ENGR 290 MATLAB Simulation for Hovercraft Design

 

 

List of Figures

Figure 2.1.1: Dimensions of Competition Track

Figure 4.1.1: Design Concept #1

Figure 4.1.2: Design Concept #2

Figure 4.1.3: Design Concept #3

Figure 5.0.1: Linear and Angular Motion Along the X and Z Axis of the Hovercraft

Figure 5.0.1.1: Dimensional Design of Hovercraft Design #1

Figure 5.0.2.1: Dimensional Design of Hovercraft Design #2

Figure 5.0.3.1: Dimensional Design of Hovercraft Design #3

Figure 5.2.1.1: Angular and Linear Motion Results Created by MATLAB Simulation for Hovercraft Design #1

Figure 5.2.2.1: Angular and Linear Motion Results Created by MATLAB Simulation for Hovercraft Design #2

Figure 5.2.3.1: Angular and Linear Motion Results Created by MATLAB Simulation for Hovercraft Design #3

Figure 8.0.1: Estimated Gantt Chart of the Hovercraft Project Timeline

List of Tables

Table 5.0.1: Inertia Calculations for Hovercraft Design #1

Table 5.0.2: Inertia Calculations for Hovercraft Design #2

Table 5.0.3: Inertia Calculations for Hovercraft Design #3

Table 5.1.1: Theoretical Results of the Hovercraft Designs

Table 6.1.1: WOT Analysis of Designs

Table 6.2.1: SWOT of Design 1

Table 6.2.2: SWOT of Design 2

Table 6.2.3: SWOT of Design 3

Table 6.3.1: Pairwise Comparison Matrix

Table 6.3.2: Normalized Pairwise Comparison Matrix

Table 6.3.3: Row Averages

Table 6.3.4: Priority Vector

Table 6.3.5: Weight Comparison Matrix

Table 6.3.6: Normalized Weight Comparison Matrix

Table 6.3.7: Row Averages

Table 6.3.8: Weight Priority Vector

Table 6.3.9: Speed Comparison Matrix

Table 6.3.10: Normalized Speed Comparison Matrix

Table 6.3.11: Row Averages

Table 6.3.12: Speed Priority Vector

Table 6.3.13: Maneuverability Comparison Matrix

Table 6.3.14: Normalized Maneuverability Comparison Matrix

Table 6.3.15: Row Averages

Table 6.3.16: Maneuverability Priority Vector

Table 6.3.17: Programmability Comparison Matrix

Table 6.3.18: Normalized Programmability Comparison Matrix

Table 6.3.19: Row Averages

Table 6.3.20: Programmability Comparison Matrix

Table 6.3.21: AHP Analysis Overall Ranking

Table 7.0.1: Components That Will be Used for Hovercraft Design 1

 

Table of Contents

 

1.0 Introduction

Page 5

 

2.0 Mission Objective

Page 6

 

3.0 Requirements

Page 7

 

4.0 Designs

Page 8

 

5.0 Theoretical and Matlab Simulations

Page 11

 

6.0 Design Selection

Page 19

 

7.0 Components

Page 28

 

8.0 Estimated Gantt Chart

Page 29

 

9.0 Conclusion

Page 30

 

References

Page 31

 

1.0 Introduction

The design and development of a hovercraft is perhaps similar to that of an aircraft or a boat in some way. Several in-depth researches have been carried out in order to understand and analyze the principle of how the hovercraft work and functions.The primary team goal is to design and build a sufficient optimized hovercraft that can finish the path and overcome obstacles in the least amount of time. The process began by brainstorming and coming up with many different designs, which eventually narrowed down to three. Decision making can be complicated; each design decision such as shape, size, and amount of elements can have an impact on the hovercraft efficiency. With the help of SWOT, WOT, AHP, and Matlab framework which guides through the design selection process, and hopefully to the best hovercraft design.

2.0 Mission Objective

The objective of the this competition is to design an build a hovercraft that:

1. Complete’s as much of the specified track as possible, operating autonomously. 
2. Traverse’s as many of the increasingly challenging obstacles along the track.
3. Complete the course in as short a time as possible (2 min. time limit per each attempt)
4. Accomplish the Objectives 1-3 without using more resources (i.e. fans and servos) than necessary. 

Score will be based on the formula 

Distance covered / (number of components * time taken) = Total Score 

The highest score wins the competition  that is why there is another objective 

5. That  achieves as high a score as possible 

2.1 The Track

The track consists of four straight aways of 235cm and three u-turns.  Along the way there will be three obstacles at the center of the straight aways, ranging in size , 1mm, 2mm and 3mm. 

