exposed to gravity doesn't change whether shooting uphill or parallel to the earth's surface.

Gravity works on all bullets the same. The time it works on them is the only factor.
Shot horizontal to the earths surface a bullet traveling 100 yards will have full effect of gravity for 100 yards.
Shot at a 45 degree angle the gravity will only have the effect of 50 yards.
If shot straight down gravity will not effect trajectory at all.
Shooting game the hold over/hold under has to take into consideration the VITAL ORGANS that are the target INSIDE the animal. A impact point that would strike the heart on a horizontal shot may miss the heart if the same impact point is used with the animal above or below the shooter at a steep angle.
Hunters always need to aim for the ORGANS where they actually are inside the animal that they are trying to strike with the bullet.
Dan

[Daryl]

YES - in concert -   Every projectile, round ball or conical falls16 feet in it's first second of horizontal flight.  As Dan noted, it's time of flight over that distance.

It's ballistic shape & speed dictate it's time of flight over a given distance.

The higher the sights are above the centre of the bore, the greater the height of the projectile in smylee's example. Thus Dan's statement about point blank range.

If a target was perfectly vertical and over 100yards away - either up or down, most shooters would be unable to hit it as the ball or bullet would be always travelling above or away from the line of the sights - ever increasing. With no horizontal component, the ball or bullet would never cross the line of sight past the initial 15 to 25 yards travel - whatever it's zero.

I increased the sight height to compensate for the short range. Yeah - it's a small picture - looked bigger while I was making it.  HA! The physics remain unchanged.

[smylee grouch]

As a side note on my first post, that 12" gong looks more like a 6x12 when viewed from the extrem downward angle. You have to hold steady for a 50 yd shot if you want to hit it with any consistancy.   My 58 hunting rifle is zeroed for 130 so I try to hold center of bottom edge or so.    Smylee

[SCLoyalist]

With respect to how fast a bullet falls, it accelerates due to gravity at 32.2 feet per second per second downward.   It's drop is a function of time of flight ( t, in seconds),  drop (in feet) = 1/2 (32.2)*t^2.   So, after one second, it will have experienced 16 feet of drop.  After two seconds, 64 feet of drop, etc.  At least, that's how Sir Isaac Newton explained it to me over a beer one night back in my college days.
 
The old Lyman BP Handbook had a fairly decent discussion of ballistics and trajectories.   Drop and "bullet path" are two worthwhile things to understand when interpretting where you're hitting versus where you're aiming.   

SCL

[credns]

It looks like we're saying that round ball or elongated bullet the same rule applies shooting level vs. up (Down) hill.

[SCLoyalist]

It looks like we're saying that round ball or elongated bullet the same rule applies shooting level vs. up (Down) hill.

Right,  whether shooting uphill or downhill or roundball or elongated bullet, you would aim a bit under the target.   What varies is how much under, and that's determined by the projectile's time of flight (in turn determined by bullet cross-sectional area and mass and muzzle velocity and distance to the target) and how much drop gravity causes during that time of flight.  The aforementioned Lyman BP handbook includes a brief discussion of the effects of shooting up/downhill in the ballistics tutorial, along with some examples and math formulas.   

Just as an example, if you were shooting at a squirrel in a tree, 25 yards away at an uphill angle of 60 degrees with a .36 cal squirrel rifle, 1900 fps mv, patched roundball,  you might want to hold about a quarter inch lower than if you were making a level shot.   If that squirrel was 100 yards away up that same hill, hold more like 4 inches lower than if shooting on the level.

 

[mjm46@bellsouth.net]

I totally understand the whole thing. My only problem is trying to find a range on the side of a hill to practice.

[Daryl]

NP - we can easily manage any angle to about 45 degrees here and the odd cliff here and there will give straight verticals or by placing the target out from the base, any angle down you want. A ZIP line would be fun for going down to check the target if you forget your spotting scope. The climb back up wouldn't be much fun in snow shoes.

[T*O*F]

Just to add a little spice to the chili...........If your hunting rifle is zeroed for "point blank range" as it should be, why not just aim dead on, regardless if your target is uphill, downhill, or level.

[Daryl]

Exactly.

[4ster]

With respect to how fast a bullet falls, it accelerates due to gravity at 32.2 feet per second per second downward.   It's drop is a function of time of flight ( t, in seconds),  drop (in feet) = 1/2 (32.2)*t^2.   So, after one second, it will have experienced 16 feet of drop.  After two seconds, 64 feet of drop, etc.  At least, that's how Sir Isaac Newton explained it to me over a beer one night back in my college days.

SCL (or anyone else), Its been a long time since I took physics and it was not my best subject.  Now that there is no grade involved I like to understand the logic of the formula, not just to memorize it for the test.  Since we know that a falling body accelerates at about 32 feet per second per second, why does the formula halve that rate?  It seems to me that a bullet would drop 32 feet in a second.  I'm wear'n a hole in my head from scratch'n.  

I'll buy a beer for anyone that can explain it to me.

Steve

[Daryl]

I didn't take physics so cannot answer that - I've never heard of 32fps/ps, but only 16fps/ps, but I do know a projectile will drop 16feet in it's first second of flight. I had thought it was 16' in the second, third, etc, seconds of flight, though, but that isn't an accelleration, only a constant drop. I think that's the same mistake Forsyth made- or maybe I disdn't usnderstand what he was writing about in 1860, either.

