EBV4.2  Exterior Ballistics Software
for the PC
Author: Ruprecht Nennstiel, Hofheim, Germany
Abstract
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.
even artillery).
The document also contains a link to an order form for the software.
Contents
Appendices
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 MSDOS
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 Vacuum Ballistics Model (VBM) introduced into physics
by Galileo Galilei, which assumes the presence of the force of gravity
only.

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 spindependent side drift.
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 semiempirical formulas. EBV4 does not support the mostly advanced 6DegreesofFreedom
(6DOF) model, as in most practical cases, the whole set of aerodynamic
coefficients applicable to this model is not available.
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
aerodynamic coefficients.
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 c_{D}
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
velocity.
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 highangle 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
created.
Comparison with other ballistics software
EBV4 is a completely menu driven DOS software. This sounds oldfashioned 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 redevelopment of EB as a WINDOWS software cannot be
done with the limited manpower 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 "stateoftheart". 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
ammunition manufacturers.
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
wind,

user defined initial conditions at the point of departure or the point
of impact,

a user defined line of sight of a firearm,

a user defined target silhouette.
Hardware requirements
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).

IBM Graphics Printer,

HP LaserJet, HP DeskJet,

HP Think Jet,

Epson Printer (9 pins or 24 pins)
Results of EB calculations can be exported via an ASCII text file, which
can be imported by most graphics and word processing software.
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
for
150. Euro,
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
here.
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
Handling

Completely menu driven (language: English)

Very user friendly

Mouse support

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
settings

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

File deletion

Viewing of parameter and configuration files
An example of an EB screen (main screen) is shown in the figure
Data Entry

Arbitrary measures (European and Anglo  American units) for parameter entry

Arbitrary projectiles (objects, point mass bullets, fragments, spinstabilized
projectiles)

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 data entry screen (entry of initial conditions) is show
in the figure .
Output

Arbitrary measures for printing and plotting

Printing and plotting of results

on screen,

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,

Impact line,

Terrain profile,

Point of aim and reference point,

Target silhouette,

Bullet impact points on a target,

Stability triangle (MPMM only)
An example of a graphics screen (a simple trajectory) is shown in the figure
.
Environment

Hardware independent

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.
XP)

Can be run in a network (network license required!)

Special program parameters available (e.g. for monochrome monitor, EMM
use,...)
Calculation

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
trajectory,

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),

inbore 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)
Miscellaneous

Completely revised user's manual (almost 300 pages in English) including
stepbystep examples

Documentation of available drag functions (as an appendix to the user's
manual)

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.
Ruprecht Nennstiel
Hofheim, Germany
For further questions and comments: send an eMail!
Update: February 07, 2013