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Delmotte – Espere 1

Introduction

The physics behind a gun and the bullets it fires helps determine the force

of impact and acceleration of the bullet. A blowgun is no different than any other

gun, as well as its ammunition. The physics applied to a normal gun also are

applied to a blowgun, and the specifications of the barrel length of the blowgun,

the length, and mass of the darts fired will also determine how much force they

have on impact, as well as how much they accelerate in the barrel. (Refer to

Appendix C for how acceleration is affected) Force equals mass times

acceleration, directly stating that mass effects force. Acceleration effects force

because a greater acceleration leads to a greater velocity, and the faster an

object moves, the more force of impact it has (Newton’s Second Law). It is

known that these three factors play a role in the projection of the bullet, but the

question is how much (Clark). The research set out to find the effect of the barrel

length, bullet length, and bullet mass on the force of impact and acceleration of

the bullet when it is fired. It was intended to find the combination that created the

highest force of impact.

A test was carried out by using the air pump to fire the dart out of the

blowgun at the center of the force plate to get the most precise force recording.

When the bullet hit the force plate, a spike would appear on the LabQuest. The

maximum value of this force spike would be recorded as the force of impact of

the bullet. In order to minimize confounding variables during testing, namely the

amount of power the user blew with, an air pump was used instead to fire the

dart out of the blowgun to guarantee the same amount of power for each trial.


The end of the blowgun was placed a set distance from the force plate to keep

the distance the same for each trial as the different barrel lengths would alter the

total distance the dart traveled for each trial. The darts and blowgun were

switched out as indicated by which trial was next, and the process would be

repeated.

This research has many applications to the real world and may have value

to hunters or the military. Even though blowguns were used for the experiment,

the physics behind the experiment remains true for real guns and bullets. This

research can help hunters or military soldiers determine what specifications need

to be changed or used in certain scenarios. If hunters need to use long range

ballistics to snipe their prey from afar, they would know which combination of

factors would allow their bullet to travel the fastest and with the most force,

allowing for a secure kill from afar. If military soldiers are in close-quarters

combat, this research will allow them to determine which combination of factors

works well in short range situations, instead of using ammunition that should be

used for a longer range scenario. This research will also be valuable to young

kids as it can be used by toymaker companies such as NERFTM to produce

powerful, but safe products. In other words, NERFTM would know which

combination of factors would cause too much force of impact, but could find

which combination allows the projectile to travel the fastest with the least amount

of force. Overall, this research will allow people to determine what factors to use

for their guns, whether it be for war, fun, or game.


Review of Literature

When shooting a gun, “the most important thing for a shooter to know

about bullets when shot is that, while in flight, they are all projectiles” (Cramer).

The bullets go through projectile motion, where they travel in a parabola,

accelerate a certain amount, travel at a certain velocity, and travel a certain

distance. If they hit an object, they hit the object with a certain force—the force of

impact. The characteristics of a gun and its bullet both affect the projectile motion

of the bullet when it is fired; these factors affect the “Science of Shooting.”

(Kramer) Actual guns and blowguns have many similar properties, so

characteristics that may make guns shoot bullets faster or farther can apply to

blowguns as well. When wanting a gun among others to shoot faster or have

more force of impact, there are three main factors: the length of the barrel, the

length of the bullet, and the mass of the bullet.

In the experiment, modifications are being made to the blowgun and the

bullets in order to gain the highest acceleration of the bullet when it is shot. The

factors of barrel length, bullet length, and bullet mass all affect the muzzle

velocity of the bullet when it is fired. The highest muzzle velocity will want to be

found as it correlates to the highest acceleration of the bullet. The change of

initial velocity to final velocity over time is equal to acceleration, so having the

greatest difference in initial and final muzzle velocities will result in the highest

acceleration. Achieving the highest acceleration will help create the highest force

of impact according to Newton’s Second Law of Motion, where force is

proportional to acceleration.


Newton’s Second Law helps explain the force of impact of the bullet when

it is fired. Newton’s Second Law is that force is equal to the mass of the projectile

times the acceleration. This can be expressed through the following equation,

where the force of the projectile (F) is equal to the mass of the projectile (m)

times the acceleration of the projectile (a).

F=ma

According to Newton’s Second Law, mass is proportional to force,

meaning that the higher the mass of the projectile being shot out of the blowgun,

the higher the force of impact will be.

In a past experiment conducted by Brandon L Clark, a university student,

the barrel length of a Mosin-Nagant 7.62x54R Rifle was tested to see if it had an

effect on the muzzle velocity. The barrel length is an important factor when it

comes to picking a firearm as the barrel length is known to be a factor “[in]

chamber pressure and the expansion of gas… [barrel length is] important in

relationship to velocity figures and generally, the longer the barrel the higher the

velocity.” (Clark) While blowguns do not have a use of the expansion of gas,

chamber pressure is important for the air being blown into the blowgun. Clark

tested this claim above in his experiment and concluded that the relationship is

linear. This means that the shorter the length of the barrel was, the lower the

muzzle velocity was of the projectile, while the longer the length of the barrel, the

higher the muzzle velocity was. He proved the claim to be correct. Relating to the

experiment, the longer barrel length will result in more distance for the bullet to

travel with it taking only a slightly longer time. The impulse of the bullet can be

found and generally the longer it takes for the bullet to travel through the barrel,


the higher the velocity of the bullet will be when it is fired. This is expressed

through the following equation where the force (f) times the amount of time it

takes for the bullet to travel through the barrel (t) is equal to the mass (m) times

the change in velocity (v).

ft=m∆v

After reviewing several of the sources, it hypothesized that the

acceleration and force of impact the projectile will travel depends on the mass of

the projectile, the size (shape/length) of the projectile, and the barrel length of the

firearm. Both the projectile length and mass and the length of the barrel will affect

the final force of impact and acceleration of the bullet when shot. It is important to

take these variables into consideration when determining the best characteristics

of a blowgun and its projectile to shoot the projectile the fastest with the highest

force of impact.

