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Introduction:

Here the report is all about experimental design analysis and design optimization of a paper helicopter model. This is entirely based on in-house experiment. A statistical data sheet and its design optimization is being carried out for confirming its optimized design. The statistical methodology taken into consideration is known as Taguchi matrix method and this report is carried out in reference with L8 (2)7 Taguchi matrix.

This report mainly consists of three parts which describes its “Design and it’s in house experiment, observing results and analysis and discussion on optimum solution” respectively, as followed by the requirements.

Process of making:

Here some steps we need to consider at the time of making the paper helicopter physically;

1. First we need to cut the paper throughout the outline of the drawing.
2. Cut it on the internal lines to give it a proper shape.
3. Both the wings should be folded in opposite directions, keeping an angle of 90⁰ to 180⁰.
4. Since we are using at least one paper clip at the tail end, we have to be very careful thet we added it or not.

Several numbers of factors are there which can affect the time of flight of the paper helicopter model;

1. Wing axial length (Long-short)
2. Body axial length (long-short)
3. Body width (Narrow-wide)
4. Weight of paper clips (one or two)

Some factors may be included in it like, paper material, taped body, taped wing, indoor and outdoor holes in the wings, etc.

The factor we considered here paper type having a important role on the experimental design. The reason behind it is the factor that effects on the aerodynamic drag, friction with the air.

The length of wings is also a parameter which needs to be considered because short sized wings reduce drag and give high rotation speeds. They also increase balance and stability in flight. But long wings are best for heavy lift and slow glide.

Some most important factors are:

1. Body axial length – It decides the center of mass of the entire design module.
2. Body width – it decides the load carrying capacity of the helicopter.
3. The paper clip at the lower end of the body is placed for stability of the paper helicopter and to shift its CG in downward direction.

Experimental Conduct:

Taguchi matrix method is used worldwide for control and design optimization of any product. It’s a technique, where we use statistics and L8 method, at the same time. In L8 method 8 experiments are done separately by varying their factors.

Now, it is our choice to take a variety of factors, since in between a very small range it is going on that is why; degrees of freedoms are taken very few no. according to which the Taguchi matrix is made.

Experimental orthogonal plan L8 is taken into consideration. Here number of degrees of freedom is taken as 3 arrays.

Table (1): L₈ Orthogonal matrix selection for control parameters or factors affecting the time of flight.

No of Exp. done	A	B	C	D
1	1	1	1	1
2	1	2	2	2
3	1	3	3	3
4	2	1	2	3
5	2	2	3	1
6	2	3	1	2
7	3	1	3	2
8	3	2	1	3

 

The response variables are the time of flight of the paper helicopter. Here these response variables are taken by the help of stop watch. It is the time between the times of releasing it from a particular height to the time of touching at the ground.

Table (2): List of control parameters for the experiment

Control parameters	Code	Low level (-1)	High level (+1)
Paper type	A	Thin	Thick
Wing axial length	B	75 mm	120 mm
Body width	C	25 mm	40 mm
Body axial length	D	80 mm	130 mm
Paper clip	E	1 no	2 no

 

In Taguchi matrix method the number of trials in doing the experiment depends upon 2^k, here ‘k’ is the number of factors affecting on the experiment. Since, there are so many factors are affecting on this experiment, so it will take too long time to perform this experiment. Therefore, 2^(k-l), here ‘l’ is the (1/2) ^l yields the fraction of reduction of number of trials.

Experiment Explanation:

In this part of this report the detail explanation of the above experiment is discussed. It also can give us some evidence that, actually the experiment physically carried out or not? There are some snap shots are also included in this part to ensure that, the all the detailing is being taken into consideration and carefully the experiment is performed. First of all, as we have selected two factors related to paper type, so two types of paper used in this whole experiment. One is marked as Normal (75 GSM) another is marked as Thick (200 GSM). If we talk about the sizes or the shapes one is smaller in size and another is larger in size like (1^st 75, 25, 80 and 2^nd 120, 40, 130 for Wing length, body width, body length respectively). At the time of performing the experiment the paper clips are also considered such that for both the cases use of paper clip was 1 and 2 respectively. The experiment is performed in a personal vacant room; no other influence of air flow was removed to make this experiment perfect.  The measurement of time is being carried out by the same person, who dropped the paper helicopter so that the timing of stopwatch on and off can be maintained properly.

