I always zero my rifles at 100 yards. My load ,out of my 243, zeroed at 100 yds drops 21 measured inches at 400 yds. Zeroed at 200 yds the group prints 1.5 inches high at 100 yds so by subtracting 1.5 from 21, it should print 19.5 low at 400 yds. I am told by a friend that I can't figure it that way but he could not explain why. If he is correct, could someone please explain it to me? Thank you in advance

He's right. You have to know your velocity and ballistic coefficient of the bullet you are using. By calculating these known numbers, your drop is more likely in the 30" mark. I just ran the numbers for my Model 7 Rem in .243. It runs right around 2800+ and my bullet drops 33.6" at 400 from a 100yrd zero. We would have to know what your velocity is in order to accurately guess (many variables, but could be more accurate than guessing) your drops. Hope this makes sense.

Tank

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I can't explain it in math terms, but if you run your data through a good ballistics program using 1 yrd increments and plot the curves, you'll have a good graphic of what is happening. I just ran a .243 100grain bullet with a .381 bc at 3000 fps sighted in at 100 and 200 and the bullet path was 18.3 inches low at 400 for the 100 yd sight in and 13.8 inches low for the 200 yd sight in.The path was 1.93 inches high at 100 using the 200 yd sight in. Looking at the plot your rifles muzzle angle from the horizontal would be different. Anybody else explain it better, jump in.

I always zero my rifles at 100 yards. My load ,out of my 243, zeroed at 100 yds drops 21 measured inches at 400 yds. Zeroed at 200 yds the group prints 1.5 inches high at 100 yds so by subtracting 1.5 from 21, it should print 19.5 low at 400 yds. I am told by a friend that I can't figure it that way but he could not explain why. If he is correct, could someone please explain it to me? Thank you in advance

you did not say at what speed your bullets was so here is what you will get with a 243 70 grain at 3650 fps with a .259 BC
zero 100 yds
200 is -1.8
300 -7.9
400 -19.6

Another thing to consdier is which zero are you talking about @ 100 yds? Bullets almost always have two zeroe points. The first zero point is usually closer than 100 yds and it's where the bullet's trajectory passes throught the scope's line of sight on the way up in it's initial path out of the bore. The bullet then crests and begins to drop to it's second zero point when it crosses the scope's line of sight again. With a 243's trajectory, the two zero points may both be close to 100 yds. They might be 100 and 110 yds or 90 and 100 yds. When zeroed at 200 yds the first zero will be between 25 and 50 yds because it requires a steeper trajectory to get the bullet to zero at 200 yds.

The answer to your question, when you change your zero, you change the trajectory and you can't compensate by doing straight math. One reason is, the bullet drops quicker, the farther down range it gets.

If you were to drop a bullet at the same exact time you pulled the triger on a gun and the gun was pointed exactly flat the bullets would hit the ground at exactly the same time. The faster the bullet is traveling when it leaves the barrel the farther it will travel, but the time of flight will be the same. Gravety pull things down at the rate of 32 ft. per second per second. So at the 1 second the bullets will be falling at the rate of 32 ft/sec. and will have fallen 16 ft. At 2 sec. the bullet will be falling at the rate of 64 ft./sec. and will have fallen 32. ft. If the gun is pointes up or down alittle every thing changes. As a rule the center of your scope is aprox. 2 1/2 inches over the center of the bore of your gun. So if you are aiming at a target where your line of sight is exactly level then the center of your rifle bore is 2 1/2 in low. So to hit the target your bore will be pointed up alittle bit and the bullet will come up 2 1/2 inches to hit the target. It would be very easy to figure how far the bullet would travel except we also have the resistance of the air slowing the bullet down. How much it slowes the bullet down depends on the diameter of the bullet, the larger the greater the resistance will be. The weight of the bullet, the heaver the bullet the better it will retain it`s velocity. The shape of the bullet also comes into play as pointed bullets will cut through the air better than flat nosed bullets. With all of these thing haveing an effect on how fast the bullet will lose velocity and people being lazy, for the most part, some math genious worked out a formula where the all of these factors could be rolled into 1 number, and called that number the Blastic Coefficient. Useing the BC of the bullet it is easy to plug into other simple formulas, along with the velocity, and get the trajectory, and the maximum point blank range of the bullet. ( The max. range you can zero for where the bullet will be no more than 2 1/2 in above or below the line of sight. 2 1/2 in is what is usually used for varminit rifles.) I could go on and write a book on it, but several other guys already have so I`ll let it go here.

21" at 400 yards is ~5 minutes(5.01) which is the amount you need to correct from the 100 yard zero. Going from 100 to 200 required a 1.43 minute adjustment(1.5" at 100 yards) which means you need to come up another ~3.5(3.57) minutes at 400 yards. 3.5 minutes at 400 yards is 14.65".