ESTABLISHING DOUBLE ZERO
If the scope on a rifle is zeroed at a range relatively close compared to the weight and velocity of the bullet, the bullet will strike high of the aim point beyond the zero range and then drop back through the line of sight. In theory, this creates a second or double zero at which the bullet would strike.
With ballistics tables, a calculator and a basic understanding of positive and negative numbers, the second zero can be roughly determined. The trajectory of a bullet is not truly parabolic, therefore the calculation cannot be depended on to be exact. However, the average hunter can get very close with this calculation.
Below is a ballistic table taken from the Hornady Handbook of Cartridge Reloading, Volume 2, Fifth Edition. The entry is for a .224″ caliber 55 grain full metal jacket boat tail bullet. This table is for a velocity of 3000 FPS from muzzle to 500 yds.
Look at the data to the right of the 50 yd. zero entry. Notice the path of the bullet is .4″ high at 100 yards if zeroed at 50 yards. At 200 yards, the bullet falls to -2.8″. Somewhere between 100 and 200 yards, the bullet drops back through the line of sight to the first zero.
Below is a diagram that demonstrates the double zero theory.
As I mentioned earlier, determining the point at which this second zero occurs exactly is virtually impossible with nothing more than a simple calculator. However, it is possible to get close.
First, we need to determine the drop of the bullet in inches from 100 yards to 200 yards. If the bullet is .4″ high at 100 yards and 2.8″ low at 200 yards, that’s a drop of 3.2″.
Next, we need to determine the drop of the bullet per yard between 100 and 200 yards. This is the point at which we throw the micrometer out the window and start estimating. As the bullet slows due to aerodynamic drag, the rate of fall per yard increases.
Back to the calculator, we divide 3.2, the fall in inches, by 100, the distance traveled in yards. Theoretically, the rate of fall is .032″ per yard. Remember, the trajectory is not a true parabola, so this rate of fall is not a guaranteed constant, but an average.
Next, we need to determine the distance the bullet would travel at the average drop/travel ratio before it drops back to the line of sight of the original zero. The bullet is .4″ high at 100 yards. dividing .4 by .032, we get 12.5. So, theoretically, when the bullet is 12.5 yards past the 100 yard mark, it is at the original zero.
Now, let’s discuss kill range. The kill range will be affected by the value of the desired MOA. If you’re after large game like deer and can accept 3 or 4 inch MOA , you’ll have a longer kill range. On the other hand, if you’re trying to make head shots on prairie dogs, you’ll need a very small MOA and have a fairly short kill range. That is assuming no changes are made to the scope from the original setting.
To make this interesting, let’s assume we’re looking for a kill range within 1 MOA. And let’s assume 100 yards for the zero. That means we have 1/2 inch of bullet rise and fall above and below zero to work in.
Go back to the ballistics table and look at the data for 100 yard zero. Notice the bullet is only .2″ low at 50 yards. That’s less than the actual diameter of the bullet and well within 1 MOA. So, we definitely have a kill range from 50 yards out to 100 yards. But, how far past 100 yards will the kill range extend?
According to the chart, the bullet will drop 3.6″ below zero at 200 yards. So, we do the same calculation we did earlier. That yields an average drop of .036″ per yard of travel. If we’re only willing to accept 1 MOA, we only have 1/2″ of drop below zero to work in. At .036″ per yard, theoretically, we have 13.88 yards past zero before the bullet drops out of 1 MOA. That gives us a total kill range of 63.88 yards starting at 50 yards.
Now, let’s discuss accepting a larger MOA. That’s going to extend the kill range significantly. Go back to the chart once more and look at the data for the 200 yard zero. Zeroed at 200, the bullet rises .7″ above zero at 50 yards and continues to rise to 1.8″ at 100 yards. 1.8″ above zero produces a 3.6 MOA. That extends the kill range for our first calculation of almost 64 yards zeroed at 50 yards to 150 yards of kill range zeroed at 200. Depending on what you’re shooting at and the accuracy of the rifle and ammunition, that’s a useable MOA.
This summer, I’ll be shooting ground hogs with a Savage Axis Youth model in .223 Remington. I worked up a load for it last year using IMR 3031 and 55 gr. NATO BALL bullets. With 21.5 grains of powder, I’m getting a group of .301″ at 50 yards. That’s a .602 MOA.
I’m going to dial my 4X16 adjustable objective scope in at 125 yards. I feel very sure the rifle and ammunition will do their job out to 150 if I do mine.