5.0
Trajectory Tables
If you have purchased this manual in book
form, and you have called one of Sierra’s ballistic technicians
for trajectory information, the trajectory tables you may receive
from our technicians are custom prepared for you using Sierra’s
Infinity software.
The basic elements of a trajectory and the information contained
in the tables are described below.
We have included the most useful trajectory
parameters (velocity, energy, drop, bullet path, wind drift and
point blank range with the zero range to maximize it) in the Infinity
tables. For each computed trajectory,
they are tabulated for the userselected muzzle velocity and shooting
conditions.
This discussion uses an example of a popular
rifle bullet to discuss each element of the baseline table and explain
the important terms.
Trajectory: The
trajectory of a projectile, in this case a rifle bullet, is the
actual path that the projectile follows after leaving the muzzle.
It is very important that this term be understood before using the
tables. The trajectory of the bullet is shaped by many factors:
gravity, altitude (air pressure), temperature, humidity, muzzle
velocity, wind conditions, and the ballistic coefficient of the
bullet itself. Although all of these have been discussed in much
more detail in previous sections, the major contributors will be
redescribed here as they affect the example trajectory.
The figure above illustrates the parts
of a trajectory as they are discussed here and used in the tables.
As soon as the bullet leaves the muzzle, gravity causes it to begin
to fall away from its line of departure. This creates the drop discussed
later. The line of departure is
an imaginary line through the longitudinal centerline (Bore Centerline)
of the bore and is the line upon which the bullet is launched. The
significance of this line will be discussed as each element of the
tables is discussed. Rz in the figure is the Zero
Range where the trajectory crosses
the line of sight on
its downward path, and R is the Range
of the bullet from the muzzle at
each point along the trajectory. Muzzle velocity, air resistance
(ballistic coefficient), and gravity are the major contributors
to trajectory shaping. Your Infinity
tables are computed for the conditions
defined in the “Trajectory Parameters” and “Environment
Parameters” sidebars associated with theInfinity
trajectory operations. The example
we will describe below uses level
fire, which means that the line between
the gun muzzle and the target is level, and the line
of departure is nearly level. In
Figure 5.01,
the elevation angle of the line of
departure is greatly exaggerated
for clarity. In practice, the elevation angle is a small fraction
of a degree. The elevation angle of this line is determined by the
sight height and
the zero range.
(Since the bullet begins falling immediately after it leaves the
bore, it must be launched with a slightly upward direction so that
it will fall back to the line of
sight at the zero range).
Now, in order to illustrate the key elements
in the Infinity tables,
let’s discuss each element. The figure below shows the header
for an Infinity trajectory
table for the Sierra .257 inch diameter, 117 gr. Spitzer Boat Tail
Bullet at a velocity that might be attained in a 2506.
Trajectory for Sierra .257" dia. 117 gr.
SPT at 2900 Feet per Second
At an Elevation Angle of: 0 degrees Ballistic
Coefficients of: 0.388
0.383
Velocity Boundaries (Feet per Second)
of:
0.362 

