Simple Ballistics

This is a follow on from a link at Alphecca to some comments about Varmint Ballistics

Current Gunzines are so much bull shite that the chances of a newcomer to shooting learning anything from them or finding references to any decent followup reading are close to zero, so here goes...

How a gun works

A gun uses heat energy stored in the powder to give the bullet energy. In this respect it is a heat engine, just like a steam engine, Automobile truck or ship engine, or a jet or rocket engine. Many of the analyses of these other engines work pretty well for guns. Go to your local public library or college library (not the magazine rack at the mall), and there should be some good references with all of the formulae and explanations.

Look especially at the pressure displacement graphs for engines (in steam engines these were called indicator diagrams. These were invented by James Watt, whose great discovery was not the steam engine (that was Newcomen) but what heat did inside an engine), and some of the ideal gas equations.

Geoffrey Kolbe at border barrels wrote and compiled an excellent ballistics handbook about 5 years ago. It is probably worth looking up his website to see if he has any left, or trying www.abebooks.com for a second hand copy.

Kinetic (movement) energy is half the mass of the object times its' velocity squared.
Therefore to double the velocity of a bullet you need 4 times the weight of powder to supply the energy.

The energy content of smokeless powders is pretty similar, weight for weight. (not volume for volume as pistol powders are porous or flattened to speed burning, as many pistol loads need to finish burning before the bullet leaves the case. with rifle loadings, some of the burning goes on up the barrel).

The efficiency of the cartridge bullet and barrel combination depends mostly on expansion ratio. (just like a car does, so a diesel with larger expansion ratio is able to turn more of the heat energy from the fuel into horse power turning the wheels, than a gasoline engine with lower expansion ratio is able to).

Each combination of case capacity versus bore volume and bullet weight has an optimum load.

This will use a powder of a given burning rate to prevent the pressures rising too high for the barrel to withstand.

Optimum barrel lengths for different loadings vary, for example the optimum, for a .22LR, is about 14 inches, beyond which the bullet begins to slow again as the gas pressure is lower beyond this point than the friction acting on the bullet.

The high thermal efficiency of a .22LR rifle is indicated (very, very approximately) by the quiet muzzle blast, most of that heat energy has gone into speeding the bullet and heating the barrel.

Compare that to a short barreled magnum rifle or pistol... Much of its energy from the powder is coming out of the barrel as flash and blast, not driving the bullet, but where high velocities with heavy bullets and a quick handling light gun are needed, there is little alternative.

Even for benchrest there is a trade off between short rigid barrels that give more stable shooting and longer and therefore whippier barrels that give more velocity and therefore less wind drift.

How to get more buck for your bang

There is some extra efficiency to be gained from:

short fat cases (better ignition as the powder is all close to the primer)

larger calibres (less cold bore area absorbing heat)

and sharp shoulder angles on the case (combustion taking place in the case not up a cold barrel)

Compare these to the means of getting more efficiency out of a diesel or gasoline engine... Higher compression ratios (more expansion) domed or pent combustion chambers as opposed to side valve combustion chambers or indirect injection diesels (less heat loss). Short stroke bores(less heat loss).

There is also some tinkering that can be done with powder. The gunwriters on the net site from Finland ( http://guns.connect.fi/gow/gunwriters.html ) says some very interesting things about cool burning powders (along with a lot of other interesting things about guns in general).

While scientists in Britain worked on a smokeless powder with exactly matched nitrocellulose and nitro glycerine contents for maximum heat value per grain (nitrocellulose burns to give excess carbon monoxide, tri nitro glycerine burns to give excess oxygen, put the two together and there is more heat energy to be had, this combination is called a Double base powder).

Mendeleyev (also spelled but mis pronounced as Mendeleev) the genius who came up with the periodic table of elements, and thus in chemistry ranks somewhere near to where Darwin does in biology, reasoned that including salts in the powder that would break down to give water or carbon dioxide, would cool the flame temperature, but, that the light gas molecules would be easier to accelerate up the barrel of the gun, so propellant effect would be the same.

Thus the Russians came up with an equally effective propellant that was a lot less aggressive to barrels and gave less heating during prolonged firing. (Cordite, as the British double base powder was called, was renowned for attacking the first couple of inches of rifling due to its' high flame temperature).

What happens to all that mass in the powder?

It becomes mass of hot gas that must be forced up the barrel behind the bullet. In other words, as charges get heavier, we have to devote more and more energy to propelling the gas itself, reckon on about half the weight of your powder charge being propelled along behind the bullet in the barrel.

When it pops out at the end, it is adding to recoil, the hotter and denser it is at that point, the more it will kick, bang and flash.

Recoil is momentum, which is mass times velocity, the faster that gas goes...

Now for something counter-intuitive (gun freaks are good at this sort of thing)

A big long posting by Boots Obermeyer over at Sniper country upsets the idea that reducing barrel friction will increase velocity.

Boots, who has probably forgotten more about guns than I will ever know, found that he was getting lower velocities (and I think lower pressures) with molybdenum disulphide coated bullets.

What he put this down to was; the slippery moly coated bullet was moving off down the barrel faster and so the powder was forced to burn in a larger volume, and therefore burned less efficiently, hence lower final velocity.

Now what about rifling?

Having to spin a bullet is a waste of energy. I'm too far away from my text books and too lazy to work out the formulae myself for how much energy is wasted.

I think we are over due a look at how to do without rifling in small arms:

it wastes energy we could use for velocity,

it complicates manufacture,

it attracts wear, erosion and corrosion, and,

it complicates accuracy, with a bullet flying a complicated 3d cork screw trajectory instead of a simple 2d trajectory (See Mann's; "the Bullet's Flight" reprinted by Wolfe).

Anyone out there want to design a streamlined aerodynamically stable projectile that does not require a heavy sabot to be accelerated up the barrel with it?

After all of that: shoot whatever does the job...