Unlocking the Mystery of Recoil

Have you ever thought about all the tests that must be used during the development of a firearm? A recently introduced test device will change the way guns are designed particularly with respect to recoil and controllability. The new device, called the Weapon Recoil Simulated Shoulder (WRSS), will aid manufacturers in making guns more controllable and at the same time assist in the development of more efficient muzzle brakes and recoil reducing devices. Data from the device will be used to assure that scopes, laser pointers, and other accessories are designed to endure the harsh environment of a weapon mount.

Since 1742 an ancient device called the ballistic pendulum has been used to find the recoil level. This shoot-from type of ballistic pendulum involves free hanging the gun from wires and firing it in mid-air. The distance the gun raises is a measure of what is called free recoil energy. The shoot-at type of ballistic pendulum is used to determine the energy of a projectile. With some minor variations and the addition of modern instrumentation, we’ve been using these methods for the last three centuries.

Controllability evaluation is more challenging. In cases where everyone fires the same weapon and ammunition and tries to evaluate controllability, a great inconsistency between shooters becomes evident. Even the same shooter does not repeat the same controllability performance. Most controllability evaluations involve little more than asking shooters how quickly and accurately they felt they could get off that second or third shot. Inconsistent results are a huge frustration to the military as controllability is important to keeping a burst of full automatic fire on target.

A few years ago, the U.S. Army’s Program Manager for Small Arms saw the need for advancement in technology and awarded a study contract to Knight’s Armament Company, Titusville, Florida. Project goals included the improvement of recoil measurement techniques and a better metric for controllability.

The engineers at Knight’s began their study with a thorough review of every recoil study report available. They found that almost all the reports had the same theme. A gun follows Newton’s 3rd law of physics: “For every action, there is an equal and opposite reaction.” The force that pushes the bullet and gun gas through the barrel and out the muzzle is equal to the recoil force of the gun. The rearward velocity of the firearm and its weight are multiplied together in a formula that gives the recoil energy. It’s hard to figure out how fast the firearm is recoiling especially if there is any device on the muzzle that diverts the gun gas from going straight ahead. Muzzle brakes and even flash suppressors turn the gas to give a forward force on the weapon that slows its recoil velocity. This is why researchers generally take the easy way out and find the energy with the
ballistic pendulum.

Knight’s engineers noted that recoil studies for the military almost always focused on the shooter. Repeated input of high levels of energy into the shoulder causes bruising and very high recoil energy can cause damage to the eye. The U.S. military measures the free recoil energy of every shoulder fired weapon it fields; classifying each into categories that limit how many rounds per day can be fired. Their table shows that if a gun develops less than 15 ft-lbs, (20 Joules) of energy, unlimited firing is permitted. The M4 and M16 fit this category. The highest level on the table is 60 ft-lbs (81 Joules), above which no shoulder firing is permitted. Knight’s testing found that a typical 3½ inch 12 gauge magnum shotgun develops 59 ft-lbs of energy which is alarmingly close to the military’s maximum.

While the energy method might be useful for making decisions about how many rounds per day are appropriate, its value is limited when studying recoil. The level of free recoil energy doesn’t tell anything about how much recoil force goes slamming into the shoulder. Here’s an example with results that may surprise you. Suppose one gun has a constant 300 pound recoil force and pushes against your shoulder for 1 inch of travel. In this case, recoil energy is calculated by a simple multiplication to give 300 inch-pounds of energy. Now take a second gun that pushes with a constant load of 100 pounds over 4 inches of rearward travel. The second gun has 400 inch-pounds of energy. It’s hard to appreciate that the gun with the lower force has significantly higher free recoil energy, but it’s true. This is what is so perplexing about the study of recoil. The energy method only tells part of the recoil story and that’s why the Army supported Knight’s investigation.

