1. ## Ballistic Coefficient

By popular demand here is the thread on BC. It should be a good topic with so many professors here

So.......does weight (or mass) have anything to do with BC???

Here is my agrument, and I think it's pretty sound.

Take 2 bullets the same exact shape and size and external coating, but one is more dense (more mass/weight) than the other. They both leave the muzzle at the same velocity. To achieve this velocity the heavier bullet needs more force to propell it. F=M(A) Conversely, to slow the heavier bullet down requires more force, which means if they are traveling through the same density of atmosphere, the lighter bullet will slow down quicker than the heavier.

Can anyone refute this?

2. You have two questions posed.

The first "does weight have anything to do with B.C. ?"

No, because you do not need to change weight to change B.C..

Changing shape or velocity can change B.C.

Second question is interesting. I'll stay out of that one.

3. BC = shape and weight used as factors in a formula, a formula that is over my head, but not over my common sense.

As I wrote on the other thread:

"Cast a lead bullet in a mold. Then, cast a styrofoam bullet from the same mold. Shoot them both out of the same barrel at the same velocities. Which one will go farther and which one will be most affected by cross winds?"

RMiller wrote:

"Put it in any ballistic calculator. Two bullets same B.C. same velocity = same trajectory regardless of weight."

This is true, because any BC assumes a specific weight.

So then, the way I see it, Weight/shape gives us BC, velocity/BC gives us trajectory.

4. Here is a ballistic calculator. http://www.eskimo.com/~jbm/calculations/traj/traj.html

Same B.C.+same velocity= same trajectory regardless of weight.

.5+3000fps=same drop at any range regardless of weight.

Change the weight if you want. It wont change the drop.

Caliber does not matter either.

5. Originally Posted by RMiller
You have two questions posed.

The first "does weight have anything to do with B.C. ?"

No, because you do not need to change weight to change B.C..

Changing shape or velocity can change B.C.

Second question is interesting. I'll stay out of that one.
Actually the second question answers the first. The analogy of the 2 bullets is an illustration of BC as related to weight.

"...you do not need to change weight to change B.C.. "

This very true, but it doesn't prove that weight is not related to BC. There are several factors related to BC and changing any one of them can change BC.

Drag which includes, size, shape and surface coating, is a factor. Weight is a factor, velocity is a factor. Change any one of these and leave the others the same and the BC will change.

If the illustration of the 2 bullets is true (which it is a mathmatical fact) than weight is related to BC, because that's what BC is. To assert that weight isn't a factor means the illustration must be refuted.

6. You started this. So here goes.

The myth of weight v mass.http://ourworld.compuserve.com/homep...ard/weight.htm

7. The two quetions are completely different.

Weight is used to calculate B.C. but weight is not needed to change B.C.

The posts I saw debate on were talking about differences in B.C. not differences in how to calculate BC.

8. Originally Posted by Big Al
You started this. So here goes.

The myth of weight v mass.http://ourworld.compuserve.com/homep...ard/weight.htm

Thank you for the link Big Al, I enjoyed reading it and will read it again with study in mind. Thanks again, I enjoy reading like this.

9. The question as to how to calculate BC uses weight, assumption for mass to get sectional density. Look at the many formulas for BC. weight is used to assume mass.

This is why we need to know if this assumption is correct.

10. From my post a few minutes ago:

"Weight/shape gives us BC. Velocity/BC gives us a specific trajectory."

This is a simple way to look at it.

From: http://en.wikipedia.org/wiki/Ballistic_coefficient

"The ballistic coefficient (BC) of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to the deceleration—a high number indicates a low deceleration. BC is a function of mass, diameter, and drag coefficient. It is given by the mass of the object divided by the diameter squared that it presents to the airflow divided by a dimensionless constant i that relates to the aerodynamics of its shape. Ballistic coefficient has units of lb/in² or kg/m²."

Mass is weight, as BigAl pointed out. "diameter, and drag coefficient" is a function of shape.

Weight/shape gives us BC.

11. Sittin' here and thinkin,' I left out density.

Weight/shape/density gives us a BC. I was assuming lead in my former post.

12. Before I read all of these I want to throw this out. This is just some thoughts I put down to formulate a reply for another individual a couple days ago.

