NON-LEAD AIRGUN AMMUNITION PROJECT



NON-LEAD AIRGUN AMMUNITION PROJECT

Joseph Ouellette, Bryan LaMora, Zach Rohlfs

Executive Summary

Team 07F proposes a two-part pellet design as a substitute for the currently produced lead pellet by the Crosman Corporation. The newly designed pellet consists of a two-part construction, a plastic outer sheath covering a solid copper core. The combined weight of 6.6 grains is well within the specified four to ten point five grains required by Crosman. Safety concerns due the bounce back of the pellet are comparable to the current lead pellet. The components of the new pellet design are non-toxic. The production of one million pellets per day is attainable using two insert molding machines at a fixed cost of six hundred thousand dollars. The estimated cost of producing one hundred pellets is $0.47. The newly designed pellet was unable to hold the accuracy that its lead predecessor achieved. Future improvements to the barrel design will need to be made in order to maximize the performance of the non-lead pellet.

Abstract

The current material of choice for the manufacture of recreational air pellet guns ammunition is lead. Lead is a material that is unsafe for humans and can lead to environmental problems. The Crosman Air Rifle Company has commissioned the research and development of a “Lead Free Substitute” for their Air Rifle Ammunition product line. Team 07F proposes the use of a two-part pellet consisting of a plastic outer shell and a solid metallic core. Initial testing has shown the velocity of the two-part pellet is within the given parameters. This new pellet design will meet the specifications for manufacture that Crosman has specified.

introduction

Team 07F is investigating an economical substitute for Lead in the production of air rifle pellets as specified by the Crosman Air Rifle Company. The new pellet must be an economical and easily manufactured Lead pellet substitute. The pellet is to function in a barrel of diameter 0.176 + 0.003/- 0.0005 inches (4.470 +.076/-.013 mm), be between four and ten and a half grains (.2592 and .68g), and have a length of 0.195 to 0.260 inches (4.95 to 6.60mm). The pellet must function at –30(F to 160(F (1(C to 71(C). The velocity range of the pellet has to function between 100 ft/s and 1200 ft/s (30.5 and 365.75 m/s). The pellet substitute can be of any shape but must remain intact after impact and have a low bounce back effect. A low bounce back effect will ensure the safety of the operator when the pellet hits a hard object. The pellet material should be non-toxic and stable in a black oxide oil environment. Final aerodynamic design should maintain the current accuracy of the lead pellet in which a shot group is within a 0.835-inch (21.2mm) diameter circle at 25 yards (22.86m). The final cost per 100 pellets should be between $0.10 and $0.80. The pellet substitute that is proposed is a two-material design that would consist of a solid metal core covered with a plastic skin. The solid metal core will provide the weight necessary to maintain the pellets accuracy and the plastic skin will allow the use of metal cores that normally would damage the air rifle’s barrel due to the metals’ hardness.

Nomenclature

A, area of a circle

AC, area of contact;

a, acceleration due to gravity;

ad, acceleration due to drag;

Cd, co-efficient of drag;

CL, contact length;

CP, heat capacity;

FP, force due to pressure;

Ff, force of friction;

Fd, force due to drag;

H, Heat;

LB, length of barrel;

LL, length of lands;

Mwt, mass of the material;

m, mass of pellet;

NL, number of lands;

P, internal chamber pressure;

R, bounce back distance;

r, radius of pellet;

T, Temperature;

tAB, time of travel from point A to B;

W, width of contact;

Wf, work due to friction;

V, velocity of pellet;

V0, initial velocity;

VR, velocity of pellet after impact;

Yi, initial height of pellet at point A;

Greek Symbols

(k, co-efficient of kinetic friction;

(, Density of air;

Brainstorming/ideas/materials

When first presented with this project we investigated the possibility of replacing the current lead pellet with a lead substitute material. Through much research we found that only a few materials were available, such as beryllium or PolyOne Ecomass, which is a tungsten powder filled polyamide. These materials are capable of meeting the weight criteria, they are non-toxic and they meet other specified criteria, the only problem is that they range in price from 12 to 17 dollars per pound. Considering the fact that lead only costs 39 cents per pound, these lead substitute materials do not meet our cost criteria.

We then discussed the possibilities of using two different materials combined together to help meet all of our requirements. We considered using BB’s currently made by Crosman Corp. and mounting them on the front of a plastic body as shown in figure 1.1.

[pic]

Figure 1.1

The plastic body would slide along the inside of the barrel and take advantage of the riffling in the barrel and the steel BB would give use the weight we desired. This pellet would weigh approximately 6 grains, it would be non-toxic and it would take advantage of the rifling in the barrel but we had concerns about it staying intact after impact and it would have a high bounce back effect due to the high coefficient of restitution of steel. This shape would also exceed our length requirements.

Our design then moved towards a metallic cylindrical core encased in plastic as shown in figure 1.2.

[pic]

Figure 1.2

The idea here is that the plastic nose would help to reduce bounce back and the steel core would give us the mass we desired while also meeting the rest of our requirements. With further investigation of this design, we realized that there would not be enough steel in the core to give us the weight we desired. The weight of this pellet is 3.67 grains. We were hoping to create a pellet that weighed around 7.9 grains which is the current weight of the lead pellets. We also wanted to reduce the surface area that is in contact with the barrel, to reduce friction.

We then decided to sacrifice some of the aerodynamic characteristics of the above design to try and increase its weight and reduce the contact area as shown in figure 1.3.

[pic]

Figure 1.3

With this design we were able to increase the weight from 3.67 grains to 5.56 grains this was a desirable increase in mass but now the bounce back effect had been increased.

Increasing mass and decreasing bounce back were the two major issues at this point we needed to address. We searched through a materials database for a material that was denser than steel and had a similar coefficient of restitution as lead. We found that copper would meet both of our requirements. Copper has a coefficient of restitution of .22, which is fairly close to lead, which is .16, steel has a coefficient of restitution of .90 and therefore making it infeasible for use. It is also more dense than steel.

With the inner material set it was now time to decide upon a plastic for the external body. We needed something that had low temperature impact resistance, low cost, easily injection molded and had as high of a density as possible. Our search led us to Xenoy 1200, this plastic is a blend of polycarbonate and polyester which has all of the characteristics we desired. Using this plastic in conjunction with a copper core resulted in a pellet weighing approximately 6.35 grains. Since this plastic is also chemical resistant it helps us to meet some of our other requirements such as being able work with black oxide oils. Figure 1.4 is a drawing of the final pellet design, please see appendix B for a detailed drawing of the pellet.

[pic]

Figure 1.4

FRICTION AND HEAT GENERATION

The Change in Heat of the pellet as it passes through the barrel is a concern since any temperature generated due to friction may exceed the melting point of the proposed plastic shin. The parameters for the calculation of heat and friction require the use of several assumptions and initial conditions. Due to the geometry of the pellet chamber the calculations for heat generation will begin at the point the pellet has taken the shape of the barrel. When the lead pellet takes the shape of the barrel the force normal to the pellets skirt is due to the pressure in the chamber. The hoop stress in the pellet due to the compression of the pellet in the barrel is also neglected with the assumption that the calculations begin when the pellet has already deformed to the shape of the barrel. The movement of the pellet through the barrel increases the volume behind the pellet so that the initial pressure in the chamber will actually decrease. To obtain the maximum temperature increase the pressure changes in the barrel will be considered constant from the instant the 24-psi (165.5kN) compressed air is released to the point the pellet is discharged from the barrel. The pressure on the skirt of the pellet at the point at which the pellet actually leaves the barrel is much less than when the pellet was in the chamber. Since the normal force of the pellet on the barrel is directly proportional to the pressure in the chamber it is expected that leaving the pressure constant will result in the maximum friction force. The temperature change due to the decrease of pressure in the chamber is also neglected. The decompressing gas would have a cooling affect on the pellet and the barrel in normal firing conditions. By setting the temperature constant the heat generated by friction will be maximized to the worst case scenario. Due to the negligible affects of gravity on the small pellet, the force of gravity was considered zero.

The first value required for the calculation of heat change and friction is the contact length (CL). The CL takes into account the rifle “Lands”. The Lands are the high areas in the barrel that the pellet skirt actually comes into contact with. The rifling of the barrel has six lands that are 0.045in (1.14mm) long. Multiplying the number of lands times the length of each land equals a CL of 0.277in (7mm) Eq (1.1).

[pic] (1.1)

The width of contact between the barrel and the pellet is 0.020in (.5mm). This width times the CL will give the Area of Contact (AC) which equals 0.00553in2 (eq 1.2).

[pic] (1.2)

To find the Force due to Pressure (FP), neglecting hoop stress, the Pressure (P) of the chamber is multiplied by the AC, when cared out equals a FP of 0.133lb Eq (1.3).

[pic] (1.3)

The Force of Friction Ff can now be obtained. The coefficient of kinetic friction (μk) between steel and lead in a dry, no oil, condition is approximately 0.4. Multiplying the μk times the FP equals a Ff of 0.0531lb (.24 N) Eq (1.4).