Problem StatementProblem Statement:


To determine the effect of barrel length of a blowgun and projectile length

and mass on the acceleration and force of impact when the projectile is fired.

Hypothesis:

The biggest barrel length of 0.6 m and the smallest projectile mass of 0.8

g and length of 0.075 m will produce the highest force of impact and acceleration

when the bullet is fired.

Data Measured:

The independent variables of this experiment were the barrel length of the

blowgun (0.6 m, 0.46 m, and 0.3 m) the length of the projectile (0.075 m, 0.07 m,

and 0.065 m), and the mass of the projectile (1.4 g, 1.1 g, and 0.8 g). The

acceleration and force of impact of the projectile when it was fired were the

dependent variables. The force of impact was measured in Newtons (N) using a

force plate. The force is given in the LabQuest when the projectile hits the force

plate after it is fired. The acceleration was measured in meters per second

squared (m/s2) and was solved for using Newton’s Second Law of Motion (see

Appendix C). The type of test used was a 3-factor DOE, which was used to

compare the values of the trials. Each DOE had 11 trials each, and three were

done to make sure the data was consistent throughout.

Experimental Design


Materials:

Northwest Territory 120V AC PumpAir Pump Cap (1/2 in diameter)(3) Blowguns (varying lengths)(5) Handmade Bullets

Vernier Force PlateLabQuestTI-Nspire CalculatorMeterstick

Procedure:

Before Firing

1. Set up low, high, and standard length blowguns (see Appendix A).

2. Set up handmade bullets (see Appendix B).

3. Set up standard trials as trials 1, 6, and 11. Use TI-Nspire calculator to randomize the rest of the trials.

4. Repeat step 3 for randomizing the trials for the other DOEs.

5. Set Force Plate onto the floor where it is laying down.

6. Plug in Force Plate into the Labquest. The Labquest should set up, and all that is needed is to press the play button when recording data.

7. Plug in 120V AC Pump. Put air pump cap on the end that blows out air.

Firing the Blowgun

8. Before each trial, make sure there is nothing on the force plate and zero the force plate on the Labquest. If negative numbers are seen on the Labquest, reverse the calibration.

9. Push selected handmade bullet through the hole of the mouthpiece of selected blowgun until the end of the bullet is equivalent with the pipe part of the blowgun and the bullet is firmly stuck inside.

10. Align the air pump cap so it’s firmly stuck inside the mouthpiece of the selected blowgun.

11. Place meter stick directly above to the force plate and measure out 30 cm above the force plate. Align blowgun so the end of the blowgun is next to the 30 cm mark.


12. When ready to fire, press record on Labquest and turn on the 120V AC Pump. Leave AC pump on until the bullet fires. When bullet fires, turn off AC pump.

13. When bullet hits the force plate, stop data recording. On the Labquest, look for a spike in the data and using the “Statistic” option, highlight the spike and look for the “max” statistic. This is the force of impact.

14. When done shooting, unlatch air pump cap from selected mouthpiece.

15. Locate and gather bullet that was fired.

16. Repeat steps 8-15 for the other trials.

Diagram:

Figure 1. Materials

Figure 1 shows the materials used in the experiment.


Figure 2. Setup to Fire Blowgun

Figure 2 shows how the procedure will look like before the bullet is shot.

This was done within the school’s gymnasium, but the picture was taken in the

classroom. The 120V AC Pump is positioned above the blowgun, with the blower

cap firmly fitted into the blowgun, the bullet is inside, and the blowgun tip is

directly placed 0.30 m above the force plate. Once ready, start LabQuest data

recording and turn on the 120V AC Pump to shoot the bullet.


Figure 3. Dart Inside Blowgun

Figure 3 shows what the bullet should look like when it is inside the

blowgun. The end of the bullet should not be positioned inside the female

reducing adapter part of the blowgun, but it should be tucked into the PVC pipe

part of the blowgun.


Figure 4. Air Pump Cap Alignment with Blowgun.

Figure 4 shows what the air pump cap will look like when firmly aligned

with the blowgun. The hole of the blower cap should be within the mouthpiece of

the blowgun, so when the AC pump is turned on, the air will blow through the

tube of the blowgun.


Data and ObservationsTable 1Value of Factors

Factors (+) Standard (-)Barrel Length (m) 0.6 0.46 0.3Bullet Length (m) 0.075 0.07 0.065Bullet Mass (g) 1.4 1.1 0.8

Table 1 shows the values that were used for the high, low, and standard

for each factor. Barrel and bullet length were measured in inches and converted

to meters and bullet mass was measured in grams.

Table 2Run 1 of Trials

TrialBarrel Length

Bullet Length

Bullet Mass

Acceleration (m/s)2

Force (N)

Bullet Mass (g)

Standard

3.3643.7

1.1

2 + + + 4.929 6.9 1.43 + + - 3.625 2.9 0.84 + - - 2.750 2.2 0.85 + - + 3.214 4.5 1.4

Standard

3.4553.8

1.1

7 - - - 2.125 1.7 0.88 - - + 2.214 3.1 1.49 - + + 2.786 3.9 1.4

10 - + - 2.375 1.9 0.8Standar

d3.455

3.81.1

Table 2 shows the results of the first 11 trials for run 1. Acceleration was

found using the formula for Newton’s Second Law of Motion (Refer to Appendix

C). It can be seen that the biggest force was produced by trial 2, or the high

barrel length, high bullet length, and high bullet mass (+, +, +) trial, with a force of

6.9N. This trial also had the highest acceleration of 4.9 m/s2. The two weakest

trials were the low barrel length, low bullet length, and low bullet mass trial (-,-,-)


and the low barrel length, high bullet length, and low bullet mass trial (-,+,-), with

forces of 1.7 N and 1.9 N respectively. While trial 7 holds the lowest acceleration,

trial 10 does not hold the 2nd lowest acceleration, as trial 8, the trial of low barrel

length, low bullet length, and high bullet mass (-,-,+) has a lower acceleration

despite having a higher force. The three standards also all have very similar

results.


