[hillbilly]

This writer gives good advice about shooting uphill or down hill, but not for the reason he lists.

It's called "A right triagle" not "gravity"


http://www.fieldandstream.com/fieldstream/hunting/article/0,13199,493239,00.html

[fish2xs]

I suppose he had to exercise brevity for the sake of page real estate. Clearly, gravity does not pull any less on a projectile fires at an angle, the way he stipulates. It is more pronounced in archery, where firing an arrow up or down hill requires aiming for a
flatter trajectory.

[tiberius]

Actually he'e sorta right when he says that "The steeper the angle of the shot in either direction, the less gravity pulls on your bullet". Note that he does not say that gravity is actually less, just that it pulls the bullet less.

To be precise, he should have added one word and made his statement "The steeper the angle of the shot in either direction, the less gravity pulls your bullet DOWN". Since obviously the TOTAL force does not change, just the "y" component.

Remember, force is a vector and when shooting up/down hill the component which causes drop is indeed less. And yes, this is drawn using right triangles :).

[Mal H]

Think of it this way: If the shot required is 100 yards long on the horizontal, the bullet will travel over the earth and be affected by gravity for 100 yards. If the shot is again 100 yards but at a 45 deg angle (up or down), then the bullet is only affected by gravity for only 71 yards (100 / sqrt 2) even though it takes approx the same time to travel the 100 yards.


|\
7 | \
1 | \ 100 yds
| \
y | \
d |____________________\
s 71 yds

(This may not look much like much of a triangle on some displays
due to different fonts used.)

[WvaBill]

"The steeper the angle of the shot in either direction, the less gravity pulls on your bullet".

If gravity were the only outside force:

No, the less gravity pulls the bullet from the line of sight. Uphill the bullet will have a flatter trajectory. It will slow faster.

Downhill, it will have a flatter trajectory and itty-bitty faster.

BTW, if a deaf person fires a gun and noone hears...:neener:

[TallPine]

quote:
--------------------------------------------------------------------------------
"The steeper the angle of the shot in either direction, the less gravity pulls on your bullet".
--------------------------------------------------------------------------------


So if you shoot straight up (the steepest possible angle) gravity will have no effect on the bullet and it will keep going forever.

:D

[Mal H]

Of course! That's why long range rockets are launched straight up and not at an angle. ;)

The small article could have been worded better, but I think the reason is as fish2xs said, not enough page space to give the wordy explanation.

[TallPine]

Well, from my experience with aircraft simulations, you do have to account for the effect of gravity that slows an object that is climbing and speeds up an object that is descending. (taking all other factors such as drag into account)

So shooting downhill should produce a slightly higher impact point than shooting uphill, since the bullet will travel the distance faster and be subject to gravity for a shorter amount of time.

But I think you would have to be shooting a muzzle loader or a bow, or shooting at very long distances, to even notice the effect.

[Black Snowman]

"The steeper the angle of the shot in either direction, the less gravity pulls on your bullet".

What he MENT was "The steeper the angle in either direction the less gravity pulls the bullet off target."

Gravity still pulls on the bullet, but when shooting up, more gravity is slowing the bullet rather than making it change direction and when shooting down it helps the bullet keep some velocity rather than changing its tajectory.

The forces you are dealing with are still gravity, drag, and momentum. How they effect each other varies depending on the tajectory.

[TallPine]

Yes, I know all that, but I am just like to pick apart syntatic flaws in statements that people make. ;)

The gravitational effect on the speed of an object varies (approximately) according to the cosine of the angle, and the effect on the path varies according to the sin.

But then of course the speed affects the path ... so it goes round and round.

[Top_Notch]

The force of gravity between two objects depends on the inverse square of their distance apart. In other words doubling the distance between two objects will reduce the force of gravity between them to one quarter of the original.

The formula for gravitational force is:

Force = G Mm/d2


So, technically, gravity does affect a bullet less shooting uphill than it does downhill. Unfortunately, the difference is neglible for the herewith discussion. As we surmised, the author used bad nomenclature to help prove his arguement. An incorrect premise but correct conclusion just means his argument is valid, just not sound.

