Hi, I always see the charts showing the giant arch of the round in trajectory charts, but always wondered why the starting point was a tad below the "0" mark..

This chart showed me what I always believed but the other charts confused me, making me think that the rounds actually climb in height if the rifle and target and at the same height.

Are the charts that we normally see based on "Prone" shooting, where someone is aiming upward?? (Description #1 in this chart shows what Im talking about.)



So is a 50/200 zero not possible when shooting like the rifle is on the 2nd demonstration in this photo?? Or any short and long range zero where the trajectory crosses (25/250 or 50/200 for example), by the trajectory I can tell this is an AR/556 demonstration, but applies to all Rifles.

VERY CONFUSED, being I would think when bench shooting or free hand shooting that the Rifle would be more like Demonstration #2, unless your shooting prone for the round to shoot upwards.

Any advice??

The top chart is correct. For a 50/200 yd zero, the 50yd mark would be where the bullet trajectory crosses the line of sight the first time ( blue line crosses the arrows).  The 200 yard mark would be where the target is. That is why the 50/200 zero works for both distances.  At 50 the bullet is still on the upward travel. By 200 it is on the way down.

You never are actually shooting as shown in the bottom picture, due to the height of the sights over the bore, specifically the rear sight.

Take a closer look at the diagram. It actually explains how it works pretty well.

You're over thinking it.

The bullet can never rise above the line of sight of the bore - there is no lift in a bullet.  Immediately after leaving the bore it is as affected by gravity as anything else and free falls downward just the same as if you'd dropped the bullet from your hand (well, except for the fact that the bore is angled up slightly as your top sketch shows)  If you leveled the bore to be dead horizontal and fired the gun, and dropped a bullet at the same instant the fired bullet left the muzzle, they would both hit the ground at the same exact time.

Look carefully @ #2.  See where the bbl is pointing?  Do you think that after traveling for 20" in a straight line @ 3200 fps, the bullet magically rises in an arc?  #1 is correct.  If the sights and the target are on the same plane, the bullet ALWAYS rises to meet the target.  Take your 50/200m zero.  The first intersection point between the Line of Sight (LOS) and the Bullet Trajectory is your 50 m mark.  The 2nd intersection point between LOS and trajectory is the 200m mark, which in this illustration happens to be the target.

I suspect you are overthinking it.

I think most charts don't care about detailing the proper relationship of the barrel because they assume you have an elementary understanding of gravity, which is acting on the projectile the moment it leaves the bore as it does not generate lift, fired parallel to the earth's gravitational field the bullet would immediately start heading toward earth and never meet or cross the line of sight.

What "matters" in trajectory charts, if anything, is the relationship between line of sight and path of the projectile, which thanks to gravity needs be fired at at least a very slight angle toward line of sight  regardless of shooter position (assuming sight is over bore and we're not laying the rifle on it's side) in order to meet line of sight at some point. Most of the time the trajectory is such that instead of meeting line of sight and falling away the projectile crosses the line of sight, and travels slightly to greatly above it before crossing it again at another distance and then traveling down away from it.

Also, scope bases / mounts have a slight angle built in - some more than others.  The angle is very slight - almost imperceptible.  However, it is there.  Install a mount backwards, and see what happens.

Replace the bullet with a  baseball. Stand in center field and throw it to home plate.  Now it's a lot easier to see that arc.

Very good analogy. Trying to get people understand  that the bullet does not rise as it leaves the barrel is a lesson in frustration sometimes.

It may also be helpful to look at a "ladder" rear sight, like on an M79 grenade launcher.  The longer range marks are toward the top, making you angle the muzzle higher to line up the front sight.

The important point is, of course, that the bullet flies in an arc, not a straight line.

I have kind of wondered about this.  I know the long range guys buy 20 MOA bases to give their scopes more room to work with - but most bases for standard rings and scopes are advertised as '0' MOA.  In reality you need something on the order of 2 MOA angularity to get a 100 yd zero.  Is this 2 moa in the bases? the rings? or is it just accommodated by the windage adjustment on the scope itself? I guess I need to go look at a scope diagram.

The only bases with an angle built in are advertised that way. Otherwise, the scope adjustments are used.