TrialBarrel Length

Bullet Length

Bullet Mass

Acceleration (m/s)2

Force (N)

Bullet Mass (g)

Standard

3.5453.9

1.1

2 + + + 4.714 6.6 1.43 + + - 4.125 3.3 0.84 + - - 3.375 2.7 0.85 + - + 2.714 3.8 1.4

Standard

3.2733.6

1.1

7 - - - 1.750 1.4 0.88 - - + 2.000 2.8 1.49 - + + 2.643 3.7 1.4

10 - + - 2.500 2 0.8Standar

d3.455

3.81.1

Table 3 shows the results of the next 11 trials for run 2. Again, trial 2 holds

the highest force of 6.6 N, as well as the highest acceleration of 4.7 m/s2. Trial 3,

the trial of high barrel length, high bullet length, and low bullet mass (+,+,-) held

the 2nd highest acceleration of 4.1 m/s2 despite being far from having the 2nd

highest force. Trials 7 and 10 held the two lowest forces again of 1.4 N and 2 N

respectively. Also, trial 8 too holds the 2nd lowest acceleration of 2 m/s2 despite


having a higher force, with trial 7 still holding the lowest acceleration of 1.75 m/s2.

The standards once again hold very similar results.


TrialBarrel Length

Bullet Length (cm)

Bullet Mass

Acceleration (m/s)2

Force (N)

Bullet Mass (g)

Standard

3.3643.7

1.1

2 + + + 4.643 6.5 1.43 + + - 4.000 3.2 0.84 + - - 2.875 2.3 0.85 + - + 3.500 4.9 1.4

Standard

3.3643.7

1.1

7 - - - 1.625 1.3 0.88 - - + 2.071 2.9 1.49 - + + 2.786 3.9 1.4

10 - + - 2.250 1.8 0.8Standar

d3.273

3.61.1

Table 4 shows the results of the last 11 trials for run 3. Trial 2 once again

hold the highest force and acceleration of 6.5 N and 4.6 m/s2. Trial 3 followed

behind trial 2 with an acceleration of 4 m/s2 precisely. Trials 7 and 10 also follow

suit by having the two lowest forces of 1.3 N and 1.8 N. Trial 8 continues the

pattern of having the 2nd lowest acceleration of 2 m/s2 with trial 7 still holding the

lowest acceleration of 1.6 m/s2. The standards once again hold very similar

results, although lower than the standards from Runs 1 and 2.


Table 5Observations for Run 1

Trial Observation

1 Bullet flew out with a loud thud.

2 Bullet flew out strongly, very loud thud.

3 Bullet flew out weakly, had a loud thud.

4 Bullet flew out weakly, quiet thud.

5 Bullet got jammed. Took 2 attempts. bullet flew out strongly, very loud thud.


7 Bullet flew out very weakly, quiet thud.

8 Bullet hit did not register. Took 3 attempts. Bullet flew weakly out with a loud thud.

9 Bullet flew out strongly, loud thud.

10 Bullet hit did not register. Took 4 attempts. Bullet flew out weakly with quiet thud.

11 Bullet hit did not register. Took 2 attempts. Bullet flew out with a loud thud.

Table 5 shows the observations made while conducting each trial for run

1. Most trials had the dart fly out of the blowgun without a problem. Some of the

darts produced a louder thud when hitting the force plate than others, such as

trial 2, while others flew out with very weakly yet still produced a loud thud.

During trial 5, the dart got jammed in the barrel of the gun and took several

attempts to fire the dart. The LabQuest failed to identify the force spike with some


trials, meaning that the “bullet hit did not register.” This resulted in the trial having

to be redone as many times until the force of impact was correctly registered.


Trial Observation


2 Bullet hit did not register. Took 2 attempts. Bullet flew out strongly with a very loud thud.


4 Bullet flew out, quiet thud.

5 Bullet got jammed. Took 3 attempts. Bullet flew out strongly, very loud thud.


7 Bullet flew out very weakly, quiet thud.

8 Bullet got jammed. Took 2 attempts. Bullet flew out, quiet thud.


10 Bullet hit did not register. Took 3 attempts. Bullet flew out weakly with a loud thud.

11 Bullet got jammed. Took 2 attempts. Flew out with a loud thud.


2. This run contained more errors than run 1 as there were a lot more jamming of

the dart in the barrel and the LabQuest not registering the impact. When the

darts fired and were correctly identified, the results were similar to run 1.



Trial Observation


2 Bullet flew out strongly with a very loud thud.



5 Bullet got jammed. Took 2 attempts. bullet flew out strongly, very loud thud.


7 Bullet hit did not register. Took 4 attempts. Bullet flew out very weakly with a quiet thud.

8 Bullet got jammed. Took 3 attempts. bullet flew out, loud thud.


10 Bullet hit did not register. Took 3 attempts. Bullet flew out weakly with a quiet thud.



3. This run also had many errors while being conducted, with the most appearing

error being that the darts were getting jammed in the barrel. The LabQuest also

had a very difficult time identifying the force of impact for trial 7, resulting in four

attempts. With successful attempts, observations of thud noise and power of dart

were similar to that of runs 1 and 2.


