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Ballistics For Dummies

by Jon R. Sundra   |  November 2nd, 2010 26

The basics that every shooter should know about the bullet’s flight from muzzle to target.


It doesn’t take a master’s degree in math or physics to understand a rifle bullet’s trajectory. The illustration above is exaggerated to show how the bullet, which is always falling away from the Line of Departure, intersects the Line of Sight at two distances, the second of which is the range at which the rifle is zeroed.

One of the most successful publishing ventures in recent times is a series of books entitled (Blank) for Dummies. Whatever the skill or knowledge you wish to acquire, there is a “dummies” book for you, including subjects like Raising Smart Kids for Dummies (honest!) and Aromatherapy for Dummies. The funny thing, though, is that these books aren’t really written for dummies at all, nor do they address subjects at elementary levels. In fact, one of the better books I’ve read on wine is Wine for Dummies.

I’m sure it will come as no surprise if I were to tell you there has yet to be a Ballistics for Dummies, so I hope you’ll accept my use of that title here with the same good humor with which it’s being offered.

Just what do we need to know, if anything, about ballistics that could make us better riflemen and more successful hunters? There are actually three aspects to ballistics: internal, external and terminal.

Internal ballistics has to do with what happens inside the rifle from the moment of ignition to the bullet’s exiting the muzzle. For the most part, only handloaders need be concerned about internal ballistics and then only because it is they who are assembling the loads that determine what those ballistics will be. You would indeed be a “dummy” if as a handloader you weren’t interested in acquiring basic knowledge about internal ballistics, particularly because much of it affects your own safety.

On the other hand, if you do all your shooting and hunting using factory ammo, there’s nothing you really need to know about what goes on inside the gun because you have no control over it. Don’t get me wrong; I would never discourage anyone from learning as much as he can about internal ballistics. It’s just that it’s not necessary in this context.

As for terminal ballistics, that’s something we have some control over but only to the extent of choosing the specific bullet, whether as a component of a handload or factory load. Terminal ballistics begins once that bullet enters the target. It is a science that is as much qualitative as quantitative because there are so many factors that affect lethality, factors that cannot be tightly controlled in a laboratory.

What’s left, then, is external ballistics, which is just a fancy term for what the bullet does from muzzle to target. We’re going to keep it simple because, frankly, simple is all I know. I mean, it took me three tries to get through remedial math in college, and I flunked physics, so take my word for it, it isn’t complicated.


These two 154-grain 7mm bullets have the same sectional density of .273, but the flatbase on the left has a BC of .433 while the SST on the right rates a .530.

To understand what happens from muzzle to target and why–or at least to the extent we hunters need to know–there are some definitions and fundamental concepts one must be familiar with before all the pieces can fall into place.

DEFINITIONS
Line of Sight (LOS): A straight line out to infinity as represented by the scope’s reticle, or the sighting plane formed when the front and rear sights are aligned.

Line of Departure (LOD): Another perfectly straight line, this one running down the center of the bore to infinity.

Bullet Path: The arc or trajectory of the bullet relative to LOS.

Drop: The actual drop of the bullet relative to LOD. I’m sure we’ve all heard someone describe a rifle as being so flat-shooting “the bullet doesn’t even drop for the first 100 yards!” Nonsense. Even with the flattest-shooting super magnum, the bullet starts dropping away from the LOD the moment it leaves the muzzle. A popular misconception is one that results from the use of the word “rises” in various ballistics charts. A bullet is always dropping, but it does indeed “rise” relative to the LOS. This seeming anomaly exists because with the scope being positioned above the bore, the only way the LOS could converge with the bullet path is to angle the sights downward. In other words, if the LOD and LOS were parallel, the bullet would exit the muzzle 11⁄2 inches low and start falling farther away from there.

Adding to the confusion is the fact that, once those sights are angled downward to converge with the bullet path at some practical distance downrange–whether it be 100, 200 or 300 yards–the bullet and LOS will have already converged once before. Whether we’re shooting a .45-70 that we want zeroed at 100 yards or a 7mm Ultra Mag at 300, this first convergence of LOS and bullet path occurs between 20 to 40 yards from the muzzle.


Both of these 300-grain .375-caliber bullets have the same SD of .305, but the spitzer boattail on the left has a BC of.493 while the roundnose rates only a .250.

In the case of the .45-70, to get it to print dead-on at 100 yards, we’d find that our bullet first converged with our LOS about 20 yards from the muzzle. From that point on, the bullet would be “rising” to where at 55 yards it would be at its highest point above our LOS–about 21⁄2 inches. At that point the bullet begins to fall relative to LOS to where the two again converge at our desired zero range of 100 yards.

