From DDWiki

Contents 1 Executive Summary 2 Customer Needs 3 How System Functions 3.1 Trigger Mechanism Function 4 Components 5 DFMA 5.1 DFM 5.2 DFA 6 FMEA 7 DFE 7.1 LCA 7.2 CO2 Emissions During Use 7.3 End of Life contingencies 8 Opportunities for Improvement 9 How Product is Used 10 Mechanical Analysis

Executive Summary

The paintball marker provides an instrument through which players can compete in simulated-combat scenarios, either for fun or for recreational competition. The average paintball marker must be reliable, simple to operate, and easily maintained. The marker is a relatively simple pneumatically actuated and controlled mechanism, a sliding venturi bolt (aka firing bolt) supplies pressure to propel the paintball and completes the loading action, a cocking bolt ensures the proper cocking of the venturi bolt. A regulator supplies pressurized gas to each mechanism. To understand these mechanics, we dismantled a store-bought marker; we then weighed and photographed each component. While the marker was disassembled, group members noted the probable means of manufacture for each component; this information was then used to present an analysis of DFM, DFA, and DFE considerations made by the OE manufacturer; these DFx analyses indicated that the marker was, in fact, sufficiently designed for manufacture, as wasted metal and plastic is kept to a minimum. The paintball marker's DFA charcateristics lean towards end-user maintainence rather than production, although production ease is addressed by modularity of the marker; the body/barrel and trigger frame modules can be assembled independently and then mated downstream, increase the efficiency of the manufacturing process. DFE analysis showed that the primary environmental concerns come from the manufacturing stage and the usage of CO2 gas during play. The greatest impact on the environment would be to implement a recycling program to encourage users of this product to turn in scrapped paintball guns for reclamation. A mechanical analysis quantified the operation of the paintball marker; we found the effective range to be 41 meters when fired straight forward from 5.5 feet (neck or shoulder height). Investigation into the operation of the marker indicated several failure modes; these failure modes were considered in an FMEA analysis to weigh the varying degree of risk associated with each failure. Ultimately, the paintball marker appeared to be a safe and reliable tool; therefore, improvement areas focus on increasing performance rather than reliability or cost.

Customer Needs

Most paintball players use their guns in tournament play at parks designed specifically for this purpose. On occasion, teams may play in uncharted forests or abandoned buildings to provide a new thrill and lower playing costs. The object of most games is to successfully shoot a paintball (the projectile) at an opposing team’s player to mark them with the paint inside the projectile. Speeds can reach up to 300 feet per second, over which the sport or play can become unsafe. Certain arenas measure and limit the users’ guns to a lower value. The first and foremost requirement is reliability and durability from a gun. There is nothing more frustrating than a gun malfunction in the middle of a game, when the user travels a significant distance to play. This quality can easily be found due to the strong correlation between price and durability. Having a good line of sight is paramount for aiming. Certain hopper and feeder designs go straight up from the gun housing, making it difficult to look at one’s target. For this reason, most designs incorporate an elbow feeder to offset the hopper towards the user. Barrel lengths will vary from 3 to 48 inches, and are usually interchangeable for a given gun. However studies have shown that no increased accuracy can be gained from a barrel longer than 8 inches. Lightness is a requirement for all levels of play, but again it is merely a question of price. Certain parts can be high strength plastics, sometimes even carbon, which would otherwise be of common metal alloys. The compressed air tank is perhaps one of the heaviest single parts on the marker. Carbon fiber is a popular alternative material for a tank, which may need to stand up to pressures of 5 ksi. More advanced users want quick adjustability of their projectile speeds. Bottom end markers require some tooling to change this setting, but more advanced markers, or aftermarket parts allow for on-the-fly adjustability even in the field. Typical low end markers use compressed CO2 (carbon dioxide), but this may cause inconsistent muzzle velocities. Advanced users will sometimes switched to compressed nitrogen, which eliminates this problem.

How System Functions

The paintball gun (or paintball marker) fires a 0.68 inch diameter paintball at speeds of around 280 fps using compressed air in a semi-automatic firing style. This means that after cocking the marker once, when you pull the trigger it will fire a paintball and also recock the marker for you. This allows the user to rapidly fire paintballs.

Before you can fire the gun, the bolt must be in the cocked position. This is accomplished by pulling the cocking pin back until you hear a click. This is only done once at the beginning of use. When the bolt is pulled back, the Venturi Bolt slides back in the marker barrel (shown in red) which allows a paintball to fall through the feed neck and into the marker barrel. The cocking pin is also connected to the striker bolt, which slides back in the striker chamber (shown in yellow) engaging the trigger mechanism (the trigger mechanism will be described separately in the next section). When the striker bolt engages the trigger mechanism, it is locked in the back position. This causes the striker spring to apply a force to the back of the striker bolt.

In this cocked position, the air reservoir (shown in blue) is filled with compressed air. This chamber is sealed off from the rest of the gun by the cup seal and valve pin assembly. This assembly is being pressed against the valve body (shown in green) by the valve spring. The valve body has three holes, one into the the air reservoir, another into the striker chamber, and a final leading up into the marker barrel. The valve pin extends through the valve body and into the striker chamber.

When the trigger is pulled, the striker spring pushes the striker bolt forward. The striker bolt strikes the valve pin, which opens the seal the valve pin and cap seal were creating with the valve body. Since the striker bolt and venturi bolt are connected, the venturi bolt also moves forward. Before the venturi bolt reaches the front position, it comes in contact with the paintball and pushes the paintball forward toward the barrel. Since the seal in the air reservior was opened, compressed air flows through the valve body into the striker chamber and the marker barrel. The compressed air that flows into the marker barrel accelerates the paintball out of the barrel, firing the paintball marker. The air entering the striker chamber forces the striker bolt back into the cocked position. At this point the valve spring pushes the cap seal and valve pin back against the valve body, sealing the air resevior again. With everything returned to the cocked position, another paintball falls into the marker barrel and the gun is ready to be fired again. The whole process from trigger pull until the gun cocks itself again occurs in less than a second.

Trigger Mechanism Function

Since the trigger mechanism could not be disassembled, a CAD model of the system was created to allow a full understanding of the function of the system.

The trigger mechanism allows the user to control when the paintball is fired by controlling the release of the striker bolt. When the paintball marker is not cocked, the parts of the mechanism are in the configuration shown in Figure 1. The blue arrows show forces on different component applied by springs. The spring against the trigger (black component) forces this trigger back into this position when no other forces are applied. The spring against the striker lock (red component) forces the pin to be on the far left part of the slot (cut through the center of the striker lock). As you can see, when the trigger is pulled the trigger does not touch the striker lock.

As said in the previous section, when the paintball marker is cocked the striker bolt "engages the trigger mechanism". This configuration of the trigger mechanism is shown in Figure 2. What this means is that the knotch on the bottom of the striker bolt "catches" the corner of the striker lock, outlined in yellow, applying a force to the left against the corner. This forces the striker lock to the left, sliding the pin to the right most position of the slot. This positions the left tip of the striker lock above the trigger.

When the trigger is pulled, it rotates the striker lock. As you can see in Figure 3, the striker lock's right corner no longer points up out of the trigger mechanism. This rotations moves the striker lock out of the way, allowing the striker bolt to move forward and fire the paintball gun. Once the trigger is released, there is are no more external forces on the system and it returns to the equilibrium posisiton shown in Figure 1.

Components

Part #	Part Name	Qty	Function	Weight (Ounces)	Material	Manufacturing Process	Photo
01	Hopper Connection	1	Connect hopper and feed neck	0.7	Plastic	Injection Molded
02	Hopper Connection Bolt and Nut	2	Apply pressure to plastic hopper connection housing	0.4	Steel	Heading and Thread Rolling
03	Stock	1	Helps stabilize gun against shoulder for improved accuracy	8.7	Aluminum	Cast
04	Barrel	1	Direct paintball exit out of marker	4.7	Aluminum	Cast and finish machined
05	Feed Neck	1	Direct paintballs from hopper into firing chamber	0.6	Aluminum	Cast and finish machined
06	Feed Neck Screw	3	Attach Feed Neck to marker body	0.1	Steel	Heading and Thread Rolling
07	MR1 2" Dovetail Drop Forward	1	Bracket to secure compressed air connection port to trigger handle	1.2	Aluminum	Cast and finish machined
08	Drop Forward Lock Screw	1	Secures Dovetail Bottom-Line to Dovetail Drop Forward	<0.1	Steel	Forging and Thread Rolling
09	MR1 Dovetail Bottom-Line	1	Connection point between compressed air and hose to marker body	3.2	Aluminum	Cast and finish machined
10	Hose Adaptor	1	Connect hose to Dovetail Bottom-Line	0.4	Steel	Forged and Threads rolled
11	MR1 Foregrip	1	Provides cover for hose connection to marker body.	4.9	Aluminum	Extruded or Cast and finish machined
12	Foregrip Fixing Screw w/washer	2	Connect foregrip to marker body	0.4	Steel	Heading and Thread Rolling
13	Braided Hose	1	Connects Dovetail Bottom-Line to marker body	1.8	Steel	Connections Headed and Threads Rolled, hose housing woven from metal sheet
14	Screw and Washer	2	Connects trigger handle to marker body	0.1	Steel	Heading and Thread Rolling
15	Handle Covers	2	Provides comfortable grip for handle	0.8	Aluminum	Cast and finish machined
16	Screw	4	Connects handle cover to handle	0.1	Steel	Heading and Thread Rolling
17	Handle Trigger Assembly	1	Allows user to control firing of paintball. Double trigger controls release of bolt, firing paintball	9.4	Steel	Cast, Finish machined, finish ground, press fitting
18	MR1 Reservoir Plug	1	Seals compressed air resevoir and includes attachment point for valve spring	0.8	Aluminum	CNC Turned
19	M5x12 Screw	1	Attaches Reservoir Plug to marker body	0.1	Steel	Heading and Thread Rolling
20	Valve Spring	1	Provides pressure against cup seal to press valve pin into valve body	0.1	5160 Steel	Coiled
21	Cup Seal and Valve Pin Assembly	1	Seals hole in valve body so air does not leak out of air reservoir	0.2	Aluminum and Plastic (Nylon)	Finish machined and ground, Injection molded
22	Valve Body	1	Routes air to Striker chamber and also to MR1 Venturi Bolt.	0.2	Aluminum	Turned and Drilled
23	Set Screw	1	Positions, orients, and secures air valve in marker body	<0.1	Steel	Heading and Thread Rolling
24	Cup Seal Guide	1	Centers Cup Seal and Valve Pin Assembly in air reservoir	0.1	Aluminum	Stamped
25	Striker Spring	1	Applies force to Striker Bolt, accelerating it into the valve pin	0.1	5160 Steel	Coiled
26	Striker Plug	1	Seals Striker chamber. Also includes a spring guide for the Striker Spring	0.8	Aluminum	Turned and ground
27	Striker Buffer	1	Helps protect Striker Plug and Striker bolt from damage during use from impact	<0.1	Plastic	Extruded
28	Striker Bolt	1	Strikes Valve Pin, releasing air from air reservoir, through valve body and MR1 Venturi bolt. Striker Bolt releases when trigger is pulled.	2.4	Aluminum	Turned and milled flat section
29	Quck Disconnect Pin	1	Secures Striker Plug to marker body	0.3	Steel	Cast
30	MR1 Venturi Bolt	1	Directs air from valve body to paintball. Also stops additional paintballs from entering chamber when firing.	1.6	Aluminum	Turned and milled
31	MR1 Pull Pin Cocking Knob	1	Connects Venturi Bolt to Striker Bolt. When Striker bolt is forced back into the cocked position by the compressed air, this pin pulls the Venturi Bolt back into the cocked position also.	0.4	Steel	Cast, Turned, Rolled
32	Marker Body	1	Houses main components of paintball gun including, venturi bolt, striker, and valve assemblies. The barrel, trigger assembly, and stock also attach to the body	14	Aluminum	Cast and finish machined
33	Misc. O-rings	11	O-rings help seal all the different chambers so compressed air does not leak out. This increases the efficiency of the paintball marker	<0.1	Rubber	Injection molded and vulcanized

**Note: Some assemblies and parts were not disassembled in order to avoid destroying the parts.

DFMA

There are two parts to DFMA: Design For Manufacture (DFM) and Design For Assembly (DFA).

