Re: 338 LM Improved gain twist barrel
Ok, before i go into the long noses and pitching moment, i might stick with the boattail theme a little longer and its relationship with pitching moment first. I only offer these "presentations" in an effort to bring value and understanding... if its not appreciated, simply dont read it...
Keep in mind that again, these forces are again symmetrical at zero yaw and therefore only apply once you have an angle of attack or yaw (which all bullets have unfortunately) directly applying to the epicylic or limit cycle precessional yaw that begins immediately upon exiting the muzzle (the wobbling football pass).
So not only does the boattail generate destabilizing magnus forces, boattails also generate negative lift or normal force, which acts in a vector that increases the pitching moment aswell (further reducing stability). The mechanism by which this occurs can be visualized by imagining a projectile flying with a small amount of yaw and realizing the angles of the fore and afterbody (ogive and boattail) and the lift vectors they generate by presenting an angle of attack to the oncoming airstream. The vector of the nose force is directly opposite the vector of the boattail force due to one having a net positive angle of attack and the other a net negative angle. So you get positive force/lift from the nose and negative from the tail. However the vectors complement rather than cancel due to them acting on opposite sides of the center of gravity- which incidentally determines the length of the moment arm. The moment arm lengths are measured from the center of gravity to the center of pressure of whatever force we are talking about, being magnus or normal force/lift etc. Therefore the sum of these lift/normal forces and moment arms determines the overall total center of pressure and the moment arm length acting upon it... collectively termed, the pitching moment. This acts to turn the bullet around rather than fly straight of course.
Now the nose length...
This shouldnt need much explanation of one can visualize the above with regard to the boattail. The Center of Pressure for the ogive section alone, lies almost exactly half way along its length at velocities around mach 2 to 4, regardless of whether its a secant, tangent, von karman, or whatever ogive.. There are subtle variances, but lets keep it simple for now. So if you increase the length of the nose, you get a greater pitching moment in at least 3 ways... First, the CoP gets further from the CoG due to the half length (CoP arm) of a longer ogive being physically longer. 2nd, you get a greater normal force due to the nose having more surface area and thus a larger lifting surface. Third, you move the overall CoG of the entire projectile REARWARD due to the volume/mass dimensions of longer ogives and pointier tips distributing less mass at the nose tip compared with their overall length.
Another destabilizing feature of the long nose but not relating to pitching moment, but which is similar to the third point in mechanism, in that it redistributes its mass and therefore axial and transverse inertias in a similar fashion. So it reduces the axial inertia and increases the transverse inertia and radii of gyration. - This happens to be compounded implicitly by less gyroscopic inertia (which is axial inertia of course ) so you must spin it faster to achieve the same gyroscopic effect. *As a side note on the same mechanism, Bore riding shanks with raised drive bands reduce available gyroscopic inertia also by having less mass along the axial extremities of the shank...
So you run into stability problems when designing long noses very easily, however the longer nose is a design parameter worth going after due to the VERY significant reductions in wave drag offered by long noses.
So increasing the length of the boattail, increasing the negative ANGLE of the boattail, and increasing the length of the nose etc. ALL act to increase the pitching moment and reduce stability, both static and particularly dynamic. So for one to be successful, one must not just find a way of reducing drag and providing adequate spin, but also very important is mitigating these moments and forces.
So these are some of the challenges faced when trying to design a projectile of +6.5calibers length and why we dont see many in existence. Not to say that its impossible, and in no way am i trying to discredit Noel Carlson, GSC or anybody else, nor prod you beta testers??? Much of what ive posted would be helpful to interested parties and i meerly offer information to those interested, certainly free information is better than living in the dark?