[pic] (1.4)

In order to relate the Friction force to the change in heat the Work due to Friction (Wf) is required. The Wf is the product of Ff, the Length of the Barrel (LB), and the conversion factor of inches to feet. The Wf equals 0.0863 ft-lb. (.117 J) Eq (1.5).

[pic] (1.5)

The Change in Heat (ΔΗ) equals the Wf. Knowing that the ΔΗ equals the product of the Heat Capacity (CP) of a material, mass of the material (Mwt), and the Change in Temperature (ΔΤ) Eq (1.6), the ΔΤ can be derived.

[pic] (1.6)

The CP values for Lead, Xenoy(1200, and Brass 330 are 0.129 J/g(C, 1.88 J/g(C, and 0.380 J/g(C respectively. The Mass of the Lead Pellet, Plastic Pellet, and the Brass 330 barrel are 0.512g (7.9 grains), 0.0418g (0.65 grains), and 185.07g (0.4 lb) respectively.

[pic] (1.7)

Using Eq (1.7) the temperature change can be found. The value of the temperature change in the lead pellet is 1.77(C (3.186(F). The temperature change in the plastic pellet is found to be 1.49(C (2.68(F), and when this change is added to the maximum working value for the ambient temperature the molding temperature of the Xenoy(1200 is not met. The Xenoy(1200 can then be used as the skin material.

BOUNCE BACK

[pic]

Figure 2.1

In order to understand how materials react to impacts, the distance pellets bounced back after impact with a hard object were calculated for many different materials. Using the charts in the FSI Airgun Ballistic Tables to determine the velocity of the pellet the instant before impact and the coefficient of restitution for many different materials, the distance the pellets would bounce back towards the operator were calculated.

Material Coefficient of Restitution

Brass 0.30

Copper 0.22

Lead 0.16

Steel 0.90

Table 1

Assuming the pellet bounces off of the target only with a velocity in the y direction, the time it takes for the pellet to hit the ground can be calculated from Eq. (2.1).

[pic] (2.1)

Where [pic]is the initial height of the pellet at point A, a is the acceleration due to gravity and [pic]is the time it takes the pellet to travel from point A to B. After calculating the value of [pic], the distance the pellet travels can be calculated from Eq. (2.2).

[pic] (2.2)

Where R is the distance the pellet bounces back and [pic]is the velocity of the pellet after impact.

With a muzzle velocity of 800 ft/s (244 m/s) and the height of the barrel being 4.5 feet (1.37m) above the ground, the bounce back for an air gun operator at 30 yards (27.4m) from the target was calculated. The lead and copper pellets were found to have a bounce back of 55.7 feet (17m) and 76.6 feet (23.3m) respectively where as the brass and steel pellets were found to have a bounce back of 105 feet (32m) and 314 feet (95.7m) respectively. As you can see, there is a possibility for the operator to be hit by both the steel and brass pellets where as there is no chance they could be hit by the lead or copper pellet.

PELLET BALLISTICS

Ballistic coefficients are an excellent way of describing a projectile. The coefficient predicts or determines many things about the projectile like velocity or how the object will behave in the air. The only problem with these coefficients is that they must be determined experimentally and are indeterminable through theoretical means. Ulterior methods are employed to discover if the proposed pellet is suitable. While not a substitute for a ballistic coefficient, the coefficient of drag makes a good approximation. This will help us to determine if non-lead pellet will travel at approximately the same velocity as Crosman’s™ pellet line.

Calculating the coefficient of drag, Cd, is not too difficult. From Fox & McDonald’s, “Introduction to Fluid Mechanics”, Cd is defined:

[pic] (2.3)

In the above defining equation for Cd, V, is the incompressible fluid speed around the pellet, A, is the cross sectional area of the pellet, Fd, is the force of drag exerted on the pellet by the fluid, and ρ, is the density of the incompressible fluid. The fluid in question is air. For this definition to hold true certain assumptions about the fluid and pellet must hold true. Firstly, the fluid must not compress or change its density due to excessive pressure, force per unit area. Second, the velocity of the fluid equates to the velocity of the pellet. Third, the coefficient of drag is constant for the varying velocity range, four hundred to twelve hundred feet per second. The force of drag is found using Newton’s first law.

[pic] (2.4)

Where m, is the mass of the pellet and a, is the acceleration of drag. The acceleration of drag derives from the velocity of the pellet. Using the following equations for the acceleration of drag:

[pic] (2.5)

[pic] (2.6)

These equations will yield a good approximation for the coefficient of drag given sufficient data. Where equation 12 finds for a given distance and equation 13 finds for a given time. However, gleaning sufficient data for the newly designed pellet is impossible.