DFM

In dissecting the paintball marker, several DFM considerations were discovered. Firstly the body, feed neck, drop forward, bottom line, foregrip, and trigger frame appear to be cast to size and subsequently finish machined for critical dimensions or mating surfaces. This decreases production time and material waste as opposed to, say, machining the body from a billet blank. The aforementioned parts appear to be aluminum, which is significantly easier and quicker to machine, and also gentler on tooling than steels and other harder metals.

A majority of the plastic components appear to have flashing lines, indicating that they were injection molded. This method of plastic forming ensures quick production, dimensional accuracy, and very minimal waste. The plethora of o-rings involved in proper function of the paintball marker share the same flashing lines, indicating that they too are injection molded and then vulcanized.

Finally, a good amount of circular cross sectioned parts appear to be turned from billet aluminum stock. Although this is more wasteful than casting, it must be taken into consideration that many of the circular cross-section components are moving parts, and therefore proper surface finish is critical to reducing frictional drag as the venturi bolt and cocking bolt slide in their bores. In this case, since casting yields poorer surface quality than turning, turning is required despite the wasted time and material.

DFA

The DFA characteristics of the paintball marker appear to be as well thought-out as the DFM characteristics. For instance, the hardware used on the marker are all Allen head screws; this is disadvantageous as compared to use of Phillips screws, whose bit will self-center in the cross-shaped insertion point in the head. Although a Phillips head screw would quicken assembly, Phillips screws are prone to stripping, leaving the end-user with a marker that is impossible to assemble or disassemble. Here, the consideration goes to product durability rather than assembly.

The design of the body and cocking/firing mechanisms appear to be well-suited for assembly. The components in these mechanisms are, for the most part, slip-fits in the bores in the body, and are retained by rapid retention devices such as cotter pins on easily removable posts. Not only does this make assembly easy (minimal hardware), it makes servicing the marker more convenient. In this area, DFA guidelines align themselves with product serviceability.

Finally, the paintball marker appears to be very modular in terms of assembly. Assembly of the trigger frame and body components are independent of each other, and can therefore occur simultaneously on separate assembly lines, creating two modules: the trigger and the body. These two can be joined downstream in the production order by a pair of long screws.

FMEA

In our Failure Modes and Error Analysis, we analyzed the ways in which the product could fail to achieve its desired level of functionality. These modes of failure could be caused by design flaws, manufacturing error, or user error. Procedurally, we looked at component layout and listed the most likely means of failure. We then used prescribed FMEA guidelines to assess the severity (S), probability (O) and detectability (D). The Risk Priority Number (RPN) was calculated by finding the product of S, O, and D. Afterwards, we outlined the ways in which to rectify the issues we described earlier, as well as whose responsibility it is to manage these problems. We decided that any RPN over 25 required corrective attention.

