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Old May 11, 2008, 06:54 PM   #1
Ballistics Student
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Trajectory of .30-30 and basic ballistics

As a mathematical exercise, I am trying to calculate when a a 30-30 150 grain round will fall to the ground. Assume I am shooting perfectly level across a flat plain, with the rifle 70 inches above the ground.

I'm a beginning student in all this, and want to fully understand how wind, heat, altitude and other variables affect a bullet's trajectory. Any suggestions about books, videos, graphs, or other sources of info?

Online calculators can give me the numbers, but I want to really understand, and be able to visualize the bullet's arc as it's affected by wind, humidity, etc...

I'm specifically interested in doing the math for the 30-30, and figuring when it will hit the ground. Since most info out there is about hitting a target (not hitting the ground!) any help would be greatly appreciated.
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Old May 11, 2008, 07:39 PM   #2
Ulrice
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I highly recomend A-Square's book "Any Shot You Want". It is a handloading and rifle manual. It goes through basic handloading; interior, exterior, and terminal balistics; velocity and pressure interpretation; effects of change in temperature, barrel length, and bullet compoents; recoil; rifle and cartrige selection; and load info from .22 hornet all the way to .600 NE.
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Old May 11, 2008, 08:01 PM   #3
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Thanks for the reply.

"Any Shot You Want" gets good reviews on Amazon, but I can't leaf thru it at my local bookstore, so before I spend $35, can you check your copy and see if it has a specific section about the 30-30 round?

I'd appreciate it...
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Old May 11, 2008, 08:25 PM   #4
Ulrice
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It dosn't have balistic info spicifically for the 30-30 but it does explain how gravity, wind, and air affect the bullet.
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Old May 11, 2008, 08:27 PM   #5
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The weight (bullet) will drop at the same velocity if it's fired from a rifle or simply dropped from your hand. Trajectory merely compensates for this. Velocity is related to trajectory NOT gravity.
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Old May 11, 2008, 10:22 PM   #6
Jim Watson
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Go to
http://www.eskimo.com/~jbm/calculations/traj/traj.html
and plug in the requested data.
Look for a drop value of 70 inches and the range at which that occurs is your answer.
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Old May 11, 2008, 10:34 PM   #7
jrothWA
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The "Dope BAg" of theAmerican Rifleman...

back in teh 70's answered this.
Basically, if a leveled barrel was fired and a second bullet was drop from the barrel the same time as fired bullet exited, BOTH would hit the ground at the same time. IT's all under gravity's influence, the horizontal velocity doesn't matter.
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Old May 11, 2008, 10:35 PM   #8
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Thanks, Jim, but I'm looking to understand the mathematics of ballistics, so I can have a more complete 'picture' of what happens as the bullet travels and is affected by various factors during its flight.

The online calculator tells me that a 30-30 150 grain bullet will drop to the ground at almost exactly 400 yards. Now I want to understand how and why, and be able to 'see' the bullet's arc.
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Old May 11, 2008, 10:42 PM   #9
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I would take the calculation for gravity to drop a 150 grain bullet to the ground and get how long it would take from 70 inches. Then work the fps curve as the bullet travels (available at the ammo manufacturers website more than likely) until you reach the timeout....that many feet is where the bullet landed.
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Old May 11, 2008, 10:57 PM   #10
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Free software on the internet can do this.... look for PointBlank.

It'll plot you a graph, and will take into account elevation and temperature too. Even differently designed 150gr bullets based on their ballistic coefficient.
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Old May 12, 2008, 07:37 AM   #11
Jim Watson
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Quote:
I'm looking to understand the mathematics of ballistics,
Hatcher's Notebook has a chapter with the equations and tables, the way it had to be done before computers.

I have seen recommended but do not own:

Rifle Accuracy Facts
This book by Harold R. Vaughn is the successor to the classic work "The Bullets Flight", by Dr. Mann; and is the result of many years of research and experimentation. The book covers internal ballistics, barrel vibration, chamber and throat design, muzzle blast effects, bullet core problems, external ballistics and many other chapters. Harold vaughn built a 100 yard tunnel for his testing and used a rail gun, shadow graphs, and other sophisticated equipment to research this project. Harold vaughn is not a backyard researcher. His background includes a MS in Aerodynamics and 35 years of work at the Sandia National Laboratories with 30 years as the Supervisor in the Aeroballistic division.

