Emilie Butler-Olimb, Molly Henderson, John Waters

Parameter Optimization

Purpose: To select the process settings so that the catapult will consistently project the inputted target distance, T.

Variables:Response variable T, target distanceFactor 1: Type of raw materialFactor 2: Location of fulcrumFactor 3: Angle of the platform

Number of Observations:(Assume a two 2 factorial with three levels)N = 2(k) = 2(3) = 8 observationsSo, for two 2 factorials there will be a total of 16 observations

Process:

1. Create the factorial design matrix. This shows the interaction of each of our factors.

Table 1

A B C AB AC BC ABC I

(1) - - - + + + - +

a + - - - - + + +

b - + - - + - + +

c - - + + - - + +

ab + + - + - - - +

ac + - + - + - - +

bc - + + - - + - +

abc + + + + + + + +

2. Assume that the main effects are what influence the outcome as opposed to the interaction effects (AB, AC, and BC) For a fractional factorial matrix, we simplified from a full factorial matrix in order to decrease the total number of trials. Below is the matrix that will be used during the

Emilie Butler-Olimb, Molly Henderson, John Waters

experimentation.Note: C = A*B Table 2

Run A B C

1 +1 +1 +1

2 +1 -1 -1

3 -1 +1 -1

4 -1 -1 +1

3. Substituting for Table 2,A = Raw Material (4 different projectiles, cancel out the fifth material, wiffle ball)

Ping Pong Ball, Normal Ball, Bouncy Ball, GolfB = Location of Fulcrum (4 location options, 1-4)C = Platform Angle (4 angle options, 1-4)

The team will perform two 4 fractional factorial experiments.

Table 3:+ Bouncy, Level 4, Angle 3- Ping Pong Ball, Level 2, Angle 1

Table 3

Run Raw Material Fulcrum Angle Distance T

1 Bouncy Level 4 Angle 3 111.5/107

2 Bouncy Level 2 Angle 1 113/117

3 Ping Pong Ball Level 4 Angle 1 118.5/116

4 **Ping Pong Ball Level 2 Angle 3 117.5/125

Table 4:+ Bouncy, Level 3, Angle 4- Ping Pong Ball, Level 1, Angle 2

Table 4

Run Raw Material Fulcrum Angle Distance T

Emilie Butler-Olimb, Molly Henderson, John Waters

1 Bouncy Level 3 Angle 4 131/130.5

2 Bouncy Level 1 Angle 2 87.5/104.5

3 Ping Pong Ball Level 3 Angle 2 127.5/124

4 Ping Pong Ball Level 1 Angle 4 116.5/111

Table 5:+ Golf, Level 4, Angle 3- Normal, Level 2, Angle 1

Table 5

Run Raw Material Fulcrum Angle Distance T

1 Golf Level 4 Angle 3 88/90

2 Golf Level 2 Angle 1 95/87

3 Normal Level 4 Angle 1 111/115

4 **Normal Level 2 Angle 3 130/127.5

Table 3:+ Golf, Level 3, Angle 4- Normal, Level 1, Angle 2

Table 6

Run Raw Material Fulcrum Angle Distance T

1 Golf Level 3 Angle 4 98.5/102.5

2 Golf Level 1 Angle 2 84/75

3 Normal Level 3 Angle 2 126/123

4 Normal Level 1 Angle 4 119/120.5

4. Once in the lab, the above steps will be performed. Table 3 and Table 4 will have 2

Emilie Butler-Olimb, Molly Henderson, John Waters

replications each. This will result in a total of 32 observations