JOHT 59: Faster Than a Speeding Bullet

[stickmaker]

The Joy of High Tech

by

Rodford Edmiston

Being the occasionally interesting ramblings of a major-league technophile.

Please note that while I am an engineer (BSCE) and do my research, I am not a professional in this field. Do not take anything here as gospel; check the facts I give. If you find a mistake, please let me know about it.

Faster Than a Speeding Bullet

In many ways, the history of speed is the history of human technological development. While this article will mention aspects of the overall history of speed, there is one class of object which will be focused on. That's because this class of object has such a long history of being pushed faster and faster that it has become synonymous with speed.

Bullets long predate firearms. Cast lead sling bullets go back well over two thousand years. There are cast 4th Century BC sling bullets with a winged thunderbolt imprinted on one side and "Take that" in Greek on the other. (Additional mottos found on ancient sling bullets were "Ouch," "For Pompey's backside" and even dexa (Catch!).) Lead is denser than most rocks, giving more punch on impact, and lead bullets cast in a mold were consistent in weight and shape, and therefore behavior in flight. However, there was a huge variation in both slings and bullets used by different slingers. Some of the latter were more than half a kilogram. (Forget about slinging it, just dropping it on someone could kill them!)

Maximum velocity of a bullet or stone from a sling is under a hundred meters per second, likely well under. Many learned modern texts make claims of around 30 m/s initial velocity, but this contradicts both ancient accounts of range and effect and modern tests. These latter agree that a good slinger is capable of more than twice that speed. (Arrows from a powerful traditional bow can slightly exceed 100 m/s. I believe the modern record is nearly twice that, using specialized equipment. However, arrows have more aerodynamic drag and slow more quickly than sling bullets.) Even with the mechanical advantage of the longer radius of throw offered by a sling, the human arm just couldn't manage anything much faster. There were other ways to launch bullets, some of which combined sling pouch and bow. (The ancient Romans were particularly good at developing such methods.) None were much of an improvement, at least in terms of velocity. However, that changed with the adoption of firearms.

It needs to be noted that before the age of modern science, measuring the speed of fast-moving, small, flying objects was pretty much impossible. There were wild speculations on how fast sling bullets went. Some accounts claimed they became white hot from air friction! (The practice by some armies of heating pottery sling bullets before launching them - using wetted sling pockets - to hopefully start fires in an enemy camp may be the root of this myth.) The arrival of firearms only made things worse. 

The first really good method to determine bullet velocity appeared in a book published in 1742, called New Principles of Gunnery. It was written by Benjamin Robins, an English mathematician with an interest in ballistics. This was a very influential book, among other things introducing military men to Newtonian physics.

 

For his work, Robins invented (or at least was the first to formally describe) the ballistic pendulum. His first version was a heavy iron weight with a wooden board covering its face. The bullet was fired into the board perpendicular to the surface and was embedded, transferring all momentum in an inelastic collision. This caused the pendulum to swing along a curved scale. Measuring the swing and doing some math gave the velocity of the bullet.

Robins' initial velocity measurements were so much higher than expected that he wasn't certain he believed them. He reviewed his procedures and his equipment and repeated the experiment. The velocities remained high.

That was not the only astounding discovery (for the time) made by Robins. He determined that the air drag force on a bullet (largely because the velocity was much higher than expected) was many times more powerful than the force due to gravity, and that it rose sharply with increased velocity, which upset many preconceptions. Robins' book started a chain of firing tests, instrumentation developments, and so on. It also contributed to the development of artillery towards the end of the 18th century and was responsible for introducing calculus to the syllabus of many military academies. In fact, Benjamin Robins is considered one of the founders of modern aerodynamics and the father of modern gunnery. Before this book appeared, gunnery was simply a matter of guesswork, though it was often educated guesswork. After this book was published, gunnery became an exact science. The work was so influential that the famous Swiss mathematician and physicist Leonhard Euler himself translated this book into German.

