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Modeling and Prototypes
4.4.1
Unit 4, Lesson 4
Explanation
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
The Unit Big Idea
The Engineering Design process is a systematic, iterative problem solving method which produces solutions to meet human wants
and desires.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
The Lesson Big Idea
At various intervals of the engineering design process, conceptual, physical, and
mathematical models evaluate the design solution.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Modeling
There are three different ways to represent our world Written & Spoken Mathematical Graphical
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Modeling
During design process, check for proper design to note areas of needed improvements: Conceptual,
physical, and mathematical models evaluate the design solution
The usefulness of models can be tested by comparing predictions to observations in the real world
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Conceptual Models
Conceptual models allow designs to
quickly be checked and critiqued so that the design may be refined and improved.
Technical sketching is a design tool used to create conceptual models
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Conceptual Models
There are several types of technical sketching:
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Isometric Oblique Perspective Orthographic
Technical sketching is a design tool used to create conceptual models
Isometric Drawings
3D drawings of objects using true measurements
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Front & side drawn at a 30o to horizontal
For more info, search for “isometric drawing”
Oblique Drawings
3D drawings with the width represented as a horizontal line.
Side view of object drawn at 45o from horizontal
For more info, search for “oblique drawing”
45˚
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Perspective Drawings
3D drawings of objects where lines converge on one or more points.
Intended to be close to the human eye in observation.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Can converge to 1, 2, or 3 points.
For more info, search for “perspective drawing”
Physical Models
Can be mock ups or prototypes. Prototype is a working model to
test a design concept through observation and adjustment
Mock up simulates the look of an object and not functional.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Mathematical Models
The basic idea of mathematical modeling is to find a mathematical relationship that behaves same way as objects or processes under investigation.
Mathematical modeling simulates how a system might behave.
Engineers use the language of mathematics to express mathematical ideas precisely.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Mathematical Models
Engineers create and use representations to organize, record, and communicate ideas.
Often symbolic algebra to represent and explain mathematical relationships.
Computers have greatly improved the power and use of mathematical models by performing long,complicated,or repetitive calculations.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Example of Mathematical Modeling
Designer wants to create hot air balloon designs without creating physical models
Algebraic formulas represents increases or decreases of lift based on inside volume or temperature
Calculations are communicated on spreadsheets or computer based simulations
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Steps in Creating a Mathematical Model
Determine the output you would like to achieve for the mathematical model and what data/information is available
Research for other mathematical models already created you can use.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Steps in Creating a Mathematical Model
Identify relationships among variables (may be related science
concepts, such as Ohm’s Law)
Create the equation that relates variables
Check accuracy of model against a similar system
or over time.
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Basic Properties of 2 & 3 Dimensional Objects
Engineers and designers must understand basic properties of 2D & 3D objects For 2D objects, one must be able to
calculate area For 3D objects, one must be able to
calculate volume and surface area These properties help determine
modifications related to function and marketability
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Calculating Area
Area is the amount of surface of a 2D object. Formulas are below. Rectangle: A = length x width Triangle: A = base x ½ (height) Circle: A = ∏ x radius 2
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Calculating Volume
Volume is amount of space a 3D object takes up. Formulas below. Rectangle Box: V = length x width x
height Pyramid: V = Area of Base x 1/3
Perpendicular Height Sphere: V = Diameter3 x .5236 Cylinder: V = Diameter2 x Length x
.7854
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
Calculating Surface Area
Surface area, the measure of how much exposed area a 3D object has. Formulas below Rectangle Box: SA = (H x W x 2) (H x D x
2) (D x W x 2) Pyramid: SA = (Perimeter of Base x ½ Slant
Height) + (area of base) Sphere: SA = Diameter2 x 3.1416 Cylinder: SA= (Diameter x Length of curved
surface x 3.1416) + (area of bottom + area of top)
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology
All Models
Important that they function as close to the real world as possible
They must be continually checked and refined during the design process.
More than one of the three types is often used for the same product
© 2011 International Technology and Engineering Educators Association, STEMCenter for Teaching and Learning™ Foundations of Technology