0.362 

0.362 

2500 

1800 

1800 

1800
Wind Direction is: 3.0 o’clock and
a Wind Velocity of 9.0 miles per hour
Wind Components are (miles per hour):
Down Range: 0.0 Cross Range: 9.0 Vertical: 0.0 Altitude: 0 Feet
with a Standard Atmospheric Model.
Temperature: 59°F
Data Printed in English Units
Figure 5.02
The header for a particular table documents
the parameters used in computing the data table that follows after
the header. The title, of course, is selfexplanatory. The Elevation
Angle defined as 0 degrees in the
above example means that the baseline trajectory for this bullet
was computed for level fire. The elevation
angle permits computing a baseline
trajectory for a shooting range that is not level. Although most
shooting ranges are approximately level, some public and personal
ranges are not.
The next two lines of the header must
be taken together in the discussion. The first of these two lines
defines the five Ballistic Coefficients
which are used to compute the trajectory.
The next line defines the velocity boundaries for the velocity ranges
within which these Ballistic Coefficients are used. In this example,
the 0.388 coefficient is used for computations when the bullet velocity
is above 2500 feet per second, 0.383 is used for calculations when
the bullet velocity is below 2500 feet per second but above 1800
feet per second, and 0.362 is used when the bullet velocity is below
1800 feet per second. As we have discussed previously, we provide
for five Ballistic Coefficient values for our computations because
our testing over the last 32 years has proven that a single Ballistic
Coefficient does not accurately model the fit of the individual
bullet drag to the G1 Drag Function. For this particular bullet
we have found that three coefficients
closely fit the bullet to the G1 Drag Function. The Ballistic Coefficients
for Sierra bullets are all measured in controlled conditions in
our underground test range. The next two lines should also be examined
together. The Wind Direction line
documents the wind direction and speed that were entered in the
“Environment Parameters” sidebar ofInfinity.
The Wind Components line
documents the actual downrange, crossrange and vertical wind components
that have been resolved from the defined wind and used in the calculations.
The next two lines define the atmospheric and temperature values
that were used in the computations. The Altitude value is the altitude
(or elevation) of the firing point above sea level, and the Temperature
value is the temperature of the air at the firing point. The last
line in the header documents the physical units used for the tabular
material to follow.
Let’s discuss the basic elements
of the trajectory table and what they represent. The figure below
highlights the basic table elements.
The Range
column documents the range distance
for which the data in the remaining columns apply. Since the basic
computations and data storage in Infinity
are in one yard (or meter) increments,
any integer printout interval value may be selected from 1 yard
up to the maximum range. In figure 5.03 the printout interval has
been chosen to be 50 yards, and this selection was entered in the
“Trajectory Parameters” side bar.
Range 

Velocity 

Energy 

Momentum 

Drop 

Bullet Path 

Wind Drift 

Time of Flight 

(Yards) 

(Ft/Sec) 

(Ft/Lbs) 

(LbSec) 

(inches) 

(inches) 

(inches) 

(Seconds) 

