With the 7mm Ultra Mag zeroed at 300 yards, first convergence is at about 40 yards. Between that point and 300 yards, our bullet path will attain a maximum height of about 31⁄2 inches above our LOS. Bottom line: Bullet path and LOS converge at two distances, the second of which is actually the zero range.

MIDRANGE TRAJECTORY
In the foregoing explanation I touched upon a term that is seldom used today, but back when I was a budding rifle geek, midrange trajectory was the criteria by which ballistic charts compared cartridge
performance. MRT is the maximum height above LOS that a bullet would impact on its way to a given zero range. Typically, ballistics charts would list 100-, 200- and 300-yard MRTs. As an example, the MRT for the 150-grain 7mm Remington Mag load as listed in the 1964 Remington catalog was .5 inch at 100 yards, 1.8 inches at 200 yards and 4.7 inches at 300 yards. That meant that if we were to zero our 7 Mag at 100 yards, the bullet path would print 1/2 inch high at 50 yards, 1.8 inches high at 100 yards with a 200-yard zero and 4.7 inches high at 150 yards if zeroed at 300 yards. Actually, the maximum ordinate occurs beyond the midpoint–like around 55, 110 and 165 yards, respectively–but in the real world the differences are insignificant.

While MRT was certainly useful information and a good way to compare various cartridges and loads, today’s system of listing a single zero distance for the cartridge in question, and the POIs both above and below LOS at various distances downrange, is far more useful.

SECTIONAL DENSITY, BALLISTIC COEFFICIENT
Once the bullet is launched, its trajectory is determined by its velocity, shape and weight. Which brings us to those imposing terms, sectional density and ballistic coefficient. Sectional density is the weight of a bullet in pounds, to the square of its diameter in inches. But forget that, it’s simply a way of expressing the weight of a bullet relative to its caliber. Take a 100-grain bullet, for example: In 7mm (.284) that would be very light indeed, but it would be quite heavy in 6mm (.243). Expressed in terms of sectional density, the 100-grain 7mm bullet has an SD of .177, but a 6mm bullet of that same weight has an SD of .242.


Progressive degrees of “streamlining” can be seen in this quartet of 7mm bullets. The RN on the left has a BC of .273; the Hornady A-Max match bullet on the far right rates a .623–more than double.

Perhaps a better perspective on what’s light and what’s heavy can be gotten by comparing bullets of the same caliber. Where the lightest 7mm bullet (100 grains) has an SD of .177, the heaviest 7mm slug–the 175-grain–is rated at .310. Conversely, at 55 grains, the lightest 6mm bullet has an SD of .133.

Because sectional density relates strictly to weight, not shape, that means the most bluntnose bullet has the exact same SD as the most streamlined bullet of that same weight and caliber. Ballistic Coefficient is a different matter entirely; it’s the measure of how “streamlined” a bullet is, i.e., its effectiveness at overcoming air resistance during flight. Computing a bullet’s ballistic coefficient is not a precise science, for there are several methodologies and no two will produce the exact same number. Further complicating things is the fact that BC changes with velocity and altitude.

I suggest that unless you’re some kind of a math weenie who likes to do computations just for the hell of it, do like everyone else and just take the bullet manufacturer’s word for it. All component bulletmakers list SD and BC for their bullets, but only Remington and Hornady among the ammo companies list the BCs for bullets used in factory loadings. This is useful information that I think all ammo companies should furnish both in their ballistic charts and on ammo boxes. Why? Because with so many folks out there owning ballistics programs for their personal computers, all you need to do is plug in muzzle velocity, bullet weight and BC and you can plot trajectories for any desired zero range.

Actually, any experienced handloader can guess rather closely the ballistic coefficient of any rifle bullet. For example, no roundnose bullet that I know of, from 6mm to .458, has a BC of more than .300. Between .300 and .400 we find the lighter-weight (lower SD) game bullets of spitzer or hollowpoint configuration. With BCs above .400, you’re getting into bullets of moderately heavy weight for the caliber and very sleek nose profiles.

Anything approaching .500 in a hunting bullet combines what are just about the optimums in SD and BC, like Hornady’s 7mm 162-grain SST at .550 and Barnes’ .30-caliber 180-grain XBT at .552. Typically, such extremely high BCs are found on boattail bullets with polycarbonate tips, like the SST. The Barnes, however, is the result of a very sleek ogive with an extremely small meplat–the diameter at the very tip of the nose.