Figure 5. Loading Process

Figure 5 shows the dart being loaded into the blowgun. The dart is placed

into the mouthpiece with the taped side facing in and pushed slightly past the

connecting joint to make sure the dart is tucked inside the actual barrel.


Figure 6. Firing Process

Figure 6 shows the process and method used when firing the blowgun

using the air pump. The blowgun was held above the force plate 30 cm above

using the meter stick, with the air pump hooked to the mouth piece of the

blowgun. Then, the air pump was turned on to fire the dart. The data was

captured by the LabQuest.


Figure 7. Analyzing Process

Figure 7 shows the LabQuest used to analyze the data. The force spike

was found on the graph and analyzed to get a precise force of impact of the

bullet. This number was recorded in our data table and the entire process was

repeated until all trials were complete.


Data Analysis and Interpretation

The trial order was randomized in order to reduce inaccuracy caused by

bias. For all three DOEs done, the standard trials were designated as 1, 6, 11. All

other trials were randomized using the TI-Nspire random function. Any duplicate

numbers were skipped until a non-duplicate number was found. The procedure

was modified to ensure it was conducted the same way every time and the data

recorded was consistent. Three DOEs were done to ensure similar numbers

were gotten throughout all three. This helps ensure the data recorded is valid.

Table 8Averages of Force DOEs

Runs First DOE (N)

Second DOE (N)

Third DOE (N)

Average Force

(N)Barrel Length

Bullet Length

Bullet Mass

+ + + 6.9 6.6 6.5 6.67+ + - 2.9 3.3 3.2 3.13+ - - 2.2 2.7 2.3 2.40+ - + 4.5 3.8 4.9 4.40- - - 1.7 1.4 1.3 1.47- - + 3.1 2.8 2.9 2.93- + + 3.9 3.7 3.9 3.83- + - 1.9 2.0 1.8 1.90

Table 8 shows the data recorded throughout the three DOEs done, and

the numbers when the data was averaged. There was a trend where the higher

barrel length trials resulted in higher forces of impact. There was also a trend

where higher bullet masses resulted in higher forces of impact. This can be

explained with Newton’s Second Law, where force is proportional with mass,

meaning higher masses result in higher force. The grand average is found by

adding all of the averages together and averaging that number; the grand

average for force was 3.34 Newtons.


Table 9Table of Standards for Force

Table of Standards (Force-N)3.7 3.8 3.8 3.9 3.6 3.8 3.7 3.7 3.6

1 2 3 4 5 6 7 8 93.45

3.5

3.55

3.6

3.65

3.7

3.75

3.8

3.85

3.9

3.95

3.7

3.8 3.8

3.9

3.6

3.8

3.7 3.7

3.6

Standards

Forc

e (N

)

Figure 8. Standards Data Force Scatter Plot.

Table 9 and Figure 8 both show the data recorded when doing the

standard trials. The values for the standards were relatively close to each other,

implying the data to be consistent. The data seems to go in a parabola; the

standards start getting higher, and then decline. Any effect that has an absolute

value that is double the range of standards is considered statistically significant.

The range of standards is 0.3, so the range of standards doubled would be -0.6

Newtons to 0.6 Newtons.

Table 10


Force DataFirst Second Third

Order Trial

Force (N)

Order Trial

Force (N)

Order Trial

Force (N)

1Standar

d 3.7 1Standar

d 3.9 1Standar

d 3.73 (+,+,+) 6.9 7 (+,+,+) 6.6 2 (+,+,+) 6.55 (+,+,-) 2.9 3 (+,+,-) 3.3 9 (+,+,-) 3.29 (+,-,-) 2.2 4 (+,-,-) 2.7 4 (+,-,-) 2.32 (+,-,+) 4.5 9 (+,-,+) 3.8 8 (+,-,+) 4.9

6Standar

d 3.8 6Standar

d 3.6 6Standar

d 3.74 (-,-,-) 1.7 5 (-,-,-) 1.4 5 (-,-,-) 1.3

10 (-,-,+) 3.1 8 (-,-,+) 2.8 10 (-,-,+) 2.98 (-,+,+) 3.9 10 (-,+,+) 3.7 7 (-,+,+) 3.97 (-,+,-) 1.9 2 (-,+,-) 2.0 3 (-,+,-) 1.8

11Standar

d 3.8 11Standar

d 3.8 11Standar

d 3.6

Table 10 shows the data recorded for force throughout the trials. Most of

the trials had generally close data, but there is an exception in the high barrel

length, low bullet length, and high bullet mass (+,-,+) trials where there is a

difference of 1.1 Newtons.


Table 11Effect of Barrel Length on Force

Barrel Length+ -6.67 1.473.13 2.932.40 3.834.40 1.90

Average 4.15 2.53

-1 10.000.501.001.502.002.503.003.504.004.505.005.506.00

2.5325

4.15

Barrel Length (m)

Forc

e (N

)

Figure 9. Effect of Barrel Length on Force.

Table 11 and figure 9 shows the effect of barrel length on force of impact.

The effect of barrel length can be found by finding the slope of the force, which is

the high value subtracted by the low value. The effect of barrel length on force is

1.62. This means as the length of the blowgun increases from 0.3 m to 0.6 m, on

average the force of impact increases by 1.62 Newtons. This effect is greater

than the range of standards doubled, making it significant.


Table 12Effect of Bullet Length on Force.

Bullet Length+ -6.67 2.403.13 4.403.83 1.471.90 2.93

Average 3.88 2.80

-1 10.000.501.001.502.002.503.003.504.004.505.005.506.00

2.8

3.88

Bullet Length (m)

Forc

e (N

)

Figure 10. Effect of Bullet Length on Force.

Table 12 and figure 10 shows the effect of bullet length on force of impact.

