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August 4th, 2021

Bullet Geometry Basics: Tangent, Secant, and Hybrid Ogives

secant tangent hybrid ogive Bryan Litz Applied ballistics 200X Berger Hybrid bullet, .308 30 Caliber

In discussions of ballistics, you’ll see references to “tangent”, “secant”, and “hybrid” bullet shapes. We know that, for many readers, these terms can be confusing. To add to the confusion, bullet makers don’t always identify their projectiles as secant or tangent designs. This article provides a basic explanation of tangent, secant, and hybrid ogive bullet designs, to help you understand the characteristics of these three basic bullet shapes.

Tangent vs. Secant vs. Hybrid
Most match bullets produced today use a tangent ogive profile, but the modern VLD-style bullets employ a secant profile. To further complicate matters, the latest generation of “Hybrid” projectiles from Berger Bullets feature a blended secant + tangent profile to combine the best qualities of both nose shapes. The secant section provides reduced drag, while the tangent section makes the bullet easier to tune, i.e. less sensitive to bullet seating depth position.

hybrid bullet

Berger Bullets ballistician Bryan Litz explains tangent and secant bullet ogive designs in a glossary section of his Applied Ballistics website, which we reprint below. Bryan then explains how tangent and secant profiles can be combined in a “hybrid” design.

How Bullet Ogive Curves are Defined
While the term “ogive” is often used to describe the particular point on the bullet where the curve reaches full bullet diameter, in fact the “ogive” properly refers to the entire curve of the bullet from the tip to the full-diameter straight section — the shank.

Understanding then, that the ogive is a curve, how is that curve described?

LITZ: The ogive of a bullet is usually characterized by the length of its radius. This radius is often given in calibers instead of inches. For example, an 8 ogive 6mm bullet has an ogive that is a segment of a circular arc with a radius of 8*.243 = 1.952”. A .30-caliber bullet with an 8 ogive will be proportionally the same as the 8 ogive 6mm bullet, but the actual radius will be 2.464” for the .30 caliber bullet.

For a given nose length, if an ogive is perfectly tangent, it will have a very specific radius. Any radius longer than that will cause the ogive to be secant. Secant ogives can range from very mild (short radius) to very aggressive (long radius). The drag of a secant ogive is minimized when its radius is twice as long as a tangent ogive radius. In other words, if a tangent ogive has an 8 caliber radius, then the longest practical secant ogive radius is 16 calibers long for a given nose length.”

Bryan Litz Explains Hybrid Design and Optimal Hybrid Seating Depths

Ogive Metrics and Rt/R Ratio
LITZ: There is a number that’s used to quantify how secant an ogive is. The metric is known as the Rt/R ratio and it’s the ratio of the tangent ogive radius to the actual ogive radius for a given bullet. In the above example, the 16 caliber ogive would have an Rt/R ratio of 0.5. The number 0.5 is therefore the lowest practical value for the Rt/R ratio, and represents the minimum drag ogive for a given length. An ogive that’s perfectly tangent will have an Rt/R ratio of 1.0. Most ogives are in between an Rt/R of 1.0 and 0.5. The dimensioned drawings at the end of my Applied Ballistics book provide the bullets ogive radius in calibers, as well as the Rt/R ratio. In short, the Rt/R ratio is simply a measure of how secant an ogive is. 1.0 is not secant at all, 0.5 is as secant as it gets.

Berger Hybrid bullet, .308 30 CaliberHybrid Bullet Design — Best of Both Worlds?
Bryan Litz has developed a number of modern “Hybrid” design bullets for Berger. The objective of Bryan’s design work has been to achieve a very low drag design that is also “not finicky”. Normal (non-hybrid) secant designs, such as the Berger 105gr VLD, deliver very impressive BC values, but the bullets can be sensitive to seating depth. Montana’s Tom Mousel has set world records with the Berger 105gr VLD in his 6mm Dasher, but he tells us “seating depth is critical to the best accuracy”. Tom says a mere .003″ seating depth change “makes a difference”. In an effort to produce more forgiving high-BC bullets, Bryan Litz developed the hybrid tangent/secant bullet shape.

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December 19th, 2020

FREE Tech Articles from Applied Ballistics — Worth Reading

Want to improve your understanding of Ballistics, Bullet Design, Bullet Pointing, and other shooting-related tech topics? Well here’s a treasure trove of gun expertise. Applied Ballistics offers dozens of FREE tech articles on its website. Curious about Coriolis? — You’ll find answers. Want to understand the difference between G1 and G7 BC? — There’s an article about that.

“Doc” Beech, technical support specialist at Applied Ballistics says these articles can help shooters working with ballistics programs: “One of the biggest issues I have seen is the misunderstanding… about a bullet’s ballistic coefficient (BC) and what it really means. Several papers on ballistic coefficient are available for shooters to review on the website.”

Credit Shooting Sports USA Editor John Parker for finding this great resource. John writes: “Our friends at Applied Ballistics have a real gold mine of articles on the science of accurate shooting on their website. This is a fantastic source for precision shooting information[.] Topics presented are wide-ranging — from ballistic coefficients to bullet analysis.”

READ All Applied Ballistics Articles HERE »

Here are six (6) of our favorite Applied Ballistics articles, available for FREE to read online. There are dozens more, all available on the Applied Ballistics Education Webpage. After Clicking link, select Plus (+) Symbol for “White Papers”, then find the article(s) you want in the list. For each selection, then click “Download” in the right column. This will send a PDF version to your device.

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September 23rd, 2018

Bullet Geometry: Tangent, Secant, and Hybrid Ogives Explained

secant tangent hybrid ogive Bryan Litz Applied ballistices 200X Berger Hybrid bullet, .308 30 Caliber

In discussions of ballistics, you’ll see references to “tangent”, “secant”, and “hybrid” bullet shapes. We know that, for many readers, these terms can be confusing. To add to the confusion, bullet makers don’t always identify their projectiles as secant or tangent designs. This article provides a basic explanation of tangent, secant, and hybrid ogive bullet designs, to help you understand the characteristics of these three basic bullet shapes.

Tangent vs. Secant vs. Hybrid
Most match bullets produced today use a tangent ogive profile, but the modern VLD-style bullets employ a secant profile. To further complicate matters, the latest generation of “Hybrid” projectiles from Berger Bullets feature a blended secant + tangent profile to combine the best qualities of both nose shapes. The secant section provides reduced drag, while the tangent section makes the bullet easier to tune, i.e. less sensitive to bullet seating depth position.

hybrid bullet

Berger Bullets ballistician Bryan Litz explains tangent and secant bullet ogive designs in a glossary section of his Applied Ballistics website, which we reprint below. Bryan then explains how tangent and secant profiles can be combined in a “hybrid” design.

How Bullet Ogive Curves are Defined
While the term “ogive” is often used to describe the particular point on the bullet where the curve reaches full bullet diameter, in fact the “ogive” properly refers to the entire curve of the bullet from the tip to the full-diameter straight section — the shank. Understanding then, that the ogive is a curve, how is that curve described?

LITZ: The ogive of a bullet is usually characterized by the length of its radius. This radius is often given in calibers instead of inches. For example, an 8 ogive 6mm bullet has an ogive that is a segment of a circular arc with a radius of 8*.243 = 1.952”. A .30-caliber bullet with an 8 ogive will be proportionally the same as the 8 ogive 6mm bullet, but the actual radius will be 2.464” for the .30 caliber bullet.

For a given nose length, if an ogive is perfectly tangent, it will have a very specific radius. Any radius longer than that will cause the ogive to be secant. Secant ogives can range from very mild (short radius) to very aggressive (long radius). The drag of a secant ogive is minimized when its radius is twice as long as a tangent ogive radius. In other words, if a tangent ogive has an 8 caliber radius, then the longest practical secant ogive radius is 16 calibers long for a given nose length.”

Bryan Litz Explains Hybrid Design and Optimal Hybrid Seating Depths

Ogive Metrics and Rt/R Ratio
LITZ: There is a number that’s used to quantify how secant an ogive is. The metric is known as the Rt/R ratio and it’s the ratio of the tangent ogive radius to the actual ogive radius for a given bullet. In the above example, the 16 caliber ogive would have an Rt/R ratio of 0.5. The number 0.5 is therefore the lowest practical value for the Rt/R ratio, and represents the minimum drag ogive for a given length. An ogive that’s perfectly tangent will have an Rt/R ratio of 1.0. Most ogives are in between an Rt/R of 1.0 and 0.5. The dimensioned drawings at the end of my Applied Ballistics book provide the bullets ogive radius in calibers, as well as the Rt/R ratio. In short, the Rt/R ratio is simply a measure of how secant an ogive is. 1.0 is not secant at all, 0.5 is as secant as it gets.

Berger Hybrid bullet, .308 30 CaliberHybrid Bullet Design — Best of Both Worlds?
Bryan Litz has developed a number of modern “Hybrid” design bullets for Berger. The objective of Bryan’s design work has been to achieve a very low drag design that is also “not finicky”. Normal (non-hybrid) secant designs, such as the Berger 105gr VLD, deliver very impressive BC values, but the bullets can be sensitive to seating depth. Montana’s Tom Mousel has set world records with the Berger 105gr VLD in his 6mm Dasher, but he tells us “seating depth is critical to the best accuracy”. Tom says a mere .003″ seating depth change “makes a difference”. In an effort to produce more forgiving high-BC bullets, Bryan Litz developed the hybrid tangent/secant bullet shape.

Story sourced by Edlongrange.
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January 16th, 2017

Sierra Offers New Ultra-High-BC 197gr 7mm (.284) MatchKing

Sierra 197gr MatchKing High BC F-Open Closed Meplat

Get ready for a revolution in the F-Open, ELR, and Long-Range Benchrest games. Sierra just introduced a new 7mm bullet with a stunning 0.780 G1 BC. This new 197-grain HPBT MatchKing is one of the highest-BC, jacketed .284-caliber projectiles ever offered to the public. By comparison, Sierra’s own advanced 183-grain 7mm Matchking has a .707 G1 BC. That means the new 197-grainer has a 10% higher BC than the already slippery 183-grainer. That’s an impressive achievement by Sierra.

We expect top F-Open and long-range shooters will be trying the new 197-grainer as soon as they can get their hands on this new projectile. They may need new barrels however, as Sierra states: “This bullet requires a barrel twist rate of 1:7.5″ or faster”. Sierra expects to start shipping these slippery 7mm 197s very soon. You can order directly from Sierra’s website, stock code #1997, $54.20 for 100 bullets.

Sierra 197gr MatchKing

Factory Uniformed Bullet Tips
Sierra has officially announced that the 197gr SMK will come “pointed” from the factory. These impressive new 197s will have a “final meplat reducing operation” (pointing). This creates a higher BC (for less drag) and also makes the BC more uniform (reducing vertical spread at long range). Our tests of other factory-pointed Sierra MKs have demonstrated that Sierra does a very good job with this pointing operation. The “pointed” MatchKings we’ve shot recently had very nice tips, and did hold extremely “tight waterline” at 1000 yards, indicating that the pointing process does seem to enhance BC uniformity. Morever, radar-derived “real-world” BCs have been impressively uniform with the latest generation of pointed Sierra MKs (such as the new 110gr 6mm MatchKing).

Here is the statement from Sierra about the new bullets:

Shooters around the world will appreciate the accuracy and extreme long range performance of our new 7mm 197 grain HPBT (#1997). A sleek 27-caliber elongated ogive and a final meplat reducing operation (pointing) provide an increased ballistic coefficient for optimal wind resistance and velocity retention. To ensure precise bullet to bore alignment, a unique bearing surface to ogive junction uses the same 1.5 degree angle commonly found in many match rifle chamber throats.

While they are recognized around the world for record-setting accuracy, MatchKing® and Tipped MatchKing® bullets are not recommended for most hunting applications. Although MatchKing® and Tipped MatchKing® bullets are commonly used for varmint hunting, their design will not provide the same reliable explosive expansion at equivalent velocities in varmints compared to their lightly jacketed Hornet, Blitz BlitzKing, or Varminter counterparts.

New product tip from EdLongrange. We welcome reader submissions.
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