Tangent ogives, or "spitzer" noses, are formed by drawing an arc (segment of a circle) with a specific radius, normally stated in "calibers". Thus, a .308 caliber spitzer bullet with a 10-S ogive would have .308 times 10 or 3.080 inch radius ogive curve. The spitzer shape is a true mathematical form without arbitrary curve changes, but the very tip may be modified into a round lead end, which is called a "semi-spitzer" shape. This is to help prevent damage to fragile, pointed lead tips.
The spitzer ogive is the most popular rifle ogive shape for general purpose high velocity shooting, followed by the 1-E round nose. The most popular radius is 6 calibers, since this generally gives the best ratio of weight range to over-all length. Corbin offers spitzer shapes in 2, 4, 6, 8, 10, and 12-S ogives. Those in between are so insignificantly different as to make them redundant. Spitzer ogives smaller than 2 approach the round nose or truncated conical in performance, and of course it is impossible to make a spiter ogive smaller than 0.5, since 1/2-S describes the same curve as a 1/2-E round nose and any radius less than half the caliber would not meet to form a bullet nose. The 6-S is standard for calibers below .458, the 1-E and 4-S are standard for .458. The 50 BMG is a special case where 6-S to 8-S bullets are commonly used.
Spitzer bullets for .458 and larger civilian arms typically become too long for the chamber, magazine, or rifling twist in 6-S or longer radius, so they are usually made in 2-S or 4-S spitzer shapes, or in 1-E round nose. The longer the radius, the less the weight can be varied for a given bullet caliber. This is because of length and stability limitations. The nose length is fixed by the ogive radius and the tip diameter, whereas the shank can vary from a minimum of about one caliber to as long as will fit in the gun and be stable with the rifling twist. The shorter the ogive radius, the greater can be the range of weights on both ends (very light bullets still have enough shank to balance a short nose, and very heavy bullet are still short enough to fit the gun with a shorter nose).
TANGENT
The ULD bullet was developed by Corbin during the Viet Nam era for both long range military sniper operations and later, applied to experimental bullets for Secret Service assignments. Some of the characteristics of the ULD or Ultra Low Drag design were also incorporated in a similar but later development called the VLD or very low drag design. Both designs are equivalent for all practical purposes, except that the full ULD specification includes a rebated boattail design instead of the standard boattail (for about 15% gain in accuracy by reducing muzzle-blast induced dispersion: the RBT step deflects most of the muzzle blast gas in a ring whereas the conventional BT tends to focus it into a ball in front of the emerging bullet, adding about 15% to the disperson or random buffeting of the projectile).
A special and somewhat different hybrid shape is called the "ULD-TIP" which includes a metal spire-shaped tip insert. This is actually a blend of three different shapes, tangent, secant, and spire.
Ultra Low Drag or ULD bullets use both a rebated boattail and a hybrid tangent-secant ogive to achieve minimum air resistance for a given weight and caliber. Their design requires a faster than usual twist rate barrel for accuracy. ULD bullets are suited to long ranges where minimum wind resistance and time of flight are desired. The ogive shape is optimized so that changing atmospheric pressure or increases in velocity due to temperature or loading variations have less tendancy to push the projectile into a state where a secondary shock wave is created at the junction of ogive and shank, as might happen with a longer radius and a sharper angle (or greater offset from tangent). One reason for seemingly random failures of other low drag secant designs has been shown to be the "on the edge" nature of the secondary shock wave, which is absent during ideal conditions but appears when the air density increases (lower altitude, high pressure front moves in, air temperature drops, etc.) or the velocity of the bullet increases slightly from loading or heating of the cartridge. By not pushing the ogive radius and intersection angle to unreliable extremes, the ULD design avoids developing the sudden change in BC that occurs when a secondary shock wave is created.
The most suitable weight range is toward the high side of the medium weights. ULD bullets are generally not suitable for "standard" twist rate rifles (such as the typical 1 turn in 14 inches to 1 turn in 12 inches), and may not be stable at all loadings in a 1 turn/10 inch barrel. Attempting to gain BC at all costs means at the cost of accuracy, as well. A high BC does not translate into high accuracy, any more than a very pointed head makes a man a fast swimmer! There are other factors to consider, including stability with practical spin rates and practical bullet lengths and weights. The "practical" part means both affordable and within the bounds of other limitations imposed by physics. The ULD is a special purpose design, not a "magic bullet" that fixes all problems. It can delivery exceptional accuracy at long range, with the proper equipment and loading, or it can be next to useless if the other factors are ignored.
