Leading Targets

[wadrew]

I was in a discussion with another shooter about leading various targets, and his idea was that his "swing" would sling the bullet at the target, like if he swung fast enough and was holding on the center of the target, he would still have his hits.

His premise was that newton's law made this happen. The bullet in the chamber is moving at 2' per second, and thus when it was launched, it would have that much lead time. My premise opposing his viewpoint was that the acceleration and gyroscpoic stabalization negated any swinging or movement of the shooter and his gun, no matter how fast. I have shot trap and rifles at moving targets, and no matter how fast I swung the gun, at the point that the bullet leaves the barrel, it must be at the right timing to meet the target.

I am really wondering if someone has some specific data relating to this sublect, mathematically provable with Vector calculations. I don't want to prove anyone wrong with their ideas as to shooting moving targets and how much to lead them, but to give them some concrete information on how to practice and how to be better at shooting the Texas Star, the Mover in Bianchi, running targets and swingers in IPSC, etc.

Basically, what I was taught, by an ex-olympic trap shooter, was, that math shots are only a necessity until a feel is developed for the various shots in that game. Most important, to align the sights, look at the leading edge of the target, move the gun through the target, and squeeze the trigger. The most important things were to have the head on the gun (because lifting the head causes the sight picture change and thus point of aim and impact are all off), and shoot through the target. The natural tendancy is to stop moving the gun when pulling the trigger. That basic act of muscle contraction makes everything want to stop, and thus, shooting behind the target.

Anyone???

[DogmaDog]

My 1/2-ass two cents:

When you swing your gun (pistol or shotgun), it is moving in an arc so that the muzzle has the same angular velocity as your moving target, but it will have a much slower linear velocity than your moving target. So you won't impart anywhere near enough of a lateral velocity component to your bullet for it to keep up with the target--you still have to lead it. You will impart SOME lateral motion to the bullet, just not enough, so your friend is right...just not right enough to hit the target.

Gyroscopic stabilization isn't a factor...you have to lead with shotguns (not gyroscopically stabilized), just as you do with rifles or pistols.

If you were shooting from at train at an antelope (say) running parallel to the tracks at the same speed as the train, then you wouldn't have to lead it, because the motion of the train would be imparted to the bullet. You'd still have to account for wind, though.

As far as actually shooting moving targets...I've never shot at clays. I've shot a few swingers in IPSC, and I've been using more of an "ambush" technique...put sight on a point where the target eventually will be, then pull trigger just before it gets there. With a swinger that might make more sense than with a clay.

DogmaDog

[wadrew]

Dude,

You're missing the point.

I've heard the train and arc swing ideas, and they are almost akin to urban legends.

Are you telling me that if you place 2 2x4 posts, one at 10 yards and 1 at 20 yards in a straight line so that the closer 2x4 completely blocks your vision of the second, that you could swing your gun fast enough, breaking the shot ANYWHERE and ever hit the second 2x4 in the center without penetrating or touching the first one?? You could swing the bullet and hit the second post??

Secondly, have you ever watched the Bianchi Cup swinger event when it is shot by the top shooters? If you have, please carefully analyze what you are saying! If you watch, they hold the gun in a steady arch, holding their dots or sights ahead of the x-ring. They are not swinging their shots onto the target like some old western. They even have "running boar scopes' that have multiple reticles with the correct amount of lead distance for leading a target moving left or right. Others will find out how many clicks left or right it takes to hold their sights on the center of the x-ring and have the correct amount of lead distance/time to still be able to hold on the center of the target and have their bullet intersect with that same point. Some people have done the math for the various shooting distances required in the Mover Event, and simply adjust their hold on the target instead of their sights.

The shotgun basics of leading a target is: 1. Mount the gun 2. align the sights 3. look at the leading edge of the target 4. move the gun through the target in a line ahead of it 5. release the shot.

"Swinging" the gun is what you see when observing someone lead and shoot a target. Leading the target produces the swinging movement of the gun.

Anti-aircraft gunners or shooting a moving target with a machine gun with tracers is another example of this incorrect thinking. Even if you are swinging REALLY FAST and holding the crosshairs on the target, the bullets will fly behind the target. It's not that they are swinging their turret really fast, it's that the target must be led. If you swing really fast THROUGH the target and shoot ahead of it, the bullets will hit it.

