Laboratory 3 Factorial Experiment: Paper Helicopter Design

Transcription

1 MTE 201: Experimental Measurement and Statistical Analysis Laboratory 3 Factorial Experiment: Paper Helicopter Design Introduction Factorial experiment design is an important technique for engineers to know for two reasons: 1. It is far more economical than one at a time testing. 2. It is the only method for detecting interaction effects Factorial experimentations are often performed by engineers who are debugging a complex problem, designing a product or optimizing a process. In this lab you will apply factorial experiment design to a VERY complex problem: How to perform a set of design changes to affect the flight of a helicopter, and how do they interact? Factorial experiments (and statistics in general) are used by engineers when the complexity level of the project exceeds the knowledge or means that they have. Lab Materials Lab Materials Provided: 2 pieces of paper 1 paper clip Tape Bring: Ruler Watch with a timer (digital) Scissors might be useful if you have them. Calculator 1

2 1. Prototype Development This is one of the fun parts of this lab, as you get to be creative. You should spend no more than 15 minutes coming up with a basic design for the helicopter. The helicopter will be released from 2 meters of height and it is supposed to move vertically and land in the circle drawn right under the release point. The success of the helicopter will be measured by the amount of time it stayed in air. Do not focus on refining the design at this stage, but rather to get a good basic design. Use only one piece of paper, save the other for the redesign later. Draw a brief description of your prototype. A quick sketch of the design, with any critical dimensions labeled is enough at this step. 2. Factorial Experiment Design 2.1 Factor Identification Identify three different factors that you think will affect the flight of the helicopter. It might be worthwhile to brainstorm for a few minutes to get a large list of factors and then pick from that list the ones that might be interesting to investigate. Record the name of each factor, its abbreviation and a brief description of it, with a sketch. 2.2 Level Selection For each factor (say A) choose two levels (e.g. A low and A high ). These levels should be feasible to construct given the time you have, and should be different enough to produce a noticeable effect. Based on the chosen levels, you will built 8 designs (2 3 ) and test them individually. 2.3 Experimental Plan Plan the experimental study. You are allowed 8 designs to investigate the three factors at two levels. You can choose n (i.e. number of trials per factor combination). Assign duties among the group members: either building the helicopter or testing. Keep in mind that your final design should be ready for the competition that is going to start at 16:15 sharp. Record the number of trials determined for each set in the following table. A larger number of trials will help you get more consistent values. You are limited with five trials for each design. In the following table the minus sign denotes the low level of that factor whereas the plus sign denotes the high level. 2

3 Design No Factorial ID Factor 1 (A) Factor 2 (B) Factor 3 (C) Trial No 1 (1) c b bc a ac ab abc Table 1: Test matrix for the factorial design 3. Factorial Experiment Complete the experiments using the guidelines in the previous section. Measure and record the time (in seconds) it takes for the helicopter to fall from a height of 2 meters. Two digits after the decimal point suffice for the accuracy. Calculate the total time and mean for each factorial ID. Trials Factorial ID Total Mean (1) c b bc a ac ab abc Table 2: Experimental Data 3

4 4. Analysis Calculate the 3 main and 4 interaction effects using the given equations. n in the following equations is the number of trials. For the variables a, b, c, ab, use the total time column of the previous table. 5. Redesign Comparing the values of effects calculated; determine the most significant factors of your design. The interaction effects (eg. AB) let you know whether there is an interaction between the corresponding factors (A and B). Using your analysis results, redesign your helicopter. Note down the level of each factor in your final design. 6. Competition Bring your best design to the final fly (drop, in fact) competition, the winning team will receive 2 bonus marks on the final grade. 7. Instructions for the write-up (due 1 week from the lab day) Provide the basic prototype that you found in section 1. (A 2D or 3D sketch with the dimensions mentioned) The three factors varied during the experiments with brief descriptions together with the low and high levels. Provide an explanation why you selected those parameters (how did you expect them to affect the flight of the helicopter) Sketch these factors on your drawing. The experimental data table you completed in section 3. 4

5 The calculation of the main and interaction effects. Your interpretation of the values of effects and the final levels that you have determined for each factor. Comment on the strengths and weaknesses (2 items per each at max.) of the factorial design technique based on your results. You are also advised to refer to online resources. 5