Form Factor in Ballistics

Comparing a Shape to a Standard

Form factor is a number that compares a projectile's drag to that of the standard reference shape used by a given drag model. It isolates the influence of a projectile's profile, telling an analyst how efficiently its shape slips through the air relative to an idealized standard. Understanding it clarifies why two projectiles of equal weight can perform very differently.

The Reference Projectile

Drag models such as the widely used G1 and G7 are each built around a specific standard projectile shape whose drag behavior is precisely tabulated. Form factor expresses a real projectile's drag as a ratio against that reference. A value of exactly one means the projectile matches the standard shape; other values scale up or down from it.

Reading the Number

A form factor below one indicates a projectile that is more streamlined than the reference and therefore experiences proportionally less drag. A value above one indicates a blunter, less efficient profile with more drag. The number is a clean, dimensionless summary of aerodynamic efficiency, stripped of the projectile's mass and diameter.

The Link to Ballistic Coefficient

Ballistic coefficient combines two ingredients: sectional density, which reflects mass relative to frontal area, and form factor, which reflects shape. Specifically, ballistic coefficient equals sectional density divided by form factor. A lower form factor raises the ballistic coefficient, so the same weight of projectile flies with less drag simply by being shaped better.

Matching Form Factor to the Right Model

Because form factor is defined against a particular reference shape, the same projectile has different form factors under different drag models. A long, boat-tailed design tends to have a form factor near one against the G7 standard, which resembles it, but a value well below one against the blunter G1 standard. Quoting a form factor requires naming its model.

Worked Example

Consider a sleek long-range projectile with a sectional density of 0.27 and a form factor of 0.90 against the G7 model. Its G7 ballistic coefficient is 0.27 divided by 0.90, or 0.30. A blunter projectile of the same sectional density but a form factor of 1.10 would yield a ballistic coefficient of only about 0.245, holding velocity noticeably worse despite identical weight and diameter.

A Common Misconception

Form factor is sometimes read as though a larger number means a better projectile. It is the opposite: a smaller form factor signals a more efficient, lower-drag shape. Confusing its direction, or comparing form factors quoted against different drag models as if they were interchangeable, leads to backward conclusions about which design is genuinely more aerodynamic.

Explore the glossary.

Source: Defense Technical Information Center (DTIC) Public Ballistics Research Archive — Government Research Publication Archive. Refer to the original for exact language.