Understanding Firearms Ballistics
This revised edition of the much acclaimed Understanding Ballistics , written by Robert Rinker, is expanded from 270 to 430 pages. The text has been improved and broadened with up-to-date information. Included are explanations of terminal ballistics, wind deflection, trajectory, ballistic co-efficients, velocity and drag and much more. The revised edition contains more formulas, more detailed examples, more charts and sketches and more technical details. The text is written in a clear understandable fashion by a shooter who knows shooters. The mathematical equations are provided, but the text is written so the reader can get the information without doing the math if he wishes.

New Exact Smallarms Ballistics, the Source Book for Riflemen.
Arthur J. Pejsa. Concise text makes ballistic theory and the laws of physics comprehensible to the average rifleman, and shows how to apply them to achieve improved accuracy. Help you predict precise bullet trajectories out to extreme ranges, with detailed data for many cartridges.


I don't know that these will teach you everything you want to know, but they are what is available through shooting sources.

There is also some explanatory material on the Sierra website.

Last edited by Jim Watson; May 12, 2008 at 08:10 AM. Reason: Found another reference book.
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Old May 12, 2008, 11:50 AM   #12
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Multiply the bullet weight by 9.8 meters per sec2/distance to the ground, and you will find the time for it to hit the ground. This time is not effected by any other factor. Wind, barometric pressure, bullet shape, etc.etc. only affect where it will hit not when.
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Old May 12, 2008, 02:36 PM   #13
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bullet weight in 'grains' or something metric?
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Old May 12, 2008, 03:36 PM   #14
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Using that equation, you would use Kg. But that won't give you the time, just the inertia force of the bullet falling. The time is not related to bullet weight, since the air resistance would be negligible at the vertical speed the bullet is traveling. Mathematically, the bullet will be accelerating toward the ground at 32.2 ft/sec/sec. This means each second it is falling, it gains another 32.2 ft/sec velocity downward. Now the rest is physics 101, someone correct me if anything below is wrong:

Distance (ft) / Time of drop (sec) = Ave Velocity

Max Velocity / 32.2 (ft/s^2) = Time of drop

Max vel = 2 X Ave Velocity (since the acceleration is linear and min velocity is zero)

Combining equations to solve for time of drop (basic algebra):


Sqr Rt (Dist. / 16.1) = Time of drop

So it would take an object about .60 sec to fall 70 inches.
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Old May 13, 2008, 01:18 PM   #15
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You're not gonna learn the ins and outs of ballistics from an internet message board. I'd suggest starting with the above-mentioned books. As much as a lot of folks would like it to be, the internet is a poor substitute for books.
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Old May 14, 2008, 12:37 AM   #16
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I agree. I'm reading Rinker's book, and have a few more coming from the library. Thanks to all who replied to this post.
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Old May 14, 2008, 01:33 AM   #17
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30+ years ago (back in the dark ages).....

Waaay before the internet, they used to teach this in high school physics class. The exact answer to your question when the .30-30 bullet hits the ground (fired parallel to the ground) is a straight calculation of acceleration due to gravity. On Earth, objects fall at 32 feet per second, per second, until a terminal velocity is reached.

Now, where the bullet lands (distance from the muzzle) will be the effect of several factors (MV, ballistic coefficient of the bullet, temp, humidity, etc.) over the time of flight. The time of flight (fired parallel with the earth) will be the same as the time of falling straight down, due to the effect of gravity.

Because of the relationship between line of sight and line of the bore (intentional) when you aim at a target level with you, the axis of the bore is actually pointed above your target, so that gravity will drop the bullet into the target at the "sighted in" distance. That is the trajectory, and the reason for it. All guns use this principle with their sights, because all bullets are subject to the pull of gravity as soon as they come out of the muzzle, no matter what speed they are fired at. The speed and the shape of the bullet have an effect on how much of an angle is needed between the line of sight and the line of the bore axis in order to obtain hits at specific distances.

I suggest you do some reseach into basic physics, including the expiriments done by Galileo at the Tower of Pisa. You ought to be able to find something about them on the Internet.
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