0 

2900.0 

2184.5 

1.51 

0.0 

1.5 

0.0 

0.000000000 

















50 

2779.2 

2006.3 

1.44 

0.53 

0.67 

0.18 

0.052837693 

100 

2661.6 

1840.1 

1.38 

2.19 

1.71 

0.72 

0.107990399 

150 

2547.2 

1685.3 

1.32 

5.07 

1.53 

1.65 

0.165600200 

200 

2434.6 

1539.6 

1.26 

9.3 

0.0 

3.0 

0.225830888 

250 

2324.4 

1403.3 

1.21 

14.99 

2.99 

4.79 

0.288887624 

300 

2216.9 

1276.6 

1.15 

22.29 

7.59 

7.07 

0.354968217 

350 

2112.2 

1158.9 

1.10 

31.36 

13.96 

9.86 

0.424288238 

400 

2010.4 

1049.9 

1.04 

42.38 

22.28 

13.19 

0.497081750 

450 

1911.7 

949.2 

0.99 

55.55 

32.75 

17.12 

0.573599874 

500 

1816.0 

856.6 

0.94 

71.1 

45.6 

21.68 

0.654111878 

550 

1719.5 

768.0 

0.89 

89.28 

61.09 

26.93 

0.738988797 

600 

1626.1 

686.8 

0.84 

110.41 

79.53 

32.95 

0.828709231 

650 

1537.2 

613.8 

0.80 

134.83 

101.25 

39.79 

0.923603742 

700 

1453.4 

548.7 

0.76 

162.94 

126.65 

47.5 

1.023986006 

750 

1375.0 

491.1 

0.71 

195.15 

156.17 

56.12 

1.130134794 

800 

1302.6 

440.8 

0.68 

231.97 

190.29 

65.69 

1.242270846 

850 

1237.0 

397.5 

0.64 

273.92 

229.53 

76.22 

1.360513639 

900 

1178.7 

360.9 

0.61 

321.54 

274.46 

87.72 

1.484836153 

950 

1128.0 

330.5 

0.59 

375.42 

325.64 

100.15 

1.615043409 

1000 

1084.8 

305.7 

0.56 

436.14 

383.66 

113.46 

1.750789074 

















Figure 5.03 













The Velocity
column is the speed with which the
bullet is moving at any given point. In our trajectory table, it
is the remaining velocity at
the printout range. Remaining velocity
is the velocity left after the bullet
has been launched with the Muzzle
Velocity and has then decelerated
(slowed down) due to air resistance while traveling the distance
to the printout range. The rate at which the bullet slows down is
related to its ballistic coefficient(s) and the properties of the
air (temperature, humidity, barometric pressure) over the path the
bullet travels.
The Energy
column, as typically used in ballistics
tables, is Kinetic Energy. Without getting involved in whether Kinetic
Energy or Momentum provides the killing power and what the mechanisms
are, we’ll discuss both.
The Kinetic
Energy of a bullet is based on the
mass of the bullet and the velocity with which it is traveling.
The mass is not identical to the bullet weight so the bullet weight
must be converted to mass before we can use it.
The mathematical formula for the mass
of a bullet is:
where: w = bullet weight in grains and
g = 32.174 ft/sec2 (acceleration due to gravity)
(The factor of 7000 converts bullet weight
from grains to pounds) The Kinetic
Energy of the bullet can then be
found from the formula:
where: m = mass of the bullet and: v =
the remaining velocity
The Momentum
column is included as an additional
measure of effectiveness. Momentum is calculated using the formula:
where: m = mass of the bullet and: v =
the remaining velocity
Drop, as
it is used in ballistic computations, is really an intermediate
parameter. That is, it is useful to calculate other parameters.
The drop of
the bullet is the vertical distance of the bullet referenced to
the line of departure from
the bore. The following figure illustrates drop when the line
of departure is horizontal. When
the line of departure is
not horizontal (tilted upward or downward), drop
is still defined as the vertical
distance between the bullet and the line of departure at any point
in the trajectory. Drop is
used in the computations of bullet
path, but otherwise it has meaning
primarily in a direct comparison of two bullets as to the shape
of their trajectories.
Figure 5.04
The values in the Bullet
Path column are the position of the
bullet with respect to the shooter’s line
of sight through the gunsights. For
the average shooter, bullet path is one of the most useful parameters
in the tables. Bullet path values
are based upon the sight height (distance of the line of sight above
the bore centerline at the gun) and the desired zero
range. These two points determine
the line of sight with respect to the gun and permit an accurate
calculation, using the drop, of the bullet position with respect
to the line of sight. The sight height above the bore centerline
can be measured for your specific firearm and entered on the Infinity
“Trajectory Parameters”
sidebar. We use 1.5 inches for the sight height for rifles and handguns
with telescope sights and 0.8 inches for rifles with iron sights
and most handguns as default values for sight height. Figure
5.05 illustrates the bullet path.
This rifle has a sight height of 1.5 inches and is zeroed at about
220 yards. The bullet path is 1.5 inches below the line of sight
at the muzzle, 1.68 inches above the line of sight at 100 yards,
7.45 inches low at 300 yards, and 21.78 inches below the line of
sight at 400 yards.
Figure 5.05
Wind Drift values are shown for the resolved
value of crosswind. The deflection of the bullet due to crosswind
is related to the crosswind velocity (or crosswind component of
a wind from any direction) and the time of flight of the bullet.
In this example, we used a 3 o’clock wind direction (crosswind
only blowing from right to left across the shooter’s line of
sight to the target) so there is little impact on the drop or bullet
path. (There could be an impact at the longer ranges due to the
increased time of flight over the slightly longer flight path.)
If we use a quartering wind (1.30 o’clock for example) there
will be an impact on the drop (increased drop), time of flight (also
increased), and bullet path (bullet shooting lower) due to the headwind
component. The Time
of Flight column shows the flight
time to the range distance in the range column.
Now, let’s discuss Point
Blank Range and the Infinity
printout features related to it.
The figure below shows a graphical view of Point
Blank Range.
Point Blank Range (PBR)
is that range distance out to which a shooter can always hold directly
on his target, with no compensation for drop, and expect a hit within
the vital zone.
Maximum Point Blank Range (MPBR)
refers to the maximum range for which the firearm can be zeroed
such that the bullet will neither rise above the line of sight farther
than onehalf the vital zone height
nor fall below the line of sight more than onehalf the vital
zone height.
“Vital Zone” refers
to that area within which an animal may be hit and the hit is quickly
fatal. In a deersized animal, that zone is approximately 10 inches
high and centered on the heart/lung area. On a prairie dog or ground
squirrel the vital zone is
much smaller, typically 2 to 4 inches in height. The concept applies
equally well to the metallic silhouette and other games. The
Point Blank Range and the Maximum Point
Blank Range values are printed as a result of running either the
Point Blank Range or the Maximum Point Blank Range Operation in
the Operations menu of Infinity. Both quantities represent the maximum
range that you can hold directly on the target and hit within the
vital zone. The difference is that, if your zero range is less than
the zero range which maximizes the point blank range (MPBR zero),
the bullet path at ranges closer than the zero range will not reach
a value as high as onehalf the vital zone height above the line
of sight. So, your PBR is less than it could be for the game you
are hunting. Running the Maximum Point Blank Range Operation in
Infinity will tell you where to zero your gun to maximize the point
blank range, as the example below shows. Note that in the example below, the bullet
path is computed for the Maximum
Point Blank Range Zero even though
the MPBR zero doesn’t lie at a printout range point. If you
wish to maximize your point blank range, and you are sighting in
on a 100yard range, simply center your group about 4.02 inches
higher than your aimpoint. (3.5 to 4.5 inches might be close enough
for most hunters!). If you have a 200yard range, you would center
your group about 4.6 inches above your aimpoint. Then you can take
full advantage of the 343 yard PBR of your rifle and load for deer.
Calculation of Maximum Point Blank Range
for a Vital Zone of: 10 inches Maximum Point Blank Range is 343.
Set Zero at 292
Trajectory for Sierra .257” dia.
117 gr. SPT at 2900 Feet per Second
At an Elevation Angle of: 0 degrees
Ballistic Coefficients of: 0.388 0.383
0.362
0.362 0.362
Velocity Boundaries (feet per second)
of: 2500 1800 1800
1800
Wind Direction is: 3.0 o’clock and
a Wind Velocity of: 9.0 miles per hour
Wind Components are (feet per sec): Downrange:
0.0 Cross Range: 0.0 Vertical: 0.0
Altitude: 0 Feet with a Standard Atmospheric
Model. Temperature: 59 F
Data Printed in English Units
Range 

