[Ron Weaver]

I am trying to assist my grandson in a school science project. I am trying to accurately determine how much further a high velocity 22 rimfire bullet will travel in the same time of bullet flight. So if you have your 10/22 zeroed @ 75 yds. with the standard velocity ammo, at what point further down range will the high velocity bullet also be zeroed? We are acting on the premis that gravity is constant, simply horizontal speed provides further down range bullet compensation due to faster flight time? HELP? We thought we had it made, chronoed at muzzle and 75yds. with both loads ( Aguila Std. & HV ), but are now struggeling with the formulas and height above bore of scope, etc. .....
HELP? Thanks,
Ron

[Jason_G]

Are you trying to compare horizontal travel of a high velocity .22 lr vs. plain jane .22 lr?

Jason

[north]

Here is a link to the winchester site. and a Picture of the page that list the difference in velosity between the two type of 22LR. Basically the HV bullet starts 105 fps faster but at 100 yards it is only going 41 fps faster.

http://www.winchester.com/products/catalog/comparerimfire.aspx?multiadd=WDIyTFItMS00K0FFQS1YVDIyTFItMS00&action=3&ctype=1&atype=4#

[rcmodel]

You might want to rethink that class project.

The way things are in the U.S. anymore, the kid's probably going to get expelled and placed in Protective Foster Care when he mentions rifles and shooting in class! :rolleyes:

http://i81.photobucket.com/albums/j219/rcmodel/KTOG/1224.gif
rcmodel

[Quoheleth]

Uhhh...can't help you on the physics, but as the husband of a 6th grade teacher---

---yeah, at the least, I would OK it with the teacher before turning that paper in. Wife has to (HAS to) flag any paper with gun-related language written by a student. There are a few exceptions: for instance, if the student is answering a question where the answer is a firearm ("Why was Custer's use of the trapdoor Springfield significant at the Battle of Little Big Horn?"). But if Johnnie writes, "Dear Santa, for Christmas I want a new Ruger M77 Hawkeye, chambered in .204 Ruger, and two boxes of the new Hornady ammo..." he's headed to the Big Office down the hall.

For your grandson's sake...check it out. (Cool project, tho)

Q

[btg3]

Your science project reminds me of some textbook ballistics problems from my first physics class in college. Calculus was a pre-requisite and I think you'll be using it in some form to get your current project squared away. Of course there may be some websites that do the math for you. Have you googled?

If you can assume the bullets have the same mass and drag coeficients it will also help. Think you can safely ignore the scope, but if you need to prove that mathematically, go for it.

If you need to punt, there are simpler science projects that can be done and still use your 10/22.
How does cleaning affect accuracy?
How does age/experience/training affect accuracy?
How does accuracy compare for different .22 loads?
Borrow a decibel meter and compare loudness of different .22 loads at varying distances from the gun.

However you proceed, be sure you use a large enough sample size to accurately represent what you are doing. I suggest a minimum of 10 shots for each condition in the experiment. (25 would be better.)

[NateG]

You could try this: http://www.modernballistics.com/download.htm and running the trajectory calculations for standard and high velocity .22 ammo. It'd also tell you the time-of-flight for each.

[RedLion]

gravity exerts a force of 32 feet per second squared so a bullet travelling 1000 yards in one second will drop 32 feet off the muzzle at 1000 yards. But the rate of its fall is not linear. The equation we used in high school was S=.5(A)(T^2) where s= distance, A=acceration(gravity), and T^2= time squared. A bullet at 1000 fps will get to 75 yards at 9/40 sec (225 feet/1000 fps=9/40). Using the equation (32)(9/40^2)=.81 feet. so a bullet travelling 1000 fps will fall .81 feet off the muzzle at 75 yards. To use a higher velocity bullet just solve for how long the higher velocity will travel in the same amount of time as the original bullet.

9/40sec=225feet /1000fps
9/40=x/new velocity 9/40sec =x/1500fps x=337.5 feet or 112.5 yards

The biggest factor is the friction caused by the air on the bullet causing it to decrease velocity more and more as the bullet travels through the air. For figuring this you will need some big calculations like calculus derived formulas with the rate of deceleration versus the rate of the bullet falling.

If your kid is still in elementary school or middle school i would just assume air resistance is negligable. the judges will be more impressed because it would be more reasonable for a kid to solve just the gravity equation than derive a new equation using calculus( I couldn't do it as a senior in physics!)

