introduction to the p5 computing laboratorylabejp/courses/1p5/lecture3slides.pdf · session 3, dbt...

Introduction to the P5 Computing Laboratory

Eric Peasley

Department of Engineering Science

Design, Build and Test

Session 3, DBT Part A

Simulating a Rocket Launch

Informal Assessment (No marks)

Session 4 & 5, DBT Part B

The Lander Controller

Assessment (15 marks)

What to do before Session 3

● Read the Introduction page 107 to 110

● Read Euler's Method 111 to 114

What to do before Session 3If you want to get started

● Work your way through the rest of the Euler section on page 115 to 117

● Read Exercise introduction 118 to 121

● The Exercises must be done in the Laboratory session

Program Design

● To make is easier to write large programs

● To improve the quality of your code

a) How well your code works

b) How understandable your code is

What is the purpose ofComments

Documentation

Final_Velocity = Initial_Velocity + acceleration * time;

Distance = Initial_Velocity * time + (acceleration *time.^2)/2;

Final_Velocity = sqrt(Initial_Velocity.^2 + 2*acceleration*Distance);

v = u + a * t;

s = u*t + (a*t.^2)/2;

v = sqrt(u.^2 + 2*a*s);

Final_Velocity = Initial_Velocity + acceleration * time;

Distance = Initial_Velocity * time + (acceleration *time.^2)/2;

Final_Velocity = sqrt(Initial_Velocity.^2 + 2*acceleration*Distance);

v = u + a * t;

s = u*t + (a*t.^2)/2;

v = sqrt(u.^2 + 2*a*s);

% u = The initial velocity in m/s % v = The final velocity in m/s% a = The constant acceleration m/s^2;% t = The time duration in seconds;% s = The distance travelled in metres

Functions

myfunction

function [x y] = myfunction(a,b,c)

INPUTa b c

OUTPUTx y

A self contained block of codeDesign Build and Test separately

The problems with LARGE programs

● The larger the program,

the more errors you get.

● The more code you have, the more difficult it is to find the errors.

The problems with LARGE programs

Program Size

How to write BIG Programs

Prog1 1 day


Prog1 Prog21 day 100 days


Prog1 Prog2

fnfnfnfnfnfnfnfnfnfn

1 day

1 day

1 day

1 day

1 day

1 day

1 day

1 day

1 day

1 day

Total10 days

1 day 100 days

Car Body Engine Gear Box Transmission Brakes Wheels etc


Engine Pistons Crank Electrical System Cooling System Fuel Delivery etc



Cooling System Radiator Fan Water Pump etc



Cooling System Radiator Fan Water Pump etc

Water Pump Impeller Housing Bearing etc

Programs

Function

Function Function Function Function

Function

Function

Function

Function Function

Function

Function

Program

Function

Top Down Design

Structures

V = [ 1 6 4 2 7 8 ]

x = V(3); x → 4

All values must be the same type and size.

You have no choice about index used.

Limitations of Arrays

Name of the structure is Element

Field Value

Symbol 'Na'

Atomic 11

Shells [2 2 6 1]

Name 'Sodium'

Structure

Structure.Field = Value

Element.Symbol = 'Na';

Element.Atomic = 11; Element.Shells = [2 2 6 1];

Element.Name = 'Sodium';

Structure

%SquareHouse(1).path = [0 100 100 0 0 0 0 100 100 0]; % squareHouse(1).colour = 'r'; % The colour to plotHouse(1).solid = 1; % Fill the square %TriangleHouse(2).path = [ -20 50 120 -20 100 170 100 100 ]; % TriangleHouse(2).colour = 'g'; % The colour to plotHouse(2).solid = 1; % Fill the triangle

