Physics of a Spudgun


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Well it's quite simple actually. Spudguns use some of the same principles as internal combustion engines. Just as burning gas forces a piston out of a cylinder it can also force out a potato. A spudgun is a device that uses some form of propellant to project a potato across the sky. Usually these devices are made of ABS plastic sewer pipe. There are several major parts of the spud gun that these pages will refer to. These parts are the firing chamber, the igniter, and the barrel.

The ignition device of a spud gun is simply put the spark generator that causes the combustion of the fuel in the firing chamber. This device is usually a charcoal grill lighter. The button on the sparker is depressed and a spark arcs across a wire lead and a ground wire. The grill sparker is installed in to the back of the firing chamber by means of threading, epoxy, and bolts. This sparker becomes a projectile if it is not well seated in the end cap of the firing chamber. It must be held firmly in place withstanding any pressure produced by the fuels being burned in the chamber. This type or igniter will work in most conditions including when it becomes wet with fuel.

Other igniters exist but are not recommended as highly as the charcoal grill sparker. The Colmen lantern spin lighter which use a flint and striker can become gummed up with some fuels and is not recommended for use in spud guns which will use hairspray as a primary fuel. This lighter must have new flints installed when they run out. This type of lighter also will fail to function when wet with fuel. The flame style barbecue lighter is a click lighter that produces a small-sustained flame. This lighter rarely misfires but is very hard to install given the high pressures it would be subjected to. Also the fuel in the lighter it self must be refilled. Some Spud Guns use a spark plug and battery setup that involves more work as well as more components. The benefits of this style of ignition system is that you have the ability to remote detonate the fuel from a safe distance. By far the push button charcoal grill sparker is the recommended igniter. It is cheap, effective, relatively easy to install and long lasting.

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The firing chamber is the larger section of the Spud Gun where the buring of the fuel takes place. It is usually a section of four inch PVC or ABS plastic pipe in schedule 40 thickness. This pipe is cut to the desired length and glued to the four to three inch reducer at the front and the female four inch clean out end cap. The rough volume of this chamber is important so take that into account when cutting the length of four inch pipe. This rough volume can be found from
V=p r2

Remember also to take into account the volume of the reducer fitting and end cap if precision is required. The best way to determine the exact volume of the chamber is to fill it with water and measure the volume of the water contained in the camber with graduated measuring devices such as beakers. This volume is important to know so that the proper proportions of fuel to air can be added for correct combustion.

Barrel

Size:

The combustion of the fuel in the firing chamber will create a set pressure that has to escape through the barrel of the spudgun accelerating the potato out at a specific velocity. The size of spudgun barrels usually range from 1.5 to 2.0 inches in diameter with 1.5 inches being the standard. The larger the diameter the less the acceleration of the spud projectile. This is due to Newton’s 2nd law F=ma which can be written as a=F/m or m=F/a. If the diameter of the barrel is increased the force acting on the spud is dispersed over a larger surface area and therefore it will have a slower acceleration and intern a lower muzzle velocity. Also with the larger diameter there is a larger projectile which will have a larger mass. This larger mass will reduce the acceleration of the spud as well. The length of the barrel is entirely up to you but remember the longer the barrel the more friction has to be overcome. It is safe to say that to an extent a longer barrel is more accurate than a short one. The typical range of barrel length is between two feet and four feet.

Rifling:

The inside surface of a barrel can be riffled or unrifled. Riffling is essentially several spirals cut into the inside of the barrel to cause the projectile to spin in the barrel. When the projectile leaves the barrel it spirals down range much like a football. When the projectile spins on only one axis, the one parallel to the axis of the barrel, it reduces the drag on the projectile. The less the drag is the farther the spud will travel and with the reduction of cross forces, due to the wobbling of the spud, a higher accuracy can be achieved. The unrifled barrel does not provide this balancing to the flight of the projectile and it therefore is unstable and less accurate as a result. However due to the difficulty of machining riffling on the inside of a 1.5 inch ABS pipe the unrifled barrel is the most common in use.

