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The Shapes Of Flight Plane Simulation

 Project Proposed By

Ali Mazahir Qamari                                                                                                                                                             B.S II 1999                                                                                                                                                                         Numerical Analysis & Computing                                                                                                                     Department Of Computer Science                                                                                                                     University of Karachi-Pakistan                                                                                                                                         Dated: October 21, 1999

Despite the forbidding mystique around the act (and word) of "writing", it is not a skill one is born with . People learn how to write, just as they learn how to read, to type, and to operate computers. Ones get better at it the more one writes. I too has obtained the same path and this was my first step towards proposing a real time project for implementation. I am thankful and grateful to Almighty Allah the omnipotent and omnipresent who has endowed us with knowledge in the patience and encourage in the accomplishment of my task.

 The idea and reference of the project proposal is taken from the NASA (National Aeronautics and Space Administration) researcher’s educator guide. The web addresses are:                        

This Project Proposal can be implemented in aviation, aerodynamics, automobile industry, train and shipping industry. Last but not the least, special thanks to my course supervisor who has endowed me with his knowledge.

Sir Dr. Syed Arif Kamal                                                                                   Associate Professor                                                                           Department of Mathematics                                                                 Univerisity Of Karachi-Pakistan                            

Back ground

The Shapes of Flight Simulation, involves students in the interaction between mathematics, science and technology as they look at the process of airplane design. NASA researchers show students & engineers the process and tools to research, develop, test and evaluate airplane design. We can observe how the engineering process compares to the scientific method. The activity involved in organizing, comparing and interpreting data. We have to investigate the glide ratio for a Prototype Model of an Airplane models and determine which glide ratio of Airplane is best beneficial for flight planes. Guisness Book of World Record was established in the 1980’s by high school students from the Hampton, Virgina for making big paper plane for experimentation.


 Every year countries spend their high cost budget over air plane machinery’s including defense and travelling purpose. Many projects fail due to non-analysis of the real time problems. Big aviation such as NASA performs prototype modeling and then implements it.


 Teachers and researchers adopt this method to guide their students the real scientific engineering methods.


 A vast revenue is save and researchers, teachers and students can learn the methods of scientific study, occurrence in nature and can program it for any aviation corporation.


 Paper planes, measuring sticks, weighing machine, chalks cost about Rs 100/-

 Risk Factors
A constant force is not used to glide the plane.
Different paper quality material.
Human error.

Experiment Material

 Electronic weighing machine for paper weight .                                                                   

Airplane pattern namely Egret, Flex , Basic Square, and Condor                                                            

1 piece 8-1/2 * 11 paper A4 size paper

Meter stick or metric tape measure.
Test flight area.
Length cord, marked off in meters, anchored to a starting line.

Terms & Ratios

Glide Ratio: The horizontal distance that the airplane will travel from a given altitude in the absence of power and wind.

Glide Ratio = horizontal Distance Flown/ Change in Altitude

Weight Paper1=10 grams i.e. 0.010 kilogram

Weight Paper2=04 grams i.e. 0.004 kilogram

Development & Design

There are four stages in the development of an aircraft, they are

  1. Concept 2. Design 3. Modeling 4. Testing


Glide different plane shapes with constant force and record their observation in a chart than predict the nature and behavior of the model. After the test run we than implement it for simulation for real time projects. 

Mathematics Standards

Science as Inquiry

Science & Technology



Calculate area for paper airplane model & wing area

NASA researchers demonstrate geometry modeling performed on the computer in the preliminary design configuration of blended wing model.



Measures launch height (altitude).

Measure horizontal distance to the nearest meter.

Physics occurs

Force, Gravitation, Air resistance


Number Operations

Calculate Mean, Median, and Glide Ratio, Ratio between total area and wing area of airplane model. Mathematics involves

Numerical Analysis


Data Analysis


Collect Data, Keep records, Graph results

NASA researchers discuss the necessary analysis performed on an unconventional configuration called a blended wing body.



Problem Solving

Determine which paper airplane design has the best ratio.

Engage in Mathematical discourse to extend understanding of problem solving and capacity to reason and communicate mathematically.

NASA researchers describe the technologies and engineering process used to research, design, develop, test and evaluate futuristic airframe concepts

Technologies provide tools for investigations, inquiry and analysis.

Test Run

The launching of the model airplanes from a constant height and with a consistent force for each trial in the experiment is necessary. For recording correct data I have taken three observations for each test flights and similar paper weight.

 Data Collection & Analysis

 Data from each flight should be collected and recorded on to the Data Sheet. I have measure the distance traveled by the model from the launching point to where the model first hit the ground. Calculate mean and median of the collected data. Then compute the glide ratio for each of the recorded observation.

 Name Of Airplane Model: Egret

Weight Paper1=10 grams i.e. 0.010 kilogram

Trial distance altitude glide ratio
1 2.92m 2.07m 1.41
2 3.06m 2.07m 1.47
3 2.98m 2.07m 1.43
mean(x) 2.98 m
MEDIAN 2.98 m

Name Of Airplane Model: Flex

Weight Paper1=10 grams i.e. 0.010 kilogram

Trial distance altitude glide ratio
1 2.10m 2.07m 1.01
2 2.31m 2.07m 1.11
3 2.22m 2.07m 1.07
mean(x) 2.21 m
MEDIAN 2.22 m

Name Of Airplane Model: Condor

Weight Paper1=10 grams i.e. 0.010 kilogram

Trial distance altitude glide ratio
1 2.06m 2.07m 0.99
2 2.12m 2.07m 1.02
3 2.11m 2.07m 1.01
mean(x) 2.09 m
MEDIAN 2.11 m

Name Of Airplane Model: Basic Square

Weight Paper1=10 grams i.e. 0.010 kilogram

Trial distance altitude glide ratio
1 2.72m 2.07m 1.31
2 2.69m 2.07m 1.29
3 2.78m 2.07m 1.34
mean(x) 2.73 m
MEDIAN 2.72 m

Name Of Airplane Model: Egret

Weight Paper2=04 grams i.e. 0.004 kilogram

Trial distance altitude glide ratio
1 2.06m 2.07m 0.99
2 1.98m 2.07m 0.95
3 2.01m 2.07m 0.97
mean(x) 2.01 m
MEDIAN 2.01 m

Name Of Airplane Model: Flex

Weight Paper2=04 grams i.e. 0.004 kilogram

Trial distance altitude glide ratio
1 1.73m 2.07m 0.83
2 1.59m 2.07m 0.76
3 1.62m 2.07m 0.78
mean(x) 1.64 m
MEDIAN 1.62 m

Name Of Airplane Model: Condor

Weight Paper2=04 grams i.e. 0.004 kilogram

Trial distance altitude glide ratio
1 1.64m 2.07m 0.79
2 1.69m 2.07m 0.81
3 1.58m 2.07m 0.76
mean(x) 1.63 m
MEDIAN 1.64 m

Name Of Airplane Model: Basic Square

Weight Paper2=04 grams i.e. 0.004 kilogram

Trial distance altitude glide ratio
1 2.01m 2.07m 0.97
2 1.89m 2.07m 0.91
3 1.94m 2.07m 0.93
mean(x) 1.94 m
MEDIAN 1.94 m


Observations, Prediction & Behavior

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