Drag Analyzer

The Drag Analyzer is a truly unique feature of Ballistic Explorer that graphically displays bullet drag versus ground velocity. Drag depends on the bullet's velocity relative to the air, the selected drag function (model), ballistic coefficient (BC), air density, range slope, and the speed of sound. Being able to display bullet drag for three traces at a time makes it easy to see how various parameters impact bullet drag at a level of detail not readily available before.

To open click Drag Analyzer... in the Tools menu.

 

The function of most of the check boxes on the Chart Controls tab are obvious when you check or uncheck them. When Velocity as Mach is checked the graph's X-axis displays velocity in Mach Number as defined by the Army Standard Metro atmosphere, which is 1120.27 f/s. When unchecked, velocity is displayed in either feet or meters per second depending on which units are selected in the Options menu.

When Add Mach 1 Bars is checked tinny vertical bars are added to the plot for each trace where the bullet experiences Mach 1 air velocity per the parameters set in the corresponding Trace window.

In the example to the right the red plot is for 95 F, which increases the speed of sound to 1165.3 f/s. The green plot is for 59 F, which is the standard Metro temperature with the speed of sound of 1120.3 f/s, and the blue plot is for 19 F, which decreases the speed of sound to 1074.0 f/s.

Remember that the bullet experiences drag due to air velocity as defined by the speed of sound, yet muzzle and downrange velocities are referenced to the ground and in units of feet or meters per second or standard Metro Mach units of 1120.27 f/s. Thus, the drag curve shifts horizontally with changes in the speed of sound and/or air velocity (head and tail winds).

Click the Velocity Range tab to access slider controls that set the maximum and minimum velocity of the graph. The graph updates as the sliders are moved making it easy to select the desired range.

 

Click the Information tab to view the Mach 1, Air Density, and Wind data for each displayed trace. Note that only the headwind or tailwind component of a wind from any direction is shown as the crosswind component doesn't contribute to drag.


The menu at the top of the window includes Options for changing the color of the plots, and buttons to Print, save the graph to a File (bmp) and open this Help page.


 

Page Directory
Details about the Drag Analyzer graph, G, Mach units, and the atmospheric model explained.
Drag versus velocity is the core relationship from which downrange predictions are made.
Long used scheme for customizing standard drag functions to fit actual bullets, but it's not so simple.

 

Background Information

Many shooters are familiarly with bullet drag coefficient graphs as shown on the left above. The formula for plotting drag coefficient vs. Mach isolates the bullet's shape so that it can be compared to other shapes. While useful in designing bullets, it's difficult to visualize the drag a bullet experiences in flight from looking at a drag coefficient graph. Taking into account all the factors affecting bullet drag produces the graph shown on the right above with drag in units of "G". It's then easy to see that drag increases as velocity increases with a large jump as velocity approaches Mach 1.

The term Mach 1 refers to the speed of sound with Mach 2 being twice the speed of sound and so on. While the term Mach can be applied to sound traveling through any medium, our focus here is sound traveling through air.

"G" represents the standard gravitational constant, which is defined as an acceleration of 9.80665 meters per second squared or the equivalent force of 9.80665 Newtons per kilogram of mass. A drag of 100 G's can be regarded as either a negative acceleration (deceleration) of 980.665 meters per second squared or a drag force of 100 times that of gravity acting on the bullet.

For a given velocity and bullet, the drag due to air resistance felt by that bullet depends both on the density of the air and the speed of sound through that air. This is why drag functions are defined in terms of Mach number rather than absolute velocity. Furthermore, drag depends on the velocity through the air rather than the velocity relative to the ground, yet we measure and calculate velocity relative to the ground. A bullet fired at 2500 fps into a 12 mph (20 fps) headwind experiences an air velocity of 2520 fps out of the muzzle. Fire in the opposite direction and the bullet experiences an air velocity of 2480 fps out of the muzzle.

The speed of sound in air is not fixed, but is affected by temperature and somewhat by humidity. As temperature and/or humidity increase the speed of sound increases. While pressure (altitude) by itself doesn't affect the speed of sound, for a given temperature and humidity above 0 %, the ratio of water vapor in the air increases as pressure decreases, and thus, the speed of sound increases slightly with altitude.

