Welcome back!  Today, let’s talk about external ballistics.

Bullet coming from S&W by Niels Noordhoek

Anything and everything on earth is affected by gravity.  Objects fall towards the earth at a constant rate, known as the gravitational constant (9.8 m/s²) .  I hear those sci-fi writers again.  Yes, if we were on the moon, or Mars, or somewhere else, that constant would be different, and the ballistic flight will be different, but let’s get there in a bit shall we?  Impatient Sci-Fi writers!  As a quick reference, Moon Gravity is roughly 1/6th that of earth, and Mars is roughly 1/3. Newton tells us that an object in motion remains in motion unless acted upon by an outside force.  So in a theoretical, gravity free environment, the projectile would just keep going straight, in the last direction it was propelled. Of course, Gravity isn’t the only thing that affects a projectile.  The medium it flies in also plays a big part, by adding drag.  The air itself slows the projectile down.  In a vacuum there would be no aerodynamic drag, and the projectile would keep its velocity, until acted upon by something else.

That Newton guy is everywhere isn’t he?

But the air is very rarely perfectly calm.  Blowing winds, or even minute changes in atmospheric pressure can affect the flight of the projectile.  Their effect is minute, but can lead to drastic changes to the flight of a projectile. Famed weapons and bullet maker Winchester makes a fantastic free Ballistic calculator.  Use it on the web, or get the App for your iPhone here.  Let’s use it for a second, and demonstrate how a simple cross wind can affect a projectile.

So for our example, let’s shoot a 180 grain projectile from a .30-06 rifle.  I see that with this bullet (I used a Ballistic Silvertip for these examples) and a gentle 5 mph cross breeze fired at a target 300m away, the bullet moves 4.2 inches off of the intended point of aim.  What happens if we push that wind up to 10 mph?  8.4 inches.  20 mph? 17.5 inches.  Now let’s keep the winds the same, but lower the weight of the projectile to 150 grains?  Care to make any predictions? At 5, 10, and 20 mph with a 150 gr projectile (all other factors remaining the same) we get a drift of 4.7, 9.5 and 19.7 inches.  Now think of your average sized human or tasty animal target.  20 inches off at 300 meters becomes a huge difference when your life, or your supper is on the line.

Now let’s combine the two.  Gravity affects the projectile, constantly pulling it towards the Earth (or Bubblegum Planet.  Don’t worry, I didn’t forget about you Sci-Fi writers).  The atmosphere itself works against the projectile, adding drag, and affecting its flight through winds or pressure changes.  So unless bullets are fired into a vacuum with no gravitational effect, something will cause their flight to change.  Countless video games have you aiming crosshairs at a target, and squeezing the trigger, felling bad guys regardless of range.  Most of these top-notch shooter games don’t have wind effects either.  I guess it would be too hard to program, and frustrating for the player to have to calculate drop and drift on the fly while moving from cover to cover in his simulated war.  I don’t know about you, but just thinking about that makes me respect the guys that do it for real just a little bit more.

And now a reader question:  @bleflarjackson asks: “How would being fired in 1/3rd G affect the behavior of a bullet? Would the powder loads have to be reduced?”

Good question.  Let’s look back and think about it.  If the gravitational constant is 1/3 as strong as that on earth, then the effect on the projectile in flight would be 1/3 as much as well.  Everything else being the same, the projectile would fly much further.   Keep in mind that the different atmospheric density on another planet, say Mars, would affect the acceleration and drag on the bullet as well.  A bullet fired on Mars would go a lot faster for a lot longer, and a lot farther than the same one fired on earth because the atmosphere is about 1% as dense.

Now the question of reducing powder loads is an interesting one.  The pressure the cartridge produces by burning the powder is constant.  It works underwater or in a complete vacuum because the powder itself provides an oxidizer, so no outside air is needed.  Whether on Earth or Mars, or in a pineapple at the bottom of the sea, that self-contained cartridge will detonate the same way every time.  Because only the ballistics are different, the powder load would not need to be reduced, unless you were trying to accomplish two things:  Match the ballistics of the projectile to how it would fly on Earth, or compensate for recoil.  The gun would only weigh 1/3 what it did on Earth, but the recoil forces would be the same.  While not a problem for smaller, simpler weapons, Large caliber guns that are on the limit of human endurance and strength on earth would be impossible to hold on to.  Artillery and other large cannons stand the chance of destroying themselves if the charges are not reduced.  There are methods of controlling recoil, but we’ll get to that in a future episode.