At the beginning of their study, Knight’s engineers instrumented both guns and shooters with the latest accelerometers, force gages and other measurement devices. Data recovered from the tests with the new instrumentation was good and certainly usable, but not remarkably better than what had been found previously with older test equipment. Their worst surprise came when they had shooters fire at full auto and filmed the target using high speed video looking for a pattern to shot placement. They were frustrated by the inconsistencies between shooters. The project results to that point were very disappointing, showing no promise to advance the technology in recoil measurement and controllability.

One of the engineers found an old Government report that talked about replacing the human shooter with a mechanical device that mimicked the shooter’s motion during firing. The metal body parts were to be connected with springs and dampers (shock absorbers) having the same characteristics of muscle and bones. Army researchers inserted a sketch of the concept in the report, but never built it. Knight’s engineers liked the idea and took it to a higher level. They also modeled the human vibrational characteristics in order to pick the right springs and dampers and then built a mechanical device with the same characteristics. This required the use of a sophisticated analytical method called modal analysis.

To understand modal analysis, you must first accept that all bodies vibrate at their natural frequency. For example, a guitar string vibrates at a natural frequency when plucked. It is also true that most bodies – guitar strings included – have more than one natural frequency, and these can occur simultaneously. The lowest natural frequency is called the first mode of vibration, followed by the second mode, etc. Each mode is at a higher frequency than the preceding one, and each has its own shape. For all bodies, there is also a natural tendency to stop the vibration called damping. Some bodies, like the Tacoma Narrows Bridge built in 1940, didn’t have enough damping and destructed when excited at its natural frequency (YouTube shows a fascinating video of the Tacoma Narrows Bridge failure.) In contrast, there is so much damping in the human body that vibration dies out quickly. To find the natural frequencies and mode shapes, engineers input different levels of vibration into a mock up weapon being held by a shooter. Each shooter was fitted with instrumentation to study the body’s response to each level of vibration. In this way, they found the vibrational modes of what the military describes as their smallest, average, and largest size shooter. Using this information, the WRSS was built to have the same characteristics.

To be able to measure controllability, Knight’s put angular measurement devices on the WRSS in order to determine the up and down movement of the end of the barrel (pitch) as well as the side-to-side motion (yaw). The WRSS precisely tracks the point of aim during and after the firing event. For hunters this information is critical for the follow-on shot. For the military this is important for controlling bursts of automatic firing, and essential to the design of muzzle devices. A precise measurement system is invaluable in the development of devices designed to reduce muzzle motion during shooting. Why? Simply because unless there are huge performance differences in these devices, even an expert shooter can’t detect changes in performance.

Besides controllability measurements, the new shooting fixture records the force on the shooter’s shoulder, the acceleration levels (g-loads) at the buttstock and on the barrel. The new WRSS has other benefits as well. Using the acceleration data, the WRSS has already been useful in solving problems with failures in gun mounted optics and other electromechanical devices. A data plot called a Shock Response Spectrum (SRS) has been used to study how many g’s the shooter, gun, and mounted accessories must endure at various frequencies. (Remember that at 1 “g” a 10 pound body weighs 10 pounds, but when subjected to 10 g’s, that same body weighs 100 pounds.) These g-levels are important to shooter reaction and more important in the development of relatively fragile accessories like scopes, laser pointers, and night vision.

Using the WRSS fixture and SRS data plots, Knight’s engineers determined the cause of a puzzling failure of a night vision scope. The scope was tested on one gun and determined to be capable of withstanding the high shock environment, yet failed when fired from a differently designed weapon of the same caliber and weight. Why the night vision scopes failed on the second gun, but held up well on the first gun, became immediately evident on the SRS data. The SRS curve of the two guns was almost a perfect match at low frequencies, but at high frequencies where electrical equipment is susceptible to failures, the second gun showed that much higher forces were being experienced.

The US Army intends to use the WRSS in its testing laboratories, and the design has been turned over to a not-for-profit organization called the Institute of Military Technology (IMT). IMT will offer the WRSS to weapons manufacturers, government laboratories and testing facilities worldwide. Commercial firearms manufacturers may also procure the WRSS from IMT for their use.