Design of Experiment (Catapult)

 For this experiment, we used Design of Experiment to find out how the arm length, start angle and stop angle of the catapult affect the distance travelled of the projectile.

We used factorial analysis to the effect of this.

 

To keep thing efficient, we split into 2 groups where one group will do the full factorial and the other group will do the fractional factorial. I was in the group doing the fractional factorial analysis.

 

To do the fractional factorial analysis, we picked 4 runs and did them both 8 times. Meanwhile, the full factorial runs would have to do all 8 runs.

To start off, we had to figure out the values of the arm length, start angle and stop angle of the catapult to determine the high and low values. In doing so, we found that the 2 catapults had differing values for the start and stop angle. This is acceptable as long as we only compare the values to each other and not the values between the two catapults.

 

Doing the experiment!

We set up the catapult at the end of the table and the tray with sand at the other end of the table. Since we were doing both full factorial and fractional factorial run at the same time, we had to vary the distance so that both catapults can get the projectile into the tray.

Full factorial data:

 

Fractional Factorial data:

To determine the effect of single factors, we added the distance travelled for all of the runs with high value and got the average; same with the runs with low value. Then, we plotted the graphs for all of the factors. We did this for both full fractional and fractional factorial.

 

A: When the arm length increases from 24.5cm to 27.5cm, the flying distance of the projectile decreases from an average of 137.33cm to 110.075cm.

B: when the start angle increases from 5 degrees to 25 degrees the flying distance of the projectile decreases from an average of 148.25cm to 99.16cm.

C: when the stop angle increases from 45 degrees to 90 degrees the flying distance of the projectile decreases from an average of 149.19cm to 98.22cm.

The graph shows the stop angle line has the steepest gradient followed by the start angle line and the arm length line indicating that the stop angle has the biggest impact on the distance traveled by the ball, then followed by start angle, and lastly the arm length.

Most impactful: Stop angle

2^nd most impactful: Start angle

Least impactful: Arm length

 

A: When the arm length increases from 24.5cm to 27.5cm, the flying distance of the projectile decreases from an average of 117.9cm to 86.6cm.

B: when the start angle increases from 10 degrees to 35 degrees the flying distance of the projectile decreases from an average of 119.8cm to 84.6cm.

C: when the stop angle increases from 45 degrees to 90 degrees the flying distance of the projectile decreases from an average of 111.2cm to 93.3cm.

The graph shows the start angle line has the steepest gradient followed by the arm length line and the stop angle line indicating that the start angle has the biggest impact on the distance traveled by the ball, then followed by arm length, and lastly the stop angle.

Most impactful: Start angle

2^nd most impactful: Arm length

Least impactful: Stop angle

 

Finding the effect of single factors:

To find the effect of single factors, we found the average at high levels for 2 factors and then high and low for each factor and the high and high for both factors. We found this for all the pairings at full factorial as well as full fractional.

Full factorial:

(A x B)

At LOW B, (runs 1 and 5) Average of low A=(229.2+99.9)/2=164.55

At LOW B, (runs 2 and 6) Average of high A=(161.2+102.7)/2=131.95

At LOW B, total effect of A=(131.95-164.55)= -32.6 (decrease)

At HIGH B, (runs 3 and 7) Average of low A=(124.0+96.2)/2=110.1

At HIGH B, runs 4 and 8) Average of high A=(82.4+94.1)/2=88.25

At HIGH B, total effect of A=(88.25-110.1)=-21.85 (decrease)

The gradients of both lines are both negative and are slightly different with a very small margin. This indicates that there’s an interaction between A and B, but the interaction is small.

 (A x C)

At LOW C, (runs 1 and 3) Average of low A=(229.2+124.0)/2=176.6

At LOW C, (runs and ) Average of high A= (102.7+94.1)/2=98.4 

At LOW C, total effect of A=(98.4-176.6)= -78.2 (decrease)

At HIGH C, (runs and ) Average of low A=(161.2+82.4)/2=121.8

At HIGH C, (runs 6 and 8) Average of high A=(100.5+96.2)/2=98.35

At HIGH C, total effect of A=(98.35-121.8)=-23.45 (decrease)

The gradients of both lines are different, one has a larger decreasing gradient and one has a smaller decreasing gradient, therefore there is significant interaction between factors A and C.

(B x C)

At LOW C, (runs 1 and 2) Average of low B=(229.2+161.2)/2=195.2

At LOW C, (runs 3 and 4) Average of high B=(124.0+82.4)/2=103.2

At LOW C, total effect of B=(103.2-195.2)= -92.0 (decrease)

At HIGH C, (runs 5 and 6) Average of low B=(100.5+105.0)/2=102.75 

At HIGH C, (runs 7 and 8) Average of high B=(96.2+94.1)/2=95.15

At HIGH C, total effect of B=(95.15-102.75)=-8.5 (decrease)

The gradients of both lines are different, one has a larger decreasing gradient and one has a smaller decreasing gradient, therefore there is significant interaction between factors B and C.

 

From the full factorial design data, it seems that the strongest interaction is between BxC followed by AxC and finally AxB has the least interaction.

 

Fractional Factorial:

(A x B)

At LOW B, (run 1) ,low A = 144.4

At LOW B, (run 6) ,high A = 95.3

At LOW B, total effect of A=(95.3 - 144.4)= -49.1(decrease)

At HIGH B, (run 7), low A = 91.3

At HIGH B, (run 4) ,high A= 77.9

At HIGH B, total effect of A = (77.9 - 91.3) =  -13.4(decrease)

The gradient of the lines are both negative and have different values.(-54.97 and -13.33)

Therefore there’s a significant interaction between A and B.

(A x C)

At LOW C, (run 1) ,low A = 144.4

At LOW C, (run 4) ,high A = 77.9

At LOW C, total effect of A=(77.9 - 144.4)= -66.5(decrease)

At HIGH C, (run 7), low A = 91.3

At HIGH C, (run 6) ,high A= 95.3

At HIGH C, total effect of A = (95.3 - 91.3) = 4.0 (increase)

The gradients of the lines are negative and positive. The values of the gradients are also different. (-68.31 and 4.00)

Therefore there’s a significant interaction between A and C.

 (B x C)

At LOW C, (run 1) ,low B = 144.4

At LOW C, (run 4) ,high B = 77.9

At LOW C, total effect of B =(77.9 - 144.4) = -66.5(decrease)

At HIGH C, (run 6), low B = 95.3

At HIGH C, (run 7) ,high B= 91.3

At HIGH C, total effect of B = (91.3 - 95.3) = -4.0 (decrease)

The gradient of the lines are both negative and have different values. (-68.31 and -4.00)

Therefore there’s a significant interaction between A and B.

 

From the fractional factorial design data, it seems that the strongest interaction is between AxC followed by BxC and finally AxB has the least interaction. The ranking of the strongest interaction for the fractional factorial design is slightly different from the full factorial design.

Here is the excel file: 

https://ichatspedu-my.sharepoint.com/:x:/g/personal/chyrvelgwyn_20_ichat_sp_edu_sg/EW5UX-aLV71IlQ_RbTA2cpgBf7vbHfsEzr4vH5StlYigiA?e=7SdOui 

I think that this experiment taught me some ways to more efficiently finding the results like splitting up the roles and more importantly to find the result with less data using the fractional factorial design. It is important to be efficient especially when you need your data to be reliable so there needs to be more runs.