The ogive, incidentally, is that part of the bullet from the bearing surface forward that forms the nose. Bullet profiles will show the ogive to be a radius or curved line, but Hornady employs a secant ogive whereby the tip of the bullet is formed by converging lines that are almost straight–like on a cone.


A bullet can be aerodynamically shaped, like the 120-grain 7mm bullet on the left, but because of its low SD or weight for the caliber, it will shed velocity much faster. If launched 500 fps slower than the 120 grain, the 175-grain bullet on the right will have caught up with the 120 at the 500-yard mark.

If we were to place a flatnose, a roundnose and a spitzer bullet side by side, common sense tells us that the spitzer is more streamlined than the roundnose and the roundnose more streamlined than the flatnose. It follows, then, that all other things equal, the spitzer bullet will drop less over a given distance than the roundnose one, and the roundnose job drops less than the flatnose. Add a boattail and you make a bullet even more aerodynamic.

As an example, let’s take the Barnes .30-caliber 180-grain X-Bullet, which is offered in both flatbase and boattail configuration. Both these bullets have identical nose profiles, so the difference in their ballistic coefficients is due strictly to their base shape. The flatbase version has a BC of .511, while the BT’s is .552. Percentage-wise, you’d think that was a significant difference, but in actual fact the BT would drop just .9 inch less at 500 yards than the flatbase, all other things being equal.

MAXIMUM POINT-BLANK RANGE
Another way of looking at trajectories is the zeroing-in of a rifle based on Maximum Point Blank Range (MPBR). Like midrange trajectory, MPBR doesn’t actually change anything regarding the bullet’s path; it’s just a different criteria for zeroing a rifle relative to that trajectory. For deer-size animals, MPBR is based upon placing a bullet in the 10-inch-diameter vital zone of a deer-size animal by holding dead-center on its chest, without having to compensate for drop.

Essentially, it’s like taking a perfectly straight, imaginary pipe 10 inches in diameter and superimposing it on a given trajectory. With the muzzle centered at one end of the pipe, MPBR is that distance the bullet would travel and still be within the confines of the pipe. Naturally, the muzzle would have to be elevated so that at its apogee, the bullet would just graze the top of the
pipe at midrange. So adjusted, MPBR would be that distance downrange that the bullet strikes the bottom of the pipe.

Consider a .30-caliber 165-grain BT spitzer bullet exiting a .300 magnum at 3,100 fps. According to the Sierra Reloading Manual, zeroing our rifle to print dead-on at 315 yards would give us an MPBR of 375 yards. With that same bullet at 2,800 fps in a .30-06, our MPBR would be 340 yards with a 285-yard zero–not as big a difference as you’d think, is it?

Most ballistic programs will compute MPBR; all you have to do is fill in the bullet weight, BC, velocity and the size of the vital zone. Naturally, you can input a four-inch vital zone if you’re hunting groundhogs or 18 inches if you’re hunting moose. Personally, I never subscribed to MPBR; I think it’s sloppy shooting. And now that we have laser rangefinders, there’s even less to recommend it.

  • Don

    WELL DONE

  • don lucas

    question: will simply adding more powder make a bullet go flatter or faster.

    • spot

      if you increase vel it will do both

    • tom

      It might, depending on circumstances. But there are so many variables that determine muzzle velocity which is what you are looking for here when seeking "flatter or faster".

    • Ed Brickey

      Faster does not always mean flatter, you begin to get into factors of twist rate and many other factors.

  • Stefan

    The ballistic diff with using rem express rifle in 22/250 55gr pap
    Or the v-max bullet same cal and grain. Thank you

  • james

    does a bullet dropped and a bullet shot from a gun drop at the same speed

    • tom

      yes. EXACTLY the same.

      • sarg

        only in a vacuumn

        • Anthony Rose

          Actually, in any medium, since both bullets are the same friction coefficient. You only need a vacuum for a bullet and something different, like a feather, to drop at (effectively) the same rate.

    • Justin

      9.8 meters/second^2 or approximately 32 feet/second^2

    • guest

      that was on Mythbusters ages ago. if you shoot a gun at the horizon, flat, and drop the bullet (just lead, no brass) at the same time, by the microsecond, they should in theory land at the same time.

    • STBro

      Velocity? No. If you go high enough and then drop one bullet and fire the other one at 17000 mph, one bullet will drop straight down until it either burns up in the atmosphere or attains terminal velocity. The other bullet will not “drop” at all since it will be in Earth orbit. Make sure to duck around 90 minutes after you fired that bullet …

  • tom

    Excellent article, thank you. I respectfully disagree that MPBR is sloppy shooting because its all about what the shooter is trying to do. Deer don't have bulls-eyes painted on them and by the time you get out your range finder (assuming you can afford one), check the range and figure out the hold-over, the deer might have moved. This is especially true in combat where another name for MPBR is battle zero.