Velocity 

Energy 

Momentum 

Drop 

Bullet Path 

Wind Drift 

Time of Flight 

(Yards) 

(Ft/Sec) 

(Ft/Lbs) 

(FtLbs) 

(inches) 

(inches) 

(inches) 

(Seconds) 

0 

2900.0 

2184.5 

1.51 

0.0 

1.5 

0.0 

0.000000000 

50 

2779.2 

2006.3 

1.44 

0.53 

1.82 

0.45 

0.052837693 

100 

2661.6 

1840.1 

1.38 

2.19 

4.02 

1.83 

0.107990399 

150 

2547.2 

1685.3 

1.32 

5.07 

4.99 

4.2 

0.165600200 

200 

2434.6 

1539.6 

1.26 

9.3 

4.62 

7.62 

0.225830888 

250 

2324.4 

1403.3 

1.21 

14.99 

2.78 

12.18 

0.288887624 

300 

2216.9 

1276.6 

1.15 

22.29 

0.67 

17.95 

0.354968217 

350 

2112.2 

1158.9 

1.10 

31.36 

5.88 

25.03 

0.424288238 

400 

2010.4 

1049.9 

1.04 

42.38 

13.05 

33.51 

0.497081750 

450 

1911.7 

949.2 

0.99 

55.55 

22.36 

43.49 

0.573599874 

















Figure 5.07 













