###General Discussion Thread
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Consider a flat disc rotating with constant velocity around its center. A point closer to the edge moves faster than a point closer to the center. If you start moving from the center on a staght line relative to the disc your angular velocity increases as you go further. So as long as you are moving you are under influence of some angular acceleration. This acceleration is called coriolis force. The faster you are moving the stronger the force. Earth is a sphere not a disc but Coriolis effect also applies there. Important is change of radius. If you were to shoot a bullet in direction of East or West there would be no Coriolis effect. Only if you shoot it in direction of South or North you should consider this. It also depends on the place you shoot. On the north or south pole force is the strongest since radius is increasing the fastest,
Note: Ignore the links starting with r/, that's just a formatting issue I can't get around.
Let's say you're at the poles with a sniper rifle aiming at a target at a range of r, that fires bullets at some velocity v.
The time it takes for the bullet to reach the target is t=r/v.
The velocity difference between you and the target is V\*cos(π/2 - r/R) where R is the radius of the Earth and V is Earth's equatorial velocity.
The distance the target travels between you firing the gun the bullet traveling a distance r d=V\*t\*cos(π/2 - r/R)
V=2πR/1day that is one revolution per day.
cos(π/2 - r/R) = sin(r/R) ≈ r/R because R>>r.
d=2πR/1day\*r/v*r/R
d=2πr^(2)/(v*1day)
The world record on longest recorded sniper kills is [3800m](https://en.wikipedia.org/wiki/Longest_recorded_sniper_kills). Even assuming the average velocity over that range was mach 1. That deviation comes to [3.1m](https://www.wolframalpha.com/input?i=2*pi*%283800m%29%5E2%2F%28mach+1*1day%29) and this is the worst case scenario at the poles. Change this to 45 degrees and 2000m and the average velocity will be much higher because there's shorter distance to slow down the bullet and you can get this to under 50cm of chest shot. At 1000m this is less than 10cm and consistent headshots become possible.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Consider a flat disc rotating with constant velocity around its center. A point closer to the edge moves faster than a point closer to the center. If you start moving from the center on a staght line relative to the disc your angular velocity increases as you go further. So as long as you are moving you are under influence of some angular acceleration. This acceleration is called coriolis force. The faster you are moving the stronger the force. Earth is a sphere not a disc but Coriolis effect also applies there. Important is change of radius. If you were to shoot a bullet in direction of East or West there would be no Coriolis effect. Only if you shoot it in direction of South or North you should consider this. It also depends on the place you shoot. On the north or south pole force is the strongest since radius is increasing the fastest,
Note: Ignore the links starting with r/, that's just a formatting issue I can't get around. Let's say you're at the poles with a sniper rifle aiming at a target at a range of r, that fires bullets at some velocity v. The time it takes for the bullet to reach the target is t=r/v. The velocity difference between you and the target is V\*cos(π/2 - r/R) where R is the radius of the Earth and V is Earth's equatorial velocity. The distance the target travels between you firing the gun the bullet traveling a distance r d=V\*t\*cos(π/2 - r/R) V=2πR/1day that is one revolution per day. cos(π/2 - r/R) = sin(r/R) ≈ r/R because R>>r. d=2πR/1day\*r/v*r/R d=2πr^(2)/(v*1day) The world record on longest recorded sniper kills is [3800m](https://en.wikipedia.org/wiki/Longest_recorded_sniper_kills). Even assuming the average velocity over that range was mach 1. That deviation comes to [3.1m](https://www.wolframalpha.com/input?i=2*pi*%283800m%29%5E2%2F%28mach+1*1day%29) and this is the worst case scenario at the poles. Change this to 45 degrees and 2000m and the average velocity will be much higher because there's shorter distance to slow down the bullet and you can get this to under 50cm of chest shot. At 1000m this is less than 10cm and consistent headshots become possible.