Charles, Charles and John,
Is it just the 'bullet design' link that's broken, or can't you even get to the home page? Please try the link again and let me know what you get. This is the first time I've heard of trouble with the site.
In the mean time, the entire 'bullet design' page is just text, so I've copied and pasted it here:
General Notes on Bullet Design
What bullets end up being is truly a compromise between aerodynamics, manufacturing, materials, interior ballistic considerations (minimizing in-bore yaw), etc.
As an air-to-air missile design engineer, I am most familiar with the aerodynamic design considerations of supersonic flight as opposed to the manufacturing. The major topics I’m going to address include:
1. What compromises are chosen and why for different bullet applications.
2. Comment on the difference between tangent/secant ogive noses from an aerodynamic design point of view.
3. Address some statements about boat-tail design that are commonly misunderstood.
First
What drives bullet design compromises?
The key driver behind most of the compromises in bullet design is the intended application of the bullet. For our purposes, the application of BR bullets can be broken up into two basic categories: short range and long range.
Match quality short range BR bullets all pretty much look alike, no matter what caliber, it’s the same basic configuration: flat base, short shank, and moderate length nose. Likewise for long range BR bullets: boat-tail, long shank, and a long nose. So why does the ‘short range class’ look so different from the ‘long range class’?
The basic reason is because the short range bullets are concerned only with hair splitting precision and consistency. The long range bullets have to compromise these qualities a little bit because of the added demand that the projectiles also have more ballistic efficiency.
For example, why don’t winning short range BR bullets use a boat-tail? Answer: because it’s easier to make flat base bullets more precisely. There are fewer steps and less variables with flat bases. Also, slower twists are required to stabilize shorter, flat base bullets. Slower twist means less dispersion due to CG offset and in-bore yaw. You see, in the short range BR game, it’s all about minimizing dispersion.
A long range BR bullet design also has to minimize dispersion. However, long range bullets have more of a need to minimize effects due to atmospheric variations as well. This is accomplished with the VLD design. The VLD design potentially compromises inherent precision by having a boat-tail and a long secant ogive nose which: requires more steps to manufacture, has potential for inconsistency, and requires a higher twist to stabilize. Faster twist rates can exacerbate CG and in-bore yaw effects induced dispersion. BUT it’s worth the compromise for long range bullets because the VLD design minimizes shot to shot atmospheric variations that are more critical than all of the other considerations at long range.
So to wrap up the first point, the compromises that we’re all aware of are driven by the range at which the projectiles are designed to be fired from.
Second
On tangent vs secant ogive nose design:
The definition and geometric description of tangent and secant ogive noses is explained here:
(
http://www.geocities.com/rocketguy_101/ogive/OgiveNoseCones.htm)
I’ll try to address the two types of ogives in terms of ‘optimal aerodynamics’.
For a given length nose, there is an infinite number of geometries to go from the meplat diameter, to the full caliber diameter. Two well known geometries are the tangent and secant ogive. Others are the cone, Sears-Haack, ¾ power law, and the paraboloid. The efficiency of the ogive design is judged by how much energy is required to ‘shock’ the air into a compression wave. In other words, the nose needs to make way for a cross section of 1 caliber in diameter to move thru the air at supersonic speed. The efficiency of the nose design depends on how ‘gently’ the nose parts the air. The less energy required to ‘shock’ the air, the less ‘wave’ drag the nose has.
At low supersonic speeds, the optimal ogive shape is a curved shape, approximating a short radius, tangent ogive. As Mach number increases, the optimal ogive begins to look more like a cone with straight edges leading to a sharp juncture with the bullet shank, ie, more like a secant ogive with a long radius.
Using mathematical techniques, ‘optimal’ ogive shapes have been designed that are neither tangent or secant. The problem with these ‘optimal’ designs is that they are only ‘optimal’ for one Mach number. That’s because the ‘optimality’ is based on the geometry of the shock cone, which changes with projectile velocity. The best the bullet designer can hope for is to go with the nose design that’s optimal for the average velocity of the bullet.
One more thing on ogive design: The value of designing a throat lead angle to match an ogive depends on how fast the cartridge will erode the lands.
Third
On boat-tail design:
Some people believe that “Boat-tails of any design should only be of any use at the transonic stage in the bullets trajectory”.
This statement is simply not true. The boat-tail design is effective at reducing drag in all speed regimes. There is much to say about the theory involved here (including why there’s dimples on golf balls), but more convincing evidence is available. Supersonic vehicles of all kinds from fighter jets to missiles to long range BR bullets are all designed with a reduced diameter after-body.
Bob McCoy’s book entitled “Modern Exterior Ballistics” is kind of like the modern bible of ballistics. Bob was a ballistics engineer at the Aberdeen Proving Grounds in Maryland for several decades. In Chapter 4 of his book titled: Notes on Aerodynamic Drag, he shows a lot of experimental data on the subject of drag. To summarize the section on boat-tails… According to all the experiments, a boat-tail angle of between 6 and 8 degrees is optimal for reducing base drag at supersonic speeds. Drag is continuously reduced as boat-tail length grows, indefinitely. The length of the boat-tail is practically limited by stability concerns.
We typically see about 0.8 caliber boat-tail lengths on well balanced designs. A projectile having a 7 degree, 0.8 caliber long boat-tail will decrease drag between 10-15%. The design is not very sensitive to the caliber of the projectile.
I looked into the effects of rebated boat-tails a while ago and found pretty much what I expected. There’s no discernable difference between rebated and conventional boat-tails, in terms of drag reduction. I spoke to a bullet smith at a major bullet company who told me about their past experiments with the rebated boat-tail. He said the comparison between regular and rebated boat-tail bullets was a wash. It’s no surprise because of the relatively minor rebate used.