Fig (1):  There are some snap shots of the experiment so that it can prove that, actually the experiment has been carried out.

Results and Analysis:

Table (3): Proposed model observation for the paper helicopter represents the results.

No of Exp. done	A (GSM)	B (mm)	C (mm)	D (mm)	E (mm)	Time of flight (sec)
1	Thin	75	25	80	1	2.39
2	Thick	75	25	80	1	1.65
3	Thin	75	25	80	2	2.12
4	Thick	75	25	80	2	1.73
5	Thin	120	40	130	1	2.61
6	Thick	120	40	130	1	2.16
7	Thin	120	40	130	2	2.33
8	Thick	120	40	130	2	2.01

 

Calculation of Main Effects:  

The main effects related to this experiment are the values of time of flight, when the factors are at high level and at the low level. If we subtract the average time of flight at low level from the high level, then we get the main effects related to the experiment.

Like,

Average time of flight when A is considered high (+) = 1.88 sec
Average time of flight when A is considered low (-) = 2.36 sec
Main effect related to the factor A = 1.88 – 2.36 = – 0.48

The negative value of the effect of control parameter indicates the slope of the line joining the high level response and the low level response is negative.

Table (4): Main effects for the experiment

Factors affecting the time of flight	Avg. at high levels	Avg. at low levels	Effect
A	1.88	2.36	– 0.48
B	2.27	1.97	0.30
C	2.27	1.97	0.30
D	2.27	1.97	0.30
E	2.04	2.20	– 0.16

 

Calculation of Interaction Effects:  

Here for this particular paper helicopter design and optimization, we were interested to implement the following interactions;

• Wing axial length Body width ( B×C)
• Wing axial length Body length (B×D)
• Paper type Number of clips (A×E)

First considering the interaction between the control parameters B and D. to compute the interaction effect for this combination we need to find out each combinations between B and D. the combinations are (B _– D _–), (B _– D ₊), (B ₊ D_–), (B ₊ D ₊).

Interaction effect (B×D) = ½ (Main effect of B when D is at high – Main effect of B when D is at low)

                                        = ½ (0.30) = 0.15

With this same method we can find out the interaction effects for different cases,

Table (5): Interaction effects calculated

Interaction effects	Estimate of the effects
B×D	0.150
B×C	0.150
A×E	0.162

 

Graph (1): Time of flight varied by factor A (Type of paper)

 

Graph (2): Time of flight varied by factor B (Wing length)

 

Graph (3): Time of flight varied by factor C (Body width)

 

Graph (4): Time of flight varied by factor D (Body length)

 

Graph (5): Time of flight varied by factor E (No of clips)

Discussion:

Here the complete discussion based on the optimal design of the paper helicopter. The best design parameter means the factors taking into consideration is to be observe carefully. Since it is completely a physically experimental testing report that is why we can’t make any assumption. We just need to find out the design among these, and conclude a final design which must have a highest flight time in air. For our proposed designs the maximum efficient model is given below,

Table (6): Table of optimum control parameter (factors) setting

Control parameter (Factors)	Optimum level
Paper type (A)	Thin (90 GSM)
Wing axial length (B)	120 mm
Body width (C)	40 mm
Body axial length (D)	130 mm
Paper clip (E)	1 no

 

Conclusion:

The software virtual design and simulation is a perfect tool to optimize any design. But the experimental design and its analysis on the context of checking some designs optimum level is the best way for tackling quality control problems effectively. Since this paper completely based on the physical experimental checkup of the design of a paper helicopter that is why there is not a single error. There is not any kind of difference between the experiment and real life implementation. Since we have checked the proposed design considering all control parameters or factors, the results are accurate in nature. For making it more appropriate all the trials are taken for more than five times and the time of flight calculated by getting their average. The result of this experimental design provides us a greater accuracy in optimization of the paper helicopter. So finally we can conclude the perfect optimum design of the paper helicopter and its design.

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