Item and Function	Failure Mode	Effects of Failure	S	Causes of Failure	O	Design Controls	D	RPN	Recommended Actions	Responsibility and Deadline	Actions Taken	S	O	D	RPN
"Barrel" Directs paintball towards target	Incomplete boring or polishing inside barrel	Premature breakage of paintball	7	Imperfection in internal surface	4	Inspecting inside of barrel	2	56	Introduce quality control measures to ascertain surface quality on inside	Manufacturing and Quality Control	-	7	4	2	56
"Striker Bolt O-Ring" Maintains pressure differentials on moving parts	Tear or rupture	Cocking action unreliable	7	Wearing of O-Ring through repeated use	2	Inspecting surface of O-Ring for indication of wear	2	28	Quality control measures to ensure smoothness of cocking bore in body or ensure quality O-ring supplier	Manufacturing, Quality Control, Supplier Logistics	-	7	2	2	28
"Pressure Tank O-Ring" Seal breakable connection between pressure source and recepticle	Tear or rupture	CO2 leakage or depressurization of gun	8	System no longer airtight	1	Inspecting hose surface for punctures	2	16	None, too rare in occurance	-	-	8	1	2	16
"Valve Body O-Ring" Maintains pressure differential between static parts and cavities	Tear or rupture	Loss of system pressure, too little cocking pressure, or too little firing pressure	7	Wearing of O-Ring through repeated use	1	Inspecting surface of O-Ring for indication of wear	2	14	None, too rare in occurance	-	-	7	1	2	14
"Firing Bolt" Supplies pressure in barrel behind paintball	Excessive friction (failure to cock)	Paintball is chopped as bolt returns to forward position	7	Bolt moves to rear position too quickly	5	Make sure chamber and components are properly lubricated	1	35	Advise users to properly clean, lubricate, and check operation of gun components after 2000 paintballs fired (about one full day’s usage)	User	-	7	5	1	35
	Excessive friction (jam)	Incapacitation of weapon	8	Lack of lubrication	2	Ensure lubrication of chamber and component	1	16	None	User	-	8	2	1	16
"Plastic Hopper Connection" Physically joins paintball hopper with loading mechanism on body	Cracking or chipping	Inability to connect hopper to paintball gun	5	Excessive mistreatment of component	1	Inspect all connectors for anomalies	1	5	None, too minor for consideration	-	-	5	1	1	5
"Braided Hose" Supply pressure to proportioning valve	Puncture or tear	Loss of pressure	8	Mistreatment of component	1	Inspect hose for tears and punctures	1	8	None, too rare in occurance	-	-	8	1	1	8
"Spring Catch, Trigger Mechanism" Enable controlled firing of weapon	Plastic deformation or fracture	Inability to fire gun	8	Uneven force distribution, Improper manufacturing methods	1	Strength test trigger mechanisms for durability, ensure quality of material	4	32	Ensure proper design of thickness of spring catch; use proper manufacturing methods to manifest spring catch on trigger rocker	Materials and Engineering (stress analysis) and Manufacturing	-	8	1	4	32

From this FMEA, we can conclude that the O-Rings are one of the biggest problem areas. However, the frequency of failure, as well as the ease of detection, make this problem a relatively minor one. Repair kits often include O-Ring replacements, so they are easily obtainable by the user. The barrel turned out to be another area of potential failure, but the detection is relatively easy, and with proper usage and care the problem should be averted. Finally, there was the issue of the spring catch on the trigger mechanism. The responsibility of ensuring its performance was up to engineers, who could find out what sort of stressors this component could take. Repeated drops, vibration analysis, and fatigue are a few of the simulations that could be run to figure out how to better this component.

DFE

When designing for the environment, there are two major factors to consider: the Life Cycle Assessment (LCA) and End of Life contingencies

LCA

The Economic Input-Output Life Cycle Assessment (EIO-LCA) website, www.eiolca.net, contains data on the most common contributors to greenhouse gases, toxic releases, and energy usage from industries and sections of those industries. We determined that a paintball gun belongs on the "Misc. Manufacturing" Industry Group, under the Sector "Sporting and athletic goods manufacturing". We allowed the simulation to pretend that an additional $1 million had been spent in this industry, then examined the energy usage required to manufacture that amount of our product (assuming all the money had been spent on paintball guns alone). The following table is from the energy usage calculation:

Sector	Total TJ	Elec MkWh	Coal TJ	NatGas TJ	LPG TJ	MotGas TJ	Distillate TJ	JetFuel TJ	Residual TJ
Total for all sectors	8.45	0.458	2.23	3.63	0.312	0.432	0.842	0.210	0.277
Power generation and supply	2.46	0.000	1.95	0.435	0.000	0.000	0.000	0	0.074
Sporting and athletic goods manufacturing	0.752	0.100	0	0.404	0.026	0.126	0.064	0	0.020
Iron and steel mills	0.510	0.025	0.024	0.434	0.001	0.004	0.003	0.000	0.017
Truck transportation	0.370	0.001	0	0.008	0.001	0.054	0.307	0	0
Plastics material and resin manufacturing	0.265	0.015	0.017	0.214	0.012	0.003	0.001	0	0.002