For any given speed, the higher or greater it's ballistic coefficient, it's coeficient of friction, resistance to drag or better ballistic form or shape(whatever you want to call it), the farther it will travel in the first second of flight, second second, etc.

In hunting senarios, we are only concerned with part of it's first second of flight - where the drop is only figured in inches or up to a couple feet for so with ranges to perhasp 200yards.  The ballistic shape, coefficient of friction in around ball is higher, the greater the diameter of the ball.  Therefore at an initial velocity of 1,700fps, a 50 calibre ball has more drop over 150yards than a .62 calibre ball. 

[Canute Rex]

4ster:

Consider that the downward velocity of the ball is starting at zero feet per second and reaching 32 feet per second by the end of  that one second.  It's speeding up (zero, .1 ft/sec, .2 ft/sec, .3 ft/sec) as it falls.

If you were driving a car around for an hour, to find out how far you went someone would want to know your average speed. What's the average of zero and 32? 16.

The distance dropped  is 1/2 GT^2. If you solve that for 32 feet of drop (G=32 ft/s2) you get the square root of 2, 1.414 seconds. Note that it took one second to go the first 16 feet, but only 0.414 seconds to go the second 16 feet. It will take even less time to go the next 16 feet, and so on.

If you fired a bullet at 1800 ft/sec, it would travel almost half a mile before it dropped 32 feet, discounting air drag. That's a big discount, as it would probably be traveling at a walking pace by then.

Have I earned my beer?

[Daryl]

The problem with gravity rules, is the bullet and round ball both have resistance to the effects of gravity.  Projectiles  in forward motion actually produce lift due to their rotational stability. Too, the direction the projectile is fired, east, west, north & south also effects the projectile's trajectory - greater or less, as well as some wind directions, reduces the effect that gravity 'should' have on the projectiles. Another change made to ballistics from the rules of physics, is elevation ASL, along with the atmospheric conditions.  All these things effect ballistics of the projectile and change the basic rules, somewhat- defying the laws of physics.

 

[Canute Rex]

Never "defying" physics Daryl, just more complications. And a wobbly hold trumps all.

I have read that long range artillerists have to account for the spin of the earth, but I've never had that problem with my matchlock.

"In this household, we obey the laws of thermodynamics!" Homer Simpson

[heinz]

Daryl, that is just wrong.  The spin geometry on the top of the spinning object that is pulling it up is exactly equal to the spin on the bottom of the spinning object pulling it down, as long as the path is parrell to the spin axis.

[Dave Faletti]

I second Canute on physics.  Daryl the 16fps is the average velocity in the first second its not the accelaration.  You start with 0 and end with 32fps. You end up with an average of 16fps hence the 16ft drop. 32fps/s is the accelaration.  Blame Newton for confusing the average guy.  As you know different bullets have different amounts of drag which is velocity dependant, and changes flight time.  With each second the bullet covers less distance but its moving faster downward so more additional drop. Drag also counters acceleration due to gravity but not significant with what we are doing.  Keeping sights low to the barrel minimizes error for any inclination/declination but decreases max point blank range.

[4ster]

Have I earned my beer?

Yes!  Now you have to collect.  I live in Washington State, but will be traveling to the other Washington in June I think.  Otherwise, PM me your address and your particular  poison.

[Daryl]

OK - but I have some questions.

The math makes sense, but how do you account for higher points of impact over identical distances when the wind blows 90 degrees from the left - or right side - one hits high, the other low? 

Once started angling lower, or angling higher, that bullet will continue to drop more or less than the other - yes, it was directed by the wind effect.  Do these ruin the exact 16feet per second rule. 

Whether it is noticable when firing a matchlock matters not. 

[Dave Faletti]

Daryl.  The accelaration due to gravity is basicly constant.  Since we aren't in a vacuum, aerodynamic drag, wind, elevation and whatever other effect we can find will all play a part in the answer.  It comes down to what the question is, the problem to be solved and the accuracy you want.  In the end you get your answer from empirical data collected at the range by shooting.  Understanding ballistics/aerodynmics helps you ask the right questions, use the appropriate resources and best use of range time. 

[Canute Rex]

I just mentioned my matchlock because that's what I've been shooting lately.

A crosswind, a cross wind, mind you, would tend to lift or drop the ball depending on the direction of the wind vs the direction of the rotation of the ball. The ball is acting sort of like a curveball thrown by a pitcher.

Let's say the ball is spinning clockwise as you look at it from the shooter's perspective. Whatever point is at the top of the ball at any moment is moving to the right, the bottom point to the left. If the wind is coming from the right, then the top of the ball is experiencing a higher crosswind velocity than the bottom. Higher velocity equals lower pressure (Bernoulli effect) so the bullet will experience a small amount of lift and will drop less than in still air. Wind from the left means the ball drops a bit more than it might. Counterclockwise spin and right hand wind means extra drop. Counterclockwise spin and wind from the left means extra lift.

No cross wind and the velocities are equal, so the pressures are equal, so no effect, just as heinz wrote.

And it's only 16 feet in the first second. In the second second (2nd second?) it drops 48 feet. It's accelerating. But two seconds would take a bullet most of a mile, so we don't have to worry about that.

Dense air or a headwind will drop the point of impact because it slows the ball down - not as much forward motion per downward motion.

Like I said, it's still physics, just more complicated physics.

Well, 4ster, I think you'll have to just owe me that beer for a while. It's a long commute from VT.