The effect of bullet length was found to be 1.08. This means as the length of the

bullet increases from 0.065 m to 0.075 m, on average the force of impact

increases by 1.08 Newtons. This effect is greater than two times the range of

standards, making it significant.


Table 13Effect of Bullet Mass on Force

Bullet Mass+ -6.67 3.134.40 2.402.93 1.473.83 1.90

Average 4.46 2.23

-1 10.000.501.001.502.002.503.003.504.004.505.005.506.00

2.225

4.46

Bullet Mass (g)

Forc

e (N

)

Figure 11. Effect of Bullet Mass on Force.

Table 13 and figure 11 show the effect of bullet mass on force of impact.

The effect of bullet mass was found to be 2.23. This means that as the bullet

mass increases from 0.8 g to 1.4 g, the on average the force of impact increases

by 2.23 Newtons. This effect is greater than two times the range of standards,

making it significant.


Table 14Interaction of Barrel Length and Bullet Length on Force.

Bullet Length(+) (-)

Barrel Length

Solid Segment (+)

4.90 3.40Line

Segment (-)2.87 2.20

-1 10.000.501.001.502.002.503.003.504.004.505.005.506.00

3.40

4.90

2.20

2.87

Barrel Length (m)

Forc

e (N

)

Figure 12. Interaction of Barrel Length and Bullet Length on Force.

Table 14 shows the average numbers for the interaction of barrel length

and bullet length, and figure 12 is a visual representation of the values. The

interaction effect can be found be finding the slopes of the two lines and

subtracting the slope of the dotted segment from the slope of the solid segment.

The interaction effect was found to be 0.41 Newtons. This is less than two times

the range of standards, making the interaction effect not significant. The two lines

are almost parallel and seem to get closer to each other as the values get

smaller. This implies that there is probably no interaction, or if there is, it’s a very

small interaction.


Table 15Interaction of Barrel Length and Bullet Mass on Force

Bullet Mass(+) (-)

Barrel Length

Solid Segment (+)

5.53 2.77Line

Segment (-)3.38 1.68

-1 10.000.501.001.502.002.503.003.504.004.505.005.506.00

2.77

5.53

1.68

3.38

Barrel Length (m)

Forc

e (N

)

Figure 13. Interaction of Barrel Length and Bullet Mass on Force.



interaction effect was found to be 0.53 Newtons. This is less than two times the

range of standards, making the interaction effect not significant. Near the low

value, the two lines are very close together. The two lines are also not parallel,

implying there may be an interaction between the two effects.

Table 16


Interaction of Bullet Length and Bullet Mass on ForceBullet Mass(+) (-)

Bullet Length

Solid Segmen

t(+)

5.25 2.52Line

Segment

(-)3.67 1.93

-1 10.000.501.001.502.002.503.003.504.004.505.005.506.00

2.52

5.25

1.93

3.67

Bullet Length (m)

Forc

e (N

)

Figure 14. Interaction of Bullet Length and Bullet Mass on Force.



interaction effect was found to be 0.495 Newtons. This is less than two times the

range of standards, making the interaction effect not significant. Near the low

value, the two lines are very close to each other, and the lines are not parallel to

each other. This implies that there may be an interaction, but the difference in the

slopes of the lines are very small, so if there is one it’s very small.


-3 -2 -1 0 1 2 3

Figure 15. Dot Plot of Effects.

Figure 15 shows a dot plot of all of the effects. Any dot that is outside the

two lines are deemed significant. As it can be seen, only the individual effects are

significant, with the effect of bullet mass being the most significant. All interaction

effects are within two times the range of standards, making them not significant.

Table 17Averages of Acceleration DOEs

Runs First DOE (m/s2)

Second DOE (m/s2)

Third DOE (m/s2)

Average Acceleratio

n(m/s2)

Barrel Length

Bullet Length

Bullet Mass

+ + + 4.92 4.71 4.64 4.76+ + - 3.62 4.12 4.00 3.91+ - - 2.75 3.37 2.87 3.00+ - + 3.21 2.71 3.50 3.14- - - 2.12 1.75 1.62 1.83- - + 2.21 2.00 2.07 2.09- + + 2.78 2.64 2.78 2.73- + - 2.37 2.50 2.25 2.37

Table 17 shows the acceleration recorded throughout the three DOEs

done, and the average of the three values. There is a trend where higher barrel

length resulted in higher acceleration values. The bullets had more distance to

-0.6 0.6

Barrel Length – Blue Diamond

Bullet Length – Blue Triangle

Bullet Mass – Blue Square

Interaction Barrel Length and Bullet Length – Black Diamond

Interaction Barrel Length and Bullet Mass – Black Triangle

Interaction Bullet Length and Bullet Mass – Blue Circle


travel throughout the blowgun, giving them more time to accelerate. The grand

averaged was calculated to be 2.98.

Table 18Table of Standards for Acceleration

Table of Standards (Acceleration-m/s2)3.36 3.45 3.45 3.54 3.27 3.45 3.36 3.36 3.27

1 2 3 4 5 6 7 8 93.2

3.3

3.4

3.5

3.6

3.7

3.8

3.36

3.45 3.45

3.54

3.27

3.45

3.36 3.36

3.27

Standards

Acce

lera

tion(

m/s

2)

Figure 16. Standards Data Force Scatter Plot.

Table 18 and figure 16 both show the data recorded when doing the

standard trials. The values for the standards were relatively close to each other,

implying the data was consistent. There is no particular pattern either. The range

of standards was calculated to be 0.27, so any effect that is outside double the

range of standards of -0.54 m/s2 to 0.54 m/s2 is deemed significant.