 

Remember that gravity is a constant.  The reason that the flight of the bullet crosses the line of sight twice (once going up and once coming down) is because we have to compensate for that gravity acceleration constant (32.174 ft/s2).  As mentioned previously a bullet fired level to the earth from a specific height and one dropped from that same height will hit the ground at the same time.  The "x" factor comes in how far the bullet will travel over that same amount of time, and this is determined by velocity.  So, as should be obvious, the faster a projectile is moving the further it can travel in the same amount of time (assuming similar aerodynamic coeffecients, i.e. BCs) before it hits the ground.  this also means that projos of differing size and weights but with similar BCs will perform essentially exactly the same as the gravitational constant doesn't care about projectile weight.  Therefore your typical "flat shooting calibers, i.e. 22-250 for instance, is flat because its time to target is low compared to a 30/30 or other big slow rounds.

If you care about energy delivery speed is where it's at.  Because Energy equals Mass multiplied by aCcereration which is multiplied by itself (squared) doubling the weight of a projectile merely doubles its energy.  If you can double its speed you multiply its energy by about 4 times.  Let's look at a chart of 40g 22LR, 22WMR, and a 5.56 Nato Round.  The 22LR has  ~1100fps/ and ~100ft/lbs energy, the  22 WMR ~2000fps and ~340 ft/lbs energy, and the 5.56 Nato 3700fps and 1200.  By comparison a 200g .35 Remington at 100 yds is going just a tic under 2000 fps and making just over 1700 ft/lbs of energy.  Divide that 1700 by the 40gr 22 WMR energy of 340 ft/lbs and you get exactly 5, the multiplication of the weight.   Speed is your friend for both trajectory and energy.

So, back to the OP, by angling our barrel with a slight incline we raise the distance from the ground that the bullet travels from, therefore giving it a longer tragectory by delaying when and from what height the bullet will eventually be falling from.  That delay is what allows us to extend the range of the projectile, and what allows a 50/200 zero.  

Thus concludes today's physics lesson.

I tell people to imagine a garden hose.

Point the hose directly at the target and the water stream will hit the ground short of the target.
Point the hose ABOVE the target the correct amount and the water stream will hit the target.

How true

I heard too old guys (older than me) at the range once discussing why a 30.06 round rose more than some other round they were shooting.

They honestly thought that the bullet left the barrel and then began to rise because of the spin imparted by the rifling

We've all heard the level barrel firing a bullet and dropping a bullet at the same time results in both bullets hitting the ground at the same time. They don't hit the ground at exactly the same time though, do they?  Seems there are some forces that come into play that actually causes the "fired" bullet from falling as fast as the "dropped" bullet.......maybe the spinning of the bullet, and as it decelerates the back end of it drops below the theoretical centerline of the bullet.........which somehow imparts "lift"........and causes it to not fall as quickly?????   Seems I read a lengthy article in Precision Shooting magazine years ago to this effect.  Maybe the Coriolis Effect had something to do with it.......or am I dreaming this?

Heh, I had this argument with my Drill Sergeant. He finally got the point but I sweated a lot for it.

Ok if you want to get even more technical there is a SLIGHT curvature of the bullet path created by the rotation of the projectile through the air, called gyroscopic drift.  The indentions left by the rifling causes the effect as the bullet is spinning at 20k and more (depending on twist rates), and the direction is always a constant; right-hand twists causes right drift, opposite for left-hand twists.  Elevation, temperature, atmospheric pressure, etc. can increase or decrease the effect.  Ask a catcher and he will tell you essentially no pitches are straight, especially fast balls, for this same reason.  

A second effect, the Magnus effect, can "stack" with the gyro drift and add a destabilizing component to the math depending on the center of gravity of the projo.  Adding to this destabilization can be when (if) the projo stops being supersonic, a problem the F4 Phantom had back in the day (it really hated going slow).

In any case at typical engagement and hunting ranges the effect is so slight as to be non-existent.  Get into long-range BR or taking sniper shots at 1500+ meters and then you actually have to care, but for the sake of the discussion here most have probasbly never experienced them enough that they would even know it.

As for firing a bullet and dropping a bullet google it on Mythbusters.  They strapped a 1911 into a sled, level to the ground.  Had ammo loaded to be perfectly repeatable.  Found how far the bullet travelled at its velocity, and set a bullet-dropping mechanism at that point of the flight.  When the trigger was pulled a signal was sent to the dropper so that both events happed as close to exactly the same time as possible. The high-speed recording shows them hitting the ground within miliseconds of each other from a height of like 3 feet.  

You can't argue with physics, you can only add factors in that take extended ranges and flight times to matter.  A 50/200 zero is nowhere near far enough to matter.

ANY two objects that become unsupported at the same time will strike the earth at the same time.  Period.  There is no lift involved in a spinning bullet, nor any other force that could keep a bullet fired at the same time another is dropped from landing at precisely the same moment, unless the rifle barrel is not precisely positioned with the bore perfectly level.