    For those who compete in matches, you'll zero based on the exact target range and use pre-computed hold-over for variable range targets.

  • Zane Smith

    Ive never got real into ballistic but i;ve always been very good with shootin but i wna tto learn the science part of ballistics cause i think it would be cool to make my own bullet. it just seems like a hard thing to learn

  • Richard Wagner

    Sectional Density is NOT the relationship of the weight of a bullet to its diameter squared. It is the relationship of the weight of a bullet to its cross sectional AREA.

  • chris

    first awesome articale n thank u, secondely im trying to understand bullistics and guns more but i dont hunt alot so do u sites any other sites were I can find more about the mechanics of deffernt types of guns and firearms?thanks!

  • Eric Lougheed

    I've found this site because I was explaining trajectory , maximum range and range safety to my wife and realised there is an aspect of bullet flight that was never touched on in my army training (now 70 yrs past):
    Rifle bullets (and artillery shells) are spin stabilised by the rifling (obvious!) and the spin imparts gyroscopic forces to the missile; any gyroscope resists changes in attitude; what is the attitude of the missile when it hits the target? I was thinking particularly of the likely wound inflicted on the unfortunate recipient of a round negligently discharged at an angle approaching 45 degrees from horizontal.
    Imagination traditionally thinks of the missile maintaining an axis identical to the line of flight, but would not the gyroscopic forces debar this change of attitude?
    Can any kind soul point me to an appropriate source of wisdom, please?

  • Turk

    Is there an equation I can use to get tha proper bullet drop on my weatherby mark v 7 mm?

    • Daniel Woodworth

      I know very little of ballistics or its terminology (hence why I’m reading an article titled “Ballistics for Dummies”), but I do have some background in physics. From projectile motion, the equation for the vertical displacement of a projectile (bullet drop, in this case), should be y = v + (gd^2)/(2v^2), where y is the bullet drop, v is the velocity at the muzzle, g is the acceleration due to gravity, and d is the range.

      That’s excluding air resistance, of course. Including it makes the whole equation rather too complicated.

  • ometaclon

    I have a question, rifling the barrel increased the range and accuracy of the bullet. That we already know. From what I understand the bullet itself is rotating as it passes through the air. I am going to assume that a tumbling bullet is not as accurate and would have less range.

    So…

    is the bullet was formed in such a way that there was a slight ridge that would allow air to continue to rotate the bullet. almost like threads on a screw. Would this in fact increase accuracy and range of the bullet because bullet it self would be carving its own path through the air?

    • Firegun

      I would say no to that due to the fact any ridge would just cause friction and the bullet would just lose velocity faster and therefore drop faster. the point of the spin is to stabalize the bullet and therefore keep the bullet in its most aerodynamic position.

    • STBro

      First, the amount of spin is so high that “adding” spin aerodynamically does not add value. For example, under certain circumstances a bullet can stop all forward movement yet still be spinning. The purpose of the spin is “gyroscopic stability (Sg).”

      To induce spin, ridges or flight surfaces would need to penetrate outside of the laminar layer and any nearby shock waves.

      There is a slight ridge formed by the rifling in the barrel. Once a bullet is fired through a rifled barrel, it is “ridged.” Due to acceleration certain soft bullet alloys may cause a bullet to “slump” and it will change its ballistic coefficient. So long as the bullet is supersonic or sonic, the airflow across those ridges does not add to the bullet rotational velocity (however any slump would cause significant effects.) It is actually a windage loss from rotational pumping. Once the bullet goes subsonic, airflow interacts with bullet ridges. However, because bullet rotational velocity is vey high to begin with, the contribution of forces from drag in slowing rotation and ridged airflow in inducing rotation are very small and can be thought of as canceling out with regards to rotational velocity (in the subsonic part of the trajectory). For most small arms trajectory models, the three degree of freedom (3DOF) model is sufficient with gravity and drag as the primary forces.

      If you are interested in detailed bullet aerodynamics and 6DOF measurements google keywords “dtic” and “a229713.pdf” for an example.

  • Mark

    If you make the bullet do work against the air, the bullet will slow even faster…

  • STBro

    Really good article, appreciate the diagram.

  • Randy

    Thank you for an outstanding article for a new long distance shooter. It’s a start to a long education I can see now.

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