Optimizing Stability and Maneuverability in the K-8/JL-8 Aircraft

1. Introduction

The K-8/JL-8, a mainstay in several air forces globally, thrives on its balanced blend of maneuverability and stability. These crucial flight characteristics are significantly influenced by the dihedral angle of the wings. While empirical data exists, a comprehensive understanding of the interplay between dihedral and its impact across different flight regimes remains elusive. Dihedral angle refers to the upward inclination of an aircraft’s wings relative to the horizontal plane. When wings have dihedral and they form a slight “V” shape. Positive dihedral (wings angled upwards) tends to create a more uniform lift distribution across the wingspan.

Asymmetric airflow due to roll or gusts causes one wing to experience higher lift than the other. Positive dihedral helps counteract this by inducing a rolling moment that tends to level the wings.This balanced lift distribution enhances overall stability during flight. Roll stability refers to an aircraft’s ability to return to level flight after a disturbance (such as a roll). Positive dihedral contributes to roll stability:When the aircraft rolls and the higher wing generates more lift and causing a restoring moment that tends to bring the wings back to level. Positive dihedral reduces the adverse effects of induced drag during turns. The upward angled wings help minimize the drag caused by wingtip vortices. Moderate dihedral angles improve the lift drag ratio and enhancing overall aerodynamic efficiency.

This paper will fills this gap by employing CFD simulations and established aerodynamic principles to explore the intricate changing of dihedral and stabilizer angle in the K-8/JL-8.

2. Motivation

K-8 Aircraft is a jet trainer aircraft, being extensively used in Pakistan Air Force. This study reflects the effect on stability and performance parameters with required suggestions for design optimization. The study is an initial step towards designing of an aircraft, hence this effort will be useful for predicting the stability of an aircraft and also preliminary designing of an aircraft. Our research can inform modifications to the K 8/JL 8 and leading to better handling characteristics for specific training maneuvers. This could translate to smoother flight experiences for student pilots and enhancing their learning and confidence. Our research can contribute to a more comprehensive understanding of the intricate relationship between dihedral angle and its impact on aircraft performance across various flight regimes. This can be valuable for both academic researchers and students interested in aircraft design and aerodynamics.

3. Literature Review

Among all the performance criteria, aeroplane having stability is the most important. If an aircraft meets specific requirements for stability and it is said to be stable. There are two more types of stability: dynamic and static.

The body’s initial reaction to any disturbance is known as static stability. Three types of static stability exist for aircraft: lateral,directional and longitudinal stability.

In the yawing axis, directional stability is defined as follows: [1]

$$C_{n_b}<0$$

The requirement states that the yawing moment plotted against the side slip angle must have a zero slope in order for the aircraft to remain stable in this specific axis. To minimise the side slip angle and return to the trim conditions and the aircraft would therefore follow the direction of the sidewind.

The stability that an aeroplane maintains along its lateral or rolling axis is known as longitudinal stability. Longitudinal stability is depends upon two factors.[1]

When the coefficient of moment is plotted against the angle of attack alpha and it indicates a negative slope when:

$$C_{m_a}<0$$

This means that in order to resist the disturbance an’ maintain stability and the aircraft must pitch down in response to each wind gust or other disturbance that forces it to pitch upward. Second and the reason for this condition is because our wings are typically positively cambered and meanin’ that even at zero angle of attack and they produce a finite amount of lift. The second requirement is:

$$C_{m_o}>0$$

It indicates that even when the aeroplane is flying at zero alpha and it will still generate some moment.

The aircraft’s capacity to maintain stability along its longitudinal axis is known as lateral stability.The prerequisite for lateral stability:[2]

$$C_{l_B}<0$$

The requirement states that the rolling moment’s slope must be negative when plotted against the side slip angle Beta. All that would happen is that the plane would roll in the opposite direction from the disturbance or gust.

4. Brainstorming

Reasons for choosing JL-8/K-8 as case study:

• It is a trainer Jet aircarft having less complexity than modern aircraft.
• Simple structure and Geometry of aircarft allows us to make simple changes.
• It is still in production.
• Not much study is done on this aircraft
• It will open a gateway for understanding stabiltiy and aerodynamic characteristics of much complex aircrafts.

