Paper Title (use style: paper title)

International Journal of Engineering Applied Sciences and Technology, 2022

Vol. 7, Issue 9, ISSN No. 2455-2143, Pages 161-166

Published Online January 2023 in IJEAST (http://www.ijeast.com)

161

ANALYSIS OF FLIGHT CHARACTERISTICS OF

PAPER AIRPLANES

Md Hasibuzzaman, Md Kamrul Hasan

Department of Mechanical Engineering

Rajshahi University of Engineering & Technology

Rajshahi-6204, Bangladesh

Abstract: The trajectory of a paper airplane is dependent

on its lift and drag performance and aerodynamic

stability. Historically, darts were the perfect choice for

distance competitions because of their excellent stability,

but John Collins has changed this tradition with his

incredible design, Susanne, by making a new distance

record in 2012. In this paper, differences between this

world record design and other typical paper airplanes are

represented using typical models of a dart and glider since

the wingspan of Susanne fits in between them. Solid

models of these three airplanes are created with Solid

Works and analyzed with ANSYS Fluent at different

attack and sideslip angles. Finally, a comparison is made

considering lift, drag, and aerodynamic stability. From the

simulated results, it is observed that Susanne performed

moderately in terms of lift and drag performance and yaw

stability; however, it possesses the maximum amount of

roll stability.

Keywords: Angle of attack, Sideslip angle, Aerodynamic

stability.

I. INTRODUCTION

The art of paper folding, or origami, evolved and became

popular within a century of the invention of paper (500 BCE).

The first folded paper glider was developed in this period

somewhere in ancient China or Japan. Since then, paper

airplanes have been used to understand the properties of air and

airborne objects [1]. Even the forefathers of modern flight used

paper model aircraft to develop their designs. Though airplane

manufacturers do not use paper-made models anymore, these

models still play a vital role in the study of Micro Air Vehicles

(MAV), and it goes without saying that paper airplanes are still

used as fascinating toys [2]. Consequently, different

competitions are arranged for paper airplanes all over the

world, focusing on two parameters of flight: distance and time.

In this paper, the differences between the current distance

record-achieving model and two other typical paper airplane

models are revealed using CFD simulation [3].

II. CONSTRUCTION

The world record model Susanne is made with an 8.5" by 11"

paper sheet, and the wingspan of this model is a bit wider than

a dart but narrower than a glider. So, to make a perfect

comparison, both of the dart and glider models are made with

paper sheets of the same dimension. The relevant dimensions

of these airplanes are given in Table I.

Table-1: Basic dimensions

Name of the

model

Wingspan

(cm)

Wing

height (cm)

Wing

area (sq

cm)

Susanne

19.9

19.1

147

Typical dart

14.48

169.2

Typical glider

19.65

14.3

229

The construction procedure of these three models is shown in

Figure 1.

Fig.1.Construction procedure of Susanne (a-e), typical dart (f-

h), and typical glider (i-n).

It is observed from practical experience that long origami

structures always tend to deform a bit when sharp creases are

International Journal of Engineering Applied Sciences and Technology, 2022

Vol. 7, Issue 9, ISSN No. 2455-2143, Pages 161-166

Published Online January 2023 in IJEAST (http://www.ijeast.com)

162

made. So, for each of these models, a certain amount of

distance is observed between the upper and lower layers of the

wings. 3D designs made by different modelling software by

folding rectangular sheets are not helpful in imitating this

practical issue [4]. As a result, solid models are created using

Solid Works to attain better accuracy. John Collins designed

his model with a positive dihedral angle to attain better lateral

stability. With the increase in dihedral angle, lift-generating

capacity decreases. So, the dihedral angle should not be very

high either. The solid models of Susanne and the typical dart

are designed with a 20° dihedral angle [7]. Since there is no

centrefold in the glider, it is practically impossible to

introduce any dihedral angle in this model. The solid models

created by SolidWorks are shown in Figure 2.

Fig.2. 3D model of Susanne, typical dart, and typical glider

(from top to bottom).

III. SIMULATION SETUP

Sufficiently spacious fluid domains (about 25 cm in the

upstream region and about 45 cm in the downstream region)

are created to get better results. A sample of a fluid domain is

shown in Figure 3. A mesh independence study is performed,

considering the coefficient of lift as a variable [6].

Fig.3 Fluid domain of typical dart.

From Figure 4, it can be seen that seven simulations are

carried out in this process. The difference between the last

four values is within the 3% tolerance limit [8]. So, the mesh

that produces 3.5 million elements is chosen.

Fig.4.Mesh independence study.

Unstructured mesh is used for simplicity. More information

about meshing is given below in table II.

Table-2: Mesh setup.

