Full Factorial Method
Full Factorial Method is a more accurate method as it takes into account all the different variation. However, it is unrealistic to do all the runs as it will take too much time. Using full factorial method, we can determine each factors significance. We found the average of all the times when the factor is high and low and plotted it as a graph.
Below is all the data and graph we collected for the Full Factorial method.
Using the graph, we can tell which factor is more significant when determining the launch distance. The graph which exhibits the steepest gradient is the factor which is the most significant. The graph which shows the most gradual gradient is the factor that is the least significant factor. From this graph, this is the order of significance with no. 1 being most important:
1)Arm length
2)Projectile weight
3)Stop angle
Since all 3 graph drawn are negative, we can say that increasing the arm length, projectile weight and stop angle will negatively affect the launch distance
This the data of the interactions between the factors:
Interactions between Factors
Interaction between A and B for full factorial:
As the graph is not going to intersect anytime soon, the interaction between this 2 factors is not as significant
Interaction between A and C for Full factorial:
As the graph is going to intersect, the interaction between this 2 factor is quite significant
Interaction between B and C for Full factorial:
As the graph is quite parallel to each other, there is little interaction between this 2 factor
Interaction graph for factors D, E and F (Full factorial analysis)
Most interaction -> Least interaction
A and C > A and B > B and C
Using the graphical method, we can deduce that the most significant interaction occurs between factors A and C as the graph for E is the steepest and the interaction between A and C graphs have the greatest gradient difference. This indicates that there is a significant interaction between factors A and C and a change in level for factors A and C has a significant effect on the projectile distance.Graph F has the most gentle gradient and the most similar gradients in the B and C interaction graph. This shows that factors B and C have the least interaction and a change in level for factors B and C would not have a significant effect on the projectile distance.
Fractional Factorial Method
Fractional Factorial method is a more realistic method to determine the effect and significance of the factors with less result at the cost of accuracy. When picking which data we want to use for fractional factorial, we have to ensure that the runs have equal high and low.
Below is our data and graph for fractional factorial method:
From this graph, we can tell that the factor with the most significance is the arm length, followed by the stop angle and lastly the projectile weight. This is because the arm length shows the steepest gradient while the projectile weight shows the most gradual gradient.
This is the data for the interactions between factors:
Interaction between the factors:
Interaction between A and B for Fractional factorial:
Interaction between A and C for Fractional factorial:
Interaction between B and C for Fractional factorial:
Interaction graph for factors D, E and F (Fractional factorial analysis)
Most interaction -> Least interaction
B and C > A and B > A and C
Using the graphical method, we can deduce that the most significant interaction occurs between factors B and C as the graph for F is the steepest and the interaction between B and C graphs have the greatest gradient difference. This indicates that there is a significant interaction between factors B and C and a change in level for factors B and C has a significant effect on the projectile distance.
Graph E has the most gentle gradient and the most similar gradients in the A and C interaction graph. This shows that factors A and C have the least interaction and a change in level for factors A and C would not have a significant effect on the projectile distance.
Reflection
This practical helps me to understand the methods to design an experiment. The experiment was fun as we get to determine how we conduct the experiment. At the start, we decided to launch the catapult at its full strength. This caused the projectile to get launched very far away and we were too lazy to keep picking up the projectile. Therefore, we decided to load the catapult at two clicks to prevent ourself from running to far to pick projectiles. We then proceed to continue with our experiment when we faced our second difficulty, our catapult exploded. We did not know what happened but i think the rubber band got dethatched. We decided to just continue with the experiment as we can finish the experiment with just one catapult. Even with one catapult broken, we are still able to complete the experiment before other groups. I think this is because we did not set the catapult to launch very far, therefore saving the time taken to retrieve the projectile, The third difficulty we faced was during the challenge. When we were told that we can get to hit lecturers with our catapults, we instantly set our catapult to hit mr ting ( no particular reason, we just want to challenge ourselves to hit the furthest target ;) ). The problem is that our furthest recorded launch was 118cm and mr ting was about 2m away. We then decided to increase the amount of clicks before we launch the projectile. During the first shot, we missed by just a little as we overshot. Therefore, we reduce the amount of clicks and successful hit mrr ting,
There are things i don't really understand about the data. For example, the arm length. I don't understand why having a longer arm length would reduce the launch distance. After much consideration, i think that it is because a longer arm length would mean a heavier weight. Therefore most of the force went to moving the arm instead of launching the projectile. This led to the distance launched to be significantly reduced.
I learnt the importance of both fractional and full factorial method and both its pros and cons. Overall, i had a lot of fun during this practical and its a 10/10 experience.
Case Study
Student ID:2122742
This is the data, graph and calculations for the case study
From the graph, we can tell which factor is more significant by the gradient of the graph drawn. From the graph drawn, the line for power have the steepest gradient, follow by the microwaving time and lastly the diameter. This means that the factor that affect the result the most is the power, follow by the microwaving time and lastly the diameter.
Interactions between factors
As the graph plotted for the interaction between A and B is intersecting, this means that this two factors interacted quite significantly.
Since the graph for the interaction between A and C is quite parallel, this means that the two factor did not interact.
Since the graph for the interaction between B and C is going to interact, this means that the two factors interaction is very less
Below is the calculations for the interactions between the factors,
Fractional Factorial
Below is the table for the fractional factorial
Below is the graph for fractional factorial
From the graph, we can tell that the most significant factor is C follow by B and then C. This is because the graph for C is the steepest follow by B and then C.
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