5. METHODOLOGY

A concise methodology adopted for out findings is as under:

• We conduct an extensive review of existin’ literature on static stability in aircraft design.
• Investigation how wing dihedral affects both longitudinal and lateral stability.
• Exploration the connection between wing dihedral and aerodynamic efficiency.
• Developing a 3D body of the K 8/JL 8 aircraft using XFRL5 software.
• Performing stability simulations using XFRL5.
• We relate the stability analysis results to established theoretical concepts.
• Computing the lift coefficient (CL) and drag coefficient (CD) for various flight conditions.
• We create a detailed CAD model of the K 8/JL 8 based on 2D drawings.
• Simulating airflow around the CAD model using CFD software.
• Comparing CL/CD ratios obtained from stability analysis and CFD.
• Investigating how small variations in dihedral angle impact stability.
• Summarize the relationship between wing dihedral and stability.
• Acknowledge any limitations in the study and suggest areas for further research.
• Recap the main findings regarding dihedral and stability and emphasizing practical relevance for aircraft designers.

5.1. Aircraft Data

Data of K-8/JL-8 provided by the manufacturer is as under [7]:

Dimensions:

Overall Length	11.6 m
Overall height	4.21 m
Wing area	17.02 m2
Wing span	9.63 m
length Wheel track	2.54 m
Wheel base	4.442 m

Weights:

Normal take-off weight	3700 kg
Useful load	943 kg
Internal fuel capacity	780 kg
Weight empty	2757 kg
Maximum take-off weight	4332 kg

Flight Performance:

Maximum level Speed	800 km/hr
Rate of climb at sea level	30 m/s
Service ceiling	13600 m
Built-in Range	1560 km
Ferry range (with drop tanks	2140 km

Airfoil data:

Wing tip	NACA 64-A-114
Wing root	NACA-64-A-212
Vertical tail	NACA-64-A-012

5.2. Aircraft Data

3-D Models of K-8/JL-8 are made on XFLR-5 and Solid Works based on above aircraft data.

Diffterent side views of models are as under:

Solidworks Model:

Side View:

Front View:

Top View:

XFLR-5 Model:

Side View:

Front View:

Top View:

5.3. Calculations and Graphs

Following are few assumpitions taken during the calculaions.

• Height of aircarft at which it flying is at 32000ft which is around 9.8km.
• Standard atmosphere is considered with density of 1.225 kg/m³
• Speed of aircarft is around 200 m/sec.
• Angle of Attack α in case of Longtitudinal Stabilty analysis range from -10 to 10 degree with increment of 1 degree.
• Side slip angle β in case of Lateral Stability ranging from 2 to -2 degree with increment of 0.1 degree.
• α and β remain constant in case of Lateral and Longtitudinal Stabiltiy Ananlysis.

XFLR-5:

XFLR-5, which is a software tool for the analysis of subsonic aerodynamics, is mainly used to in our research study to find effects of dihedral angle of wings on Longtitudinal and Lateral Stability of K-8/J8.However,Lift to Drag ratio CL/CD, measure of the aerodynamic efficiency of an aircraft, is also calculated to show a general effect on perofmance of aircraft by changing dihedral of wing.

Longtitudinal Stability Analsysis:

Angle of Attack $\alpha$ in case of Longtitudinal Stabilty analysis range from -10 to 10 degree with increment of 1 degree.

S.NO	DIHEDRAL ANGLE	Cm0	Cma
	0	-0.00377	0.013115
	3	-0.04266	0.019135
	6	-0.00190	0.02093

Following figure shows how the Cm related to Alpha in case of K-8/JL-8.

Figure 1 shows aircraft is unstable in longtitudinal direction.

Following figure shows relation relation of pitching Moment M to angle of attack alpha.

If an aircraft is longitudinally statically stable and a small increase in angle of attack will create a nose down pitching moment on the aircraft and so that the angle of attack decreases. Similarly and a small decrease in angle of attack will create a nose up pitching moment so that the angle of attack increases.But in this case it is vice-versa.

6. Analysis of Analytical Work

A comprehensive analysis of graphs and calculations obatined from XFLR-5 and CFD is as under:

7. Comparison of Literaute Review and our Findings

Based on the findings from our analytical work and the literature review , here’s a comparison between them:

• Longitudinal Stability Literature suggests that longitudinal stability is crucial for an aircraft’s equilibrium an control. Our findings align with this and indicatin’ that the K 8/JL 8 is initially unstable longitudinally due to a negative C_mo and a positive C_ma which contradicts the typical definition of longitudinal stability.
• Effect of Dihedral Angle increasing the dihedral angle tends to improve stability and as supported by literature that discusses the positive impact of dihedral on lateral stability. Our data reflects this trend , showing a move towards positive values for stability effects.
• Studies confirm that pitch instability can arise when the aerodynamic center (AC) is ahead of the center of gravity (CG) and as disturbances increase the angle of attack and leading to a nose up pitching moment.Our analysis indicates that the K 8/JL 8 exhibits this behavior and making it difficult to control.
• The literature review and our data both suggest that an increase in dihedral angle enhances lateral stability C_lb which is consistent with the general understanding that a negative in the longitudinal axis indicates stability.
• Both our results and literature indicate that aerodynamic efficiency, measured by the CL/CD ratio, decreases with an increase in dihedral angle and which could be due to increased induced drag.
• Comparative studies between CFD and XFLR 5 show that while both can predict trends in aerodynamic performance and difference in absolute values can occur due to differences in the precision of the methods.
• The inherent stability of an aircraft and as discussed in literature and is determined by its configuration and including geometry and weight and and CG location. Our findings on the K 8/JL 8’s instability due to the AC being ahead of the CG corroborate this principle.
• These points provide a comprehensive comparison of my findings with established literature and highlighting the importance of dihedral angle of aircraft configuration on stability and control.

8. Results

Following is result of our finding keeping in view literature.

• The K 8/JL 8 exhibits initial instability in the lateral axis and with a negative C_mo and a positive C_ma contrary to the expected behavior for stable longitudinal flight.
• Increasing the dihedral angle from 0 to 6 degrees influences C_lb to approach a positive value and indicating a trend towards stability and while C_ma becomes more positive and suggesting an increase in instability.
• The aircraft’s aerodynamic center (AC) located at 1.14m ahead of the center of gravity (CG) at 1.396m implies inherent pitching instability. Any disturbance increases the angle of attack and leading to a nose up moment and further instability.
• Lift is directly proportional to the angle of attack and the nose up pitching moment is directly proportional to lift when the AC is ahead of the CG. This configuration amplifies disturbances rather than dampening them.
• Initially and the K 8/JL 8 is laterally stable and as indicated by a negative rolling moment coefficient C_lb and which aligns with the expected behavior for stable lateral flight.
• An increase in the dihedral angle enhances lateral stability by causing C_lb >to become more negative and thus improving the aircraft’s ability to return to level flight after a disturbance.
• Considering both stability and aerodynamic performance and a dihedral angle of 3 degrees is optimal for the K 8/JL 8. It provides a balance between the positive stability effects and the minimal impact on aerodynamic efficiency and making it the most suitable choice for maintaining controlled flight.

These results reflect the relation between aircraft design parameters and stability characteristics and highlighting the critical balance required for stable flight dynamics.

10. Conclusions

Conclusion of this research study shows following critical points:

• The K 8/JL 8 shows initial pitch axis instability with a negative C_mo and a positive C_ma and which shows aircraft is unstable in
• An increase in dihedral angle from 0 to 6 degrees shifts C_mo towards a positive value and suggesting a move towards stability and but also C_m1 increases positively and contributing to instability.
• The AC located at 1.14m ahead of the CG at 1.396m indicates a tendency for pitch instability and leading to control challenges if the aircraft is disturbed.
• The aircraft exhibits lateral stability and as shown by a negative C_lb
• which is enhanced by increasing the dihedral angle and thus improving roll stability.
• A dihedral angle of 3 degrees is seemed optimal and balancing the need for stability in both the pitch and roll axes while maintaining good aerodynamic performance.
• This research Paper provide a good overview of how dihedral angle effects the Stability and aerodynamic effeciency of aircraft specially K-8/JL-8.

11. Further Research

This research paper will open a gate way for other researchers to investigate the relationship between dihedral angle of wing aircraft to enhance design of aircraft.

Future research should be based on optimizng control and stabilty of aircraft.

Acronyms

Some of the acronyms used in the paper are as follows:

α	Angle of attack
β	Side slip angle
Q	Dynamic pressure
Λ	Sweep angle
Γ	Dihedral angle
Xcg	Centre of gravity location
Xac	Aerodynamic centre location
Xnp	Neutral point location
Ix	Moment of inertia about x
Iy	Moment of inertia about y AR Aspect ratio
b	Wing span
c	Mean aerodynamic chord
S	Planform area
M	Mach no
W	Weight of the aircraft
m	Mass of aircraft
Y	y-direction force
Z	z-direction force
L	rolling moment
M	pitching moment
N	yawing moment
ϕ	Bank angle
ψ	Yaw angle
CL	Co-eff of lift
CD	Co-eff of drag