The ballistic pendulum worked and was fairly accurate, but there were problems. Even for handguns, the rig was massive. Kinetic energy increases in direct proportion to the increase in mass and with the square of the increase in velocity, so rifles greatly added to the problems. Canon - their projectiles no faster than those of sidearms but far more massive - were much worse than rifles when it came to catching what they tossed. In 1781 a ballistic pendulum was constructed with the intent to measure the velocity of cannon balls massing just 1.4 kg; it had a pendulum massing about 315 kg. During the period of 1842 to 1847, Major Alfred Mordecai from the United States Army tried to determine the muzzle velocity of larger guns using a ballistic pendulum massing over 4215 kg. This was mounted between two large brick towers. The rig could only measure velocities for 32 pounders at most. It was estimated that a ballistic pendulum to measure velocities for the largest weapons then in use would require towers as large as those on the Brooklyn Bridge!

Later methods measured - through various means - the time required for a bullet to traverse a carefully measured distance, the most successful ones using electricity. Most modern devices - usually called chronographs, because the heart of each device is a clock capable of accurately and precisely measuring tiny intervals of time - still use this method, usually through light. Photosensors detect the reduction in ambient light as a bullet passes over the beginning of the measured distance to start an electronic timer, and the similar sensor at the end of the distance stops the clock.

Early black powder firearms had muzzle velocities under 300 m/s (which is a fortunate coincidence, because at speeds much higher than this the pure lead of early bullets begins to strip off and deposit in the bore in excessive amounts). Later black powder guns generally topped out a little under 700 m/s, and required either hard lead alloy bullets or a paper-patched ball to avoid leading the barrel. (Note that many muskets - smoothbores without rifling - had bores deliberately larger than the bullets. In large part the extra room helped with loading when the bore was fouled with powder residue in battle, when cleaning was unlikely. The patch filled in the gap to make a seal, as well as reducing leading. 

Keep in mind that, given the long and widespread history and variety of intended of usages of black powder firearms, the range of variation in performance is huge. Therefore, these statements should taken as generalizations.

More powder won't increase velocity by much over these values, and requires either very strong firearms or a huge risk. One reason for the non-linear speed increase is that kinetic energy increase mentioned above. Doubling projectile velocity (in a very simplified situation) requires four times the chemical energy converted into motion. Even loading four times the powder behind a bullet won't actually double the velocity, because of multiple, limiting factors. For example, a short barrel provides less working distance. However, a very long one many result in a lower muzzle velocity, due to the drag of the bullet down the bore as the gas behind it expands and exerts less force. Maximum velocity results usually come from a bore length designed for the powder charge, or vice versa. Even some modern firearms are referred to as "overbore" if the cartridge they use contains more powder than can be efficiently burned in the bore. Many magnum handguns are like this. Which is why many magnum cartridges gain significant bullet velocity in the longer barrels of rifles. Just don't go too long... (Many lever-action carbines with barrels under twenty inches are chambered in .357 Magnum, .44 Magnum and so forth.)  

More modern propellants than black powder made achievement of velocities over 600 meters per second not only practical but easy. By the early Twentieth Century velocities for lightweight bullets in front of large powder charges were exceeding 900 mps. Specialist firearms - such as early anti-tank rifles - could exceed this, though at the cost of fast wear and a very short service life. Today the absolute best performing normal rifles can just break 1300 mps. 

However, also working against high velocities for bullets is the fact that a projectile driven by expanding gasses can't move any faster than the speed of expansion of those gasses. That speed in turn depends on the molecular weight of the gasses and the chemical energy released, which in turn depend on the propellant composition and combustion temperature. There is also the limitation of how quickly the propellant combusts, which rises with chamber pressure. Bullet velocities can approach the burn rate of the propelling powders but never exceed or even match those. Given the inefficiencies involved with transferring energy to a projectile, that means 1350 mps is a rough, practical limit. The absolute limit for smokeless powders appears to be around 1600 mps, and for that you need specially formulated propellants and carefully designed firearms.

One trick to increase bullet speeds is the squeeze bore. For this, the bore of the firearm is tapered, and the bullet designed to squeeze smaller as it traverses the length. Again, this technique is very rough on the gun, which consequently has a very short operational life.

