Aim Above or Below?

[huntersjournal]

A controversial issue

If the target is not at the same level as the shooter, should he aim the rifle above or below the critical point?

As you can see in our (exaggerated) graphics, when you aim horizontally using a properly calibrated scope, the barrel of the rifle tilts slightly upwards to compensate for the parabolic effect. In other words, the bullet crosses the sight line immediately after you pull the trigger and travels above that line most of the time.

If you follow our sight-in adjustment guidelines, as described in another article, both lines will intersect at the vital zone at about 250 to 300 yards. For a target located about 100 yards, the bullet will hit 3 inches above the crosshairs’ center.

However, what happens when you are lying on the top of a hill and the game moves in the valley below? What if it is you in the valley and a sovereign reindeer roams a mound?

Here is a typical story:

A hunter, standing at the foot of a hill sees a white-tailed doe on the top. He focuses slightly behind the shoulder bone of the deer, fires and… The female deer flees as the bullet raises dust behind her. Missed miserably. But, why?

To understand the reason we must consider which factors affect the trajectory of a bullet. These are:

• Thrust
• Rotation
• Nutation (pitch)
• Air resistance
• Gravity
• Mass
• Shape of the bullet
• Initial velocity
• Length

(Actually, there are only two important factors: the ballistic coefficient of the bullet and its velocity.)

Modify one of these factors and the outcome will vary as well. For instance, if you adjust the scope for a cartridge that leaves the muzzle at 1063 yards per second and then use another cartridge that develops an initial velocity of 890 yards per second, the impact at 250 yards will hit about 4 inches below.

Normally, when we sight-in a rifle both target and barrel are more or less at the same level.

However, when shooting upwards, we are modifying several factors at once: gravity and air friction, among others. A bullet fired upwards tends to slow down due to gravity. Conversely, if fired downwards, it tends to accelerate.

To counteract the effect, always aim below the desired point when shooting upwards or downwards

In real life, the effect becomes important when the angle between the target, gun and the horizontal line across the muzzle exceeds 30 degrees.

Now, by way of entertainment, consider this ballistic question:

If you fire horizontally and drop another bullet with similar characteristics from the same height, which one reaches the ground first?

[aznighthawk]

I apologize in advance. My wife went to a Halloween party and left me at home to baby sit (Trade off for getting to go to the range in the morning to shoot my hand loads). Anyways, I got bored. If it gets a little incoherent towards to end I blame Miller High Life. (If you hated high school physics you might want to skip this one)
“However, when shooting upwards, we are modifying several factors at once: gravity and air friction, among others.”
Good luck modifying gravity. Drop a rock off your roof and time how long it takes to hit the ground. Do the same thing the next day and you will get the same amount of time. Acceleration due to gravity never changes as long as the earth does not gain or lose mass and you do not increase or decrease your distance from the centre of the earth. It does not matter if you launch a projectile above or below the horizontal; gravity has the same effect. The projectile launched straight up will lose 9.81 m/s of velocity in the first second. A projectile launched straight down will gain 9.81 m/s in the first second. Both accelerations have the same direction and magnitude.
How is air friction different depending on if you aim up or down? Is the air just above the horizontal plane where the shooter is located a different density than the air just below it? Is there wind that only affects the air above the horizontal? The more important question is how are you modifying it by shooting upwards or downwards?
“ A bullet fired upwards tends to slow down due to gravity. Conversely, if fired downwards, it tends to accelerate.”
First of all both bullets undergo huge decelerations due to air resistance (even the one fired downward). The bullet fired downward is travelling much faster when it leaves the barrel than the terminal velocity it would achieve if dropped from rest. For this reason the upward force of air resistance exceeds its weight, resulting in a net upward force and acceleration. Since the acceleration is in the opposite direction of the bullet’s velocity it slows down. You would get a similar result if you tried to throw a piece of paper downward as fast as you could. When it left your hand it would be travelling the same speed you could throw a baseball, but it would quickly slow down to its terminal speed and float the rest of the way to the floor.
A 270 caliber bullet leaves the barrel around 3060 ft/s and by the time it is 200 yds down range it is travelling around 2639 ft/s. During this time its average velocity is 2850 ft/s [vavg = ½(vf +vi)]. Using the equation t = d/vavg you can find that it takes the bullet 0.211 seconds to travel the 600 ft. Now that we know the initial and final velocity, and the time it took we can find acceleration using (a = v¬f – vi/t). The average deceleration of the bullet due to air resistance during the first 0.211 second is 1995 ft/ss.

