Cast Boolit Design parameter question

[AKbushman49]

While working with Tom Myer's Cast Bullet Design Program. A couple of questions came up. What is the significance of the CG (Center of Gravity) and CP
(Center of Pressure) relationship? When looking at other bullet designs in the program this relationship between CP and CG is not always the same. Is CP a calculation of bullet compression when fired? I realize that CG (center of gravity) refers to bullet balance, and designing a bullet longer changes that parameter. But CP doesn't maintain the same relationship/ratio to CG. (provided bullet length the only parameter changed). Hence my question. Thanks in advance.
bushman

[Outpost75]

The distance between the CG and CP is the radius of gyration and bullets having a shorter rg tend to be more stable than those which do not, having a less favorable ratio of axial to transverse moments of inertia. Good sources for further explanation would be in an aerodynamics textbook or artillery manual.

Google rhe search terms nutation and precession.

[Tom Myers]

While working with Tom Myer's Cast Bullet Design Program. A couple of questions came up. What is the significance of the CG (Center of Gravity) and CP
(Center of Pressure) relationship? When looking at other bullet designs in the program this relationship between CP and CG is not always the same. Is CP a calculation of bullet compression when fired? I realize that CG (center of gravity) refers to bullet balance, and designing a bullet longer changes that parameter. But CP doesn't maintain the same relationship/ratio to CG. (provided bullet length the only parameter changed). Hence my question. Thanks in advance.
bushman

Bushman,

C.P. refers to "Center of Pressure"

The Center of Gravity of a bullet is the point at which all the weight of the bullet seems to be concentrated. That is, there is as much weight ahead of the bullet's center of gravity as there is behind it. You can call it the balance point. To calculate the center of gravity of a bullet, the weights of each of it's components must first be calculated(base band, gas check shank, each body band section , each groove section, crimp groove section, front band, bore ride section, ogive section and tip section) and then each weight multiplied by it's distance from the base is added to a total and the total is averaged to find the center of gravity. The center of gravity of a bullet is important to stability not because the bullet balances there; but because, when a bullet wobbles or gyrates in flight, the axis of the bullet will rotate only about the center of gravity (C.G.).

The Center of Pressure is similar to the center of gravity except that the forces involved are the air pressure forces acting on the surface area of the bullet as it is in flight. The center of pressure of a bullet is the point at which all the air pressure forces on the bullet seem to be concentrated. That is, there is as much air pressure force on the bullet behind the center of pressure as there are ahead of it.

Calculating the center of pressure is similar to calculating the center of gravity except that, instead of weight, we use area or profile and multiply the profile area of each bullet section by it's distance from the base, add them all together and calculate the average center or geographical center of the bullet. This is the point at which all the air pressures on the bullet is centered. (C.P.)

After exiting the rifling of a barrel, the bullet is spinning at a very high rpm rate. The bullet becomes a miniature gyroscope. A gyroscope does not want to change it's orientation and, as the spin stabilized bullet moves along the curved path of the trajectory, it maintains a slight nose-up attitude as the trajectory path continues to bend downward from the initial launch angle. This nose up attitude causes air pressure to act on the lower surface of the bullet. The farther from the center of gravity that the center of pressure is, the more leverage the air pressure has against the stability of the bullet and the easier it is to start the bullet oscillating about the center of gravity.

So, the closer the center of pressure is to the center of gravity, the harder it is to destabilize the bullet. The result of a stabilized bullet is an accurate bullet.

After incorporating the ability to caluclate the center of pressure into the bullet design software it became evident that, for the most part, inherently accurate bullets maintained a center of pressure close to the center of gravity while bullets that were difficult to find an accurate load for tended to have the center of pressure further from the center of gravity.

You will notice that the Ranch Dog bullets all have the C.P. quite close to the C.G. this is one of the contributing factors to the stellar accuracy of Michael's innovative wide meplate concept.

I know that this has been a long winded explanation to your question. Hopefully it was not too rambling and will help you to understand the concepts behind the reasoning.

If you have any further questions or do not understand some things, please do not hesitate to ask.

Hope this helps.

Respectfully,
Tom Myers

Link to Precision Cast Bullet Design (http://www.tmtpages.com/#advanced)

[AKbushman49]

Tom & Outpost,
Thanks, I figured/guessed that you'd want the two parameters as close together as possible, but wasn't sure why. By the way, Tom Awesome Program! I can foresee lots of time working with it.
bushman

[wquiles]

Thank you Tom. Post like yours are why I love this forum so much :awesome:

[Wolfer]

Yes, that was an extremely informative post written in laymans terms.
Thanks Tom.

[c1skout]

And people think we just wanna put holes in stuff.

[Dthunter]

Well said Tom! Another really good source of information on bullet design and external ballistics as it pertains to bullet form factor is "Brian Litz" books APPLIED BALLISTICS. He put allot of pertenant information into laymans terms. His books deal with j-word bullets, but the physics is the same. They are a very interesting read!

[SgtDog0311]

Bushman, Tom's customers need to form a users-support-group. When not sharing tips or resolving each other's questions, members could sympathize with each other's shooting related additions... or just be good 'enabling' friends!

Tom, Another good treatise to be sure. I was wondering: your program shows to have a calculation for optimal twist rate. Is that a Greenhill formula you’ve plugged into the software?

This sure looks like a good investment for anyone frequently looking at new molds and trying to select the optimal bullet design!

[Tom Myers]

Bushman, Tom's customers need to form a users-support-group. When not sharing tips or resolving each other's questions, members could sympathize with each other's shooting related additions... or just be good 'enabling' friends!

Tom, Another good treatise to be sure. I was wondering: your program shows to have a calculation for optimal twist rate. Is that a Greenhill formula you’ve plugged into the software?

