Bullet FlightBallistics will be covered in detail in a section devoted to the subject. For now I'll only discuss a few fundamentals. The moment a bullet leaves the barrel it begins to fall. I have been to the range and heard people talking about how their [insert bullet here] climbs for the first 50 yds. or so. The laws of physics do not work differently for these people or their guns. They just don't understand the relationship between the line of sight (LOS) and the bullet path (BP).
The LOS is perfectly straight. The sights on a rifle are on top of the rifle. If they are straight, and the bullet is always dropping, then the only way the two paths will ever intersect is if the LOS is adjusted to cross the BP at some point. That is exactly what we do. If the rear sight post is raised then the LOS will cross the bullet path. In fact, it crosses the bullet path twice. The bullet will steadily drop until it crosses the LOS again. I'll include a picture when I can get it scanned. If any of you have one scanned feel free to donate it!
The point at which the two paths cross the first time is referred to as "battle sight zero" in the US Army. If an M16's sight's are adjusted until they are "zeroed" at 25 meters, they will also be zeroed at 250 meters (where the two cross again). This means that out to 25 meters the rifle will shoot low, between 25 and 250 meters the rifle will shoot high, and after 250m the rifle will shoot low again. This is what people are referring to when the say that their "bullet climbs after so many feet". Their sights are pointed down at an angle like everyone else's.
- Between sights and the first intersection, bullet is BELOW LOS.
- LOS crosses BP, after first intersection bullet is ABOVE LOS.
- Bullet drops more and crosses the LOS. After this the bullet is below LOS again.
Bullets do not drop at a constant rate. As soon as a bullet leaves the barrel it is a prisoner of gravity and drag. The longer a bullet flies, the longer it is exposed to gravity, and the farther it will drop. When a bullet leaves the barrel it is moving very fast. It covers the first 30% of it's maximum range very quickly. Accordingly, the effect of gravity is very small during this period. In proportion, the drag effect is quite high. As the bullet slows the proportional effects of drag and gravity swap places. Once a bullet has flown 60% of it's maximum range, drag is very small, and gravity is causing the bullet to drop very fast. These topics will be discussed in greater detail in the section titled "Exterior Ballistics".
Advanced Marksmanship By David Reed
Most of the data and discussions which follows is taken directly or paraphrased from the Sierra Rifle Reloading Manual 3rd Edition. I have many books and manuals but Sierra's is by far the best. If you do not have this manual then I urge you to get it. All reloading manuals contain extensive disclaimers and Sierra's is no exception.
I am providing this information because I have not found it elsewhere on the Web. It would take days to convert all of their data to HTML and it would be full of errors, piss them off, and keep you from buying their book! These pages should not be considered a worthwhile substitute for their manual. They do good work and I encourage you to support them by buying their manual. I think I paid around $34.95 US for it and as I mentioned, it is my favorite. Speer, Nosler, and Hornady also have good references. When I need data, I usually compare all of them.
I've tried many bullets and can't honestly say that any brand is better than any other for my purposes. My .300 Win. drops everything I shoot with it. I have favorite bullets for each rifle that I own. It might surprise you to know that one of my guns shoots 180gr round nose bullets better than any other bullet I've tried! Don't be to quick to assume that a match grade bullet will fly better than others in any particular rifle. Bullet weight has a lot to do with it. (See section on rifle tuning where I discuss harmonics.) Try them all and decide for yourself. When the manufacturer recommends a bullet for a particular purpose don't try to read to much between the lines. A hollow point bullet is designed to expand rapidly, but if you are shooting whitetail with a .300 that is not a disadvantage! And now, on to exterior ballistics . . .
- Ballistic Coefficient
- Altitude and Humidity
- Uphill/Downhill Shooting
- Wind Effects
Ballistic CoefficientRather than try to calculate ballistics for every bullet made, it is easier to compare the ballistics potential of the bullet in question to one standard bullet. The potential of the standard bullet can be calculated very precisely. The drag deceleration of another bullet can be compared to this standard to produce a factor for calculating deceleration. This factor is known as the Ballistic Coefficient. It simple terms the BC of a bullet is a measure of it's efficiency. If we compare several bullets all fired at the same muzzle velocity, then the higher the BC of any bullet, the flatter it shoots, the better it bucks the wind, and the better it retains its velocity as it travels downrange.
For a given bullet fired at a known muzzle velocity, the BC of the bullet determines its trajectory. This is because drag is the strongest force acting on the bullet, and the BC governs the amount of drag. The effect of the BC enters mainly through the time of flight. The drop at any range is nearly proportional to the square of the time of flight. It is clear that a bullet with a shorter time of flight will drop less than one with a longer time of flight. Time of flight is affected by drag, because drag slows a bullet down. Since the drag gets less as BC gets larger, larger BC means less drop.
Time of flight also depends on muzzle velocity (MV). A large heavy bullet typically has a high BC (Inertial), but you cannot get the MV very high on a heavy bullet. So a high BC bullet may drop more than a lighter bullet fired much faster. For a comparison to be fair, you should also compare the final velocity and energy at the range in question.
It should be evident that between 600 and 1000 yards, the heavier bullet is actually moving faster and of course, carrying more energy. We should also note that after 1000 yds, the heavier bullet will be flatter than the lighter bullet, but this is pretty much out of the effective range of the rifle.
Look for the higher BC, but don't wear blinders. Consider MV, energy, and final velocity when choosing a bullet.
Altitude & HumidityDrag depends on the density of air and on the speed of sound. These depend on temperature, humidity, and barometric pressure. Sierra uses standard factors in their ballistics tables. The values are:
Altitude: sea level
Pressure: 29.53 inches of mercury (Hg)
Temperature: 59 degrees F.