Acceleration due to gravity: -32.2 ft/ss
Acceleration due to air resistance: -1995 ft/ss
The average acceleration due to air resistance is almost 62 times greater than the acceleration due to gravity during the first 200 yds of the bullets travel.

“To counteract the effect, always aim below the desired point when shooting upwards or downwards”
Let me try to explain why you aim below the desired point when shooting upward or downward.
Case #1: You fire at a target directly above you. If you are using your hunting rifle you will hit high. This is because your hunting scope is adjusted to compensate for drop due to gravity. When you aim straight up the bullet does not follow a parabolic path and gravity only causes it to slightly slow down while it travels in a straight line path.
Case #2: You fire at a target directly below you. This bullet also travels in a straight line path. Your hunting scope is not set up for a bullet that travels in a straight line, but for a bullet that drops below its initial straight line path due to gravity. For this reason you hit high again on your first shot and then adjust on your second shot by aiming below your target.
Case #3: You aim horizontally at a target 200 yds away. Earlier we found that it will take the bullet 0.211 seconds to get there. Using the equation d = 1/2gt2 + vit we can find that the bullet will drop 8.5 inches below its initial straight line path due to gravity. When you sighted your rifle in at 200 yards you already adjusted for this drop so you didn’t have to think about it. When you see the bulls eye in the cross hairs your barrel is actually aimed 8.5 inches above your target. (You can apply that last sentence to case #1 and #2 if it didn’t make sense the first time.)
Final analogy: You want to hit a target by throwing a baseball. If you are standing on a cliff and the target is directly below you, you throw directly at the target or just drop the ball while holding it above your target. If you are throwing at a target on a flat field that is 40 yards away you throw the ball with an upward angle so it will drop into the target. Since most of our rifle shots are more horizontal than vertical we set up our scopes to compensate for that drop.
Case 1 and 2 are very unlikely in a hunting situation. They help to illustrate the point that as your shot angles get more extreme you have to aim further below your intended point of impact to compensate for the bullets flatter trajectory.
If you want to get scientific you only need to worry about the horizontal distance to the target when calculating bullet drop for typical hunting ranges. You can find this by multiplying the actual distance (range finder reading) by cosine (angle above or below horizontal). They now have range finders that already do this for you with a push of a button.
“If you fire horizontally and drop another bullet with similar characteristics from the same height, which one reaches the ground first?”
They will hit at the same time. Acceleration due to gravity is independent of horizontal motion.

[shootinfool]

Aim low with either shot. The reason for this is that gravity only affects the bullet for the real linear distance to the target. Even though you range the target at 500 yards, if the degree of the angle is 30 gravity will only affect the bullet for 433 yards. If you take the COS of the angle you are shooting and multiply it by the ranged distance it will give you the distance you should correct for. In this case if you ranged the animal at 500 and corrected for 500yds then you will be shooting over your target. This is a much simplified version. Hope it helps.

[aznighthawk]

I could have done a simle post but that would not have killed a night of baby sitting. Hopefully there is a couple of people out there who prefer to know how things work over being spoon fed the simplified answer.

[maintguy47]

Use a range finder or throw a rock at em

[aznighthawk]

A range finder that compensates for shooting angle above or below the horizontal. Forgot that part .

