The document describes a research project to design an improved helicopter. Researchers at Flinders Engineering tested different helicopter designs and recorded flight times. The student is asked to choose variables to change, such as blade length or base size. Flight time data for different variable values will be collected and graphed. A quadratic model will be fitted to the data to determine the optimum design configuration.

1. Quadratics
Modelling Task
23 September 2013
New improved helicopter
design identified by ASMS
students
Jo Kellaway, Maryann Doolette, Maja Williams
In exciting news from the Flinders Engineering Research labs, a innovative new design for a helicopter has been
developed. Associate Professor Susan Hyde has greeted the knowledge with delight, stating that her trips to and
from the Education Department Head Offices in Flinders Street will be much more pleasant.
However, with any new design there will always be challenges and the final configuration of the design is still being
investigated.
A number of designs were tested to determine the most efficient and safest structure for the project. Changes were
made and optimum time in the air were recorded.
Researchers believe that they are close to producing the perfect helicopter.
You are one of the researchers on this project and you want to find out the optimum configuration so Susan can fly
most efficiently.
Below are several templates for your helicopter, showing various aspects of the design that you can change. You
need to consider what variables you wish to consider. You might look at size, weight (e.g. by adding components)
etc.

2. Quadratics
Modelling Task
Here the length of the blades have been changed or the size of the base etc.
(NOTE: The dotted lines need to be cut and the solid lines need to be folded. See the diagram below for final
shape.)
List several variables that you could change. Identify the ones that you will concentrate on.

3. Quadratics
Modelling Task
Draw up and make your helicopters based on the variables you will change. Find an appropriate spot that is not
going to interfere with other classes and drop your helicopter. Time how long it takes to reach the ground. Repeat
with other helicopters with different values for your chosen variable.
Record your results below.
Variable Value
Time of Flight
You need to find a model to map this data so you draw a graph to represent it. Use the axes on the next page to
help.
From your graph, what do you think is the best type of model for your data?
Estimate the x - intercepts of your graph. Use these to write an equation for your model in factor form.

4. Quadratics
Modelling Task

5. Quadratics
Modelling Task
From your graph, what are the coordinates of the maximum result?
What does this mean in the context of the problem?
Use the coordinates of the maximum and your equation in factor form to find the model that fits this data.
Enter the data into your calculator and use it to find the equation of this relationship.
Why might the models that you get be different?

6. Quadratics
Modelling Task
Using either of the two models, determine the range of values that your variable can take where the model is valid.
Why is this the range of possible values for the model?
Consider the model that you have developed. What are its limitations? When will it work and when will it fail? Are
the answers that you have obtained reasonable?What other assumptions have you made?