SO, when I shoot a swinging target in IPSC, I am only producing a swinging motion with my gun BECAUSE I am shooting a little ahead of the A-zone or right at the leading edge of it in order to have my shots in the MIDDLE of the A-zone.It's playing catch-up to get the gun ahead of the target, but the swinging is only the product of that movement, by moving it THROUGH the D, C, and A-zones and calculating the speed of the target, distance from it, and how much lead I think it needs. SOME shooters will hold their gun still and wait for the swinger to come to them, however, if they hold the gun still and shoot at the center of the A-zone, their bullet will be NOT int the center of the a-zone but on the edge or even in the C or D-zones, depending on the distance from the target and at what warp speed it's rocketing back and forth at. Some people have to wait for the swinger to 'stall' or stand still at the edge of it's arch, just so that they can shoot it like it's standing still.

Please understand, I am not looking for a literary hostile discourse with anyone, I am hoping to catch someone who knows the math involved. MOSTLY because I want to know the amount of lead differences of a target moving towards me versus one moving away from me, as in the mover, it will move towards the centerline and then away from it. How much? What is the equation that lets me input my velocity, distance, and target distance from the centerline.

Other things to take into consideration:

Bullet flight time-- how long does it take for the bullet, standing still, to accelerate and leave the muzzle.

Firing pin Lock time-- how long does it take for the firing pin to begin moving forward, strike the primer, and ignite the primer.

Ignition time-- how long does it take for the primer, once struck, to ignite the powder sufficiently, building pressure, and break the bullet loose from the bullet-to-case-fit, and the tightness of the crimp.

Hammer/sear/trigger lock time-- how long does it take for the hammer to fall once the nessary amount of disengagement from the sear.

Our own reaction time-- how long does it take from seeing the triggering event, nerve impulses and muscle contractions that make the trigger finger move.

SO, leading the target not only has to do with once the bullet leaves the muzzle, but how much mechanical movement time there is from when your gut tells your finger to squeeze the trigger and when it does, when the gun does it's various locktime components, so on and so forth. Does this mean that all the lightweight hammer/sear/trigger parts will automatically make you shoot faster?? That's a common misconception. What it can help improve is the reduction of lock-time and decrease the severity of a flinching motion. It really gets into timing and what you learn to shoot with.

Hey, I tend to be a windbag, but I can only hope that this helps, and someone else joins in the discussion that has done the 'nerd work', and has the results to show for it.

Just remember, it's not where the dot/sight WAS when you pulled the trigger, but where it LIFTED from. That's where the shot WILL be. If you pull the trigger on the leading edge of the target, and the sight/dot LIFTS FROM aywhere else other than where you pulled the trigger, you probably froze (stopped) moving with the target and flinched. And believe me, it always moves, sometimes almost not at all, and sometimes a little, and sometimes, a lot.

Nothing really TRULY stops anyway. So why waste time trying to stop anything? Stopping the gun on a target and shooting, waiting for everything to settle and break the second shot, is a waste of time. Moving through it and breaking/calling the shots in the desired place is much smoother and ultimately, faster. Ever seen the drivers who stop completely before turning? What fools! Ever seen the one who puts the car sideways and accelerates through the corner? Which do you think is faster? Who on earth would want to stop their gun/dot/sights/body for anything?? Running and moving faster sure helps stage times, but to stop is to lose. Heard of Musashi? The "stopping mind" is slower. How about the "stopping gun"? Seen the guy who can move and stop really fast? Looks fast, for sure. It's not as fast as the guy who still moves quickly, but doesn't stop, but kinda floats through the positions. Run, Stop, Shoot=slow. See+shoot=fast.

-Drew

[kevin c]

I'm not a physicist or a mathematician, but perhaps there's a mix up about momentum and vector forces affecting the flight of the bullet. Momentum may keep a bullet moving in one direction, but it's the direction of the forces applied to the bullet that determine its actual flight path. In shred's example, there are three objects (target, gun and bullet) in linear movement, with vectors easily defined. In the second scenario, there's the target moving in a line, but the gun with the bullet still in it turning in an arc. Perhaps there's some confusion about what affects the bullet's movement in each case.