Face sizing

0.001m

Number of inflation layers

Growth rate

1.2

Max face size

0.01m

To get better results, meshing is performed separately for each

of these angles mentioned before. A sample of the generated

0.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

0 2000000 4000000 6000000 8000000

COEFFICIENT OF LIFT

NUMBER OF ELEMENTS

International Journal of Engineering Applied Sciences and Technology, 2022

Vol. 7, Issue 9, ISSN No. 2455-2143, Pages 161-166

Published Online January 2023 in IJEAST (http://www.ijeast.com)

163

mesh in the cross-section of the left wing of a typical dart is

shown in Figure 5.

Fig.5.Mesh generated at the cross-section of the left wing of

typical dart.

ANSYS A fluent solver is used to run these CFD simulations.

To conduct an accurate simulation, several factors have been

taken into consideration. Inlet airspeed is kept at 5 m/s for

each of these simulations to avoid the issue of flutter [10].

Boolean is chosen during the creation of the fluid domain to

subtract the internal volumes of these models from the

surroundings to attain simplicity. For the lift and drag related

simulations, the angles of attack are changed from 0° to 30°

with an interval of 10° and from 30° to 50° with an interval of

5° to find out the exact angle of attacks for stall conditions.

Similarly, stability-related simulations are run with a 5°

sideslip angle interval. The turbulent model is selected

according to the simulations carried out by NG et al. [9]. The

solutions are generally converging on the boundary conditions

of the solver, which are given below in Table III.

Table-3: Solver setup

Velocity of flow

5m/s

Time

Steady

Pressure

1 atm

Turbulent model

Spallart-Allmaras (1 eqn)

Wall roughness

constant

0.5

Fluid

Air

Density of fluid

1.225 Kg/m

Viscosity

1.7894e-5 Kg/m-s

To obtain accurate values, iterations are continued until the

values stabilize. Figure 6 represents the output of the

coefficient of lift of Susanne at 40° AOA.

Fig.6. Coefficient of lift of Susanne at 40° AOA

IV. ANALYSIS OF LIFT AND DRAG COEFFICIENTS

It is a common practice to use the lift and drag coefficients of

an aircraft to analyze its flight performance. Mathematically,

lift and drag coefficients are expressed in following equations

[4].

ρV

(1)

ρV

(2)

Where,

Reynolds number, density of fluid(kg/ m3), inlet air

velocity(ms-1) ,height of the wings(m), dynamic

viscosity(kg/ms), coefficient of lift, coefficient of drag, lift

force, drag force, surface area are expressed by Re

,ρ, V, D, μ, C

, C

, F

, A gradually.

Figure 7 shows that, for each of these models, the coefficient

of lift increases with the increment of the angle of attack.

However, at a certain angle (around 35° AOA), stalling

Occurs in all of these models, and the coefficient of lift starts

to fall. At a 0° angle of attack, lift generated by the glider and

the dart is nearly zero, but due to the aligned lower portion of

Susanne, it is capable of generating a significant amount of lift

at this position. On the other hand, from Figure 8, it is clear

that coefficients of drag increase slowly with angle of attack

and exhibit rapid growth after a while. Besides, from Figure 9

it is calculated that the values of the maximum lift-drag ratio

for dart, Susanne, and glider are 3.31, 3.95, and 5.08,

respectively, and the optimum angle of attack for dart and

glider is nearly 10°, whereas for Susanne this angle is 0°. In

addition, it is observed that, at the maximum lift-drag ratio

point, the typical glider model possesses the highest amount of

lift in relation to drag. The typical dart model, on the other

hand, can achieve the least amount of lift among these models.

International Journal of Engineering Applied Sciences and Technology, 2022

Vol. 7, Issue 9, ISSN No. 2455-2143, Pages 161-166

Published Online January 2023 in IJEAST (http://www.ijeast.com)

164

Fig.7. Lift curves of paper airplane models

Using the values of the lengths of these paper airplanes (Table

1) and flight speeds (5 m/s), relevant Reynolds numbers are

obtained from the following equation,





Re

(3)

Where, Reynolds number, density of fluid(kg/ m3), inlet air

velocity(ms-1) ,height of the wings(m), dynamic

viscosity(kg/ms)are expressed by Re ,ρ, V, D, μ, gradually.

Fig.8.Drag curves of paper airplane models.

Fig.9.Drag vs lift curves.

The density and dynamic viscosity of air in this case are 1.225

kg/m3 and 1.7894 kg/m3, respectively. According to equation

3, the relevant Reynolds numbers for the dart, Susanne, and

glider are 99265, 65378, and 48947, respectively. From the

experiments of Chen and Lie [11], it is seen that for the

models of similar Reynolds numbers, the relevant values

(maximum lift-drag ratio, angle of stall, and optimum angle of

attack) are similar. To represent the properties of the fluid

domains of these models at the maximum lift-drag ratio point,

relevant figures of pressure contours are given below. Pressure

contours are created at the midsection of the left-wing of each

airplane and shown in Figure 10, Figure 11, and Figure 12.

From these figures, the difference in pressure generated

between the upper and lower surfaces of the wings can be

observed.

Fig.10. Velocity contour of Susanne at 35° AOA.