Projectile Motion:



If physics has taught man anything other than that gravity works it would be that a projectile follows a parabolic path when launched. This is because the force of gravity is independent to the force of the combustion in the firing chamber acting on the projectile. Using physics it is possible to calculate the distance that the projectile will follow one fired. If a pressure gage is inserted into the firing chamber so that it can take a reading of the max pressure build up before the spud is propelled out of the barrel several equations can be applied and ultimately the distance traveled by the spud can be found. It is important to place the pressure gage in a fitting or thicker part of the firing chamber so that it will not be blown out of the chamber as a projectile. The preferred type of gage to be used is one that pushes a peg to the highest pressure and then stays requiring that it be reset after each use. Otherwise you would have to estimate the max pressure by inspection of the dial during firing. Once this max pressure is obtained you can use it to calculate the force on the spud in the barrel.


F=p*c (1)

Where F is the force in Newton’s on the spud in the barrel, p is the max pressure in the firing chamber in Pascal’s, and c is the cross sectional area of the spud in the barrel. To convert psi into Pascal’s multiply by 6.895E3. Remember that the cross sectional area of the spud is the cross sectional area of the barrel. This is found by using


c=p *r2 (2)

Where c is the cross sectional area of the barrel, and r is the radius of the barrel in meters used.

Once the force on the spud projectile has been found Newton’ second law can be applied


F=m*a (3)

Where force F in Newton’s, is equal to mass m in kg, times acceleration a in m/s2. The mass of the potato can easily be found by finding the mass of the whole potato before being cut in the barrel and then taking the mass of that potato after being cut and to find the mass of the potato being shot out of the barrel. Set m*a equal to the above equation p*c after making the substitution for c and solve for a. This gives


m*a=p*p *r2 ® (4)

a=(p*p *r2)/m (5)

After taking the mass of the projectile potato, m in kg, you will have the pressure in the chamber, p in Pascal’s, prior to firing the spud, the radius of the barrel, r in meters, and the mass of the potato shot. From all of the above equations it is possible to find the acceleration of the potato down the length of the barrel given by equation (4). This is of course assuming a frictionless barrel. In order to calculate the friction of the spud in the barrel it is suggested that a spud projectile of average size and density be puled out of the barrel by use of a hook through the spud and attached to a fish weighing scale. This will give the kilogram force needed to overcome fiction in the barrel but it must then be converted to Newton’s by multiplying the value times g.


W*g=N (6)

W is the weight read from the scale in kg, g is the gravity constant =9.81m/s2, and N is the force of the kinetic friction of the potato in the barrel in Newton’s. So from the previous calculation of the kinetic fiction N of an average spud projectile it is possible to find the true acceleration of the spud as it passes down the barrel from this equation.


m*a =(p*p *r2)-N ®

a=[(p*p *r2) -(W*g)]/m (7)

Where a in m/s2 is the acceleration of the spud in the barrel, p is the max pressure in the firing chamber given in Pascal’s, p is the constant » 3.14, r is the radius of the barrel in meters, W is the weight given by forcing an average potato out of the barrel with a scale in kilograms, and m is the mass of the potato projectile.

Where not quite done yet! We still have to find the velocity of the potato now as it leaves the barrel. This commonly referred to as muzzle velocity. This can be found from the equation


V2 = Vo2+2*a*x (8)

Where V is the muzzle velocity, Vo is the initial velocity before firing or 0, a is the acceleration found above, and x is the length traveled by the spud or the barrel length. This yields the following equation.


V2 = 2*a*x (9)

After substituting in a from equation (7) in to equation (9) You get


V2 = 2*x*{[(p*p *r2) +(W*g)]/m} (10)

From this muzzle velocity V can be found by taking the square route of both sides




V= Ö (2*x*{[(p*p *r2) +(W*g)]/m}) (11)

Once the muzzle velocity V in m/s2 is accurately calculated being careful to have the correct unit conversions the following formula can be applied to find the distance that the spud could travel if there is no air resistance or drag.


R = [V2/g]*[sin (2q )] (12)

Where R is the range in meters, V is the muzzle velocity of the projectile, g is the gravity constant = 9.81 m/s2, and sin (2q ) is the sin of 2 times the launch angle q . When (11( is substituted into (12) the following equation results.


R = {[Ö (2*x*{[(p*p *r2) +(W*g)]/m})]2/g}*{sin (2q )} (13)



Again to summarize:

V– Muzzle velocity (m/s)

x– length of barrel in (m)

p– Max firing chamber pressure in Pascal’s or (N/m2)

p – » 3.14

r– radius of barrel in (m)

W– weight shown on scale when pulling spud out of barrel (kg)

g– gravity constant = 9.81 (m/s2)

m– mass of the spud projectile in (kg)

R– is the range of the projectile in (m)

q – is the launch angle

R– is the range of the projectile in (m)



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