If I got Newton right, a bullet will only travel in a straight line if the force vectors on it are parallel to its line of flight. Any force that is applied, only at an instant (puff of wind, hitting a twig) will deflect it off that first line of flight onto another STRAIGHT line. A force applied constantly to the bullet during/along its flight will make it CURVE off its orginal course, (eg, good old gravity).

In the first situation, the movement of the bullet is out of a barrel that is aimed (is stationary) to some point on or ahead of the target. The force applied to the gun to get it moving with the train is a past event , so the bullet leaves the barrel in a straight line. It travels to the aiming point in a straight line, and a lead is only needed if the target is moving relative to the gun/train (the antelope may have to run into the bullet, or, in another sense, run into the zeroed sights of the gun).

A gun barrel turning through an arc, though, is, in a sense, constantly having a force applied to it as it turns (we can consider it anchored at the breech end). Think of a ball, better yet, think of a bullet, tied to the end of a string that you whirl around your head. The ball/bullet wants to go straight, but the force of your pulling on the string makes it turn in an arc. Let go of the string and the ball flies away in a straight line because there isn't any force being applied off the axis of the line of travel (at 90 degrees in this case) to make it curve.

On firing, the bullet starts down the turning/arcing barrel, and turns through that same arc because the bore applies a lateral force to the bullet in the direction the barrel is turning (though not at 90 degrees like the string). But as soon as the bullet leaves the barrel, that lateral force is no longer being applied, and the bullet keeps on going straight (except for gravity, precession, and god knows what else) from then on. So essentially, the bullet only is curving while it's in the barrel.

So, yes a bullet can curve in flight, but only by using forces applied after the bullet leaves the barrel (such as gravity). After that, it's (mostly) straight.

My understandng is that the lead needed on a moving target is a fixed distance based on how the bullet's flight time and the movement of the target make them meet at the same point in space. How you get that lead is a matter of an individual's own technique, but I would guess that the faster the target is moving across the shooter's field of vision, the bigger the lead is going to need to be, and, by sweeping the gun through the target, the shooter naturally speeds up the sweep to catch up with the faster target, and, since reaction time for the shooter is probably close to fixed, by the time he pulls the trigger, the gun will have swept further ahead of the fast target than the slow, and thereby give him the extra lead needed for the faster bird. But I can't even imaging an equation that would describe that.

My apologies to the physicists for my crude approximations. This is as good as I unnerstannit m'self.

[DogmaDog]

Dude, You are missing the point.

I'm telling you that a bullet's velocity relative to the ground is equal to it's velocity relative to the gun plus the gun's velocty relative to the ground.

I'm telling you that, yes, if you swing your gun fast enough, you could hit the post behind that other post (though there must be a straight line from the muzzle of the gun to the target post at the time the bullet leaves the barrel--kevin c is correct that once the bullet leaves the barrel, it will travel on a straight path).

I'm also telling you that in all practical cases, you just can't swing your gun fast enough...angular velocity and linear velocity aren't the same. The velocity imparted to the bullet by the motion of the gun is negligible, but it is there. In theory, if you are shooting while running to the right, you would need to "lead" your targets by shooting slightly to the left so the bullet hits the middle of the A-zone. In practice, shooters just aren't running that fast, and if they are, the targets are so close that the lead required is much smaller than the error in targeting anyway.

If you've ever played hockey, though, these kinds of leads (due to motion of the shooter) do come into play--in order to pass to a stationary team mate as you zoom by, you have to pass a little "behind" him.

So here's a formula for leading that ignores any component of bullet velocity induced by movement of the gun/shooter:

Where

d = distance to target

v(t) = velocity of target (linear velocity, moving tangentially to the shooter's line of sight)

V = velocity of bullet (assumed to be constant...for IPSC purposes, this is probably reasonable)

L = required lead, given as a distance to aim in front of the target, at distance d.

L = d/V*v(t)

So your lead for a target at 100' distance, moving at 10' per second, when shooting a bullet going 1000' per second is 100/1000*10 = 1 foot. It will take 1/10th of a second for the bullet to get 100', and in that same time, the target will move 1', so that's how much you have to lead.

If you're shooting a swinger, v(t) becomes a sine function, and it gets a little more complicated.