Another trick is the discarding sabot. A tough but light casing (aluminum and some polymers are common) encloses a long, slender, dense projectile. This gives a low total weight and a large base area for the expanding gasses to work on, but once the projectile leaves the bore the outer casing falls away. This gives a very aerodynamic shell moving at very high speed. 

Gas propellants have been evaluated for artillery and tank guns. Besides providing a faster speed of combustion and a lower molecular weight, this would also allow tailoring the muzzle velocity by injecting just enough propellant. However, so far this trick hasn't provided enough benefit to compensate for the disadvantages. The biggest one being the need for new or modified equipment.

While these techniques do provide significant increases in projectile velocity, they still are limited by the speed of combustion of the propellant. 

One of the most difficult things to convince early critics of rockets about was that a rocket could exceed its exhaust velocity. Part of this is because a rocket gains velocity by a different mechanism than bullets do. A well made rocket can, in fact, make a change in velocity much greater than the exhaust velocity. Because of this people who understand rockets have long thought that a rocket gun would prove superior to a conventional firearm. (How long? Buck Rogers was using a rocket gun in the late Twenties, and was likely not the first.) However, the acceleration of a rocket is inherently lower than that of a bullet (though some rockets have been flown which pulled hundreds of gees, that pales before firearms, which can accelerate a bullet at tens of thousands of gees). 

The (in)famous Gyrojet pistol and rifle were seriously limited by this. The weapons were smoothbore, the spin provided by canting the rocket ports at the rear of the projectiles. Those "bullets" were rather large, since they had to carry their propellant with them. They didn't reach maximum velocity - or maximum spin - for some distance after leaving the muzzle. This made them less effective at short ranges than a traditional firearm the same size and weight, since they were still gaining speed. Because they didn't spin up to full speed until some time after leaving the muzzle they were also much less accurate, since they didn't properly stabilize until physically beyond where the shooter could affect the path. Finally, once the fuel burned out you had a low-density projectile (bullet in front and hollow rocket in back) with a large frontal area. This was not conducive to velocity retention.

Rockets do have advantages, of course. They got us to the Moon, after all. They have also given us the fastest speed (relative to the Earth) for any large object humans have made. The Stardust sample-return capsule was the fastest man-made object ever to reenter Earth's atmosphere (12.4 km/s at peak). This was faster than the Apollo mission capsules and 70% faster than the Shuttle Orbiter.

This brings up an interesting point. More people have walked on the Moon than have driven faster than 1200 kph. (This may no longer be true when you read this, since land speed record attempts are ongoing.) Going fast in space is easy. Without friction you just keep building speed for as long as you can produce thrust. On the ground, you have multiple sources of friction. Especially if you're on wheels. Friction eventually balances thrust, setting the ultimate limit for speed. 

Aircraft remove all sources of friction save for air resistance and internal engine friction. Small surprise that early aircraft soon eclipsed the speed of automobiles and trains. Today, the fastest manned aircraft ever to fly is the now-decommissioned SR-71, which could exceed Mach 3. The X-15 rocket plane - actually a winged, suborbital spacecraft, rather than an aircraft - came close to Mach 7. The Shuttle (or Space Transportation System Orbiter, also now decommissioned) hit Mach 25 (8,200 m/s) during reentry. In orbit, it was actually traveling at around 8,100 m/s. To reenter the atmosphere, the Orbiter fired its Orbital Maneuvering System rockets - the smaller nozzles at the rear - to slow below orbit speed, removing about 300 mps. However, as it dropped it picked up speed from the fall; hence the reentry velocity being higher than the orbital velocity. (These numbers will vary depending on the Orbiter and the mission flight profile.)  

Most of those reading this probably know that a few ground vehicles have exceeded the speed of sound. You're probably also aware of the first supersonic flight. However, how many of you know what was the first object to exceed the speed of sound (~330 m/s)? It wasn't a bullet. Many early firearms could throw bullets faster than this velocity, even muskets. However, they came much later than the accomplishment. 

The first man-made object to exceed the speed of sound was likely a piece of rope or cord. You see, the crack of a whip is the sonic boom produced when the tip exceeds the speed of sound. 

