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

demonstrationIndustrial Application 3-D Laser Scanner

y

The (x,y) axis

x

z

x

y

The x,y,z axis

Home made scanner and description of 3D axis

Setting up the coordinate plane on isometric graph paper

Developing the isometric drawling using the measuring machine

Using orthographic drawing and aerodynamic principals

Wind tunnel

Design of Wind tunnel

Setting up Airfoil

Testing the airfoil

3d laser scanner

Calibration

Scanned image

Industrial Engineering with Linear and Quadratic models

Linear and quadratic equationsPaper helicopter demonstrationData collection (wing length/time)Predictions from dataTest predictionsRevision with new modelWorksheets

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

Paper Helicopter demonstration

Data Collection

0

0.5

1

1.5

2

2.5

3

winglength

1234

Tim

e (sec)

Prediction from Data

0

0.5

1

1.5

2

2.5

3

wing length

12345

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)

Tim

e (sec)

0

0.5

1

1.5

2

2.5

3

3.5

winglength

123456

Tim

e (sec)

For a six inch wingspan a prediction of 3.2 seconds was made

This did not work

A new model was needed

0

0.5

1

1.5

2

2.5

3

winglength

123456

Tim

e (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 ActivityDifferent equations are used in different

situations.Siege weapons and their usesBallista linear modelsSlope (slope formula, trig models, linear

regression)Trebuchet quadratic models

Different equations are used in different situations.

Linear Equations Quadratic Equations

Siege weapons and their usesIn 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.comhttp://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.

riserunangle

rise

run

opposite

adjacent

Slope Tangent

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

Model Trebuchet Large scale model

Models Can lead to Future Designes

Make sure you know what is going to happen ------------------- or at least have an idea !

Industrial Engineering Game