Order TrialAcceleration

(m/s2)


(m/s2)


(m/s2)1 Standard 3.36 1 Standard 3.54 1 Standard 3.36

3 (+,+,+) 4.92 7 (+,+,+) 4.71 2 (+,+,+) 4.645 (+,+,-) 3.62 3 (+,+,-) 4.12 9 (+,+,-) 4.009 (+,-,-) 2.75 4 (+,-,-) 3.37 4 (+,-,-) 4.872 (+,-,+) 3.21 9 (+,-,+) 2.71 8 (+,-,+) 3.506 Standard 3.45 6 Standard 3.27 6 Standard 3.364 (-,-,-) 2.12 5 (-,-,-) 1.75 5 (-,-,-) 1.62

10 (-,-,+) 2.21 8 (-,-,+) 2.00 10 (-,-,+) 2.078 (-,+,+) 2.78 10 (-,+,+) 2.64 7 (-,+,+) 2.787 (-,+,-) 2.37 2 (-,+,-) 2.50 3 (-,+,-) 2.25

11 Standard 3.45 11 Standard 3.45 11 Standard 3.27

First Second Third


Table 19Acceleration Data

Table 19 shows the data recorded for force throughout the trials. The

acceleration varies greatly in the high barrel length, low bullet length, and low

bullet mass trials and the high barrel length, low bullet length, and high bullet

mass trials.


Table 20Effect of Barrel Length on Acceleration

Barrel Length+ -4.76 1.833.91 2.093.00 2.733.14 2.37

Average 3.70 2.26

-1 10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

2.26

3.70

Barrel Length (m)

Acc

eler

atio

n (m

/s2)

Figure 17. Effect of Barrel Length on Acceleration.

Table 20 and figure 17 show the effect of barrel length on the acceleration

of the bullet. The effect of barrel length was calculated to be 1.45 m/s2. This

means as the barrel length increases from 0.3 m to 0.6 m, on average the

acceleration of the bullet increases by 1.45 m/s2. This is more than double the

range of standards, making this effect significant.

Table 21


Effect of Bullet Length on AccelerationBullet Length+ -4.76 3.003.91 3.142.73 1.832.37 2.09

Average 3.44 2.52

-1 10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

2.515

3.44

Bullet Length (m)

Acc

eler

atio

n (m

/s2)

Figure 18. Effect of Bullet Length on Acceleration.

Table 21 and figure 18 show the effect of bullet length on the acceleration

of the bullet. The effect of bullet length was calculated to be 0.93. This means as

the bullet length increases from 0.065 m to 0.075 m, on average the acceleration

of the bullet increases by 0.93 m/s2. This is more than double the range of

standards, making this effect significant.

Table 23


Effect of Bullet Mass on AccelerationBullet Mass+ -4.76 3.913.14 3.002.09 1.832.73 2.37

Average 3.18 2.78

-1 10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

2.7775

3.18

Bullet Mass (g)

Acc

eler

atio

n (m

/s2)

Figure 19. Effect of Bullet Mass on Acceleration.

Table 23 and figure 19 show the effect of bullet mass on the acceleration

of the bullet. The effect of bullet length was calculated to be 0.4. This means as

the bullet mass increases from 0.8 g to 1.4 g, on average the acceleration of the

bullet increases by 0.4 m/s2. This is less than the range of standards doubled,

which makes this effect not significant.


Table 24Interaction of Barrel Length and Bullet Length on Acceleration.

Bullet Length(+) (-)

Barrel Length

Solid Segment (+)

4.34 3.07Line

Segment (-)2.55 1.96

-1 10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

3.06833333333333

4.34

1.96166666666667

2.55

Barrel Length (m)

Acc

eler

atio

n (m

/s2)

Figure 20. Interaction of Barrel Length and Bullet Length on Acceleration.



interaction effect was found to be 0.34 m/s2. This is less than two times the range

of standards, making the interaction effect not significant. The two lines are not

parallel, implying that there may be an interaction.


Table 25Interaction of Barrel Length and Bullet Mass on Acceleration

Bullet Mass(+) (-)

Barrel Length

Solid Segment (+)

3.95 3.46Line

Segment (-)2.41 2.10

-1 10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

3.455

3.95

2.10166666666667

2.41

Barrel Length (m)

Acc

eler

atio

n (m

/s2)

Figure 21. Interaction of Barrel Length and Bullet Mass on Acceleration.



interaction effect was calculated to be 0.09 m/s2. This is less than double the

range of standards, which makes the interaction effect not significant.

Graphically, the lines look parallel, with both lines having almost the same slope.

There is probably no interaction effect.


Table 26Interaction of Bullet Length and Bullet Mass on Acceleration

Bullet Mass(+) (-)

Bullet Length

Solid Segmen

t(+)

3.75 3.14Line

Segment

(-)2.62 2.41

-1 10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

3.14333333333333

3.75

2.41333333333333

2.62

Bullet Length (m)

Acc

eler

atio

n (m

/s2)

Figure 22. Interaction of Bullet Length and Bullet Mass on Acceleration.

Table 26 shows the average numbers for the interaction of bullet mass


interaction effect was calculated to be 0.2 m/s2. This is less than double the

range of standards, which makes the interaction effect not significant. The lines

are almost parallel to each other, which imply there is a small to no interaction.


-3 -2 -1 0 1 2 3

Figure 23. Box Plot for Acceleration.

Figure 23 shows a box plot of the effects for acceleration. Only two of the

effects were significant: the effect of barrel length and the effect of bullet mass.

The effect of barrel length was the farthest away from two times the range of

standards, making it the most significant effect. The effect of bullet mass and all

of the interaction effects are less than two times the range of standards, making

them not significant. The interaction of bullet length and bullet mass was the least

significant.

