Reloading: ‘Ballistics for Dummies’ Part I

Webster’s Dictionary tells us that this word means the science that studies the movement of objects (such as bullets or rockets) that are shot or forced to move forward through air or space. The word is ballistics.

To summarise, it’s that part of handloading and shooting that is governed by rules based upon equations or formulae using the basic principles of physics. With modern computing available to all of us there’s no reason to bore you with line after line of equations. I’ll simply stick to the principles involved. For our purposes there are two connected categories, internal and external. Put simply, the first deals with the addition of energy and stability to the projectile and the second deals with its progressive loss due to external factors.

THREE TIMED ELEMENTS OF INTERNAL BALLISTICS

Pulling the trigger and releasing the sear initiates the first calculation point – lock time. The primer strike stops the clock and detonates the explosive. Enter sector two, from the primer strike to the movement of the base of the projectile. Our primer blast initiates the deflagration of the propellant, thereby generating the gas pressure engine that drives the bullet. The level of pressure is a function of the type and volume of the propellant together with available case volume, bullet containment and weight, as well as the firearm dimensions. The third and final sector is the time taken from the first movement of the base of the bullet until it exits the muzzle.

 

PRESSURE, CIP VS. SAAMI

The cartridge Maximum Average Pressure (MAP) is the relevant figure quoted by both the European CIP (Commission Internationale Permanente pour l’Epreuve des Armes à Feu Portatives) and American SAAMI (Sporting Arms and Ammunition Manufacturers’ Institute). Whilst the two bodies both employ piezo pressure transducer technology, CIP and SAAMI also recognise data from the copper crusher process (the measurement of deformation of a copper pellet – although only rimfire for CIP).

In any event, their methodology differs. CIP also generally quotes it’s results in bars or megapascals (multiples of atmospheric pressure) whilst SAAMI uses psi. Take .308 Win as an example, CIP quote 4150 bar, 61000 psi MAP whereas the comparable transducer figure from SAAMI is 62000 psi. It is fair to observe that SAAMI generally quote a higher figure. To their credit, the CIP database is more detailed, including proof data for pressure and Kinetic energy. On the other hand, SAAMI quote data for various bullet weights in each calibre. Only a few manuals take the trouble to quote such data. My favourite, Modern Reloading Second Edition from Richard Lee carries both SAAMI PiezoTransducer psi and Copper Crusher Units of Pressure, cup. As a crude rule of thumb, the cup number is around 10% less than the comparable psi. Links:- http://www.cip-bobp.org/home http://www.saami.org/

 

WINDING IT UP

So, we’ve kicked the butt of our projectile. Adding spin is necessary in order to create flight stability as we accelerate it along the barrel. The crude rule of thumb is that, for a given calibre the rate of twist should get tighter as the projectile weight increases. The relationship between calibre and bearing length is another factor. As we know, the common nomenclature gives us the length of rifling that will produce one revolution i.e. 1 to 10 gives us one whole turn in 10”. Rates of twist vary from antique Marlin 444’s with 1 in 38” to modified AR’s with 1 in 7”. At the slowest end we have the risk of basic instability, the projectile rotating too slowly to overcome the effects of bullet shape, gravity and atmosphere.

From my unintended experiments in .44 Rem Mag I can confirm that around 35000 RPM is the slowest rate that will reliably create stability over the shortest ranges. At the other extreme, massive muzzle velocity and very tight (say 1 in 8” can create over stability and excessive centrifugal force; sufficient even to cause the bullet to blow up. Over stability generally becomes an issue only when the trajectory of the projectile becomes extended, the induced stability fighting the upsetting forces created by drag and gravity, almost inevitably inducing tumbling. Two formulae have become established as a means of establishing an approximation of suitable rates of twist based upon calibre, bullet weight, length, external factors and a number of constants. The earliest is the Greenhill Twist Rule, and more recently, the Miller Twist Formula. Both are well documented on the web with ‘ready reckoners’ available to take the misery out of doing the maths!

As our projectile departs the muzzle we can complete the most popular and simple equation, that for muzzle energy. We have E (muzzle energy in ft/lbs) equals V² (velocity in fps squared) x M (bullet weight in grains) all divided by 450,240.

 

FLYING SOLO – THE TAKE-OFF

Our projectile now departs the comfortable mechanical order of the rifled barrel and takes on the external forces that exist en route to the target. The rifling has done its job and our pill is spinning on its’ axis. As the bullet base passes the muzzle crown the first input is that from the pressure cone of gases that not only continue to apply an accelerating force for several inches but also overtake it. (In artillery shells it can extend for many yards). If the muzzle is close to the ground the cone will be deflected and in turn, apply a minute degree of yaw to the projectile. From the onset the bullet is not actually pointing in the direction of travel.

As a result a secondary motion is now induced, axial precession. Here a second axis of rotation is not along the centreline of the bullet but at a slight yaw angle to it, causing the tip to describe a small circular motion. Any crosswind and the reaction of the spin will induce not just drift, but another yaw moment, described as the Magnus Effect.

 

THE F W MANN CORKSCREW

A third motion may also be induced whereby the entire projectile describes a spiral (corkscrew) motion around the true line of trajectory. Firing a tracer round makes this motion easy to spot. This motion was first written up by Dr Franklin W Mann in The Bullets Flight after he placed a series of intermediate boards between muzzle and target, then drew a thread through all of them to illustrate the actual trajectory. He was amazed by this result, especially since, for a given arm and ammo, the track was often repeatable shot after shot. Next month, we conclude the trajectory stuff.