Jesse SmithIndustrial Engineering Measurement in the 3D Coordinate plane Industrial Engineering with Linear and Quadratic models Historical Engineering Activity Industrial Engineering Game
Measurement in the 3D Coordinate plane • The x,y,axis • The x,y,z axis • Measurement in 3 dimensions • Manufacturing in 3 dimensions Wind tunnel demonstration • Industrial Application 3-D Laser Scanner
The (x,y) axis x y
The x,y,z axis z y x
Industrial Engineering with Linear and Quadratic models • Linear and quadratic equations • Paper helicopter demonstration • Data collection (wing length/time) • Predictions from data • Test predictions • Revision with new model • Worksheets
Linear Equations • Y=mx+b form • Can be used to predict linear data
Quadratic Equations • y = ax2 + bx +c form • Used as one way to graph data in a non linear form
Data Collection Time (sec)
Prediction from Data Time (sec) This line shows that the predicted flight time for a 5 inch wing should be 3 seconds------- after testing it proved almost true ( 2.9 seconds)
Time (sec) For a six inch wingspan a prediction of 3.2 seconds was made
A new model was needed Time (sec) This is clearly not a linear function. A quadratic model might be used to predict the optimal wing length. Before going to an optimal measurement a ROBUST design based on a linear model might be used
Robust Design Sometimes the optimal is not the best. If a design falls within the acceptable operating parameters and is more efficient to produce, then it might be more economically feasible to use this design. 1 hour to produce 2 minutes to produce Which one would you choose ?
Historical Engineering Activity • Different equations are used in different situations. • Siege weapons and their uses • Ballista linear models • Slope (slope formula, trig models, linear regression) • Trebuchet quadratic models
Different equations are used in different situations. Linear Equations Quadratic Equations
Siege weapons and their uses In Medieval warfare it was sometimes necessary to lay siege to an enemy fortification. e.g. a castle. ?
Several Devices were developed to help deal with these situations. The other was the trebuchet. One of these was the ballista. www.trebuchet.com http://members.lycos.nl/onager/ballista.html
The Ballista could fire directly at a target (Linear Model) http://members.lycos.nl/onager/ballista.html
By knowing the height of the target and the distance tables could be developed slope and angles could be compared. opposite adjacent rise run Slope Tangent rise run angle
The Trebuchet could fire in a high arc. (Quadratic Model) www.trebuchet.com
Buy building models improvements can be made on existing designs as well as planned objects Large scale model Model Trebuchet
Make sure you know what is going to happen ------------------- or at least have an idea !