How big is the effect of shooting downhill?

[Canute Rex]

Or uphill, for that matter.

I was out back shooting yesterday. I usually shoot offhand at 50 yards with a 6 o'clock hold on one of those Shoot-n-see targets with an 8" black area. I went up closer to 25 yards because there's a shoot coming up with a 25 yard competition. Suddenly my 6 o'clock hold was hitting at...6 o'clock. I tried putting the x-ring on top of my front sight and that worked. You'd think that a rifle sighted in for 50 yards would shoot a little high at 25, or am I missing something?

I looked around and noticed, looking back at my usual 50-yard spot, that it was three or four feet higher than the ground my bullet trap sits on. Add the difference between the 18" on center height of my trap and my rifle at my shoulder, maybe 3 1/2 feet, and I was shooting on a six to seven foot downslope at 50 yards. At 25 yards I was on level ground with the bullet trap, so I was aiming down maybe 3 1/2 feet.

Sometimes I have competed in woods walks where the target/gong was uphill or downhill from me. I have always wondered about point of aim in those situations.

How much difference does relative height make at various ranges? I am interested to hear people's experiences and any hard numbers anybody has come up with. 

[roundball]

Once an firearm is sighted in on the horizontal, it's POI will always be higher in both cases if the firearm is then shot at an uphill or downhill angle, and by the same amount in each case...there are numerous explanations and charts on the subject via Google but essentially its the change in the effects of gravity due to the change in angle that gravity is able to place its force on the projectile

[longcruise]

It's not the three or four feet that is getting you.  Your gun is shooting just as it should if sighted for 50 yards.  The path of the bullet is an ever increasing arc as it leaves the barrel.  The line of your sights crosses that arc at two places.  If you were holding at 6 O'clock and hitting a bit high at 50, then your gun is probably shooting dead on at about 25 yards, a bit high at 50 and once again, dead on at about 75 or 100 depending on the velocity of the ball.

[SCLoyalist]

How much difference does relative height make at various ranges? I am interested to hear people's experiences and any hard numbers anybody has come up with.  

My copy of the Lyman Black Powder Handbook has a section on ballistics, including a couple of pages devoted to effects of uphill/downhill shooting.    An example they give is if you're shooting a minie ball at 1200 feet/sec mv, at a 45 degree angle up or down,  at 100 yds the bullet will hit about 4 inches higher.   Unless you're involved in the Battles of Bunker Hill or King's Mountain, you're probably not going to be shooting that long a distance at that steep an angle.

As to the rifle being sighted in for 50 yds, and whether it should hit high/low at 25,  it depends on factors including muzzle velocity and caliber.     The "Bullet Path" (height of the bullet above or below the line of sight as you're looking through the sights) is the parameter you're interested in.    A .495 RB fired at 1600fps muzzle velocity if sighted in (assuming a 'center hold' sight picture) at 50 yds will be  0.15" high at 25 yds.    If sighted in for 50 yds at 2300 fps mv, it would, at 25 yds, be 0.16" low.  

Anyway,  the Lyman BP handbook does discuss the math of bullet trajectory,  if you've a few hours to dig into it.

SCL

[Canute Rex]

Thanks for the responses. It seems that the uphill/downhill factor is insignificant in all normal situations, and that I'm experiencing the bullet arc. Hmmm....

Now I get to decide whether to adjust my sights for a dead on hold at 50 and drop the sight picture a fraction of an inch at 25, or just leave it alone. I'll read back through the archives for the arguments on that.

Thanks again.

[Roger Fisher]

'We' try to hold dead on since the difference is not enough to worry about on most  primative targets. 

[Dphariss]

If the rifle shoots flat to 50 yards horizontally it will be very close to the same POI at that range even at a steep angle.
The up hill down hill thing is more important when the trajectory is high due to low velocity or longer range. I never varied my hold when shooting squirrels be they in a tree overhead or on the ground at my level But the range was not sufficient cause any significant change in trajectory, at least not enough to cause a miss a squirrels head.
Some one needs to do some actual testing on this.
Also remember in shooting game that if above the animal creating much of an angle that one must place the shot higher to get to the organs the projectile must destroy.
If shooting down at 45 degree angle at a deer and hold as if shooting horizontal the projectile will likely undershoot the heart/lungs.
If shooting from below some compensation is also needed.
So the hunter must aim for the internal organ he wants to hit, imagine where it is from his position and pick a spot on the animal that will place the bullet at the point he desires inside the animal.

