EBV4.2 - Exterior Ballistics Software
Author: Ruprecht Nennstiel, Hofheim, Germany
for the PC
This document discusses the various features of the Exterior Ballistics Software
EB. This program is capable to calculate exterior ballistic trajectories
of projectiles moving through the atmosphere using one out of three different
physical models. The main application of
the software are bullets, fired from small arms and exterior ballistic
problems in the field of forensic ballistics. However, the software can also be applied to larger calibers (e.g.
The document also contains a link to an order form for the software.
What is EB?
EBV4 (the letters stand for Exterior Ballistics Version 4) is the
fourth version of a computer program, which runs on all IBM MS-DOS
PCs or compatibles. It calculates trajectories of bullets or other objects
(e.g. fragments) moving through the atmosphere. EBV4 can be applied to
any of three physical trajectory models:
The MPMM also takes into account the lift force, but assumes that
the yaw angle (the angle enclosed between the tangent to the trajectory
and the bullet's longitudinal axis) remains small over the whole trajectory.
The application of the MPMM is restricted to conical and ogive nose
shapes, for which the necessary aerodynamic coefficients can be estimated
through semi-empirical formulas. EBV4 does not support the mostly advanced 6-Degrees-of-Freedom
(6DOF) model, as in most practical cases, the whole set of aerodynamic
coefficients applicable to this model is not available.
The Vacuum Ballistics Model (VBM) introduced into physics
by Galileo Galilei, which assumes the presence of the force of gravity
The Point Mass Model (PMM), which assumes the presence of
two forces: the aerodynamic drag and the force of gravity.
The Modified Point Mass Model (MPMM), which additionally
considers effects of spin, e.g. the spin-dependent side drift.
In most practical cases, the PMM will be adequate for bullets
fired from small arms. When using the PMM, bullet side deviations
are exclusively caused by cross wind.
Normally negligible influences of other forces - at least for "stable"
bullets - (Coriolis force, Magnus force, Pitch damping force,...) remain
unconsidered. However, when applying the MPMM, EB is capable to
determine bullet stability (static and dynamic) from an estimate of the
How does EB calculate a trajectory?
The differential equations of exterior ballistics are numerically solved
by a 4th order Runge - Kutta procedure with variable step size.
The method (which is a standard in numerical mathematics) has been optimized
for maximum speed without loss of accuracy.
The calculation of bullet drag - which is generally the major force
- is based on drag functions, giving the drag coefficient cD
as a function of the Mach number Ma. The software package already contains
drag functions of numerous hand gun bullets, either determined and published
by ballistic research institutes or resulting from measurements of the
author. Of course, the user may add his own drag functions. When using
the advanced MPMM, the other necessary aerodynamic coefficients
are estimated by empirical formulas from projectile geometry and the instantaneous
Any parameter influencing a bullet's trajectory within the chosen physical
model, can be adjusted freely by the user (weather conditions - even as
a function of the altitude, terrain profile, initial conditions, firearm
line of sight parameters,....). There is no limitation for the value of
the departure angle (flat or high-angle shooting).
As an improvement with respect to previous versions, EBV4 is capable
of running simulations, considering ballistic perturbations and
errors of the shooter, resulting in bullet dispersion at the target, similar
to the dispersion, which must be expected in a real shooting situation.
Who uses EB?
EBV4 has been especially designed to handle exterior ballistic problems
of bullets fired from small arms, although atmospheric conditions can be
determined correctly up to altitudes of 90 km, which is sufficient even
for artillery shells.
The software package contains multiple drag functions for small arms
bullets and a library with more than 1800 ballistic coefficients.
Thus EBV4 may be used (and is used) by ammunition manufacturers,
manufacturers of handguns and manufacturers of handgun accessories.
EB is also well suited to satisfy the needs of interested hunters
or sportsmen. However, it must be pointed out that EBV4 is a professional
tool and requires some knowledge concerning exterior ballistics.
EBV4 has been especially designed for the necessities of forensic
ballistics and indeed, almost 80% of EB users are members of forensic
(police) laboratories in Germany, Europe, USA and all over the world. Forensic
Ballistics is also the author's background. A
bullet's trajectory can be reconstructed from a measurement of the impact
angle at the crime scene. Calculations can be embedded into a real life
situation and a ballistic reconstruction of a shooting incident can be
Comparison with other ballistics software
EBV4 is a completely menu driven DOS software. This sounds old-fashioned in the
world of modern WINDOWS software. EB as a very specialized program has been
developed in the late 80's and early 90's. A great amount of features were added
over the years so that almost all exterior ballistic problems can be solved with
the software. On one hand a re-development of EB as a WINDOWS software cannot be
done with the limited man-power of a single programmer, on the other hand the
large necessary time - investment would only result in a "nicer
looking" program, but not in additional program features.
Any person having
a basic knowledge of ballistics and of working with PCs will be able to
work successfully with EBV4. By means of very fast graphic presentations,
the user has excellent control over the results of the computations.
EBV4 is fast, accurate and "state-of-the-art". Calculation times for
trajectories are considerably smaller than the real flight time of the
bullet under consideration. In many computations, experiments and comparisons
with other sources, EBV4 has proven to yield accurate results.
EBV4 has mainly been developed for the professional user in the field
of small arms ballistics and for the forensic ballistician. EBV4 is a professional tool for the professional user and goes far
beyond the capabilities of exterior ballistics programs offered by various
As far as the author knows, EBV4 is the only exterior ballistics program
on the market, which is capable of reconstructing a trajectory from
findings at the impact point (backward calculations) and the only exterior
ballistics program capable of running simulations.
The operator of EB can model specific complex conditions including:
a user defined terrain profile, where shooting occurs,
a user defined atmosphere - even as a function of the altitude -, including
user defined initial conditions at the point of departure or the point
a user defined line of sight of a firearm,
a user defined target silhouette.