Restrictions for prototyping a pellet are present since velocities, times and distances are needed. An alternative is the use of a fluid-modeling program. One such program, Fluent, models the flow of air around stationary objects in space. Due to the small nature of the pellet faulty data maybe returned. To avoid faulty data collection the pellet size was scaled using its Reynolds number to a larger more acceptable size. Now both pellets get modeled using the same tools. When calculated the Cd for Crosman’s pellet equaled 0.47 with the new pellet design equal to 0.56. These coefficients of drag are found using a two dimensional analysis of Fluent at a steady state. The steady state assumption is safe since the coefficient of drag is constant for the velocities used. Two-dimensional approximations will yield slightly higher Cd values than a true three-dimensional analysis. This is due to the object in question being treated as having infinite depth. With both pellets being relatively close in terms of the coefficient of drag, the expected velocity reduction of the new pellet should be close to that of Crosman’s but slightly quicker. Preliminary results from the prototyped pellet shows; the non-lead pellet flies up to one hundred feet per second faster than Crosman’s pellet travels. The consistency in regards to velocities of the pellet varies too much. One explanation being proposed is the hardness of the plastic is too high and therefore, rifling in the chamber of the barrel does not occur. The lack of rifling causes the pellet to tumble and throw off the velocities. This tumbling effect would also explain the poor accuracy of the pellet as well.

FINAL DESIGN PROPOSAL

The final design is a pellet that meets the requirements set forth by the Crosman Corporation. The pellet is a safer design for the environment by eliminating the use of lead. The new design is able to function in a .177 caliber barrel and has a weight of 6.8 grains is near the middle of the specified range. The new pellet will function at a wide range of muzzle velocities and works well with black oxide oils. The pellet also has a low bounce back effect and stays intact after impact.

The calculations discussed above show that the pellet will not leave residue in the barrel. This is due to the nature of the plastic combined with the minimal heat rise due to friction that the pellet sees. Over time, if the pellet left residue in the barrel, the gun would see a decrease in performance over time. Eventually this performance decrease could result in a blockage of the barrel. However, since our pellet stays well within the acceptable temperature range, there is no fear of this occurring.

There always exists the possibility that the user will do something accidentally or misjudge the distance that they are from a target. This led us to calculate the bounce back distance using the coefficient of restitution. This factor is one of high importance for Crosman; after all, if a young adult or teen were to misuse the air gun and fire too closely to an object the results could be catastrophic. With this in mind, the pellet was designed to closely resemble the bounce back characteristics of the lead pellet while still meeting the other design requirements. The bounce back consideration is one of the main reasons why copper was chosen for the core material. Other reasons why copper was chosen is because it meets our density requirements, it is a reasonably priced material per pound and is easy machined.

For some air gun users, performance is an important factor in the purchasing of a pellet. To this extent, the ballistic coefficient is an important factor in choosing a pellet. Since the ballistic coefficient is an empirically found value the coefficient of drag was used as an estimate. Looking at the two values found in Fluent of ~0.47 for the current pellet Crosman uses and ~0.56 for the newly designed pellet. The two values differ by less than 20 percent, which is not too severe. However, the new pellet design is slightly lighter in weight, which could pose possible problems during flight. The results of Fluent are useful for making a hypothetical guess about the new pellet design. The new pellet design should behave in a similar fashion to that of the current pellet employed by Crosman.

TESTING

There are three different aspects of the pellet that need to be tested in order to determine how well the design requirements have been meet. First, the pellets must be able to group within .835 inches (21.2mm) at 25 yards (22.86m). Second, the pellet must have a low bounce back effect. Last, the pellet must be able to function at velocities between 100 and 1200 ft/s (30.5 and 365.75m/s).

The accuracy of the pellets or grouping is tested by placing a paper target at 25 yards (22.86m) from the muzzle and firing five pellets with the airgun clamped in a vise as shown on the right hand side of figure 1.5. The maximum spacing between holes in the target from the pellets must be less than .835 inches (31.2mm) to meet Crosman specifications.

The bounce back effect is measured with the same set-up used for measuring accuracy except the paper target is replaced with a steel slab. Five pellets are then shot at the steel slab and the bounce back distance is then measured.

The pellet functionality at different velocities is measured using different airguns with muzzle velocities varying from 100 to 1200 ft/s (30.5 and 365.75m/s). The velocity of the pellets is measured with a light screen as shown on the left-hand side of figure 1.5.

