Round ball ballistics.

[FL-Flintlock]

Quick rule of thumb calculation for uphill/downhill is to shoot as if the target were at 90% the actual distance.  IE:  Target at 200yds, shoot as if it were at 180yds.

[Larry Pletcher]

Canute,
I appreciate your explanation. I'd also like to add that a "cross wind" usually isn't kind enough to blow uniformly all the way to the target.  Winds can quarter from any direction, vary in speed up or down, leaving you with different conditions from firing point to the target. A steady crosswind blowing at 90 degrees along the balls path would be great, but it almost never is that simple.

Bench shooters at Friendship will usually place 5 windflags between them and the 100 yd target.  It's common to see flags blowing opposite directions at the same time.   Reading windflags and shooting accordingly is a great skill.  Most competitors pick a wind or flag condition that reoccures, adjust sights for that condition, and wait for that condition to shoot. Having 45 minutes to fire 5 shots sounds like planty of time, but sometimes the shooter is well inside the last minute to fire the last shot. And he may have to settle for a less than ideal condition to fire that one.

I'm not good at this. Imagine that you're sitting there sights on the target, watching the flags.  There is a lull in shooting as shooters wait.  Your flags still aren't right, but you suddenly hear a bunch of guns around you firing.  And the mind games begin.

Regards,
Pletch   

[heinz]

Daryl, that is absolutely right
When the wind blows from 90 degrees the effects of the spin are changed because thhe wind is not parrallel to the flight axis.  If the ball is spinning clockwise and the wind is from the right the wind velocity across the top of the ball turning into the wind is, relative to the surface of the ball, faster than the surface velocity on the bottom of the ball, turning with the wind. The velocity difference will cause lift in the direction of the higher velocity.

Think about this, when you are driving down the road at 50 miles an hour the bottom of your tire where it contacts the road, is not moving relative to the road. That magic spot just sits there while the spot before it come down and touches and the spot behind it goes up and away.  The top of the tire relative to the road is moving at 100 miles per hour.

[Dphariss]

The second one is from a ballistics calculator I have the other from
http://www.handloads.com/calc/


The table above gives an indicator as to why the RB is so short ranged note the drop from 275 to 300 yards.




I have no idea which one is correct suspect its the bottom one though. Most ballistics programs have problems with the RB.

Dan

[Daryl]

Mine lists 1.24" drop at 120yards, 1.97" low at 125 yards from a 110yard zero. (all else being equal, ball weight, BC, vel.)
Sight height I set for .75", 70F and 2,000ft. ASL. Also - 1 second of flight at 330yards with 12.3feet total drop. Remaining speed of 699fps - like a .38 S&W factory load bullet - or .455 Webley. 2 seconds of flight = 530yards, 45.9feet low and still 505feet per second speed. This is actual total drop, not trajectory, which takes into consideration sigths, line of sight, rise and fall of the ball due to sight in range - the drop at that 530yards is only 42.1feet, 3.8feet less. When it's coming down, it's coming down.

[Dr. Tim-Boone]

Some times it is hard for old cops and lawyers to hang in there conceptually with laws of nature......    . They are used to thinking of legislative laws that you can break and pay a simple fine for..... Try breaking the law of gravity from the top of a 10 story building!! 

[Daryl]

Well, it isn't the fall that will kill you.

[Canute Rex]

More math, but here's something to think about:

Imagine that instead of you aiming down that the direction of gravity was swinging away from you like a pendulum. There would be less downwards force and a little forward force. The effect of gravity will vary by the cosine of the downward angle.

If you are aiming down at 45 degrees, COS 45=0.707, so the apparent force of gravity on the ball will be 70% of normal. 30% of the force will effectively be pulling the ball forward, so your loss of velocity due to air drag would be slightly less as well.

30 degrees down and the ratio is 0.866 down force.

So FL-Flintlock's rule of thumb of 90% is reasonable.

10 degrees down gives you 0.985, so the effect is about 1.5% different from horizontal.

And Pletch, yes, I remember from when I was doing more range shooting seeing the little streamers on sticks all the way out to the targets, blowing this way and that. One of the problems with ground level wind is turbulence. 200 feet up it tends to be straight and laminar, but at rifle height the wind has an up component and a down component, and burbles and eddies like a stream.

I need to look into wind drift more. 2.24" of drift at 50 yards would give you a bad day. I tend to go at that intuitively, but some real numbers would help.

[Jerry V Lape]

Canute Rex, I think your statement is in error.  If you are shooting downward, gravity is still acting straight down and will add its normal  downward acceleration during the short time interval the projectile is flying. This acceleration will probably not completely offset the wind resistance, frictional forces slowing the bullet.  But since gravity is a vertical force only, there is no way it is adding to the forward (horizontal motion) of the projectile.  I think you are confusing this with a  diagram showing the vertical and horizontal components of the bullets path. 

[Dphariss]

Here are a couple of more from the website with 110 yard zero with sea level for altitude rather than 4000.





Sight height is probably a little low but the data is generally valid since raising the sights to .75 only changes the 110 yard mid-range by .1". Also shows why a 110-130 yard zero is useful in a hunting rifle.