Naturally, the process of casting and molding the aluminum components of the paintball gun needs a lot of electricity. Additionally, the transportation of material and the finished product requires energy, not to mention the plants that process the component materials. Next is a table of how much greenhouse gas is produced as a result of creating this product:

Sector	GWP MTCO2E	CO2 MTCO2E	CH4 MTCO2E	N2O MTCO2E	CFCs MTCO2E
Total for all sectors	718	574	91.3	27.4	25.2
Power generation and supply	207	205	0	0	2.49
Waste management and remediation services	56.2	8.88	47.2	0.068	0
Truck transportation	51.7	50.9	0.079	0.710	0
Iron and steel mills	40.3	40.3	0	0	0
Sporting and athletic goods manufacturing	35.4	35.4	0	0	0

The best method for reducing environmental impact is clearly to cut down on the necessity of electricity consumption for the manufacturing of paintball guns. Second, the amount of waste produced by the manufacturing process must be limited. This may be accomplished by designing for manufacturing such that very little aluminum is discarded after being cast into the components. Lastly, more efficient storage of parts and/or the finished product could cut down on the number of trucks needed for distribution.

As for toxic releases, the mining of aluminum was the largest contributor of land releases, accounting for 60.5 kg. The manufacturing process and aluminum refining contributed to a good portion of the water releases, 2.09 kg and 1.68 kg respectively. Total air releases was mainly affected by the manufacturing process (68.9 kg) but power generation (30.9 kg) and plastics manufacturing (13.5 kg) also contributed. It is interesting to note that replacing some aluminum parts with plastic ones may not be as effective as previously thought. There is less land and water toxic release, but the air would experience a heavier concentration of toxins as a result. Still, the waste produced by aluminum mining, as well as the land damage done, can not easily be ignored.

CO₂ Emissions During Use

The typical tank of CO₂ has a 20 oz. capacity. This is due to the fact that under hotter than ideal temperatures the gas expands and the pressure inside the tank may exceed structural limitations. According to the National Sporting Goods Association, more than 8 million people participated in paintball games more than once in 2006. If we assume the majority of those players are casual players who play no more than 5 times a year, we can estimate our total paintball tanks used total to be about 50 million (including regular and one-time players). This would mean the total carbon dioxide emissions from paintball is 1 billion ounces, or 62.5 million pounds of CO₂. The average player also uses up to 2 tanks of CO₂ per day. Our total then is over 125 million pounds of CO₂ annually. The underlying assumption here is that all of the carbon dioxide in the pressurized tank is released after a full usage.

End of Life contingencies

As the FMEA above showed, the fact that much of the paintball gun is made of sturdy, lightweight metal does not prevent failure from occuring. Therefore, the implementation of plastic parts to reduce the amount of aluminum may not be the best option. Most of the essential components undergo dramatic forces; it would be very difficult and perhaps not cost-effective to use a high-strength plastic. However, the O-Rings can be improved upon so that they have a less negative impact on the environment.

From the FMEA, we showed that the O-Rings in various spots can often be the cause of eventual failure. Repair kits for paintball guns often include a supply of O-Rings, to replace worn or ruptured ones. These O-Rings are presumably thrown out once they become useless. Since recycling is not as popular an option as dumping used items in the trash, developing biodegradable O-Rings may be a better choice.

As for the reuse/recycling of aluminum and steel parts, assigning a partial refund to turning in used paintball guns may encourage the user to trade in their "useless" gun for a new/better one. Most of the parts of the old paintball gun are likely to still be functioning and in good condition. These can be put back into the assembly portion of the lifecycle, necessitating the production of fewer overall parts. This takes away from the toll on the environment inflicted by virtually every stage of production. The effects of additional transportation would be negligible, as trucks delivering shipments could also pick up the used parts while they were there.

Opportunities for Improvement

Although the paintball marker is a very simple, very reliable instrument, there are a number of manners in which to improve it's design and construction. The path this group intends to follow is improvement in paint delivery methods. A standard paintball marker is limited to firing a single paintball at a time. Additionally, there is no spray to the shot; one ball will hit only one target. This will be rectified using a shotgun style approach in which one cartridge will disperse many paintballs over a wide field, increasing the probability of a hit on the opponent.