EBV4 still is a DOS application but runs on all IBM PC's or compatibles
and is nearly independent of the available hardware.EB has been tested under DOS, Windows 3.x, Windows 95, Windows 98, Windows NT, Windows
Me, Windows 2000 and Windows XP.
Graphics on paper (as a screen dump) is only possible, if the printer
is compatible with one of the following printer types (most printers are
at least compatible with one of the printers listed below).
Results of EB calculations can be exported via an ASCII text file, which
can be imported by most graphics and word processing software.
IBM Graphics Printer,
HP LaserJet, HP DeskJet,
HP Think Jet,
Epson Printer (9 pins or 24 pins)
How can I get EB?
EBV4 is commercially available from the author and will be accompanied
by an electronic English user's manual and a short German version. A single
user's license, which allows EB to be run on a single PC, can be purchased
special rates are available for multiple licenses or a network installation.
For further information on pricing and payment regulations please refer
to another chapter.
If you are interested in EBV4 or need further information, send an email
to the author.
A test version of EB, containing only a few basic features of the software
is now available. If you want to download this test version, please click
If you are convinced that EBV4 will be a valid working tool for your
work, please visit the order page.
Summary of EB main features
An example of an EB screen (main screen) is shown in the figure
Completely menu driven (language: English)
Very user friendly
Context sensitive help at keystroke (F1, F11 - keys) on screen (in English!)
Help on errors, warnings and other messages
Configuration file selection at program start, allowing 'personal' configuration
Four user types (hunter/sportsman, advanced, ballistician, forensic scientist)
Storage and retrieval of calculations on (hard) disk
Storage and retrieval of parameters on (hard) disk
Importation of ASCII text files to a table
Exportation of ASCII text files with user adjustable column separator
Viewing of parameter and configuration files
An example of a data entry screen (entry of initial conditions) is show
in the figure .
Arbitrary measures (European and Anglo - American units) for parameter entry
Arbitrary projectiles (objects, point mass bullets, fragments, spin-stabilized
Specific drag functions for selected bullets
Standard drag functions (e.G. G1 function, drag coefficients for spheres,. . .)
Supports the concept of ballistic coefficients (bc):
Estimation of the bc from velocity vs range tables,
Library with more than 1800 coefficients,
User entry of bc
Standardized or user defined terrain
Standardized or user defined atmosphere conditions (up to 90 km altitude)
User defined troposphere (lowest layer of atmosphere)
Standardized or user defined line of sight of firearm
Standardized or user defined target silhouette
An example of a graphics screen (a simple trajectory) is shown in the figure
Arbitrary measures for printing and plotting
Printing and plotting of results
on an external printer at any port,
printing to an ASCII text file
Printing of a trajectory in various coordinate systems
Selection of print sets for trajectory printing and ballistic table printing
User defined print size
Trajectory printing with space or time increments
Multiple graph menus (MPMM only)
Fast and universal graphic presentation of results
Manipulations of graphs:
Examination of graphs with a graphic cross cursor
Zooming of graphs
Screen dump of graphs on a graphics printer
Inclusion of lines and graphs in a plot:
Line of sight,
Point of aim and reference point,
Bullet impact points on a target,
Stability triangle (MPMM only)
Requires less than 1 MB hard disk space
DOS application, requires DOS 3.x or higher
Can be run as a DOS Application under all known WINDOWS operating systems (e.g.
Can be run in a network (network license required!)
Special program parameters available (e.g. for monochrome monitor, EMM
Three physical models: vacuum ballistics, point mass model (PMM) and modified point mass model (MPMM)
Optimized fast and accurate Runge - Kutta integration
Five calculation type groups:
Zeroing a gun,
SFC - from the point of departure (PoD) to the point of impact (PoI), single
TFC - from PoD to PoI, ballistic table,
SBC - from PoI to PoD, single trajectory,
TBC - from PoI to PoD, ballistic table
Zeroing a gun:
by entry of the zero range,
by entry of the maximum summit height,
from the evaluation of a ballistic target group,
from the entry of the line of sight parameters
Calculation of single trajectories, forward:
by entry of the departure angle (deterministic or probabilistic),
correction of the sights,
by entry of an aiming point (deterministic or probabilistic)
Calculation of ballistic tables, forward
by a variation of the departure angle (deterministic),
from the entry of an angle of departure (probabilistic; regarding ballistic
perturbations and errors of the shooter),
from the entry of the point of aim (probabilistic; regarding ballistic
perturbations and errors of the shooter),
Calculation of single trajectories, backward:
by entry of the initial conditions at the PoI
Calculation of ballistic tables, backward
by a variation of the impact velocity
iterative reconstruction of a trajectory
Simulations (probabilistic view of exterior ballistics)
Considers the following ballistic perturbations
variations of the muzzle velocity,
variations of the angle of departure and the azimuth (due to barrel vibrations),
variations of the drag force,
variations of wind speed and wind direction,
variations of the lift force,
bullet static and dynamic unbalances (MPMM only),
in-bore yaw (MPMM only).
Considers the following errors of the shooter
aiming error and sighting error,
canting of the gun.
Determination of ballistic perturbations:
from an evaluation of a ballistic target group
Determination of the errors of a shooter:
from an evaluation of a shooter' s target group
Estimation of gyroscopic and dynamic bullet stability (MPMM only)
Completely revised user's manual (almost 300 pages in English) including
Documentation of available drag functions (as an appendix to the user's
Short version of user's manual in German (included in English manual)
EB Version 4.21 now also available on CD, including the user's manual as
a PDF file.
For further questions and comments: send an eMail!
Update: February 07, 2013