Rifle ballistics question

[duelist1954]

I have a question about rifle ballistics that I hope someone here can help me with.

I have been running some numbers for muzzleloader round ball ballistics through a ballistics calculator, and there is something that I don't understand.

Even though I'm running numbers for a muzzleloader, I see the same thing with centerfire cartridges, just not as dramatic.

Here is the situation:

When I run the numbers based on a 100 yard zero, it shows the drop at 200 yards as 28.5 inches.

But, when I run the same numbers based on a 200 yard zero, it shows the rise at 100 yards as only 17.1 inches.


Should the two numbers be the same. If the bullet drops 28.5 inches between 100 and 200 yards, shouldn't it hit 28.5 inches high at 100 yards if I have zero'd the rifle at 200 yards?

Obviously I'm not understanding something, and I'd appreciate getting educated.

Thanks

 

[JeffG]

But, when I run the same numbers based on a 200 yard zero, it shows the rise at 100 yards as only 17.1 inches.

Is there a large target tolerance programmed in? If your target tolerance is say, an 8 inch bull, it could account for it. Yes, the numbers should be the same. The calculations sound like they are splitting the difference between rise and drop. I doubt if projectile drag and deceleration would be programmed in for those short distances. If it is calculating projectile flight in a modified bell curve, (coehorn mortar) you have a very intelligent unit.

 

[redneck2]

Yes, the numbers should be the same.

Uhhhh. No. The trajectory is parabolic. That’s why I like to have maximum point blank range on a hunting firearm

 

[duelist1954]

Thanks Redneck. I found my answer.

 

[JeffG]

Uhhhh. No. The trajectory is parabolic. That’s why I like to have maximum point blank range on a hunting firearm

You are right, I countered my own answer...

 

[Varminterror]

No, the numbers should not be the same. Your sight offset explains the “crossing paths” difference, but remember - 17” at 100 is 34” at 200. So you’re really talking about 28” vs 34”, not 28 vs 17. Folks get too confused when talking about trajectory in inches, instead of angular dispersion.

Your 100yrd zero requires the barrel be angled upward towards the optic’s LOS sufficiently to overcome the drop of the projectile at the given range, 100yrds, as well as the optic height above the bore. The ballistic calculator is starting with the ballistic coefficient and muzzle velocity in a formula to determine the time of flight, which then correlates to a gravitational drop. That drop plus the sight height is then used to determine the elevation correction to hit the LOS at 100. When you move out to 200 yards, the time of flight increases so the drop increases, but the sight height contribution is cut in half, so you see a little different behavior.

Your “peak” of the trajectory is where you start for your gravitational drop velocity. The acceleration due to gravity is always the same, the farther out your zero, the more your barrel has to angle upward, the farther down range your peak. So then your gravitational drop acceleration yields a lesser drop velocity at farther ranges. So in a 100yrd zero, you peak around 60yrds, and by 200yrds, it has 140yrds to have built up downward velocity. Zeroed at 200, you peak somewhere around 175, and are still on your way up at 100.

So no, you should not see the same numbers, or even perfectly similar angular dispersion.