Disregarding the possibility of a shotgun-style paintball marker, there are numerous ways to improve upon the stock design. No consideration appears to be made in mass reduction. The body is cast oversize; many of the reciprocating parts are solid metal. Reducing mass would not only facilitate maneuvering the marker, but would likely also increase the marker's rate of fire. A less massive marker would be cheaper to manufacture and ship to retailers as well.

How Product is Used

Markers must be stored in an ‘un-cocked’ position, with the safety switch in the ON position, no compressed air connected to the system, and with the barrel safety plug pressed into the end of the barrel. Most manufacturers require that moving parts be lubricated with the provided or recommended lubricants before each use. Caring users will disassemble several parts of their guns internals, to go through the lubricating steps. This will ensure longevity of the marker. Next, the user will check to have proper pressure in their gas canister, and an abundance of ammunition for the upcoming usage session. When users arrive to the arena, or playing area, overalls or certain special outer wear is put on by the users to attenuate the impact of the projectiles. A mask is the most important piece of protective equipment, guarding the eyes, face and sometimes ears from impact. Welt and ‘black and blue’ spots are common marks caused by being hit with a projectile. Most right handed users will hold the handle with their right hand, use their middle and/or index fingers to operate the trigger, and look down the length of the barrel with their right eye, with the left eye closed. While operating the markers, and trying to mark opponents without being marked themselves, users may perform intense physical activity such as running, jumping, diving and crawling. Some of this may include dirt, when done in an open forest-like area. This aspect of the product usage requires the most out of the marker. The marker must be durable enough to not get damaged, while having a constant supply of air and paintballs to fire in any orientation.

The SPYDER MR1 Manual recommends the following official usage steps and precautions: http://www.spyder.tv/section/support/manuals/mr1.pdf

Mechanical Analysis

The paintball gun has a muzzle velocity of around 280 fps (85 m/s). Using this velocity we can find the firing range of the paintball gun. Below are a list of vairous constants and useful values to use in the following analysis.

v = 85m / s
ρ = 1.119kg / m³
μ = 1.84E − 5N * s / m²
mass = 0.0032kg
diameter = 0.3048
A = .5 * π * r² = 0.0365m²
a_g = 9.87m / s²

First we need to know the time the paintball is in flight. To do this, we can assume that it is being fired from a height of 1.68 m (5.5 ft) and only being affected by gravity in the y-direcction. There will be some affect due to drag in the y-direction, but it is small enough to be neglected in this calculation.

y₂ = y₁ + v_y1 * t + 0.5 * a_g * t²

Take y1 as 0, y2 as 1.68 m, and v1 as 0. From this we get that t = 0.58 s. So the paintball is in the air for 0.58 seconds before it reaches the ground if it is shot horizontal from a height of 1.68 m.

Now that we know how long it will be in the air, we can find the distance it will travel. At 85 m/s, the force due to drag will have an affect on the velocity and therefore the distance the paintball travels. So first we must find the force due to drag.

F_d = 0.5 * C_D * ρ * v² * A

To find C_D for a sphere, we need to find the Reynolds number.

Plugging in the values for these variables, we get a Reynolds number of 1.6E6. From a chart of drag coefficients for spheres, at this Reynolds number we get a coefficient of drag of 0.4. We will assume that the drag coefficient stays constant at 0.4 at any Reynolds number during flight. This is a fairly valid assumption since the coefficient of drag is at around 0.4 from 2000-1.6E6. With this drag coefficient, we can find the force due to drag.
Using this force, we can find the accelleration in the x-direction due to drag.

a_D = − 0.00868 * v²

Now that we have the accelleration as a function of velocity, we can find the velocity as a function by time by doing the following integral and solving for velocity.

Taking v₀ as 85 m/s, integrating, and solving for t we get.

Now that we have the velocity in terms of time, we can integrate to find the distance.

Taking t₀ as 0 and t_f as 0.58s, we get

x = 41m

So the range of the paintball gun is 41 m, or 134 ft, if the gun is fired horizontally from 5.5 ft high. This distance will be greater or less depending on the angle of the gun when fired.