Figure 3.5

rESULTS

Eight pellets were machined and tested using the aforementioned testing procedures. The pellets were each weighed and shot with the same rifle. Three pellets were shot through the mussel velocity light screen to obtain the pellet velocity. The data in table 1 shows the velocities and weights of each pellet:

Velocity ft/s Weight in grains

1 565 6.2

2 554 6.6

3 498 6.6

Table 1

The five remaining pellets were shot to obtain the accuracy of the new design. They produced a shot pattern approximately 4 inches (10.16 cm) in diameter. Thirty-five more pellets were machined to obtain a larger sampling for the accuracy testing. With the results of the first eight pellets it was determined that a reduction in pellet diameter was needed. The thirty-five new prototypes were on average 0.178 inches in diameter a difference of 0.002 inches. The accuracy of the pellets was improved and resulted in a shot pattern with a diameter of approximately 2 inches (5.08 cm).

Possible error in the results is directly attributable to the machining process and the large variance in the shape of each pellet. Multiple machinists worked on the plastic bodies and copper cores. Slight differences in cutting of the plastic and metal ensured that there was no consistent shape in the pellet bodies.

MANUFACTURING BUDGET:

The manufacturing of the non-lead pellet would be out sourced to Empire Precision Plastics. Empire estimates they will need two production lines consisting of molding machines with 64 cavity molds and robotics for loading the pellets in order to meet Crosman’s required one million pellets per day production. Tooling costs are estimated to be $300,000 per line. Material and labor cost for production equate to $0.47 per one hundred pellets.  

CONCLUSION

Team 07F is investigating an economical substitute for lead in the production of air rifle pellets as specified by the Crosman Air Rifle Company. It is the recommendation of Team 07F that a two-material pellet be used as a substitute for the lead pellet currently in production. This two-material design would consist of a solid metal core covered with a plastic skin. The solid metal core will provide the weight necessary to maintain the pellets accuracy. The plastic skin will allow the use of metal cores that normally would damage the air rifle’s barrel due to the metals hardness.

Three areas of concern in the initial design and material selection phase where drag, bounce back, and temperature rise. To ensure the new design at least performs as well as the current pellet design, the drag coefficients were required. These calculations were obtained using Fluent software but due to the pellets size and the fact that Fluent treats the pellet as an infinite wing, the result are inconclusive.

The bounce back distance is needed in order to protect the user of the air rifle from the possible bounce back of a pellet that hits a hard surface. The bounce back was determined using the coefficient of restitution for the metal in question. It was determined that copper was the closest in bounce back as that of lead. Steel on the other hand was nearly four times the bounce back distance of lead.

Friction forces due to the pellet traveling through the barrel will generate heat. To ensure this heat generation will not melt a plastic pellet skin and leave residue in the barrel, heat rise calculations were made. It is calculated that the plastic pellet will have a maximum heat rise of 1.49(C (2.68(F) in contrast to the lead pellets is 1.77(C (3.186(F) heat rise. The GE resins Xenoy( 1200 meets the requirements for heat resistance, impact resistance, and injection molding ease.

As a result of testing, it has been proven that our pellet design meets most of the requirements set forth by Crosman. The pellet functions in .177 caliber riffles, they meet the weight, length and shape requirements and have a shot start force of less than 24 lbs. (106.75 N). The pellets function between 100 ft/s and 1200 ft/s (30.48 m/s and 365.8 m/s) and works well with black oxide oils. The pellet stays intact after impact, the material is non-toxic and has a low bounce back effect. Although this pellet design meets most of the requirements, it does not meet all of them. The pellets are supposed to be able to be accurate within .835 inches (21.2 mm) at 25 yards (22.86 m). We were only able to obtain a shot grouping of 2 inches (50.8 mm). Part of this is due to the manufacturing process. With insert molding technology, the pellets will be able to be made more accurately and consistently than we were able to obtain in the machine shop.

It is the determination of this team that utilizing the current barrel design will not provide the accuracy results Crosman is requiring. To fully realize the potential of the new pellet a new rifling pattern should be developed.

Acknowledgments

Team 07F would like to thank the following individuals:

Edward Shultz, Chief Engineer from the Crosman Air Rifle Company, for the help he has given and the use of the Crosman facilities.

Dr. Ghosh, team advisor, for all the time he spent assisting our team and the guidance that he provided.

Rick Wilson, Vice President of Engineering, Empire Plastics

References

[1] Hibbeler, R.C., 1974, Engineering Mechanics Dynamics, Prentice-Hall, Upper Saddle River, New Jersey, Chap. 15.

[2] Brychta, F.S., 1994, FSI Advanced Airgun Ballistics, Firearms & Supplies, Hancock, Michigan.

[3] Brychta, F.S., 1993, FSI Airgun Ballistic Tables, Firearms & Supplies, Hancock, Michigan.

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