With all of the effects, they can be put into the predication equation and

parsimonious equations to get good predictions of trials values (see Appendix D)

-0.54 0.54

Barrel Length – Blue Square

Bullet Length – Blue Diamond

Bullet Mass – Blue Triangle

Interaction Barrel Length and Bullet Length – Black Square

Interaction Barrel Length and Bullet Mass – Black Triangle

Interaction Bullet Length and Bullet Mass – Black Diamond


Conclusion

The purpose of the experiment was to find the effect that barrel length,

bullet length, and bullet mass had on the force of impact and acceleration of the

bullet when it was shot. The hypothesis was that the longest barrel length of 0.6

m, the longest bullet length of 0.075 m, and the lowest mass of 0.8 g would have

the greatest force of impact and acceleration. After the data recording and

testing, the hypothesis was rejected. The combination of the longest barrel length

of 0.6 m, the longest bullet length of 0.075 m, and the highest bullet mass of 1.4

g resulted in the highest force of impact and the highest acceleration. It was also

noted that all of the factors had a positive effect on the force of impact and

acceleration. This means as the factor values were increased, the force of impact

and acceleration also increased, so the highest factor values would result in the

highest force of impact and acceleration. For force, only the individual effects

(effect of barrel length, bullet length, bullet mass) were significant, and the

interaction effects were not. For acceleration the individual effects of barrel length

and bullet length were significant, and the effect of bullet mass and the all of the

interaction effects were not significant.

The higher values for the factors that resulted in greater results were

understandable. According to Newton’s Second Law of Motion, force equals

mass times acceleration, therefore the more mass the bullet had, the higher its

force should be. This correlates with acceleration, since force is proportional to

acceleration, so a higher force would result in a higher acceleration. The length

of the bullet coincides with mass. The longer bullets had slightly more mass than


the standard or shorter bullets. The length of the barrel determined the amount of

distance the bullet traveled in the barrel. In the experiment, the longest barrel

allowed the most distance for the bullet to travel within the barrel. The higher

distance traveled resulted in a higher final velocity, which led to the bullet having

a higher acceleration (refer to appendix E) The higher amount of acceleration

allowed the bullet to accelerate more over time while traveling through the barrel,

and it left the barrel at a higher velocity, and it hit the force plate with a higher

force. This is why trials in the experiment that had the high barrel length generally

had a higher force of impact than trials with the low barrel length.

There may not be much research about blowguns, with blowguns having

been more popular in older warfare. Today, blowguns have seen limited use in

combat. However, blowguns share many similar properties to actual guns, and

the data in the experiment can be applied to the properties of real guns. The

results recorded in the experiment do agree with current work relating to guns. In

a study done by student Clark L. Brandon of the University of South Florida, the

highest barrel length of the Mosin-Nagant rifle resulted in the highest muzzle

velocity and the highest force of impact. This result is the exact same as the

result in the experiment as both the barrel length of the Mosin-Nagant rifle and

the blowgun had a positive effect on the force of impact of the bullet. In Cramer’s

book The Science of Shooting, he states that bullets are heavily affected by

gravity due to their mass. This is shown in the experiment as the bullets with

more mass had more force due to gravity having a greater impact on them.


With this research, guns can be modified in order to give the bullets shot

the highest amount of force of impact when they are shot. This can result in the

most effective and lethal bullets when used for hunting/shooting purposes. The

research also proved bullets with higher masses had a higher force of impact,

and in the field, different guns of varying barrel length can be combined with

bullets of different mass to find the most effective combination.

There were weaknesses in the experiment. Only 5 bullets were made for

the different bullet types, and as they were repeatedly used through the three

DOEs, they gradually wore down. The worn down bullets became harder to

shoot, and had to be adjusted so they slid down the barrel easier. These

adjustments may have altered the pressure it required to push the bullets down

the barrel, and may have affected the force of impact and acceleration of the

bullet when it was shot. Also, the ideal impact zone for the bullet was the center

of the force plate, but the bullets did not always hit the center, as they did sway

during the time it took them to travel to the force plate. This may have ended up

in a difference in the registration of force when the bullet hit the force plate.

Finally, when the force plate was zeroed, the force did not always stay at 0

Newtons. The value of the force swayed from -2 to 2 Newtons. This may have

affected the final force registered, and made it less or greater than it actually

was.

Research could have gone further by testing the factor’s effect on the

accuracy of the bullet when it is shot. A higher force could result in more effective

bullets, but the bullets must be able to hit their target first. Accuracy could easily


be tested by adding a laser sight onto the blowgun and having it aimed at a

target. The bullets could be marked so that the bullets show a distinct track which

the distance from the target could be measured for accuracy. Velocity could have

been found by shooting between two sensor gates to find the time it took for the

bullet to travel from gate to the other. This would allow an equation to be used to

solve for velocity. Finally, the distance the bullet travels through the air could’ve

been tested. It is important for soldiers to know the range of their gun, because

having a range advantage is valuable in gunfights as it is important to know how

far the gun can shoot while still being effective. The distance of the blowgun

could’ve been easily tested by simply shooting it at a 45 degree angle (to get the

greatest distance) in an area where wind resistance would not be too much of a

variable.

The research could prove valuable to any sort of activity that includes the

usage of guns. It could help people consider the factors of the gun that can help

make it more effective before they buy it, which based on the research: a gun

that has a longer barrel, and can shoot longer and higher massed bullets. This

could help the military decide the most efficient guns (high barrel length and

ability to shoot high caliber bullets is ideal) to distribute to their soldiers. Whether

guns are used in hunting, warfare, or just shooting at targets, having the best gun

can provide the most effective and satisfying results.


Appendix A: Making the Blowguns

Materials:

(3) ½ in diameter 2ft length PVC Pipes(3) ½ x ¾ Female Reducing AdapterRuler (1 in precision)Black MarkerElectric Saw

Procedure:

Be aware of safety precautions. Use Electric Saw with care/guardian supervision.