Kinetic energy is a very good way to do damage to a target. Researchers - for both military and civilian applications - have tried multiple tricks to give bullets a higher velocity than a chemically powered gun can provide. There have even been studies of dropping objects on targets from orbit. (One concept was named Hammer of Thor.) 

The technique of using a gaseous propellant was mentioned above, as well as its limitations for field deployment. Researchers in laboratories are a bit less constrained than artillery or tank crews, and have used this concept to produce high velocities. However, they have also come up with another trick which works even better. For such things as studying asteroid impacts, they use an explosive charge to drive a piston into a tube of hydrogen gas, which then launches the projectile. Because of the extremely low molecular weight of the working fluid, these light gas guns can reach muzzle velocities in the low end of the velocities of potential impactors, and are improving steadily. 

A device which is a combination of traditional gun and jet engine is the ram accelerator. The launch tube and projectile effectively form an inside-out ramjet. The tube is filled with a fuel-air mixture, and a propellant charge starts the projectile forward. The fuel-air mixture compresses as the projectile moves down the bore, and ignites once past the constriction, the detonation forming a standing shockwave at the rear of the projectile. The pressure from this forces the shell down the tube. Since the combustion is moving with the projectile, you don't have the propagation speed limitation of conventional firearms. This concept was originally developed with the intent of replacing sounding rockets, which gives you an idea of the muzzle velocity. Accelerations of over a hundred thousand gees and muzzle velocities of over 5,000 mps are expected for the larger, longer ram accelerators.

The stresses involved in such a device are stupendous. When asked what would happen if the blast from the initial propelling charge flashed past the projectile and ignited a detonation in the fuel-air mixture ahead of it, one of the developers stated that no malfunction of the launcher was worse than normal operation. The last I heard, ram accelerators were still under development. 

When chemistry won't do the job it's always a good idea to try physics. Electric cannon are still not quite at the deployment stage, despite being worked on for about a century. One major problem is dumping enough electricity fast enough into the launcher to do the job. Having the launcher survive such treatment is even more difficult. 

Some electric launchers work like a solenoid, and are often nicknamed coilguns. These work by using electricity to generate a magnetic field which interacts with the projectile much as the rotor of an electric motor does with the magnetic field produced by the windings, except the force generated is linear rather than circular. They are simple and generally easy and cheap to build, but have lower performance than some of the other alternatives. 

Another version of electromagnet launcher is the railgun, so named because the projectile is positioned between two conductive rails. This works very much like a linear induction motor, and can be thought of as a variation on that device. These launchers are very hard on their rails, and rarely shoot more than three times before needing refurbishment. Muzzle velocities are already very high and climbing with development. Much of the research for these is focused on improving the working life. 

Some electrical accelerators use the electricity to vaporize material - reaction mass - at the rear of the projectile or on the face of railgun-like rails, turning it into an electric rocket. If the material becomes a conductive plasma, no physical contact between projectile and energy source is necessary, eliminating that source of drag. Because the power is coming from outside, the projectile can actually be supplied with more energy than an equivalent mass of chemical propellant carried on board would produce. Any propellant container on the rear of the projectile can be dropped like a discarding sabot once the launch is over, reducing drag.

For all of these, the energy supply is the limiting factor. Which is likely why the US Navy has made the most progress with fielding a large working electric gun. If you're on a ship, getting enough electricity for your weapon is greatly simplified over doing the same job for artillery in the field. Especially if that ship is nuclear.

Studies have been made to evaluate using ground-based lasers to supply energy to large rockets, in a variation on the theme of the third version of electric canon described above. The on-board propellants - perhaps plain water, but more likely hydrogen - would be chemically inert or at least far less toxic and energetic than traditional chemical propellants. With an external power supply, more energy can be delivered to the rocket than the same mass of chemical propellants could provide. The lasers might be electrically or chemically pumped; the exact nature of the power source is irrelevant. They would beam energy to the working fluid, heating it to vapor and possibly even dissociating the molecules, perhaps even creating a plasma.

So there you have a very brief overview of the history of projectile speed and how it is produced and measured. This runs almost thirty-five hundred words (somewhat longer than typical for these articles) yet has just barely scratched the surface. If there is sufficient interest I may go into more detail on certain aspects of the human quest for speed in the future.