Figure 2.1: Dimensions of Competition Track

3.0 Requirements

Considering the requirements of hovercraft, there are three major and distinct components that are involved in the entire mechanism,  a platform, a motorised fan and a skirt. Hovercrafts can also be called as Air Cushioned Vehicle (ACV) that are designed to travel on land, snow, water and other surfaces like mud, grass and quicksand (Jeong and Chwa, 2017). The smooth air cushion can be of different materials as per the purpose of the ACV. However, it is necessary to take care of certain requirements that are involved in the making of the hovercrafts to handle the speed and strength required by the hull considering the availability of the components and intermediate fabrication skills. In the words of Iventosch et al., (2019), as hovercrafts serve different purposes, it is necessary to ensure the implementation of certain factors like military surveillance near coastal areas, transportation purposes in snowy regions and flood rescue operations. Among the three major components stated above, the fan bows the air beneath the platform that are trapped and grounded by the skirts. The region where the air is trapped is the plenum chamber and the air that is blown inside form rings that is circulated at the base of the skirt and through this the air beneath keeps escaping (Foraker et al., 2016). Along with this, under laid are the requirements that are to be met by hovercraft before it functions:

•     It is necessary to maintain the hover-height by containing the cushion of the air under the craft.
•     It must have the ability to contour over the hindrances or obstacles across its path.
•     Ability to regain the original shape after deformation and also focusing on providing stability.

     The power-to-weight-to-strength and power-to-weight ratio are required to be determined in order to handle the structural strength of the hovercraft. 

4.0 Designs

Figure 4.1.1: Design Concept #1

Figure 4.1.2: Design Concept #2

Figure 4.1.3: Design Concept #3

5.0 Theoretical and MATLAB  Simulations

In the previous part of the report we dipics  three designs of the hovercraft that will be tested and simulated to expand on the decision making on  our final design. To do this we set on using newtonian methods to solve for angular acceleration and linear acceleration of each design. After solving for both angular and linear acceleration MATLAB would be used to simulate the velocity and displacement over time of each design and each type of motion. 

The goal was to find the acceleration, velocity and displacement  of the hovercraft to both the translational motion (the x direction)  and the rotational motion (?, along the x and z axis).

Figure 5.0.1: Linear and Angular Motion Along the X and Z Axis of the Hovercraft

To calculate the angular acceleration of the hovercraft, the newtonian equation  of inertia was used Inertia = Torque x Angular Acceleration .  We had the weight of all the components and the dimensions were determined for each design, with this data we were able to calculate the Inertia of each part with the equation Inertia = Mass * Meter2, the sum was then recorded. The torque was more difficult to calculate as the only data that was given for the thrust was the air flow. With the help of an online airflow calculator [1] the force was calculated for the AFB1212SH fan. With the force known for the fan, the Torque could be calculated with Torque = [perpendicular] Force * Meter, trigonometry was used for forces that were not perpendicular. With inertia and torque both calculated, the angular acceleration could be calculated.

To calculate the linear acceleration, the simple newtonian equation of  Force = Mass * Acceleration  was used.  In this context the acceleration that we are looking for is in the forward front direction of the hovercraft. Due to this fact the force that is used is the backwards force applied by the AFB1212SH  fan(s). With this force the total mass was calculated and used to calculate the forward linear acceleration.

5.0.1 Inertia Calculations for Design Concept #1

Figure 5.0.1.1: Dimensional Design of Hovercraft Design #1

 

Table 5.0.1: Inertia Calculations for Hovercraft Design #1

Parts	Inertia (kgm2)
Sensor- 25cm	0.000312
Sensor 15cm x2	0.000225
Servo 15cm	0.001
Fan	0.009
Body	0.014
Battery x2	0.00185
Total	0.0264

5.0.2 Inertia Calculation for Design Concept #2

Figure 5.0.2.1: Dimensional Design of Hovercraft Design #2

 

Table 5.0.2: Inertia Calculations for Hovercraft Design #2

Parts	Inertia
Battery x2	0.00185
Sensor 25cm	0.000312
Sensor 15cm x2	0.000221
Body	0.014
Fans x2	0.064
Total	0.080

5.0.3 Inertia Calculation for Design concept #3

Figure 5.0.3.1: Dimensional Design of Hovercraft Design #3

 

Table 5.0.3: Inertia Calculations for Hovercraft Design #3

Parts	Inertia (kgm2)
Sensors x4	0.00125
Fan x2	0.06
Battery x2	0.002
Body	0.017
Total	0.080