[Hkmp5sd]

Essentially, what you are look at is bullet drop. All forces actiing on the bullet can be considered the same whether firing horizontal or at an upward angle due to the distances we are talking. Gravity is a constant (unless we want to include the Theory of Relativity). Muzzle velocity, drag, etc are the same.

Bullet drop is how much a bullet falls when fired from a rifle that is horizontal to the ground. When firing at an angle, the only thing changing is the actual distance the bullet travels. Since it is traveling a shorter horizontal distance, gravity has less time to pull it downward, resulting in it hitting the target higher than your point of aim.

Which is why when you are compensating for bullet drop in an uphill or downhill shot, you aim low for both.

[Carlos Cabeza]

when you are compensating for bullet drop in an uphill or downhill shot, you aim low for both.

Good answer !

Simple, and to the point.

[bountyhunter]

Actually he'e sorta right when he says that "The steeper the angle of the shot in either direction, the less gravity pulls on your bullet". Note that he does not say that gravity is actually less, just that it pulls the bullet less.

No, gravity pulls on the bullet exactly the same in either case.

The reason that it LOOKS like the bullet is falling less due to gravity from your viewpoint as you shoot uphill, is that the triangle formed is rotated and that means the gravity "force vector" has a smaller component in the direction your eye now sees as "down". That is because the direction you now see as "down" no longer is straight down towrd the earth's center. In fact, the force vector (and thus the force of gravity) has not changed at all nor has the distance that the bullet moves downward from its straight line path it would take without gravity. However, the direction of gravity is now acting at an angle to the "down" direction your eye is expecting the bullet to fall.

It just looks like it falls less because of the shooter's altered perspective.

A good way to see the "limiting case" would be to fire the bullet straight up from the earth. You would see zero "drop" due to gravity from your perspective because gravity's effect is working straight back towrd your eye. But, the bullet will also kill you when it falls so it's not a good experiment to actually try to perform.

[bountyhunter]

when you are compensating for bullet drop in an uphill or downhill shot, you aim low for both.

That is correct. The gun is "sighted in" to compensate for the full downward drop amount and rotating the flight path up or down reduces the amount of drop distance that will lie along the direction at a right angle to the sights (ie, what looks like "down" from your new perspective). Less downward travel means higher POI, so you have to aim lower.

[bountyhunter]

Bullet drop is how much a bullet falls when fired from a rifle that is horizontal to the ground. When firing at an angle, the only thing changing is the actual distance the bullet travels. Since it is traveling a shorter horizontal distance, gravity has less time to pull it downward, resulting in it hitting the target higher than your point of aim.

Nope. Even if the target is exactly the same distance from the muzzle along the path of the bullet, you still have to aim low for either an uphill or downhill shot.

Here's how to see why it is true. Suppose that for your gun, in a hundered yard horizontal shot, the bullet will travel 3" downward before it hits the target.

Twist the thing into an uphill shot at 45 degree angle, but still put the target exactly 100 yards from the muzzle.

Same flight time, bullet still drops 3" downward from the straight line trajectory line.

However, notice (nothing up my sleeve) it doesn't look like 3" to your eye. Take a 3" toothpick and look at it at straight from the side. Rotate it 45 degrees to your sight line. It now looks .707 X 3" tall from your perspective.

Same with the bullet shot. same shot, same distance, same flight time: but, looking through the scope from your perspective, the bullet only drops 3 X .707 = 2.1".

Since the scope is dialed in to compensate for the full 3" drop, if you put the crosshairs on the target for the "45 degree uphill shot" with these ballistics, it will hit 0.9" high at the target.

[Hkmp5sd]

Nope. Even if the target is exactly the same distance from the muzzle along the path of the bullet, you still have to aim low for either an uphill or downhill shot.

