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Stats Assignment 1 – The DOE Project Assignment

OVERALL AIM: To design and conduct a two-level, three factor, full factorial experiment (replicated) to characterise the operation of Mark II catapult (e.g., factorial regression analysis) with a view to meet the distance (Range) specification of 2800mm + 200mm. A two to three-member team is required for each campus. Table 1 shows the list of participates of statistics assignment 1.

BACKGROUND: The focus in your assignment is on the distance the projectile travels (this is known as the Range, abbreviated as R in Figure 1), when it is being launched via the famous Massey Mark II catapult (Figure 1). From high school physics we know that when a projectile is launched at an angle α, at velocity v, from a height h, subject to simplifying kinematics assumptions, the range R would be given by the below equation (eq 1), where g is the gravitational constant. A calculator that incorporates equation 1 is available in https://www.omnicalculator.com/physics/projectile-motion.

L is the length of the catapult base (see Figure 1).

positions

You will appreciate that calculating the initial velocity v of our projectile (Figure 1) using our physics and advanced calculus knowledge would be quite challenging, and even if some of us can still do that, we would be making overly simplifying assumptions. On top of that, the relationship between R and v (eq 1) is too theoretical (for our airflow practice golf balls and the squash balls, the physics assumed in equation 1 will not hold very true). See Appendix A.

So, what can we do? We would plan a statistically designed experiment to understand how the catapult works! That is what operator 1 (Block 1) and operator 2 (Block 2) need to do, in this assignment. A third person can join in the experiment. This basically means, three people would be sharing the same data. If a third person is available, s/he can document the catapult firing procedure and protocols. This ensures that operator 1 and operator 2 would do the exact same thing, when they conduct their respective eight trials. The third person would conduct 25 confirmation runs.

The factors, their two levels are shown in Table 2. The response is the range (R), which is the landing distance from the base of the catapult.

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