5.1 Theoretical Results 

	Design #1	Design #2	Design #3
Power consumption	15.04W	19.39W	19.41W
Area of base	13.57m2	13.57m2	19.63m2
Weight of base	0.5kg	0.5kg	0.6kg
Mass	1.510kg	1.863kg	1.977kg
Total Airflow from thrust	3.203M2/min	6.406M2/min	6.406M2/min
Total Airflow from lift	3.203M2/min	3.203M2/min	3.203M2/min
Thrust applied by fan(s)	5.3N	7.48N	10.6N
Force applied by gravity	14.81N	18.27N	19.39N
Total Inertia	0.0264kgm2	0.080kgm2	0.080kgm2
Torque applied for one fan	0.795Nm	1.06Nm	1.325 Nm
Angular Acceleration	30.16rads/s2	13.24rads/s2	16.54rads/s2
Linear Acceleration	3.51m/s2	4.01m/s2	5.31m/s2

Table 5.1.1: Theoretical Results of the Hovercraft Designs

5.2 MATLAB simulations 

The MATLAB simulation was used to elaborate on the data collected in the theoretical calculations. The theoretical calculation gave us the angular and linear acceleration of each hovercraft design. With the addition of MATLAB we will not only be able to see the the acceleration over time of each hovercraft but to be able to calculate and represent velocity and displacement over time of each design.  For better visual effects the value at three seconds is shown. Note that these calculations do not take into consideration drag and friction, which will affect the results in the real world .

5.2.1 MATLAB simulations of Design #1

Figure 5.2.1.1: Angular and Linear Motion Results Created by MATLAB Simulation for Hovercraft Design #1

5.2.2 MATLAB simulations of Design #2

Figure 5.2.2.1: Angular and Linear Motion Results Created by MATLAB Simulation for Hovercraft Design #2

5.2.3 MATLAB simulations of Design #3

Figure 5.2.3.1: Angular and Linear Motion Results Created by MATLAB Simulation for Hovercraft Design #3

6.0 Design Selection

6.1 WOT Analysis

Table 6.1.1: WOT Analysis of Designs

DESIGN 1

DESIGN 2

DESIGN 3

 

SPEED

2

1

1

 

NUMBER OF PARTS

2

2

3

 

MANEUVERABILITY

1

2

3

 

WEIGHT

1

3

3

 

PROGRAMMABILITY

2

3

3

 

TOTAL

8

11

13

1: best,         2: ok, 3: worst

6.2 SWOT Analysis

Table 6.2.1: SWOT of Design 1

Strengths Maneuverability is high. Lightest hovercraft design. High angular acceleration.	Opportunities  The number of parts could be decreased by using one sensor. Known grading scheme  Known track Known obstacles
Weakness Programmability is relatively difficult. The number of parts is relatively high	Threats Other groups with a similar design.

 

Table 6.2.2: SWOT of Design 2

Strengths High Velocity.	Opportunities  Known grading scheme  Known track Known obstacles
Weakness Programmability. Largest mass.	Threats Other groups with a similar design.

 

Table 6.2.3: SWOT of Design 3

Strengths Low number of parts. High velocity.	Opportunities  Known grading scheme  Known track Known obstacles
Weakness Maneuverability. Programmability. Largest mass.	Threats Other groups with a similar design.

6.3 AHP Analysis

Table 6.3.1: Pairwise Comparison Matrix

	Weight	Speed	Maneuverability	Programmability
Weight	1	2	1/2	4
Speed	1/2	1	1/2	3
Maneuverability	2	2	1	3
Programmability	1/4	1/3	1/3	1
Sum	3.75	5.3333	2.3333	11

 

Table 6.3.2: Normalized Pairwise Comparison Matrix

	Weight	Speed	Maneuverability	Programmability
Weight	0.2667	0.3750	0.2143	0.3637
Speed	0.1333	0.1875	0.2143	0.2727
Maneuverability	0.5333	0.3750	0.4286	0.2727
Programmability	0.0667	0.0625	0.1428	0.0909
Sum	1.0000	1.0000	1.0000	1.0000

 

Table 6.3.3: Row Averages

Weight	0.3049
Speed	0.2020
Maneuverability	0.4024
Programmability	0.0907

 

Table 6.3.4: Priority Vector

0.3

0.2

0.4

0.1

 

Table 6.3.5: Weight Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	1	3	3
Design 2	1/3	1	2
Design 3	1/3	1/2	1
Sum	1.6667	4.5	6

Table 6.3.6: Normalized Weight Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	0.6	0.6667	0.5
Design 2	0.2	0.2222	0.3333
Design 3	0.2	0.1111	0.1667
Sum	1	1	1

 

Table 6.3.7: Row Averages

0.5889

0.2518

0.1592

 

Table 6.3.8: Weight Priority Vector

0.59

0.25

0.16

 

Table 6.3.9: Speed Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	1	1/3	1/4
Design 2	3	1	1/3
Design 3	4	3	1
Sum	8	4.3333	1.5833