[Der Aulte Jaeger]

WaidmannsHeil,
The hardest part is estimating the slope or the angle up or down from where you are shooting to your target, more on that in a minute. In either case it's the "horizontal" distance to the target that counts, and whether you are shooting up or down, it decreases. Now to that estimation: depending on your height and arm length, reaching out and touching the slope in front of you gives some accuracy in estimation. If I am standing straight and reach out and touch it then that's close to a 60 degree slope for me if I recall right. Better yet get a tilt meter such as one finds for sale for sailing and jeep 4wd activities and use it. It's a curved level, simple,and works up through 55 degree if you get the right one. This little device is easy to carry and sighting over it a few times in the mountains will give a big assist in estimating angles. Other pocket devices but heavier, are the old Military, Forestry and Surveying compasses, mainly Bruntons. Suunto also makes a combo inclinometer/compass that's super nice also.

Now to simply the trig tables to the point they are relatively useful in a quick estimation situation as it's the angle and cosine that I use to determine relative range. Say you are shooting up a 30 degree slope. I found the cosine and rounded it off to .9. I multiply that
x actual range. If your rangefinder says 300 yards, shoot as if it was a 270 yard shot, or .9 x 300
= 270 yds. Next try a 45 degree slope down. Your range finder says 400 and the cosine is .707 so I rounded to .7 for math in the head purposes. .7 x 400 = 280 yards so you'd shoot as if the 400 yds were actually just 270 yds. The last number I carry in my head is .9 for those shots in that 60 degree realm. We are talking about shooting over a ledge and in this case figure a 500 yard shot at a trophy sheep. The cosine is rounded out is .5 x 500 yds for a much shorter shot of 250 yds. Truth is very few will ever get a chance at that 60 degree or greater slope but I like the 1, 2, 3 aspects of ranging for slope which by the way is the third calculation I make in my head behind range and wind. I also use a 1,2,3 approach for both of them.

[southwind]

This is simple. Gravity is the issue! shoot the horizontal distance at targets above or below you which is normally going to be holding low.

I have never met anyone who can accurately judge percent of grade, so take a good rangefinder with angle compensating mode and you will be fine.

Keep it simple, leave the books, manuals and calculators at home.

[Der Aulte Jaeger]

I hope you didn't take away from what I wrote that one needs extra equipment, books, calculators, etc.

This is simple. Gravity is the issue! shoot the horizontal distance at targets above or below you which is normally going to be holding low.

I have never met anyone who can accurately judge percent of grade, so take a good rangefinder with angle compensating mode and you will be fine.

Keep it simple, leave the books, manuals and calculators at home.

First let me address "percent of grade," which is a far different beast than slope angle which is what we are working with. Finding someone who can estimate percent of grade is harder than pulling hen's teeth!

I do agree that gravity is the issue and so much so that most others pale in comparison. The method outlined by me above, requires less complex equipment weight wise than even you suggested carrying, a, "rangefinder with angle compensating mode." The small pocket sized slope angle device I indicated above is really light and small, runs about $10, is super reliable and between it, good scope sighting in procedure, and using your basic duplex scope, eliminates the need for a rangefinder with angle compensation. I suppose that many of the more "expensive" range finders of today are really great but thus far I've gone through a couple Bushnells that both experienced the same problem in that after less than a season of use started degrading in ability to "range," distances over 175 yds or so. I do like using a rangefinder since if they work as advertised, should be more accurate than my method with the duplex crosshairs for those shots beteen 300 and 500 yards, where I just might take a shot with near bench rest wind conditons, and near bench rest stability of rest, etc. My carbine is very capable but between the conditions and my limitations, the rangefinder is just an extra bit of sprinkles on the icing of the cake.

I really do like your last statement, southwind, "Keep it simple, leave the books, manuals and calculators at home." My method, at most, requires a small 3x5 card taped to your stock and when incuding a slope measurement device, either as part of your compass, or seperate the weight added is in the ounce or two category and there is no need for books, manuals or calculators, or worse yet "unreliable equipment!"

As for estimating slope angle, carry a slope angle measurement device around for a week or two in the mountains and you will also learn how to estimate angles somewhat correctly! I had professor in geology teach me that years back during grad studies in geology and forestry. Like all things, "practice makes perfect!"

[JLROOT]

Now I remember why I hated science class!!!!

My head hurts.

Just one time for the slow kid (me):

If shooting up hill do I aim low or high? Same question for shooting down hill.