Low Length Blowgun

1. Using the ruler, from the tip of one of the PVC pipes, measure out 1 ft. Mark where a foot is with the marker.

2. Using the Electric Saw, cut where the mark was made. The resulting PVC pipe should be 1 ft long.

3. Attach one of the Female Reducing Adapters to one end of the 1 ft PVC pipe.

Standard Length Blowgun

4. Using the ruler, from the tip of one of the PVC pipes, measure out 0.5 ft. Mark where 0.5 ft is with the marker.

5. Using the Electric Saw, cut where the mark was made. The resulting PVC pipe should be 1.5 ft long.

6. Attach one of the female reducing adapters to one end of the 1.5 ft PVC pipe.

High Length Blowgun

7. Attach one of the female reducing adapters to one end of the 2 ft PVC pipe.


Diagram:

Figure 24 shows what the blowguns should look like in their completed

form.


Appendix B: Making the Bullets

1. Take 2x2” post-it note and roll from one side to the other to make a cylindrical shape

2. Checking fitting for the ½” diameter barrel.

3. Adjust the size of cylinder until it fits snuggly into the barrel. Cylinder should fit easily into barrel but not fall out if shaken or pounded.

4. Tape the loose edge of cylinder for stability and support.

5. Add appropriate amount of cotton depending on desired mass into cylinder and push to one end of the cylinder. Add ½ a cotton ball for the 0.8g dart, 1 cotton balls for the 1.1g dart, and 1(½) cotton balls for the 1.4g dart.

6. Tape over the end with cotton to prevent it from flying out when fired from blowgun. This will be the tip or front of the dart.

7. Cut off any loose edges of tape to prevent jamming in barrel.

8. Cut off other end of cylinder to desired size. Cut a ½” off for the standard dart and 1” off for the low dart. The high dart will remain at 2”.


Appendix C: Newton’s Second Law

The acceleration was found using Newton’s Second Law. According to

Newton’s Second Law of Motion, “acceleration is produced when a force acts on

a mass” (“Second Law of Motion”). This can be expressed using the following

equation, where the acceleration of the object (a) is equal to the force that is

acted up the object (F) divided by the mass of the object (m).

a= Fm

After the force was recorded for every trial, the acceleration of the bullet

was found using this equation. Below is a sample equation using the numbers

from the first DOE standard trial.

a= Fm

a=3.71.1

a=3.4

Figure 25. Sample Equation.

Figure 25 shows the equation shown above when applied to the first DOE

standard trial. The force recorded was divided by the mass of the bullet, making

the acceleration 3.4 m/s2.


Appendix D: Prediction Equation and Parsimonious Prediction Equation

In the data analysis, the prediction equation was used to find predict

certain values of a trial. It was found using the following equation, where y equals

the grand average (ga) plus half of all of the effects (effects) plus “noise” (noise).

y=ga+ 12

(effects )+noise

Below is the equation used with the data from the acceleration DOE, since

there were effects that were significant and not significant.

y=2.98+ 12

¿

y=4.99

Figure 26. Prediction Equation Acceleration example.

Figure 26 shows the predication equation being applied to the effects that

were found in the experiment. All values were used on the trial with high barrel

length, high bullet length, and high bullet mass.

The parsimonious predication equation is very similar to the prediction

equation. The only way it is different is that the non-significant variables are

excluded from the equation and it only tests the grand average, the significant

effects, and “noise”. It can be expressed with the following equation, where y is

equal to the grand average (ga) plus half of the significant effects added together

(“significant effects”) plus noise (“noise”).

y=ga+ 12¿

Below is the equation used with the data from the acceleration DOE, since

there were effects that were significant and factors that were not significant, so it


can properly demonstrate the exclusion of non-significant factors.

y=2.98+ 12 (1.44(1)+0.92(1)+0.68(1))+noise

y=4.5

Figure 27. Parsimonious Predication Equation Acceleration Example.

Figure 27 shows the parsimonious predication equation being applied to

the significant effects that were found in the experiment. The significant effects

were the effect of barrel length, the effect of bullet length, and the interaction of

barrel length and bullet length.


Appendix E: Velocity and Acceleration

In the experiment, the longer barrel lengths of the blowguns resulted in

higher final velocities. The equation of velocity explains this, where the velocity

(v) is equal to the distance (d) over time (t).

v=dt

Below is a sample equation using the high barrel length (0.6 m) with a set

time of 1 second.

v=0.61

v=0.6m /s

Figure 28. Sample Equation for Velocity.

Figure 28 shows the velocity solved with a distance of 0.6 m and a time of

one second. Using this velocity, the acceleration can be solved for, and generally

a higher final velocity results in a higher acceleration. This can be expressed

through the following equation where the acceleration (a) is equal to the change

of velocity (v) over time (t).

a=∆vt

Below is a sample equation where the initial velocity is 0 m/s, the final

velocity is 5 m/s, and the time is one second.

a=5−01

a=5m /s2

Figure 29. Sample Equation for Acceleration.


Figure 29 shows the acceleration solved with an intial velocity of 0 m/s,

and final velocity of 5 m/s, and a time of one second.


Works Cited

Clark L. Brandon. Effect of Barrel Length on the Muzzle Velocity and Report from a Mosin-Nagant 7.62x54R Rifle. 1st Edition. Tampa: University of South Florida. May 2011. 40 Pages. Print.

Cramer, John. Why You Can't Shoot Straight: The Basic Science of Shooting. First Edition. Los Gatos: Smashwords. 2011. 5-8. Print.

Klatt, Mercer. “Ballistics.” The Internet Pathology Laboratory for Medical Education. 2015. Web. 24 March 2015.

"Second Law of Motion." Newton's 3 Laws of Motion. Teachertech, n.d. Web. 7 May 2015.

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