You lost me on this one. If the target is 100 yards away horizontally and you move it to a distance of 100 yards at a 45 degree angle, the distance the bullet travels horizontally is less. It does not matter if the angle is down or up, the bullet drop would be the same. If you aim dead center of the bullseye, the bullet will strike high. To compensate, you aim low.

Did you think I said something different? (upon re-reading my post, it may be viewed as saying the actual flight time is less. That is not what I meant. Poor choice of words on my part.)

[bountyhunter]

Since it is traveling a shorter horizontal distance, gravity has less time to pull it downward, resulting in it hitting the target higher than your point of aim.[QUOTE]

Maybe I misunderstood this. The bullet is actually in the air the same amount of time in all cases and gravity acts on it exactly the same resulting in the same total downward movement from the straight line trajectory drawn out from the bore axis ( drop distance measured toward earth center). The point of understanding why it will always hit high is that small vertical ditance is "shrunk" in the perception of your aiming line if it is rotated in either direction to your line of sight. As if taking a pencil and looking at it side on, then rotating it. The "length" appears to get shorter to your line of sight. The vertical drop component of the flight does the same thing, meaning your sights are no longer correctly compensated when the flight line is not at a right angle to the direction of gravity.

[QUOTE]You lost me on this one. If the target is 100 yards away horizontally and you move it to a distance of 100 yards at a 45 degree angle, the distance the bullet travels horizontally is less. .

True. I was saying the total distance the bullet traveled from muzzle to target was the same. If you resolve the distances along horizontal and vertical vectors, the horizontal vector is shorter as you rotate the gun up or down. Total flight distnce is the same, flight time is the same.

It does not matter if the angle is down or up, the bullet drop would be the same. .

That's true. If you draw a straight line out from the bore of the gun and measure how far below the bullet is below that when it hits the target, the distance dropped in the direction straight down toward earth center is always the same. It just appears less to the shooter's eye because he is looking at that "length" rotated at an angle to his eye line. And regardless of which way you rotate it, it always gets shorter than the length you would see at 90 deg to your eye.

If you aim dead center of the bullseye, the bullet will strike high. To compensate, you aim low.

True. Regardless of whether you are shooting uphill or downhill.

[SteelyDan]

TallPine:

You have to re-read your first sentence.:)

Sounds like the kind of thing I would have written...

[tyme]

Ignoring aerodynamic effects...

x = v * t * cos (theta)
y = v * t * sin (theta) - g * t^2
(I hope those are right...)
Which you can use to get theta and t for any (x,y) and velocity you feel like.
You could even jam the aerodynamic equation in there to get more accuracy.

But intuitively, it'll take longer for the bullet to hit a target that's 45 degrees above horizontal because the gravitational acceleration eats more significantly into the component of the velocity that's directed toward the target. So you have to overshoot the 45 degree target more. Overshooting, as has been pointed out, typically means vertical overshoot, not angular overshoot.

It's the time in flight that affects vertical drop distance, not the distance. And the distance isn't a line (segment) either, it's actually a curve, so talking about straight line distances is deceiving.

[TallPine]

Dan: nice catch!

I actually meant to do that as a joke ... really ... how come you don't believe me ... :D


Now, I can't believe that no one has mentioned the effect of the lunar phase on bullet trajectory - the moon's gravity could pull your bullet either up or down. :neener:

[ceetee]

So is it best to shoot at high tide, or low? Ebb or neap? As an FNG, I expect the answers to these and many, many more...

[Hkmp5sd]

Let's not forget that time isn't a constant. Time flows different for the each of the participants, the shooter, the downhill target and the uphill target. Good old theory of relativity doncha know.

[RustyHammer]

Same applies to golf shots ... simple physics.:D

[bountyhunter]

Actually, golf is different: it's something like you have to take one club longer for each ten yards of rise in the green's elevation and one club shorter if the green is at a lower elevation. It's because raising the green makes it intercept the flight of the ball farther back up the trajectory curve, lowering it means it hits the turf farther out on the flight curve. It doesn't matter for me because I always skull it.