Ballistic Explorer uses an advance hybrid atmospheric model that accommodates the Metro standard sea level conditions for which the official SAAMI drag functions are calibrated, yet uses the modern ICAO atmosphere for deviation from standard Metro conditions while incorporating real world humidity levels. ICAO specifies an improbable humidity of 0 percent to avoid dealing with the complex relationship between humidity, temperature and pressure as it affects the speed of sound. While the effect of humidity is small, it's well understood and our atmospheric model takes it into account.

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Drag Profile

The above graph shows drag at standard Metro conditions for the standard G1 and G7 projectiles, which by definition have a BC of 1.000. While G1 is the standard drag function for all sporting bullets, looking at the drag plots and the two projectile's shapes G1 doesn't seem to be remotely similar to G7, which is for VLD (Very Low Drag) bullets. However, scaling the G7 drag by changing it's BC to 0.500 results in the following graph.

While the drag plots differ above Mach 2.6 (2913 f/s) and below Mach 1.6 (1792 f/s), they are almost identical between those two points. What this means is that there's no practical difference in trajectory predictions made from using G1 versus G7 in the velocity range where the plots overlap. Use any accurate ballistics program and start off with a muzzle velocity of 3,000 fps with a G1 BC of 0.500 and compare drop to that produced by a G7 BC of 0.250 and you'll find they are within 0.1 mils out to about 1,200 yards under standard conditions. This relationship holds true for all conditions as long as the 2 to 1 ratio of G1 to G7 BC is maintained. However, consider that the absolute velocity of the overlapping region changes as the speed of sound changes.

This explains why G1 has served shooters so well even for bullets that look a lot more like the G7 projectile than the G1 projectile. Only with muzzle velocities well over 3000 f/s and/or shooting to ranges where remaining velocity drops well below 1792 f/s would trajectory predictions be significantly more accurate using G7 than G1, and then only if the actual bullet's drag characteristics matches the G7 drag function.

It's not the magnitude of drag that distinguishes one drag function from another, as that can be scaled by ballistic coefficient, it's the shape of the drag versus velocity curve, or what can be called the drag profile that makes the difference. The graph below compares the G1, G6 and GL drag functions.

Being G1 is officially the standard for all sporting bullets, it's good to include it as a reference when looking at the drag profiles of other drag functions. G6 is described as being for flat base and sharp nose bullets, while GL is described as being for exposed lead nose and HP bullets. To give the drag functions similar scale for comparison, the G1 was set to a BC of 0.500, and both the G6 and GL BC values were set to give an equal time of flight at 1500 yards starting off at 3200 f/s muzzle velocity under standard Metro conditions.

While finding the BC value for equal time of flight is easily done, you can also open the Explore display and use the BC slider control to manually adjust the scale. Once you click on the BC slider you can use the mouse wheel to change the BC value of the selected trace. As the slider is moved, all open displays, including the Drag Analyzer update giving you great visual feedback. In the same way you can use the Temperature and Altitude sliders to see how these parameters effect bullet drag. Check the Add Mach 1 Bars box on the Drag Analyzer and you can see how the speed of sound changes as you adjust the Temperature slider.

Lapua has made a number of custom Doppler radar derived drag functions available in recent years, which can now be used directly in Ballistic Explorer. There's no better way of understanding how these compare to G1 than to load them into the Drag Analyzer and have a look at them. The graph below compares the G1, N522, and S538 drag functions.

N522 is Lapua's product code for their .366" 220 gr Naturalis (product number N PL 9202), while S538 is Lapua's product code for their .224" 55 gr FMJ (product number 4 PL/HL 5005). By defalt, these custom drag functions have a BC of 1.000 as these bullets act as their own standard. However, you can set the BC of these drag functions in Ballistic Explorer just as you would any other drag function. For example, advanced users could use a Naturalis drag function as the standard for other Naturalis bullets for which there is no custom drag function. To do so you need to meassure MV and downrange velocity or TOF, and then calculate ballistic coefficient based for a Naturalis drag function, such as N522.

When comparing drag functions you can use the slider controls on the Velocity Range tab to view the velocity range you expect to use when shooting. That gives you more detail of the velocity range that has the most affect on your shooting.