Structural ArrayEvery element of the array contains a structure

rotatepicabout rotateabout

Translate

rotate

House

House(1) path col solid



““

““

““

““


Functions

Structural Array

Programming is easier if you organise your data and code

Simulating a Rocket Launch

Saturn V Rocket

0 20 40 60 80 100 120 140 160

0

20

40

60

80

100

120

140

160

Real World Problem

mdvdt

= Th(t ) − k v2 − m g

Real World Problem

mdvdt

= Th(t ) − k v2 − m g

dvdt

=Th(t ) − k v2

m(t )− g

dydt

= f (t , y) y ( t 0)= y0

Initial Value Problem

Find y (t )when

Euler's Method

t 0 t1

δ t

y0

y1

t2 t 3

y2

y3

t0 t1

δ t

y0

y1

What is the slope of the line ?

t0 t1

δ t

y0

y1Slope=

y1− y0t 1−t 0

=y1− y0δ t

What is the slope of the line ?

What is ?dydt

What is ?dydt

dydt

= k = slope

t0 t1

δ t

y0

dydt

= f (t , y) y (t 0)= y0

t0 t1

δ t

y0

dydt

= f (t , y) y (t 0)= y0

dydt

(t 0) = f (t0, y0)

t0 t1

δ t

y0

dydt

= f (t , y) y (t 0)= y0

dydt

(t 0) = f (t0, y0)

slope = f (t0, y0)

t0 t1

δ t

y0

y1

dydt

= f (t , y) y (t 0)= y0

dydt

(t 0) = f (t0, y0)

y1− y0δ t

= f (t0, y0)

slope = f (t0, y0)

t0 t1

δ t

y0

y1

dydt

= f (t , y) y (t 0)= y0

dydt

(t 0) = f (t0, y0)

y1− y0 = δ t f ( t 0, y0)

y1− y0δ t

= f (t0, y0)

slope = f (t0, y0)

t0 t1

δ t

y0

y1

dydt

= f (t , y) y (t 0)= y0

dydt

(t 0) = f (t0, y0)

y1− y0 = δ t f ( t 0, y0)

y1− y0δ t

= f (t0, y0)

slope = f (t0, y0)

y1= y0+δ t f ( t 0, y0)

dydt

= f (t , y) y (t 0)= y0

y1= y0+δ t f ( t 0, y0)

t0 t 1

δ t

y0

y1

t2 t 3

dydt

= f (t , y) y (t 0)= y0

y1= y0+δ t f ( t 0, y0)

t 0 t1

δ t

y0

y1

t 2 t3

y2y2= y1+δ t f ( t1, y1)

dydt

= f (t , y) y (t 0)= y0

y1= y0+δ t f ( t 0, y0)

t0 t 1

δ t

y0

y1

t 2 t 3

y2

y3

y2= y1+δ t f ( t1, y1)

y3= y2+δ t f (t 2, y2)

Using Euler's method to solve y'(t) = f(t,y) y(0) = y0

1. Initialize the values.

2. Repeat for each time step.

3. Store the current values for plotting later.

4. Evaluate the current value of f(t,y).

5. User Euler's formula to evaluate y for the next step. y = y + dt*f(t,y)

6. End of repeat.

7. Plot the date.

Top Down Design of Euler's Method

The Design Cycle

Design

Start with a simple design

Design Build


Design Build Test


Design Build Test

Debug


Design Build Test

Debug

Make the design more complex

Design Build Test

Debug

Add additional feature to the design

Saturn V Rocket

Design Build Test

Debug

Constant Acceleration

Constant Acceleration

dvdt

= a wherea is a constant

v = u+at

s = ut+12at2

Design Build Test

Debug

Thrust Stops after 150 seconds

Thrust Stops after 150 seconds

dvdt

= a

v = u+at

s = ut+12at2

t < 150

dvdt

=−g

v = u−g t

s = ut−12g t2

t ≥ 150

Design Build Test

Debug

Variable Mass

Design Build Test

Debug

Force of Drag

Assessment

No formal assessment for session 3

Get a demonstrator to comment on your program

READ PAGE 119

How to get GOOD MARKS

Practice 2

Debugging

introduction to the p5 computing laboratorylabejp/courses/1p5/lecture3slides.pdf · session 3, dbt...

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