Table 6.3.10: Normalized Speed Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	0.125	0.0769	0.1579
Design 2	0.375	0.2308	0.2105
Design 3	0.5	0.6923	0.6316
Sum	1	1	1

Table 6.3.11: Row Averages

0.1199

0.2721

0.6980

Table 6.3.12: Speed Priority Vector

0.12

0.27

0.70

 

Table 6.3.13: Maneuverability Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	1	3	3
Design 2	1/3	1	2
Design 3	1/3	1/2	1
Sum	1.6667	4.5	6

Table 6.3.14: Normalized Maneuverability Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	0.6	0.6667	0.5
Design 2	0.2	0.2222	0.3333
Design 3	0.2	0.1111	0.1667
Sum	1	1	1

 

Table 6.3.15: Row Averages

0.5889

0.2158

0.1592

 

Table 6.3.16: Maneuverability Priority Vector

0.59

0.22

0.16

 

Table 6.3.17: Programmability Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	1	2	3
Design 2	1/2	1	2
Design 3	1/3	1/2	1
Sum	1.8333	3.5	6

Table 6.3.18: Normalized Programmability Comparison Matrix

	Design 1	Design 2	Design 3
Design 1	0.5455	0.5714	0.5
Design 2	0.2727	0.2857	0.3333
Design 3	0.1818	0.1429	0.1667
Sum	1.8333	3.5	6

 

Table 6.3.19: Row Averages

0.5890

0.2972

0.1638

 

Table 6.3.20: Programmability Comparison Matrix

0.59

0.30

0.16

 

Table 6.3.21: AHP Analysis Overall Ranking

	Weight (0.3)	Speed (0.2)	Maneuverability (0.4)	Programmability (0.1)	Final Score
Design 1	0.59	0.12	0.59	0.59	0.496
Design 2	0.25	0.27	0.22	0.30	0.247
Design 3	0.16	0.70	0.16	0.16	0.268

Design 1 is the preferred design based on the AHP analysis. It had the highest score for the weight, maneuverability and programmability sections of the AHP analysis. This is the design that will be constructed for the project.

7.0 Components

Table 7.0.1: Components That Will be Used for Hovercraft Design 1

FAN

SERVO

BATTERY

SENSOR

 

NAME: AFB1212SH Newtons: 5.3N AMOUNT: 2 DIMENSIONS: 120x120x25mm TOTAL MASS: 396g

NAME:  HS311 AMOUNT: 1 DIMENSIONS: 39.88x19.81x36.32mm MASS: 43g TOTAL MASS: 43g

NAME: GENS 450 AMOUNT: 2 DIMENSIONS: 56x31x10mm MASS: 33g TOTAL MASS: 66g

NAME: GP2Y0A02YK0F AMOUNT: 3 DIMENSIONS: 29.5x13x21.6mm MASS: 4.8g TOTAL MASS: 14.4g

8.0 Estimated Gantt Chart

Figure 8.0.1: Estimated Gantt Chart of the Hovercraft Project Timeline

9.0 Conclusion

In conclusion, the first hovercraft design has a substantially lower score for the WOT Analysis than the other designs. In addition to this, the SWOT analysis has also shown that the first design is better overall than the other two designs. Also, the AHP analysis has proven that hovercraft design one is better than its counterparts and the most efficient. This hovercraft will offer increased maneuverability, speed and have a lower weight than the others.  Matlab and other simulations have shown that the torque of design one is lower than the others and the angular acceleration is higher than the other designs. Should the Gantt Chart be accurate, the hovercraft will be on schedule and teamwork is crucial for this hovercraft to function as intended.

References

Fu, M., Zhang, T. and Ding, F., 2019. Adaptive Finite-Time PI Sliding Mode Trajectory Tracking Control for Underactuated Hovercraft With Drift Angle Constraint. IEEE Access, 7, pp.184885-184895.

Jeong, S. and Chwa, D., 2017. Coupled multiple sliding-mode control for robust trajectory tracking of hovercraft with external disturbances. IEEE Transactions on Industrial Electronics, 65(5), pp.4103-4113.

Iventosch, J., Dutton, J.E., Matthews, S.D., Gorsev, P.K. and Schwartz, R., Pensa Systems Inc, 2019. Recognition and prediction of semantic events learned through repeated observation. U.S. Patent Application 16/533,764

Foraker, J., Lee, S. and Polak, E., 2016. Validation of a strategy for harbor defense based on the use of a min?max algorithm receding horizon control law. Naval Research Logistics (NRL), 63(3), pp.247-259.

 

[1]Online Engineering Calculator. Airflow Conversion Calculator https://www.engineering.com/calculators/airflow.htm. Retrieved february 2020.