Dan

[T*O*F]

Thanks for the responses. It seems that the uphill/downhill factor is insignificant in all normal situations, and that I'm experiencing the bullet arc.

Actually, it can be a huge factor.  The simplest example is a bowhunter in a treestand.  They almost always shoot over the deer.

It has to do with the "Time of flight" of the projectile as illustrated in this picture.
The steeper the angle, the more pronounced the effect.  Same for uphill, just flip the picture.  The mind tells you that since the target is 150 yards away from your muzzle, you would hold high.

[D. Taylor Sapergia]

Excellent illustration TOF!  The example is identical for shooting a flintlock as it is for a longbow.  
One thing that adds another complication to the thing, is the height off the barrel of the sights.  The closer your sights are to the bore, the easier it seems to me is the sighting to point blank.  In other words, The line of sight and the line of the ball are closer together to the point blank spot.  

[Jerry V Lape]

TOF is correct with the diagram but not correct about time of flight being equal for both AB and AC.  That is physically not possible as the ball upon exiting the muzzle has only one velocity.  Distance AC is still longer. 

What TOF has correctly drawn is a vector diagram.  The distance AB is the horizonal distance that gravity acts on either shot AB or AC.  However our shooter has estimated his shot AC as 150 yds and applied that hold to his sight picture.   But the horizontal is only AB of 50yds.  If he held as if it were a 50 yd shot he would hit correctly.   Interestingly, if the wind is strong enough to be a factor he would need to adjust for wind on the 150yd distance with the sights held for the horizontal of 50yds.  And your group size on AC is still going to be the same as for your 150yd groupings. 

Leupold is making a rangefinder which measures the downward angle (or upward) and reading out the horizontal distance to give you the correct information for your sight picture.  So far no one has a good wind detector which can be equally as important or more so with wind deflection on long range shots.

[T*O*F]

TOF is correct with the diagram but not correct about time of flight being equal for both AB and AC.  That is physically not possible as the ball upon exiting the muzzle has only one velocity.  Distance AC is still longer.

I think I beg to differ.  Velocity has nothing to do with it.  It's all about gravity.  Gravity starts acting on both as soon as they leave the muzzle.  If fired simultaneously, both would hit the target at the same instant.

[Joey R]

Back when I shot 3-D outdoor archery matches there was a woodchuck target with the shooting stake placed 3 feet from the target. It gave the newbies fits when they shot the target with the 10 yard pin. I scored 10's on that target everytime by using my 60 yard pin setting.( Past experience 

[Jerry V Lape]

TOF,   Perhaps if you considered your example this way it would help.   First the formula  (distance = time x velocity.)

If the horizontal distance were 50 yds and you fired a muzzleloader with a velocity of 1500fps the time of flight would be a little more than 0.1 seconds.  

150ft / 1500fps = 0.1 seconds   (actually a little longer because you have some velocity decay due to wind resistance)

If the slant range were 150 yds in order for the ball to cover that distance in 0.1 seconds it would have to be traveling  4500fps.    There is no way you can get your old muzzlestuffer to accomplish that.  

450 feet /0.1 seconds = 4500fps  

Don't confuse this with  the old classroom example of a bullet fired absolutely horizonally at the same time a second is dropped vertically from the same height.  In this case they both would reach the ground, assuming the ground is level, at the same time.  The classroom example is useful to demonstrate that gravity is a constant separate from horizontal velocity.  Hence, your diagram is valid, but not the statement beside it.

[T*O*F]

Don't confuse this with  the old classroom example of a bullet fired absolutely horizonally at the same time a second is dropped vertically from the same height.  In this case they both would reach the ground, assuming the ground is level, at the same time.

Jerry,
I did and you're correct.  I started to add that example but figured it would cornfuzle everyone even further.
I bow to your superior wisdom.

