# Shooting accuracy on a moving target

1. Mar 2, 2012

### wheels25

My buddy and I are planning on doing a shooting competition at our local gun club and need some help. I have asked around school (i am a junior in college) but no one seems to be able to come up with a formula for me. I am looking for a formula to figure out how much to lead a moving target by so when my projectile hits it will be at my desired bulls eye. The example i gave people was "my bow shoots at 300fps and assuming a deer is walking perpendicular to me at 5fps at a distance of 20ft how much do i lead it by?" I know at a short distance like this it will not matter much but i am more interested in a formula so that when we go rifle shooting on moving targets at 600+ meters and only have one shot we don't miss. Also all this is just assuming it is a calm wind day on flat land and assuming i have a perfectly consistent shot each time. Also please forgive my lack of knowledge i am a psychology major so please try and answer as simply as possible i am not familiar with physics. Thank you for any help you can provide

2. Mar 2, 2012

### nDever

Welcome to the Physics Forums.

If you know for certain that your bow shoots arrows at an initial velocity of 300 ft/s, and your moving target moves at a constant velocity of 5 ft/s, all you would need is the distance from the target and you would be close to getting a lead time. Remember too, that as the arrow travels through the air, gravity is still acting meaning that the arrow is being pulled down. This may mean that you would either need to be elevated a bit or aim your bow at an angle before you shoot the arrow or else you may wind up landing below the bullseye. Again, it depends on how far you are from the target.

3. Mar 2, 2012

### A.T.

How much time will the arrow need to travel 20ft if it goes at 300ft/s ?
How far will the deer move in that time if it moves at 5ft/s ?

For longer ranges you need a good estimate of the average velocity, not just the initial one.

4. Mar 5, 2012

### wheels25

If I know my target distance how do I calculate my lead?

5. Mar 5, 2012

### Bobbywhy

wheels25, Welcome to Physics Forums!

For a good theoretical description of the problem see:
http://en.wikipedia.org/wiki/Fire-control_system

For some detailed calculations see:

Calculating Lead For Projectiles, From Unify Community Wiki
Author: Daniel Brauer
These functions calculate an intercept point based on the current positions and constant velocities of a shooter and a target, along with a projectile speed. They're really good for shooting asteroids with machine guns, but won't work as well for targets that can dodge.

Last edited by a moderator: May 5, 2017
6. Mar 5, 2012

### wheels25

another friend of mine suggested this - please let me know if this is correct? knowing that my bow shoots 300ft/sec and my target is moving 5ft/sec at 20 feet away I would divide 300/20 and get an answer of .06666 then multiple that by my targets speed of 5ft/sec .06666x5 to get an answer of 0.3333 meaning i lead my target by 0.3 feet (4inches??) would this work???

7. Mar 5, 2012

### jim hardy

A question well stated is half answered.