As far as lock time, time for the bullet to accellerate, decrease in bullet velocity with distance, etc., they are all negligible at the velocities and distances usually encountered in action pistol sports.

DogmaDog

[DogmaDog]

OK, did a little math, and came up with a solution to the two post problem.

Short answer: if you can swing your gun at about 456 rpm or faster, you can hit the second post at 20 yards. (The muzzle must be moving sideways at almost 160 fps, for a muzzle 40" from it's pivot point). I'm going to go watch Saturday Night Fever a couple times, and then go practice at the roller disco to see if I can get it.

Obviously, we don't swing our muzzles anywhere near that fast, and any leads we would need due to our own motion are negligible.

Anyway, as far as other things you want to time (lock time, how long the bullet takes from chamber to muzzle, etc.) I suspect they are all so short compared to bullet flight time to the target, and to reaction time as to be negligible as well.

For example, the time the bullet spends in the barrel is about 0.0004s. This is assuming a 5" barrel with a bullet undergoing constant acceleration from 0 to 900fps in the first 2" of barrel, and then from 900 to 1000fps in the last 3" of barrel (somebody once told me a bullet attains about 90% of it's velocity in the first 2" of barrel)

I'm using the equation d = [(V0 + Vf)/2]t, where V0 and Vf are starting and ending velocities, d is distance, and I"m solving for t, time.

Anyway, the time the bullet is in the barrel is about .4% of the time it takes to get 100' downrange.

So the L = d/V*v(t) equation is probably as close an approximation as you need given you will be estimating it all by eye and instinct, anyway.

DD

[TDean]

Drew, you're giving me a headache again!!

Maybe a few more Mac'njacks will help?

During a walkthrough at Area2, Dave S. asked me if I was going to lead the mover (about 15 yds). That struck me as odd since I don't have much experience with trap or Bianchi. I said hell no! I'm just going to put my front sight on the target, track with it and pop the shot. He said "..I really think you should lead it, but do what you want.." I figured he was just trying to do the supersquad-voodoo-thing on me, so I ignored his advice. Sure enough, I hit behind the target and nailed a no-shoot that was moving with it.

The sideways velocity of my gun (bullet) was slower than the velocity of the target.

Once the bullet left the bbl, it was still moving slower (sideways) than the velocity of the mover.

I should have led the target a little. C-zone maybe.

[eric nielsen]

If you're that curious, do a web search for "principles of naval fire control" or similar phrases.

It's all right there, courtesy of the US govt.

[uSS Mahan DDG-42]

[TDean]

Cool stuff here....

I want to take this class...

Naval Science 202

[mcginnes]

Check my math, but:

If the end of the shooters barrel is moving at 1 m/s* then the lateral velocity** of the bullet would be 1 m/s.

If the bullet is moving at 300 m/s, and the target is 10 meters away, the flight time for the bullet is 1/30 sec or .0333 sec. Given the 1 m/s lateral velocity from above, the bullet will impact the target 3.33 cm ( about 1.3 inches) past where the gun was pointing when the bullet left the barrel. This is, or course, in full swing. To correct for this, make sure your bullet exits the barrel .00333 seconds before your gun is pointed at your intended point of impact.

If the target is 10m away, and moving at 10m/s, your correct lead is 30cm and not the 33cm you might expect (about 12 vs. 13 inches). And try not to puke on the RO's shoes.

* I’m working in meters, because the math is a lot easier. Given, two targets that are 2 meters apart on center, 10 meters from the shooter, and the end of the shooters barrel is 1 meter from the shooters pivot point, and it takes .2 seconds at a constant velocity to get from the center of one target to the center of the second target, then the barrel is moving at 1 m/s. There is a lot of guess work there, but the barrel moving at 1 m/s seems about right to me.

** Tangent to the arch of the barrel tip, and perpendicular to the axis of the bore, at the point the bullet left the barrel, and moving in the direction of the swing.

[shred]

Yeah, but what about lateral wind-resistance? :D

[EricW]

Anybody played with the lead calculator on the Pact MkIV?

[mcginnes]

Yeah, but what about lateral wind-resistance? :D

Don't be silly. I'd need the Ballistic Coefficient of the bullet to figure that out.