• Ken Kraushaar

The Earth is Flat?


I recently came across an old argument during a search I did on the Coriolis effect from the flat earth society. In one particular post, I read the following as an attempt at proving the earth was flat by referencing shooting:

“They might need to factor in wind speed and distance. Bullets shoot in a straight line so there is no curvature to factor unless you are confusing fiction with reality as seen in the movie Wanted.”- anonymous

Unfortunately for this poster, rifles/bullets do not actually shoot in a straight line. The weight of the bullet via the force of gravity, (which is a constant 32.2fps due to the centripetal force caused by the earth's rotation), actually causes the bullet to drop a significant amount before impacting the target.

For example, we'll use the same information I used in the post regarding adjustment of collimators. keep in mind, a collimator only aligns the scope's retical with the bore of the barrel. we still have to account for the initial drop of the bullet at 100 yards:

Here is the mathematical equation for finding out the amount of adjustment in Minute of Angle (inches) you will need to make in order to get your bullet within 1 or 2 inches of the intended zero, before you ever shoot your rifle at the range:

A= 4m+h/r/100

h= the distance in inches above the bore diameter

m= midrange trajectory in inches at "R"

R= Range in yards

A= Angle in minutes between the collimator and the line of sight.

For this equation we will assume we have a "known" mid-range trajectory. in days past this was included in reloading guides or it was data provided by ammunition companies on the box. we'll assume a range of 300 yards, with a scope height of 1.5" above the center bore with 1/4 MOA adjustments, and a starting velocity of 3000fps.

We'll use the following taken from an old Hornady reloading manual:

ex: 30 caliber 150 grain spire point bullet

Range @muzzle @100yards @200yards @ 300 yards

Velocity (fps) 3000fps 2730 2470 2230

Energy (ftlbs) 3000ftlbs 2483 2033 1656

Drop (inches) 0 2.09" 9.48" 23.62"

Midrange Traj 0 .52" 2.37" 5.90"

So we can see that the mid-range trajectory is 5.90". as a side note, you can figure out the mid-range trajectory by dividing the drop by 4. for example 23.60 / 4 = 5.9 which is the listed mid-range trajectory for this bullet.

So we now know that:

h=1.5"

m=5.90"

R=300

So we can plug it into the equation:

4(5.90")+(1.5") / 300/100 which would then be 23.6"+1.5" / 3 which then becomes 25.1 / 3= 8.366666667 or rounded to 8. now multiply 8 by the number of clicks (4) or 8*4=32 clicks "up" to bring the adjustment close to a zero at 300 yards.

even at 100 yards, if we plug in the numbers, 4(.52)+(1.5) = (2.08")+(1.5") or 3.58" / 1 which then equals 3.58, or roughly 4 inches low, so we multiply by our clicks 4*4=16 clicks "up."

There is a separate equation for figuring out the angle without the midrange trajectory, which simply uses the drop, which most ballistics programs can now provide.

That equation is A=100(D+h) / R

So again: D=23.62" h=1.5" and R=300 yards.

A= 100(23.62+1.5) / 300 -> A= 100(25.12") / 300 -> A=2512 /300 -> A=8.37 or A=8 (rounded.)

Now multiply the adjustment by 4 clicks and you get 32clicks "up" for the adjustment, which is the same as our last equation.

This creates the illusion of being able to point straight at a target, but in reality we are still arcing the bullet using trajectory to compensate for gravity, not unlike shooting a cannon or an arrow. It’s being lobbed at the target. The effect of wind, using match grade bullets, is dependent upon the bullet’s ballistic coefficient, or its ability to travel through the air, which is a different force at play all together.

This can further be seen by using an angle indicator and measuring the starting angle of the rifle, when shooting it straight with no adjustment, and then again after the angle has been changed, and you would have a rifle that has been adjusted several degrees from the original measured angle. This is even more pronounced when we shoot at longer distances, and is actually observable in footage readily available on youtube, which shows the bullet arcing towards the target, not unlike an arrow.

When you factor in the Coriolis effect, which in shooting, only becomes necessary when you are shooting at distances greater than 1000 yards, you are accounting for 1) spin drift, which is caused by the lateral deflection the bullet caused by the Coriolis effect, and the rotation of the earth, which is a constant speed of 460 meters per second (or 1028.99mph). If you are facing west, in the northern hemisphere, then you have to account for the target actually moving incrementally towards you, and a rightward deflection, and if you are facing east, then you are accounting for the earth rotating away you as you shoot. If you are in the southern hemisphere, then you would have to account for a lateral deflection to the left. The longer the distance, the more compensation for both spin drift and the earth’s rotation you have to make.

Again, this is not movie magic, these things are actually observable and quantifiable. Take for instance, something simple: storm rotation. From NOAA we find: “The reason is that the earth's rotation sets up an apparent force (called the Coriolis force) that pulls the winds to the right in the Northern Hemisphere (and to the left in the Southern Hemisphere). So when a low pressure starts to form north of the equator, the surface winds will flow inward trying to fill in the low and will be deflected to the right and a counter-clockwise rotation will be initiated. The opposite (a deflection to the left and a clockwise rotation) will occur south of the equator.” -http://www.aoml.noaa.gov/hrd/tcfaq/D3.html

These same forces are at play when we are shoot.

Now, the poster was right, you cannot arc a bullet in the manner that they do in the movie “Wanted”, but you are actually shooting at angle, even at short distances, when you are shooting at a target; this poster, possibly was conflating the mythbusters episode which proved you cannot “bend a bullet” while shooting at a target.

The only exception to this rule would be shooting something like a .416 barrett, or a .50caliber BMG, which travel at a speed of 2,750fps, and 2978fps, respectively (depending on the bullet weight,) at a distance of 100 yards. In these cases, the impact would be high at 100 yards because gravity hasn’t yet overcome the speed of the bullet by the time it gets to 100 yards, though at further distances, again, the impact would observably drop depending on the distance as an effect of gravity caused by centripetal force of the earth’s rotation. Otherwise, we would not have to factor in velocity when shooting either, and the bullet would keep going at a constant speed.

For more information on the topic of the Coriolis effect on shooting, please check out Bryan Litz’s books and posts on the topic, as he is extremely detailed when it comes to long range shooting and computations regarding the subject.


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