Secondly just because you can change numbers in a calculator program on line and get a particular result doesn't mean bullet weight does not effect ballistic coefficient.

Weight does have a grand effect on a BC number and that is well supported by the laws of science. Also The I in the formula is form factor and it is not effected by weight, only by shape and surface of the projectile.

Newton left us with several myths. Among these are: The law of inertia; An object, which contains mass, will remain at rest until acted upon by some force or field. An object which contains mass when set in motion, will continue in motion in a straight line, until altered by external force or field. Inertia at rest, inertia in motion.

The greater the mass of an object the greater its inertia and the greater its resistance to a change in velocity. Heavy things are hard to get moving and hard to stop once they are moving. This is momentum, which is defined as mass in motion.
Momentum (P) is mass (M*V) velocity. Mass is the object weight in pounds/ the acceleration of gravity which is a constant. ( G=32.14 feet per second squared)

Heavier bullets will give up velocity at a slower rate than light bullets because of this inertia in motion or momentum.

W=Weight. W matters.
__________________________________________________ ____________________

The Ballistic Coefficient of a bullet is depends upon its weight, its cross-sectional area and its shape. BC or C=W/I*d^2

W is the weight in pounds.

I is a number called the form factor which depends on the bullets shape.

D^2 represents the cross-sectional area (diameter squared)

The weight and cross-sectional area can be represented by Sectional Density (SD)

There are standard drag models represented by G1, G3, G4, etc

There are different BCs for different velocities.

There is no such thing as an absolute and invariable ballistic coefficient (BC)

BCs can change with (1) Altitude (2) Temperature (3) Atmospheric pressure (4) Humidity.

BCs for a given bullet are calculated at a specific velocity. As the velocity changes, the BC changes. (This is because as velocity changes the aerodynamic drag.)

Air resistance on a projectile in flight is dependent on several factors. (1) Shape and diameter (2) Velocity (3) Air density (4) the local velocity of sound {Mach number }(This is from temperature, pressure and humidity)

C=W/I*d^2

The ratio of weight to the square of the diameter is W/d^2 is called Sectional Density (SD) therefore we can substitute SD into the equation.

BC=SD/I
I is a form factor or coefficient of form derived from a aerodynamic model by comparing a test projectile to a standard projectile.

All bullet companies calculate BCs for their bullets at standard atmosphere.

Altitude: Sea level
Temperature: 59 degrees F (15 C)
Pressure:29.53 inches Hg
Relative Humidity: 78%
Air Density: .0751 lbs/ft^3 (cubic foot)

13. Originally Posted by RMiller
Here is a ballistic calculator. http://www.eskimo.com/~jbm/calculations/traj/traj.html

Same B.C.+same velocity= same trajectory regardless of weight. This will be with different diameter.

.5+3000fps=same drop at any range regardless of weight.

Change the weight if you want. It wont change the drop. If you change it without changing either of the other two, to keep the same BC, it will change the drop.

Caliber does not matter either.
Yes it does, that is diameter.

If you change the I or form factor you change the BC.

IF you change the d or diameter you change the BC.

If you change the W or weight you change the BC.

Do you deny the fromula(s) are valid?

Do you have a fromula you would like to post?

14. I have never once commented on how to calculate BC.

It seems most of these posts are how to calculate BC.

I have only ever talked about getting different BC without changing weight.

If I am shooting a .5 BC bullet in my 30-06 now, I do not have to go up in weight to find a bullet with a higher BC. So in my example weight has nothing to do with BC.

15. Originally Posted by RMiller
I have never once commented on how to calculate BC.

It seems most of these posts are how to calculate BC.

I have only ever talked about getting different BC without changing weight.

If I am shooting a .5 BC bullet in my 30-06 now, I do not have to go up in weight to find a bullet with a higher BC. So in my example weight has nothing to do with BC.
Sorry, my mistake then. I though that was what I read. What did I do, waste my noodle?

16. Weight is NOT mass. I do not care what you think you know about this subject. Read the link and rethink your position on this myth. This is why many times BC calculation fall down when tested on a Doppler radar range.

Remember, assume makes an," ass (of) you, me"

17. Originally Posted by Murphy
Sorry, my mistake then. I though that was what I read. What did I do, waste my noodle?

I would say not.

