1. Lecture_1a

# 1. Lecture_1a - ME303 MME University of Waterloo Prof...

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Unformatted text preview: ME303, MME, University of Waterloo. Prof. Serhiy Yarusevych Significance of Engineering Mathematics Relevance? Relevance? Can you think of any non-trivial modern engineering design that does not involve mathematical analysis? Mechanical Engineering Design Mechanical Engineering Design Problem Analysis Design, Optimization, & Validation Validation Final Design Approach to Engineering Design Approach to Engineering Design Problem Analysis and/or Design Evaluation Physical Modelling Modelling Mathematical Modelling Modelling Physical Modelling Physical Modelling Build a scaled model or a full-scale prototype scaled model or full prototype Test in a laboratory Modify the design based on the results and test again the design based on the results and test again Scale the optimized design to a real system Pros: reliable results (if done properly) Cons: expensive and time consuming Mathematical Modelling Mathematical Modelling Derive mathematical equations that describe system mathematical equations that describe system performance Solve the equations to predict system behaviour Modify the design and modify the equations Pros: design can be done “on paper” before building Cons: - uncertainty in the results - a realistic model may involve complex math realistic model may involve complex math Modern Engineering Design Process Modern Engineering Design Process Mathematical Model Numerical Solution Experimental tests Final Design Example: Plane Design Exam Example: Plane Wing Design Example: Plane Wing Design Example: Wing Design Example: Wing Design Proposed profile Example: Wing Design Example: Wing Design Simplified Mathematical Model (neglect friction) Example: Wing Design Example: Wing Design Refined Mathematical Model (neglect small swirls) Example: Wing Design Example: Wing Design airfoil Experiment Example: Wing Design Example: Wing Design Experimental Results Example: Wing Design Example: Wing Design www.aerospaceweb.org Mathematical model: plane Mathematical model: plane Example: Wing Design Example: Wing Design Model: 12 ft http://windtunnels.arc.nasa.gov/ Full scale:80 x 120 ft http://windtunnels.arc.nasa.gov/ Summary: Summar Mathematical models are widely used in modern engineering design and analysis Thus, need to know how to formulate and solve mathematical models ...
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