## Tuesday, January 11, 2011

### Testing Firearms: Measuring Bullet Velocity - II

In our previous post, we studied the first accurate method of identifying bullet velocities: the ballistic pendulum method. While the ballistic pendulum method was accurate and remained in use for many decades, it wasn't initially adopted all over Europe perhaps because the inventor was English. Instead there were some other methods developed in some other countries of Europe, all of which were developed after the ballistic pendulum method. Some of these were not as accurate, but were still preferred over the ballistic pendulum method, perhaps because of nationalistic reasons. The interesting thing about these methods is that while they were more inaccurate than the ballistic pendulum method at the time they were invented, they laid the foundations for more modern and accurate methods of determining bullet velocities.

In 1767, an Italian named Mattei came up with a method to measure bullet velocities. His method consisted of a vertical paper cylinder which was mounted on a wooden frame. The frame was made to rotate by using a cord and a weight. Once a uniform known speed was attained by it, the bullet was fired through it, perpendicular to the axis of the cylinder. The bullet passed through the paper cylinder and left two holes on the surface. The two holes gave the arc through which the cylinder had rotated as the bullet passed through it. By computing the length of the arc and knowing the diameter and the rotational speed of the cylinder, one could compute the bullet velocity. However, this method's precision was dependent on three factors: (a) the diameter of the cylinder, (b) knowing the rotational speed accurately and (c) the uniformity of the rotation. This machine was also not very effective against faster moving bullets, because it could not measure times less than 1/30th of a second, during which time a modern bullet, such as that fired by an M-16 rifle, could easily cover 100 feet (30 meters), which means you'd have to use a cylinder at least 100 feet in diameter to measure the speed of an M-16 bullet reasonably. It was also very hard to make sure the cylinder was rotating uniformly and so the device was not very accurate either.

In 1804, a French officer named Colonel Grobert invented another method to determine bullet velocity based on similar principles as Mattei's method. In Grobert's method, two large disks about 6.5 feet in diameter, made of cardboard, were attached to the same horizontal axle. In Grobert's original design, the two disks were placed 13 feet apart. The axle was rapidly rotated by means of an endless chain in combination with a flywheel and a windlass. When the rotation of the axle was judged to be at a constant speed, the tester then aimed at the disks and fired a shot through them. The bullet pierced through both disks, but since they were rotating rapidly, the exit hole through the second disk was not in the same line as the exit hole through the first disk. By looking at the positions of the two holes, one could determine the angle of revolution. Since the distance between the two disks was known and the speed of rotation was also known, the tester could calculate the bullet velocity. However, this method had the same weaknesses as the Mattei method described above.

The next step to correct these above problems was invented by another French officer, one Colonel Dabooz, in 1818. His method involved a gravity apparatus to measure bullet velocities.

His apparatus consisted of two screens, two pulleys, a cord and a counterweight. In his method, a fixed screen was placed precisely 50 yards from the muzzle of the firearm to be tested. Directly in front of the fixed screen was another screen, which was suspended by the cord. The cord passed through two pulleys and the other end was right in front of the muzzle of the gun and was tied to a counterweight, which held the movable screen in place. The firearm was aimed at the screens. When the firearm was discharged, the bullet would cut the cord as it left the barrel. This would release the movable screen, which would start falling. The bullet would travel 50 yards and pass through both screens. Since the movable screen was falling during this time, the hole in the movable screen would not be at the same height as the hole in the fixed screen. Knowing the acceleration due to gravity and measuring the distance between the holes in the two screens, the tester could calculate how much time the bullet took to travel 50 yards and from this, he could calculate the bullet velocity. This method had the advantage that a constant acceleration was imposed on the falling screen (since acceleration due to gravity remains constant), which made the time measurement more reliable. To measure the velocities of faster moving bullets, the distance between the two pulleys could be increased and reasonably accurate measurements could be made. The one error in this method is that it assumed that the movable screen would begin to fall as soon as the bullet passed through the cord.

The reader might note that while these three method use different ideas, they have one thing in common: they all measure the time taken for a bullet to travel through a known distance and from this, they determine the bullet velocity. This is unlike the ballistic pendulum method, which uses the principle of conservation of momentum to determine the bullet velocity. While these methods were not as accurate as the ballistic pendulum method when they were invented, they laid the foundation for the concept of cronographs. With the invention of electricity, the cronograph concept became more practical and more accurate and it eventually replaced the ballistic pendulum method. We will study practical cronographs in the next post.