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Multiple (stepped) Ballistic Coefficients

Sierra Bullets has been using G1 based stepped BC values for decades. They discovered early on that few bullets exactly matched the G1 drag function to the accuracy they were able to test to, so they publish what amounts to a custom drag function for each of their bullets.

The above graph shows a plot (red) of the stepped G1 BC values for the 0.308" 155 grain Sierra PALMA MatchKing (#2156) compared to the plot (green) of a single G1 BC of 0.476 that produces an equal time of flight to 1000 yards, and to the plot (blue) of a single G7 BC of 0.238 that also produces an equal time of flight to 1000 yards. You can easily see the BC steps in the graph and how those steps follow the G7 plot closer than the G1 plot. The Sierra PALMA (#2156) is one of the bullets Bryan Litz tested for his book Applied Ballistics For Long Range Shooting, and he also found it better matched the G7 drag function.

The velocity ranges given in a stepped BC are not absolute values, but are relative to the standard Metro speed of sound, which is 1120.3 f/s. As an example, the first step of 2700 f/s divided by 1120.3 f/s is Mach 2.41. In the graph below the temperature has been increased to 95 F.

At 95 F the speed of sound increases to 1165.3 f/s, so Mach 2.41 is now 2808 f/s and you can see in the graph the first step occurs at that velocity. In addition to the change in the speed of sound, the air is only 92.4 percent as dense as under standard conditions. The combined effect is to reduce drag at 3000 f/s (ground velocity) from about 59 G's down to about 52 G's, or about 11.8 percent.

The change in the speed of sound and drag changes the range at which the bullet's velocity drops into the transonic range. Assuming a muzzle velocity of 3200 f/s, then at 59 F the PALMA drops to Mach 1.2 (1344 f/s) at 1081 yards, but at 95 F it drops to Mach 1.2 (1398 f/s) at 1102 yards.

The velocity ranges given in a stepped BC are relative to the air, yet we measure muzzle velocity and calculate downrange velocity relative to the ground. For the graph below the temperature is set back to the standard 59 F, but a 30 MPH (44 f/s) tailwind has been added for all three traces.

Being the air velocity is 44 f/s less than the ground velocity the first step of 2700 f/s now happens at 2744 f/s ground velocity. The drag on the PALMA at 3000 f/s (ground velocity) has been reduced by about 1 G. Assuming a muzzle velocity of 3200 f/s, the range at which the bullet's velocity drops into the transonic range increases from 1081 to 1115 yards.

At first glance that doesn't seem right as in the prior example an increase in temperature to 95 F reduced the drag at 3000 f/s by about 7 G's, yet only extended the transonic range from 1081 to 1102 yards. However, the temperature increase also increased the speed of sound from 1120.3 to 1165.3 f/s which puts Mach 1.2 at 1398 f/s. In the tailwind example the PALMA drops to 1398 f/s at just 1074 yards, but that's Mach 1.25 when the speed of sound is 1120.3 f/s.

A common criticism of stepped ballistic coefficients has been that they cause abrupt changes in downrange velocity and drop predictions. While that can be demonstrated using arbitrarily large steps, the graphs below demonstrate no such issue with steps for an actual bullet. In fact, even in the velocity graph where the G1 plot deviates past 1000 yards the plot for the PALMA closely follows the G7 plot.

Some bullets do match the G1 drag function quite well, even boat-tail bullets as can be seen in the graph below.

The above graph shows a plot (red) of the stepped G1 BC values for the 0.308" 165 grain Sierra Spitzer BT (#2145) compared to the plot (green) of a single G1 BC of 0.406 that produces an equal time of flight to 1000 yards, and to the plot (blue) of a single G7 BC of 0.208 that also produces an equal time of flight to 1000 yards. The BC steps are quite small and the red plot follows the green G1 plot much closer than the blue G7 plot.

Changes in air density, air velocity, and the speed of sound combine to increase the difficulty of making first shot hits at ranges where the bullet drops into or through the transonic velocity range. With the Drag Analyzer you can visualize the relationship between various drag functions and conditions at a level of detail far grater then with other types of graphs, and perhaps improve your shooting.

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