You might want to double check my work because I have been out of standard kinetics for about a year and a half now. Just look up physics and kinetics and you'll have the equations. And remember to have fun with the project:)

[jmorris]

I helped out my brother in law with a similar project (used paint balls) a few years ago. Once he has figured out the calculations you can check his work at http://www.eskimo.com/~jbm/calculations/traj_card/traj_card.html FWIW he had more fun learning to run the lathe and mill building our test rifle than he did doing the math after we collected the data, but it was the project he picked out.

[Jim Watson]

Hatcher's Notebook has the ballistics tables for manual calculations. Very tedious but more educational than feeding numbers into a computer program.

[glennv]

I teach physics so PM me if you need help with the calculations.

[Six O'clock Tactical]

Yeah, unless you want to try teaching a 6th grader discreet mathmatics and differential equations of motion, just stick to gravity.

Redlion, the friction is actually a negligable effect on the bullet compared to the reaction of the phase change of the atmosphere in front of the bullet. Ballistics are more of a pressure issue with turbulent flow drag equations than simple friction coefficients, especially when you crest over transonic velocities and the properties of fluids are completely altered at those speeds.
Also, 32 fps/s is an accelleration, not a force, as the units for force are N. (F=ma) In one second the bullet would be in freefall at a rate of 32fps, it would have fallen only 16 feet.
(Just a quick refresher for those who dont use this info every day) :-P
Good to see you tried to remember though... always a positive thing to exercise the brain.

Also, you will need to consider that the force required by an object to proceed through a fluid is logrithmic to its velocity, and the force derived from momentum is just proportional to the velocity, so the faster bullet will have a greater negative acceleration than the slower bullet, and this of course will change logrithmically. When you get below transonic speeds though, ballistics takes another wild turn as fluid compressability properties change. I have the mach number property charts... dunno where they are though...

Anyway... stick with gravity and MAYBE a very simplified momentum equation, and I doubt theyll take into consideration the properties of supersonic flow while grading a 12 year old.

[gravis86]

RedLion is spot on, except that you need to start using vectors, assuming that the bullet will not be fired perpendicular to the gravitational force.

He is assuming that you fire on a level plane, but you won't be. A bullet travels up at the beginning of its trajectory, so that means it is fired at an upward angle.

It's a lot more complicated than the traditional High School formula.
http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

[Mike OTDP]

I'd edit the experiment to permit the use of forces parallel or perpindicular to the line of flight. The math will go a lot easier that way.

Now, one option that you might want to explore is to shoot both cartridges at the same distance, then use the difference in bullet drop to figure out the difference in velocities.

[BP44]

Sorry I cant be of help but I wanted to say that it is great that you are helping your grandson with this, it really makes me feel good about life agian. I am not being sarcastic this is really cool:) and

[JackOfAllTradesMasterAtNone]

Helping your grand son that is.

I think you've got enough of the math and other sources in this thread to get you in the right direction.



I really like helping my boys with school projects like this, although this sort of thing doesn't come along all that often. My youngest was involved in Destination Imagination for a while. He came home one day with need to build a Rube Goldberg machine. I said, Huh? A what? He had already sketched something out. I wasn't allowed to do any of the work or make design changes. That weekend we had a crash course on power tool use in my shop. I held things in place for his own safety, other than that he did all the manufacture/assembly. As pretty much the leader of his 5th grade team, they won districts and state and made a really good showing at Globals largely due to how his machine functioned. It was the pinacle in the skit.

Your grand son, learning the effects of acceleration, velocity and gravity, upon flight of a bullet, Or any flying object for that matter for a school project is cool. :D

RCMODEL- The way things are in the U.S. anymore, the kid's probably going to get expelled and placed in Protective Foster Care when he mentions rifles and shooting in class! Man, You've got that right! We live in a small rural farmland community so we're lucky to get to know most of our kid's teachers. Come to find out some are even hunters/shooters. But we have figured out some of the 'Tree hugger/Vegan/Save the Wales' types that we tip-toe around to make sure either of our boys are not arrested and slipped into a straight jacket just for talking with their buddies about their new hunting rifle as reward for getting straight "A's".

-Steve

[Hoser]

Any chance you are the same Ron Weaver of STC fame?