This sure looks like a good investment for anyone frequently looking at new molds and trying to select the optimal bullet design!

John,

Thanks for the enthusiastic comments about the Bullet Design Software.


The previous module versions used a more simplified version of the equations that did not use an editable stability factor to optimize the values.

http://www.tmtpages.com/draw/HelpfilesAdv/bullet_paramaters.gif

I have recently updated the Advanced and Professional Cast Bullet Design (http://www.tmtpages.com/#advanced) modules with an enhanced optimum twist rate, bullet length and minimum muzzle velocity calculator based upon a projectile gyroscopic stability factor.

http://www.tmtpages.com/draw/HelpfilesAdv/AdvStability.png

The algorithms used are variations of Don Miller's modifications of the Greenhill equation that considers the muzzle velocity and weight of the bullet along with the bullet length and twist rate to calculate a Gyroscopic Bullet Stability Factor.

For those that are mathematically inclined here is a link to the page in the Cast Bullet Design online help files (http://www.tmtpages.com/draw/HelpfilesAdv/hlp_cast_bullet1.htm) that describe each variation of the formula that is used to calculate one value when the other three are known.

[SgtDog0311]

Sent you a PM Tom.

[runfiverun]

Tom's new bullet program is about 5 light years ahead of the design pro program that I use.
I discussed it with him briefly when he was working on finishing it.
it's designs, extra programs, and it's ease of use are far ahead of the older program I use.

[SgtDog0311]

Thanks runfiverun. Gonna call Tom this afternoon. Trying to decide between that "basic" and the "advanced". I'm a little scared of my own capabilities with a software program that does just about anything but bout got myself talked into it.

[DrCaveman]

Can you elaborate about the "profile" dimensions used in calculating the CP? Is this the forward facing profile, as in: the total area of exposed material as viewed from the nose of the boolit?

I am not an aerodynamics student, but i am suspecting that turbulent effects may have an effect here that i am not considering. At face value, the explanation of CP vs CG would suggest that a dual ended wadcutter is optimal. Since that is surely not the case, can someone explain how the profile dimension is determined?

[Tom Myers]

Can you elaborate about the "profile" dimensions used in calculating the CP? Is this the forward facing profile, as in: the total area of exposed material as viewed from the nose of the boolit?

I am not an aerodynamics student, but i am suspecting that turbulent effects may have an effect here that i am not considering. At face value, the explanation of CP vs CG would suggest that a dual ended wadcutter is optimal. Since that is surely not the case, can someone explain how the profile dimension is determined?

DrCaveman,

Below is an excerpt from an old post that I wrote that may more fully explain the methods used to determine Center of Gravity and Center of Pressure.
One should not place a great amount of emphasis on the CP CG relationship as it is one of many small variables that individually have an effect upon bullet stability.
These factors are included in the Bullet Design Calculations because they CAN be calculated and experience has shown that there is a trend toward better bullet accuracy when the difference between the two is small rather than large.



In order to determine the effect of the Center of Gravity on the stability of a bullet, the relationship of the CENTER of GRAVITY to the CENTER of PRESSURE of that bullet design would need to be determined.

The Center of Gravity and the Center of Pressure on a projectile such as a double ended wad-cutter would be at the same point. However, if the projectile is composed of different profiles on the nose and base, then the CG and CP would be at different points on the projectile.


When a spin stabilized bullet travels along the trajectory path, the gyroscopic effect of the spin tries to keep the bullet in the initial nose-up position acquired by the required sighting elevation.

This slight nose-up attitude presents the PROFILE of the bullet to the pressure of the Ballistic Wind of the trajectory. The base of an average bullet has a larger PROFILE than the nose which applies more Ballistic Wind pressure to the bullet base and tends to lift the base of the bullet more into alignment with the path of the trajectory. However the downward angle of the trajectory is constantly being increased by gravity so the spin stabilized bullet never quite catches up and is always traveling in a slightly nose-up attitude in relation to the trajectory path.

Depending upon the design of the bullet, the Center of Pressure is usually closer to the nose of the bullet than the Center of Gravity.

A rotating bullet is seldom, if ever, perfectly balanced and it gyrates and precesses around the CG of the bullet as it travels along the trajectory.

If the Center of Pressure is not at the same point as the Center of Gravity, the pressure of the Ballistic Wind acting upon the Center of Pressure will tend to increase the unbalanced condition of the bullet.

The distance from the Center of Pressure to the Center of Gravity may be considered as a lever to unbalance the bullet. The larger the distance between the two, the longer the lever, resulting in a larger destabilization force.

So, the generally accepted theory is that, the closer the Center of Pressure to the Center of Gravity, the more potential for a stable bullet.

You can determine the Center of Gravity by balancing a bullet on a knife edge.
You can determine the Center of Pressure by balancing a cardboard cutout of the Profile of the bullet on a knife edge.

The "balance point" of a bullet would be the center of mass or center of gravity ( CG )
The Center of Gravity may be calculated by finding the average of the distances from the bullet base of the Center of Gravity of each of the shanks, bands, grooves, bore rider, nose, etc that make up the design of that particular bullet.

The Center of Pressure may be calculated by the determining the balance point of the entire PROFILE of the bullet and can be defined as the average of the distances from the bullet base of the Area Center of each of the various section profiles of the bullet.

A suggested procedure to move the center of pressure closer to the center of gravity on an existing design would be to produce that design in a hollow base version with the hollow base cavity volume calculated to bring the Center of Gravity to coincide with the Center of Pressure.

[madsenshooter]

I can't help but wonder if the CP/CG relationship is what makes the 311414 and B&M 311169, Squibb designs, stop shooting accurately above 1500fps or so. I'll ponder that for awhile.