Fig.11. Velocity contour of typical dart at 35° AOA

0.2

0.4

0.6

0.8

1.2

0 10 20 30 40 50 60

COEFFICIENT OF LIFT

ANGLE OF ATTACK

Typicl Dart

Susanne

Typical Glider

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60

COEFFICIENT OF DRAG

ANGLE OF ATTACK

Typicl Dart

Susanne

Typical Glider

0.2

0.4

0.6

0.8

0 0 . 5 1 1 . 5

COEFFICIENT OF DRAG

COEFFICIENT OF LIFT

Susanne

Typical Dart

Typical Glider

International Journal of Engineering Applied Sciences and Technology, 2022

Vol. 7, Issue 9, ISSN No. 2455-2143, Pages 161-166

Published Online January 2023 in IJEAST (http://www.ijeast.com)

165

Fig.12. Velocity contour of typical glider at 35° AOA.

V. ANALYSIS OF AERODYNAMIC STABILITY

Like all other actual airplanes, paper airplanes represent three

basic types of movements with respect to the X, Y, and Z

axes. These movements are named as pitch, roll, and yawn

respectively. The moments and moment coefficients

associated with these three axes, explain the characteristics of

the stability of an aircraft. In this paper, analysis of

aerodynamic stability is conducted according to the procedure

of Nguyen et al. [6]. All the stability related simulations are

performed at 0° AOA at different sideslip angles [5].

According to the angle convention, a negative yawing moment

is generated by the relative wind when an aircraft flies with a

positive sideslip angle. To bring back stability (to make the

fuselage aligned with the direction of the relative wind), a net

positive restoring yawing moment is needed. For positive

sideslip angles, the higher the value of the positive yawing

moment, the higher the degree of yaw stability[12]. The

yawing moment coefficient is represented in the following

equation

ρV

(4)

Where, C

= rolling moment coefficient, L= rolling moment,

N= yawing moment, b= wingspan, S= wing area

Figure 13 represents the yawing moment coefficients of these

paper airplanes with respect to the sideslip angle. From Figure

13, it can be seen that the typical dart is the most directionally

stable model because of the huge centerfold, which acts as a

radar. Susanne’s yaw stability performance is quite similar to

the dart just because of the presence of the centerfold, though

it is not that stable. At a 10° sideslip angle, its yawing moment

coefficient is 21.89% lower than that of a dart. On the other

hand, a typical glider possesses the lowest amount of yaw

stability with the lowest yawing moment coefficient, which

is 82.16% lower than Susanne at a 10° sideslip angle.

Fig.13.Yawing moment coefficient vs sideslip angle

To achieve roll stability, the values of the rolling moment

coefficient should be as negative as possible while increasing

the positive sideslip angle. The rolling moment coefficient is

expressed in equation (5).

ρV

(5)

= Vawing moment coefficient, L= Rolling moment, N=

Vawing moment, b= Wingspan, S= Wing area

Fig.14. Rolling moment coefficient vs sideslip angle

Figure 14 depicts the rolling moment coefficients of these

models for different sideslip angles. This figure shows that

Susanne possesses the best roll stability among these models,

followed by the typical glider and the typical dart. Susanne's

rolling moment coefficient is 59.72% lower than that of a

typical glider and 86.85% lower than that of a typical dart at a

10° sideslip angle. It is clear that Susanne possesses excellent

roll stability because the wings are attached to the fuselage

with a positive dihedral angle and because of the moderate

length of the wingspan. Though the typical dart model is also

designed with the same dihedral angle as Susanne, its

wingspan is the shortest among these three models and it

possesses the lowest amount of roll stability.

-0.025

-0.02

-0.015

-0.01

-0.005

0.005

0 5 10 15 20

ROLLING MOMENT COEFFICIENT

SIDESLIP ANGLE

Typical Dart

Susanne

Typical Glider

International Journal of Engineering Applied Sciences and Technology, 2022

Vol. 7, Issue 9, ISSN No. 2455-2143, Pages 161-166

Published Online January 2023 in IJEAST (http://www.ijeast.com)

166

VI. CONCLUSION

After the analysis of lift and drag performance and

aerodynamic stability, the differences between these three

paper airplanes can be easily observed. Though the typical

dart model holds the lowest lift-drag ratio, it shows the

maximum amount of yaw stability. Because of these reasons,

darts can follow a smooth trajectory and travel a moderate

amount of distance. The typical glider model is best at

generating lift in terms of drag, but it shows considerably poor

performance in terms of stability, like all other paper gliders.

As a result, gliders are not so good at traveling linearly, but

they represent excellent performance for being airborne for a

long time. Finally, it goes without saying that Susanne is the

most optimistic model to break a distance record. Though this

model’s lift-drag ratio at the optimum angle of attack position

is 46.26% lower than the glider and 17.86% higher than the

dart, it represents excellent yaw stability and the best roll

stability among these models. All of these factors contributed

to this model setting a Guinness World Record for distance.

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