This gives an indication of why commonly used RBs will not shoot past 1000 yards.

Dan

[Daryl]

I use only 3 flags over 100 yards when shooting seriously.  More might work for some people, not me.  With the swirling winds on our range, more flags are too distracting. I did set up 5 flags once, and had reversals on every flag in 5 shots with no 2 flags pointed in the same direction at the same time that I saw.  The berms protecting us from the pistols and visa-vis, cause this I assume, long with the bush not to far away.  On the other side of the berm , 45 degrees to the prevailing wind, is a narrow pistol range, then a 12feet high wall, then another narrow pistol range with berms at the 50yard line and along it's far side. This raises havok with the wind, usually starting around 11:30 through to 12:30 in the day.

I found by raising the POI (zero) a bit at a time, I could figure maximum range of a projetile if fired on a flat plane, to strike the ground.  Of course, this is theoretical representing the longest possible ball and none would stike higher. All low shots would hit low as would all higher projected shots- like a morter.  It also had my .69 making over yards with  165gr. of 2F.  More powder would thoeretically give greater range - a few feet further could be all.
With a 1000yard zero - at 20 yards is would have to be, according to the program, 6' + 1/4" high.
At 610 yards, it would be 1,428.19" high, which is 119feet. The wind drift would be 50.2feet at 1,000yards.  It would take 5.359 seconds to travel that 1,000yards, terminal velocity would be 308 feet per second.  It would have a total drop of 305.36 feet. Now, something doesn't sound right, but that's what the program says. It works very well indeed with other rifles I have shot at fairly long range.

My program shows a .50 having a maximum range of 830 to 834 yards, which sounds about right.  The maximum height of travel to that is at 540yards - 953.77", which is 79.5 feet(rounded) It's terminal velocity would be 300fps and time of flight is 4.368 seconds.

When I adjusted my program to 0ft. ASL, my velocities were reasonably close to Dan's program. Wind drift is within 1/2".

The difference between .5" above the centre of the bore and .75" above the centre of the bore, was only 3/10" at 100 yards.

[Canute Rex]

Jerry,

Maybe I wasn't being clear. The pendulum thing was an attempt at visualizing the gravity vector vs the bullet path. A failed attempt, I guess.

Imagine shooting straight down a 200 yard deep well. You wouldn't have to account for bullet drop because the force of gravity would be in line with the path of the bullet. In fact, the bullet velocity wouldn't reduce as much as it would if fired horizontally, because you would add the acceleration of gravity to the speed of the bullet. If you stuck a chronograph down at the bottom of the well you'd find that the final speed of the bullet would be higher than the same bullet/load fired horizontally for 200 yards. It would be falling as well as shooting, so to speak. This would be tiny over a couple hundred yards, but still there.

Now imagine shooting 200 yards down a 45 degree hill. You'd be halfway in between shooting parallel to the force of gravity and perpendicular to it. Gravity would be pulling on the bullet at a 45 degree angle (roughly, due to arc) to the bullet's path. The bullet would experience less  pull perpendicular to its path. 0.707 as much. It would also be falling, somewhat, in it's path to the target, and thereby losing less speed. Less perp. force = less drop and less loss of velocity = shorter time to target = less drop, so it's a two-fer.

Does that make more sense?

Good thing I shoot horizontally at targets; this is too complicated. Important for hunters in the mountains, though.

[Jerry V Lape]

Canute Rex,

Now we are in agreement.  And I have taken more than one shot down a 200yd deep well, the most extreme being approx 250 yd line of sight but only 65 yd horizonal distance.  Shot 2 inches below my normal point of aim and hit an inch above it.  The angle was so steep I used the toe of my boot as rifle rest while sitting on the edge of the rim.  The angles like that are similar to tree stand shooting I suppose, as the vital area is greatly narrowed from above.  From that angle it is best to get a going away or head on shot as it provides a larger (longer) target area to give you a little leeway on point of impact.  AZ provides a lot of opportunity for cliff shots. 

[huckfinn]

http://www.chuckhawks.com/shooting_uphill.htm

Take a second to read this about shooting uphill/downhill.  


It says that the effect of gravity on the projectile only has to do with the horizontal distance, not the line of sight distance.  Leupold has a scope that will measure the
line of sight distance but will correct for the 'true ballistic range."  A 400 yard line of sight shot is equivalent to a 335 yard horizontal shot in terms of bullet drop.  

Do you remember the "monkey and hunter" question in physics?  

[Daryl]

That gravity only works over the horizontal distance only, is a given as far as bullet or ball drop is concerned. That is why a ball or bullet shot over a 400yard distance at an angle of 45 degrees, up or down, experiences the gravity of only about 200yards - and therefore exhibits drop for the actual horizontal distance only. The actual horizontal distance changes with the angle, also a given.

[Vomitus]

  Hey Gents, Thanks for posting these tables on the fifty. I see now why I have some issues at 75 yards. Yep, shooting over the small gongs(egg) at this distance.Interesting chart,thanks.
(I now got to figure out how to get 1900FPS outta my Beck!)

[Daryl]

100gr. of 2f should get her close, LB - maybe 110gr.