X-PLane 9.7, By Laminar Research

Flight Simulator Design guru Austin Meyer of Laminar Research added the functionality to fly around on Mars to the X-Plane Simulator back in the year 2000.  He wrote an essay on what it was like to fly on Mars, and although the physics of free flight are different from that of ballistics, they do share enough similarities for us to draw a comparison.  Here’s an excerpt on learning to fly on mars:

“Sound easy? IT ISN’T, BECAUSE WHILE YOUR GRAVITY (WEIGHT) IS ONLY ONE-THIRD OF EARTH’S, YOUR ==>INERTIA<== IS STILL THERE IN FULL FORCE! So you are flying with only 1/3 the total lift of what you are used to having to stay in the air, which seems fine UNTIL IT COMES TIME TO TRY TO TURN OR FLARE!!!!! THEN you see that while the lift for STAYING airborne is only 1/3 of Earth’s, the INERTIA, and thus the lift needed to CHANGE DIRECTION (this includes the landing flare!) IS STILL THERE IN FULL FORCE! The problem is, you DON’T HAVE THAT KIND OF LIFT, SINCE THE AIR IS SO THIN!
Bottom line: All airplanes on Mars are AIRBORNE TITANICS: Ripping blissfully along, unaware of their impending doom due to their inability to TURN against their tremendous inertia.
Landings are impossible without arresting gear. If you can work the flare out right (it IS possible with advance planning) then you will touch down doing about 400 mph. Now how do you stop?
…
Speaking of which, CRASHES are interesting. No air drag to slow the tumbling planes down, and little gravity to drag them to a stop against the ground! Crashes look like “the Agony of Defeat” from the Olympics where the guy on the downhill ski-jump bites it near the top of the ramp and tumbles on and on and on, powerless to stop an accident that started hundreds of yards earlier! (though on mars, at 400 mph, your plane will tumble across the plains for MILES!)”

Read the whole thing here, and while you’re there, download the free demo of X-plane 10, and try your hand at the world’s best desktop flight simulator.

So now we know a little bit about how a bullet flies, let’s think about a common problem.  How does one aim a ballistic projectile?   Because bullets will fly in a curved path (usually downwards towards the ground, unless yet again those Sci-Fi Writers have added multiple gravity sources to their bubblegum planet) getting that projectile to its intended target is a tricky problem.  Adjusting the point of aim upwards will allow the projectile to fly further along its arc before it impacts the ground, or its target.  This is taken to extremes with long-range artillery.  These guns shoot in high arcs, taking the range of their projectiles into the many tens of Kilometers, with the ability to clear cities, mountains, and anything else underneath them.  Some of them get so large, and the ranges so extreme, that their orientation to the rotation of the earth has to be taken into effect, because the target will have rotated out-of-the-way of the projectile by the time it gets there! Aiming is accomplished by knowing the ballistic trajectory of our projectile, and predicting where the projectile will be along that trajectory when it reaches the target.  Being able to guess or measure the range to the target is the key here to being accurate. Recent advances in laser rangefinding technology has pushed the prices down far enough that this is now available to the common hunter and sport shooter.

Of course, guessing the range and predicting bullet drop at that range is merely half the battle.  What about drift due to wind or other atmospheric phenomena?  Well, there lies the secret art of shooting.  Reading and predicting the wind and how it will affect your projectile is the mark of a true shot.  A Marksman develops the ability to read the clues around him, and around his target.  From the sway of trees, billowing of clothing, even the shimmer of a heat mirage in very long-range shooting will tell a shooter how the bullet will react as it flies.  Of course, for you Sci-Fi people, the indicators would change depending on the atmosphere and gravity of your planet.

So that’ll wrap things up for this episode.  Tune in next week for more External ballistics where we’ll discuss stabilizing our projectile against all of these outside forces.  The projectiles fight back!