Fun With Math and Guns

You have just been shot at by a sniper. Luckily he missed and when you heard the bullet go by you started counting and the estimated time between hearing the bullet and hearing the gun report was approximately 2.5 seconds. How far away do you look for the shooter? Given some approximate knowns:

V1 - Speed of sound is ~ 1100 ft/sec

V2 -Avg speed of bullet over distance is ~ 2400 ft/sec

T1 – Time from hearing bullet to hearing gun report ~ 2.5 sec

T2 – Time it takes the bullet to travel from the gun to your position ~ ?

Total Time = T1+T2

Calculate T2 = T1*(V1/V2)

T2= 2.5sec*(1100 ft/sec / 2400ft/sec) = 1.14 sec

Total Time = 2.5sec + 1.14 sec =3.64 sec

Distance to shooter = 3.64 sec * 1100 ft/sec = 4004 ft

Convert to yds – 4004 ft / 3 ft/yd = 1334 yds

So to simplify the equation

Distance to shooter = (T1+(T1*0.458))*366

(2.5+(2.5*0.458))*366 = 1334 yds

So you look for your shooter about 1300 yds down range.

Memorization chart using this equation.

 

 

Remember these are approximations based on sniper rifle velocities but good enough for the field. In fact one could say about 260 yds per 1/2 second or 520 yds per second.