40
1-800-338-3220
40
1-800-338-3220
FOUR DEGREES 
OF FREEDOM
HORNADY BALLISTICS APP WITH 4DOF
®
WHY 4DOF
®?
Modern sniping and long-range shooting demands 
have surpassed the capabilities of traditional Ballistic 
Coefficient (BC)-based calculations. While custom 
drag modeling has addressed some of the limitations 
of BC, it still falls short in accurately modeling the full 
dynamics of a bullet in flight.
As a bullet travels toward its target, its nose is rarely 
perfectly aligned with its trajectory throughout the 
entire flight. Instead, the bullet exhibits “wobbling” 
motions, known as precession and nutation, around 
its flight path. This misalignment is quantified as 
the “angle of attack,” which represents the angular 
difference between the bullet’s orientation and its 
trajectory. Any angle of attack introduces additional 
forces—beyond drag—that act on the bullet and 
influence its path. To accurately predict a bullet’s 
trajectory, these forces must be accounted for in the 
modeling process.
The 4DOF (Four Degrees of Freedom) bullet library 
goes far beyond the limitations of BC and even 
custom drag profiles. Each bullet is characterized 
by over 400 unique properties, including mass, 
inertial characteristics, drag coefficient (Cd) versus 
Mach number, and other aerodynamic factors. This 
advanced modeling provides a far more precise 
representation of a bullet’s flight dynamics compared 
to using a single BC value or a custom drag profile 
that ignores additional forces acting on the bullet.
Discover the cutting-edge advantage of the Hornady Ballistic Calculator with 4DOF®, 
tailored to meet the precision demands of law enforcement professionals. With an entire 
playlist of informative videos, you can explore how 4DOF® offers unmatched accuracy 
and reliability in the field.
Scan the QR code or visit HORNADY.COM/QR/4DOF-OVERVIEW to dive into the details 
and experience the difference 4DOF® can make.

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