You may think that if you develop a load at lower elevations and then go to the mountains on a hunt, that your round will shoot flatter. The air is less dense, however it will probably be colder, thus offsetting the difference. What may surprise you is that a bullet will shoot flatter in humid air than it will in dry air. That is because the molecular weight of water is less than the molecular weight of dry air. Therefore the BC increases when we go from dry to more humid air. However the difference is pretty small and probably not worth figuring out. The most dramatic effect on bullet performance is a change in altitude provided that the temperature increase is not that great. If you sight your rifle in on a cold day, and go to the mountains and it's not that much colder, you will see a difference in trajectory. The best way to calculate the difference is to use a ballistics program. You'll find a freeware/shareware version to download on my home page. If you would like one for Windows, I highly recommend JBM's On Target! Ballistics software. The author is very knowledgeable and his program is based on solid physics. It is the best ballistics program that I know of.
You should try to prepare a table which shows how your rifle will shoot over a reasonable range of altitudes. Once you commit to memory the altitude effect, you will be close enough to make accurate shots. The very best way is actually test your rifle under conditions that are close.
Shooting Uphill/DownhillBullet drop does not change very much when shooting uphill/downhill. But the rifle will appear to shoot high. In fact it shoots high by almost the same amount whether you are shooting up or down. Therefore you must adjust your hold or change your scope when taking shots at high angle, especially as range increases. If you know what the drop (d) is for your bullet at any given range, you can use the following table to calculate the amount your bullet will shoot high, in inches.
Think about a 600 yd shot downhill at 40 degrees -- Instead of a 50" correction we are talking about a 40" correction. Check your tables or ballistics program for your rifle. If you would like to know what it is right now, then try JBM's online ballistics calculator! Just use your "back" button on your web browser to return.
Wind EffectsThis is a big one. You must understand wind effects to shoot well. Formulas abound for this, but as we'll see, exact calculations are of little use. There is no substitute for practice. For our purposes we will refer to wind direction using the clock method. 12:00 is straight in the face, 6:00 is on the back of the head. Vertical deflection of bullets is very slight, at most a few inches at long ranges with 20+ winds. We will ignore head & tail winds (HTW) in this discussion. You will have to find the right place to hold, or adjust your sights slightly, for this component. If we discount HTW, then the wind effect of a 2:00 wind is the same as a 4:00, 8:00, and 10:00. Thus we only need to remember wind adjustments for 1,2, and 3:00. To be exact, you could calculate wind using 2:15, 1:48, etc. Those of you who are sailors know that wind is constantly shifting. Anywhere you are shooting, the wind at the target will always be different than the wind where you are shooting from. It changes all the way to the target. It may be 2mph where you are, 7mph halfway down range (from a slightly different direction), and 5mph at the target (from a slightly different direction). Usually the wind clocks or veers. Over a period of 10 minutes lets say, the wind will be 7mph for 3 min., then clock 5 degrees to the right for 5 minutes, then veer back to the left 5 degrees. Frequently there will be a brief lull in the wind, then it will reappear from the new direction. Aviators know this too. The wind swirls across the earth in large systems, each made up by an almost infinite number of microsystems. When on the water, you can see "wind lines". They look like areas of the water that have ripples. On big grassy fields you can see this too.
In the morning, when the sun comes up, the air and ground begins to warm. As the ground warms, convection currents form cause air to move uphill. The western slope of a hill will have stronger currents than the eastern slope.
In the evening, the opposite occurs. If you are near the water, the land - sea heat differential effect also occurs. Warm air rises over the ground and is replaced by cooler air over the water. This is known as an offshore breeze and occurs mid-morning. As the ground cools in late afternoon, the reverse occurs, although not as strong. After the sun has gone down is when the onshore breeze gets stronger. During the day, late morning - through afternoon, you are in the doldrums where nothing much is happening (minus the presence of a system). A shooter must study these winds as they swirl along the ground.
Shooters cannot see ripples in the water, they must look for other signs.
Mirage's move with the wind just like grass does. When shooting across flat ground you can see the shimmer of the heat rising off the ground. If the shimmer is straight up, there is less than 2mph wind. The mirage will lean away from the wind up until about 20mph when it disappears almost completely. Watch trees and grass. With a 2-4mph breeze the grass will move and you will see the eddies of air moving the ground. Fields are excellent places to read the wind because you can see the air currents. The leaves will also shimmer and and small limbs will move. 5-9mph and the grass starts to lean pretty well. Smaller limbs on the trees are moving constantly and thicker limbs barely move. 10-14mph and the thicker limbs are moving and the grass is being pushed strongly during the stronger gusts. 15-20mph and the trees are swaying and the grass is in constant motion.
Be aware that trees block the wind on fields. The windward side of the field will not have as much air as the leeward because the trees are blocking it. As you look across the field you will be able to see the stronger air moving at the center and leeward sides. (Pronounced "looward"). Now that you understand a bit about reading wind, you can see why complex calculations are fruitless. You must average these effects, always giving more credence to wind that is closer to the target (where the bullet is moving slower). Only with practice will you become good at this. For target shooters, those who can read wind well will always outshoot those who can't, all other things being equal. Wind has a dramatic effect on long range shots.
Recall that I said we would only consider winds from 1, 2, and 3. Look at a ballistics table for your bullet and use these factors to determine crosswind. (Or use JBM's)
If your bullet moves 36" inches at some range with a 3 or 9 wind, then it will move about 18" with winds at 1,5,7, or 11. You only need to remember wind effects for your bullet at each range where wind is an issue. Then remember two other numbers -- 50% and 90%, 1/2 and "almost all of it". Now look downrange and average it all out, come up with your number, and shoot. If you have time, figure windage for lulls and strong winds both. If you can't get your shot off in a lull, you'll have to adjust, but you'll know how much.