Help with Ballistics and Math for a AP Physics Project

[whiskeylima]

I am helping my son with an AP Physics project. He is an avid silhouette shooter and he chose a shooting related project.  He is trying to calculate:

The amount of kinetic energy (in either ft pounds/sec or newton meters/sec) necessary to knock down a full size ram at 200 meters.  We have read on a forum that handgun silhouette shooters calculated,  depending on the overhang of the foot, it takes approx. .8-1.0 ft pounds/sec of kinetic energy to consistently knock down a ram. He is trying to put to paper the physics / math reason for this.  He will then load, shoot, chrono a series of different rounds and determine what combo of bullet weight and velocity works.

This may be a long shot but if anyone can help,  its the 50 pound brains on this forum.  You also gotta appreciate a kid and teacher that is completely focused and interested in this project.....and fully supportive of it.  

[zeus]

I would think the force required is directly related To point of impact in relation to the targets true center of gravity location. As in a hit to the top of the back will help tip easier than a hit to the bottom-middle area in my limited ram experience years ago. Add that with the placement of the feet on the rail, it would vary In my mind. I would hold the foot placement as a constant and assume full contact on the feet/rail. Then you could use the weight in relation to the area of the feet and work out from there possibly? A hit to the top breaks the foot contact whereas a hit to the bottom may try to slide it on the rail somewhat which brings in a friction coefficient rather than broken contact from a high hit. He will have to assume some constants like full contact etc where he has some control of the variables that are actually within his ability to control.

[bradshaw]

May 23, 2018 21:46:25 GMT -5 whiskeylima said:

I am helping my son with an AP Physics project. He is an avid silhouette shooter and he chose a shooting related project.  He is trying to calculate:

The amount of kinetic energy (in either ft pounds/sec or newton meters/sec) necessary to knock down a full size ram at 200 meters.  We have read on a forum that handgun silhouette shooters calculated,  depending on the overhang of the foot, it takes approx. .8-1.0 ft pounds/sec of kinetic energy to consistently knock down a ram. He is trying to put to paper the physics / math reason for this.  He will then load, shoot, chrono a series of different rounds and determine what combo of bullet weight and velocity works.

This may be a long shot but if anyone can help,  its the 50 pound brains on this forum.  You also gotta appreciate a kid and teacher that is completely focused and interested in this project.....and fully supportive of it.  

*****

I am not aware of a mathematic formula or answer to the question of force required to topple a 55 pound ram. First, there is a ram set “full foot” on a flat steel rail. Then, there is the adopted IHMSA rule to overhang the back side of front and rear feet 1-inch, a rule intended to prevent Rocks & Dynamite loading in a quest to reduce “ringers”----targets hit but not knocked over.

Zeus describes areas relevant to TARGET INERTIA: top of the back topples with less force; low belly requires more force, etc. Lateral aspects relate to inertia as well: shoulder hit=higher target inertia; rump=lower target inertia.

And then the BULLET. As I came to silhouette with considerable handgun hunting under my belt, many of my bullets included pure or soft lead cores. Other silhouetters chose hard-cast bulets, in the theory the harder bullet would hit harder. Perhaps the harder bullet hit harder----with short IMPACT DURATION. A soft bullet of same weight at same velocity exhibits longer DWELL TIME. Many silhouetters have seen the puff of gray smoke as a hard bullet vaporizes on steel and the silhouette remains standing, or takes its sweet time to fall.

One projectile which defies the PLASTIC DEFORMATION/DWELL TIME behavior is the French 12 gauge shotshell loaded with a steel ball bearing. Vicious impact and barrier penetration. The steel ball does not break, chip, warp, crack or peel. I suspect the steel ball bearing preserves momentum to overcome inertia of the ram.

Your son may have opened a can of worms, and those worms are ready to lead him on an adventure.
David Bradshaw

[potatojudge]

Speaking of cans of worms, that's where experiment design comes into play. Gotta reduce or account for as many variables as possible or you'll have a hard time applying your findings in general terms.

Stipulate things like point of impact a "hit zone" or at least limit to the top half of the target (kicking the feet out from under the target with a low hit is a whole other experiment), measure the force with which your given load and bullet strike (perhaps a steel ram hung on a long cable as a pendulum and measure maximum deflection of the plate?- this would account for dwell time of the bullet/energy imparted to the target since some of the 1/2MV squared of the bullet velocity and weight will be lost to heat, deformation, and continued motion of the bullet), if the feet are set off the rail then measure the angle the ram must tilt to fall over. Chrono the loads at 200 meters then make reduced loads that hit with the same velocity at 25 meters to simplify shooting and measurements.

[jsh]

I sent you a PM with some info from a mentor of mine. He is a hands on IHMSA shooter, also a retired professor.
Jeff

[whiskeylima]

Thank you all for the replies. We are making some progress forward. The teacher did suggest the development of a ballistic pendulum but I am not sure that is in the cards. My son will need to make some broad assumptions else this will get way too complicated. He initially wanted to try and determine the force necessary to move the animal based on the height of the hit but quickly got a headache with the variables. We may go the route of assuming a "dead center" hit, and assuming the pads on the feet are full set and are 4" x 5", calculating the force necessary to move the animal straight back off of a 4" rail. I appreciate his interest and desire to try this, but he is quickly realizing this is way more complicated than he initially thought.

[Ken O'Neill]

Way in the back of my mind, I seem to recall someone doing a "study" that suggested that hollow points exhibited a longer dwell time and were therefore more effective. His conclusion, reached during the '80's. I have no opinion.
Your son's physics project is fraught with potential variables ... gives me a headache. Where's Werner von Braun, when we really need him?