[Canute Rex]

I guess the principle is that when you shoot downhill the angle between the gravity vector and the ball's kinetic energy vector is smaller. If you shot straight down there would be no bullet drop at all, the two vectors being parallel. Just keep your toes out of the way.

On a pragmatic front, now I have the counter-intuitive task of adjusting the sights. If the ball is crossing the line of sight at 25 yards, going over by ~4" at 50 yards, and (theoretically) crossing again at 75 yards, then I need to file down the rear sight by maybe a sixteenth. (27" sight radius) That would put me slightly under at 25 yards and dead on at 50. That is, if the ball is still on the rise at it hits 50 yards.

Now I'm thinking that my muzzle velocity must be low for there to be that much difference between 25 and 50 yards. I'm using a 490 ball (175 grains) and 65 grains of 3F. I cut down a bit on the powder to save my cranky right shoulder. Ideas? Suggestions? Two cents?

[SCLoyalist]

Using the numbers in the Lyman BP Handbook (which are probably ballpark within 10 percent or so of what your gun is doing),  the load you described ought to be giving you a muzzle velocity around 1525 fps.  (If you have access to a chronograph, it would be a good sanity check before doing any rambunctious sight filing.)  

Rather than file down the rear sight, you might see if you can find a taller front sight, or an adjustable rear sight to save on filing.   Track of the Wolf (and no doubt other suppliers) has a bunch for most sizes of dovetails, including just a front sight base that you could solder your own custom height blade in.  Increasing the height of the front sight should give you a bit more immunity to heat mirage, too.

Once you get the front/rear sights altered where you're hitting dead center at 50 yards with that load and a center hold sight picture, the Lyman tables say that at 25 yds the bullet path will be 0.23" (high),   50 yds will be 0" (dead on),  75 yds bullet path will be -1.94" (low), and 100 yds will be 6" low.      

Good luck.  SCL

[Jerry V Lape]

And shooting almost straight down, which I have done on a deer approx 175 yds below my perch on  a cliff edge is extremely difficult to figure out unless you are lined up with the long axis of the animal.  The shot was so vertical I was resting my forend on the toe of my boot which was hanging over the edge.  I held off  (below) the near side of the deer and hit almost on top of his back.  This was with sights zeroed for 200 yds.  Lucky guess on my part as the effective width of the vital area  was probably less than 5 inches from that angle.  If you can find a cliff to practice vertical shots, try it and see how difficult the vertical position is.  It would make a wonderful target presentation for a club shoot if you had the terrain for it.  Even a 25yd vertical at a target the size of a ground hog  will challenge most since they never practice it.   

[Daryl]

For our black powder shooting, Taylor's mention of the height of the sights is a very important one. A similar effect comes from a 6 o'clock hold in this instance, as this was Canute's method of sighting.  To hit 4" high at 50 yards, the ball would be approximately 2.2" high at 25 yards, not zero'd.  From my own testing, I know most of my rifles, if zero'd at 25 yards, I mean actually zero'd, as in the horizontal line disecting the centre of the group, they will be no more than 1/2" high at 50 yards. With normal sight height- raising the barrel or lowering it slightly, 20 degrees makes not enough difference to see on the target - perhaps 1/4".

 Suffice to say that shooting uphill or downhill, the shot will go high. The higher the sights, the higher the ball or bullet will strike.
Dan also spoke of shooting squirrels up in a tree - with the barelycorn-type sights, set low on the barrel, he also is spot on.

[Canute Rex]

Thanks, SCLoyalist, for the hard numbers. From looking at this chart and that, I'd say I'm getting somewhere around 1500 fps.

Daryl, 2.2" high sounds about right, as I wasn't really dead on at 25 yards. I had sort of a mini-6 o'clock hold. I was using one of the repair dots from a Shoot-n-see, which is about 2" diameter, and I was sitting that on top of the sights, roughly speaking. Roughly.

Like a lot of other people  on this site I need to wear glasses for long distance work (and short distance work) and I have to make a focusing choice between the front sight, the rear sight, and the target.

[Daryl]

Front sight sharp - target and rear sights fuzzy - standard rules of engagement.