Doesn't temperature, altitude, barometric pressure, and humidity also factor in when calculating bullet arc and drop?

When I went Deer hunting a couple of years ago I Zeroed my rifle (Remington 30-06 and a Leupold optic) during the summer in Boulder City, NV (elevation around 2500 feet) at about 115 degrees with very low humidity.

When I got to the hunting area in Elko, NV during the fall, (elevation around 5000 feet) at about 75 degrees and higher humidity, I checked Zero on my rifle before opening day and the Zero was off by quite a bit.

The optics or sights are above the bore by, say, 2 inches, so::

1.   At the muzzle, the bullet would hit two inches below the point of aim.

2   In order for the point of impact to be the same as the point of aim at, say, 50 yards, the bore must be angled up relative to the line of sight.  If it didn't the bullet would strike more than 2 inches below the point of aim.

3.  If the bullet has another zero at, say, 200 yards, then between the first zero at 50 and the second zero at 200 the bullet MUST be above the point of aim.

The first depiction is correct but is, as has been mentioned, exaggerated.


Brian

well.........this is getting off topic from what the OP asked......but...... I'll disagree with the statement that a bullet dropped and one fired level will strike the ground at EXACTLY the same time. It may have with the projectile that the Myth Busters used, if it were indeed a .45acp. I don't think a subsonic projectile, and a pistol bullet at that, is subjected to the forces that I was referring to in the article that was published in Precision Shooting. It's been years ago though, so I cannot recollect the details of the article.  I'm suggesting that a bullet has lift, and is going to "fly" above the centerline of the bore, of a perfectly level barrel. I'm saying the article referenced various forces/conditions, that affected the flight of a bullet, and "caused" it to fall at a rate slower than what a stationary bullet of the same weight would. It did have something to do with the rifling grooves engraved into the bullet jacket (and most rifling being right hand), along with the bullet spinning in the neighborhood of 200,000 revolutions.
   I don't have but about 100 to 150 issues of Precision Shooting, but I'll look and see if I can find the article.

Yes, however their direct effect on the bullet at typical hunting distances is pretty miniscule. 40° of temp change especially from excess of 100° to cooler probably had a significant effect on the powder burn and your velocity.

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Understood. I probably should have stated that I know about certain zero's and trajectories, just why the barrel is always below the 0" mark in all charts, didnt know if "Prone" was being accounted for.

Just always wondered why it was aiming upwards when if your shooting, being I feels as if #2 is how you're holding it, although I KNEW #2 was wrong by, well, it says itss Wrong and looks wrong with an Arch that would defy gravity.

The main thing that threw me off was the over exaggeration of the Bore Aiming upward in Pic#1

Thanks for clearing it up, basically, the rear and front sight being set at different heights makes sense to me on the bore aiming upward.

Thanks again guys!!

I did find the articles that I mentioned in the previous posts. The April 1996 and Sept 1996 issues of Precision Shooting have articles titled "The vertical component of wind drift" and "The vertical component of wind drift.....revisited".  April article written by Richard Near and the Sept article by Robert L. McCoy. The gist of the articles are that wind from the right will cause vertical lift to bullets fired from right hand twist barrels. Test were performed by the military at Aberdeen Proving grounds, back in the mid 60's that proved this theory. The test were done with 308 Win and 300 Win Mag. At 1000 yards a 10mph wind from the right caused a 4 inch plus reduced drop.  
 I'm guessing that reduced drop would result in longer flight time. Minuscule perhaps, but time none the less. That example is would appear to be the result of an outside variable though..........so my recollection of the article was wrong. (it's been almost 2 decades so cut me some slack)

The "lift" you mention is related to the effects of wind that also induce a number of other effects, including increased bullet yaw and destabilization of the bullet as it flys.  At all but the longest of ranges, these effects are trivial in the vertical and only slightly noticeable in the horizontal.

And please keep in mind that sights do not take into account wind - that's the shooter's job.  The original post was about idealized trajectories as applied to sight alignment, and our discussion has drifted far from that, into some pretty high-level applied physics.  There are some great references on these physics questions, but they all pretty much evenly agree that any vertical component of bullet flight variance is very small at practical distances.  Interestingly, very low drag (VLD) bullets experience more problems from these wind interactions, mostly due to the Magnus effect (which is basically the effect mentioned in your later post).  Magnus causes right-hand spun bullets to rise (a little) in a left-to-right wind, and DROP (again, a little) in a right-to-left wind.