18. The most comprehensive piece on BC that I am aware of is in the Sierra Edition V reloading manual. My guess is there is over 50 pages on it.

For me an interesting concept pointed out in the Sierra manual is that the BC of a specific bullet changes with its velocity.

For example, a 308 168 matchking has a BC of:
.462 above 2600fps
.447 2100-2600fps
.424 1600-2100fps
.405 1600 and below

19. I have no idea if this has to do with BC or not, but I decided to post it to add fuel to the fire. If you look at the factory long range ballistics, which are published in the back pages of Guns & Ammo Annual, and Petersen's Rifle Shooter Annual magazine, you will notice something about most cartridges. In this case, I will pick one cartridge out of the bunch.

.300WM

1. Federal 180-grain A-Frame, sighted at +1.7" 100 yards, zero at 200.
2. Remington 200-grain A-Frame, sighted at +1.8" 100 yards, zero at 200

180 grainer
Muzzle = 2920 fps, 3409 foot-pound
100 yd = 2687 fps, 2887 foot-pound
200 yd = 2466 fps, 2432 foot-pound. Bullet drop = 0 (zero)
300 yd = 2256 fps, 2035 foot-pound. Bullet drop = -7.4"
400 yd = 2056 fps, 1690 foot-pound. Bullet drop = -21.6"
500 yd = 1867 fps, 1393 foot-pound. Bullet drop = -44.1"

200 grainer
Muzzle = 2825 fps, 3544 foot-pound
100 yd = 2595 fps, 2989 foot-pound
200 yd = 2376 fps, 2506 foot-pound. Bullet drop = 0
300 yd = 2167 fps, 2086 foot-pound. Bullet drop = -8.0"
400 yd = 1970 fps, 1722 foot-pound. Bullet drop = -23.5"
500 yd = 1783 fps, 1412 foot-pound. Bullet drop = -47.9"

-The 200 grainer (similar construction, same caliber) is loaded 100 fps slower. It's BC should also be lower, but I didn't check to see by how much.
-The 200 grainer should be longer than the 180 grainer, and of higher SD
-The 180 grainer has higher BC, but lower SD
-From the muzzle out to 500 yards, the 200 grainer keeps ahead on energy
-From the muzzle out to 500 yards, the 180 grainer keeps ahead on velocity
-Out to 300 yards, both strike the target within 1" from each other.
-------
If you look at the ballistics for all the cartridges there, you will come upon several loads where two similarly constructed bullets (same brand). Of the same caliber, and one heavier than the other-with the lighter loaded a little faster than the heavier one: the lighter one sheds velocity at a faster rate than the heavier one, and that somewhere around 300 yards both are traveling at speeds very close to each other. Since the maximum distance I may ever take a shot on moose is 300 yards (maybe), I prefer a heavier bullets over lighter ones.

20. Originally Posted by RMiller
The two quetions are completely different.

Weight is used to calculate B.C. but weight is not needed to change B.C.
I guess we have a problem with semantics...or... what the question is.

The original posts that started all this were...

{...... and weight (or mass) is a factor in BC.} by me and...

{"and weight (or mass) is a factor in BC."

It's a factor in SD(sectional density) and energy calculations,but not in BC(ballistic coefficient). SD is moot too,as it does not factor integrity.}

by another poster.

The issue was does weight (or mass) factor into BC, and the simple answer is *yes*. By every formula and and written explanation I have ever read.

Originally Posted by Big Al
Weight is NOT mass. I do not care what you think you know about this subject. Read the link and rethink your position on this myth. This is why many times BC calculation fall down when tested on a Doppler radar range.
Big Al, you sure wont get an argument from me on this. My HS teachers and college professors did a good job of making this very clear to me. So yes technically we are talking about Mass. Weight (in our world) is the effect of the Earth's gravity on Mass. We measure it (i.e. 168 grains) and us it in the equation for Mass. Hence for practicle purposes and layman's terms I have used the term weight, because essentially there is no difference in the quantitative value of weight or mass in the BC equation. I will use the more proper term "Mass" from now on.

Also, I'm not sure what you're getting at about BC calcs falling down when tested at a doppler range?

OK then, so the original once again was and is.... "Does Mass factor into BC?"

Anyone think it doesn't?

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