ULD
Source: DAVE CORBIN
Secant ogives can be a bit deceptive, in regard to ogive curve versus the actual bullet shape or length, because, unlike a tangent ogive spitzer curve, the secant curve radius is only one of two specifications required to identify the shape. The second specification tells where the bullet shank intersects the nose curve. In a tangent ogive (standard spitzer), the ogive always joins or "intersects" the shank at precisely 180-degrees. That is, there is no offset from the smooth nose curve to the straight part of the bullet. The start of the nose arc begins where the shank ends. But this is not true for a secant ogive.
A standard spitzer, or tangent ogive, is a special case of the secant ogive where the angle of intersection is 180-degrees, or the offset from tangent is zero. All other possible intersections are secants. So the term "tangent" identifies a specific shape when combined with a radius for the nose curve, because the offset (or angle of intersection) is known and always fixed at zero or 180-degrees. But a secant ogive can be offset any amount from tangent, so specifying the ogive (such as 14-S or 18-s) does not tell us the bullet shape or length by itself. A 14-S spitzer is almost impossibly long in the nose, but a 14-s secant can be any length right up to the spitzer length (but is always shorter, since the secant ogive is "slid back" toward the base of the bullet by some amount, intersecting the curve at some angle other than 180-degrees). We have to specify the angle, or the amount of linear offset, in order to get the complete picture.
The reason for secant ogives is to try to pull a fast one on Mother Nature, by making the nose angle a little sharper without making the bullet too long for stability, and yet not creating such a sharp junction that a secondary shock wave is created. The junction between the smooth ogive curve of the nose and the straight shank will create a shock wave if the bullet travels fast enough, the air is dense enough, and the angle is sharp enough. This can create a situation where the secant ogive gives you better BC than the same over-all length of a tangent ogive (which would have a longer radius), but it might drop suddenly if the weather changes, you travel to a lower elevation, or you load to a higher velocity. Secant ogives therefore carry their own risks if pushed very far, so you seldom see consistent results from secants over 14-18 calibers of radius and angles of intersection over five degrees. For instance, a 14-S X .014-inch offset defines Corbin's standard Ultra Low Drag bullet shape in any caliber, and it seems to wring the maximum BC out of most calibers without the shifting atmospheric/velocity secondary shock wave problem. But a longer radius usually requires a sharper junction to keep the over-all bullet length reasonable, and the sharper junction begins to generate the higher drag secondary shock wave with changes in atmospheric pressure or loading velocity.
SECANT
Typically, benchrest bullets for under 200 yard shooting don't need to exaggerate the BC, and can gain more by using the lowest practical spin rate. Therefore, a 6-S ogive would be entirely practical. Many clients choose a 7-S custom ogive, or the 8-S ogive. A few choose the ULD (Ultra Low Drag, developed by Corbin for military and Treasury department sniper applications many years before the very similar VLD popular with civilians). But even though the ULD is our design, we feel strongly that it is not appropriate for medium and short range (100-300 yard) target shooting simply because it forces the shooter to use a longer bullet than necessary, which in turn requires a faster twist barrel, which in turn exaggerates any jacket wall eccentricity. So why do it? Who cares about the BC, if you are not shooting in a gale wind, at 100-300 yards? If you can read the mirage and the wind flags like a high power shooter, then you can certainly take advantage of the slower spin that stabilizes a normal weight 6-S bullet.
But the ULD design will help at 500-1000 yards (and of course, with 50 caliber benchrest at 1000-2000 yards, it will become a necessity as soon as enough other good shooters catch on). At some point, the bad effect of more spin balances the bad effect of wind drift on a lower BC bullet, and you choose the lesser of the two evils. This is no different from other bullet design fields, where you are always choosing between two contradictory values and trying to balance their bad effects in order to get the most use from their good effects.