Modeling and Prototypes - Technology Engineering and Design › uploads › 9 › 6 › 7 › 4 › 967428 › ... · much exposed area a 3D object has. Formulas below Rectangle Box:

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.


The Lesson Big Idea

At various intervals of the engineering design process, conceptual, physical, and

mathematical models evaluate the design solution.


Modeling

There are three different ways to represent our world Written & Spoken Mathematical Graphical


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


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


Conceptual Models

There are several types of technical sketching:


Isometric Oblique Perspective Orthographic

Technical sketching is a design tool used to create conceptual models

Isometric Drawings

3D drawings of objects using true measurements


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˚


Perspective Drawings

3D drawings of objects where lines converge on one or more points.

Intended to be close to the human eye in observation.


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.


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.


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.


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


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.


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.


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


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


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


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)


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


Documents

Modeling and Prototypes - Technology Engineering and Design › uploads › 9 › 6 › 7 › 4 › 967428 › ... · much exposed area a 3D object has. Formulas below Rectangle Box: