Stability Derivatives of a Delta Wing with Straight Leading Edge in the Newtonian Limit

This paper presents an analytical method to predict the aerodynamic stability derivatives of oscillating delta \ud wings with straight leading edge. It uses the Ghosh similitude and the strip theory to obtain the expressions for\ud stability derivatives in pitch and roll in the Newtonian limit. The present theory gives a quick and approximate \ud method to estimate the stability derivatives which is very essential at the design stage. They are applicable for \ud wings of arbitrary plan form shape at high angles of attack provided the shock wave is attached to the leading \ud edge of the wing. The expressions derived for stability derivatives become exact in the Newtonian limit. The \ud stiffness derivative and damping derivative in pitch and roll are dependent on the geometric parameter of the \ud wing. It is found that stiffness derivative linearly varies with the pivot position. In the case of damping \ud derivative since expressions for these derivatives are non-linear and the same is reflected in the results. Roll \ud damping derivative also varies linearly with respect to the angle of attack. When the variation of roll damping \ud derivative was considered, it is found it also, varies linearly with angle of attack for given sweep angle, but with \ud increase in sweep angle there is continuous decrease in the magnitude of the roll damping derivative however, \ud the values differ for different values in sweep angle and the same is reflected in the result when it was studied \ud with respect to sweep angle. From the results it is found that one can arrive at the optimum value of the angle of \ud attack sweep angle which will give the best performance

Oscillating supersonic delta wing with straight leading edges

A Supersonic similitude has been used to obtain stability derivatives in pitch and roll of a delta wing with straight leading edge for the attached shock case. Ghosh’s strip theory is been used in which strips at different span wise locations are independent of each other. This combines with the similitude to give a piston theory which gives the closed form of solution to stability derivatives in pitch and roll. Some of the results obtained have been compared with those of Hui et al ,Ghosh and Lui &Hui. Results have been obtained for supersonic flow of perfect gas over a wide range of Mach numbers, incidences and sweep angles

Estimation of damping derivatives for delta wings in hypersonic flow for straight leading edge

Accurate estimation of the aerodynamic stability derivatives of airplanes is essential to evaluate the performance of the aircraft, whether civilian or military. Theoretical prediction methods for the dynamic stability derivatives at high angles of attack have not advanced, and in the present paper, an attempt has been made to study the effect of damping derivatives for delta wings for different angles of incidence, and the Mach number for a wing whose leading edge is straight. In this paper, the flow is considered to be unsteady flow and also considering the effect of the Leeward surface along with the shock waves and the expansion waves. The theory developed in the present paper considering the unsteady effects, the results have been estimated for speed flows for air assuming the air to behave as perfect gas for a range of angle of incidence and the inertia level. The results show that for Mach number M = 7 and above the damping derivatives become independent of inertia level. Increase in the damping derivatives is substantial when the angle δ is increased from 5 to 10 degree

Oscillating supersonic delta wings with curved leading edges

In the present study Supersonic similitude has been used to obtain stability derivatives in pitch and roll of a delta wing for the attached shock case. A strip theory is used in which strips at different span-wise locations are independent. This combines with the similitude to give a piston theory. The present theory is valid only for attached shock case. Effects of wave re ection and viscosity have not been taken into account. Some of the results have been compared with those of Hui et al (1982), Ghosh (1984), and Liu and Hui (1977). Results have been obtained for supersonic ow of perfect gas over a wide range of Mach numbers, incidences and sweep angles. A good agreement is obtained with Hui et al in some special cases

The computation of stiffness derivative for an ogive in the hypersonic flow

Expression for Stiffness derivative for an Ogive is derived with the suppositions of the arc on the nose of the cone from the air is being considered as perfect gas and the viscosity being neglected, the motion is quasi-steady, and the nose deflection angle of the Ogive θ is in such a way that the M2 after the shock is > 2.5. It is seen that due to the increment in angle θ, the stiffness derivative increases linearly due the progressive increase in the plan form area of the nose shape. The results indicate that there is a 38 percent increase in the stability derivative when the flow deflection θ was enhanced in the range of 5 to 10 degrees. With the further enhancement in the flow deflection angle θ from ten degrees and above, does not yield substantial increase in the stability derivative. Due to this change in the surface pressure distribution will lead to shift the location of centre of pressure, from the hinged position h = 0.5 to 0.8. The centre of pressure also has shifted towards the downstream, which lies in the range from h = 0.72 to 0.85

Analysis of damping derivatives for delta wings in hypersonic flow for curved leading edges with full sine wave

In this study, an attempt is made to evaluate the effect of first arched ends on the damping derived due to the pitch rate aimed at the variable sine wave bounty, flow deflection angle δ, pivot position, and the Mach numbers. Results show that with the escalation in the bounty of the complete sine wave (i.e., positive amplitude) there is an enlightened escalation in the pitch damping derivatives from h = 0, later in the downstream in the route of the sprawling verge it decreases till the location of the center of pressure and vice versa. At the location where the reasonable force acts, when we consider the stability derivatives in damping for the rate of pitch q, there is a rise in the numerical tenets of the spinoffs. This increase is non-linear in nature and not like for position near the leading edges. The level of the stifling derivatives owing to variations in Mach numbers, flow bend approach δ, and generosity of the sine wave remained in the same range

Analytical estimation of stability derivatives of wing with curved leading edges at hypersonic mach number

This paper focusses attention on the influence of prominent curved ends to restraining deprived owing to the transverse frequency for the numerous amplitude, flow rebound perspective δ, hinge location, and the inertia. In the current learning by the consequence of expansion fan on the expansion side (i.e., Leeward surface) are neglected. Outcomes of the demonstration are that with the increase of the amplitude of the half-sine wave, there is a progressive increase in the-hampering spinoffs from k = 0, advanced to the TE, it declines up to the whereabouts of the normal force location and just opposite trend. At the place of k = 0.4, while we deliberate the permanence spinoffs in curbing for the pitch q, there is a reduction in the mathematical tenets of the derivatives, and this trend continues till k = 1 towards the trailing edge. This upsurge is not linear and not like for position near the foremost edges. The change in the enormousness of the inhibiting results because of the deviations in the Mach (M), flow deflection angle δ, and the amplitude of the sine wave persisted in the identical kind

Estımatıon of hypersonıc unsteady and qausı-steady dampıng derıvatıves for a delta wings at large incıdence

This paper presents results of quasi-steady and unsteady damping derivatives of a delta wing whose leading edge is straight. Results are computed for a wide range of Mach numbers and angles of attack. Here the contribution to the damping derivatives due to the rate of change of angle of attack is estimated separately. The results show that with the increase in Mach number, there is a progressive decrease in the damping derivatives for both the cases (i.e., unsteady and quasi-steady). With the further rise in the Mach values, the magnitude of decline has diminished for Mach number M = 10 and above the state of steady-state is achieved. For the entire range of the Mach number, the location of the center of pressure remained unchanged for a fixed value of the flow deflection angle δ. For the lower flow deflection angle of the wing, the magnitude of the damping derivatives is smaller as compared to the higher values of δ. The contribution to the damping derivatives from the rate of change of angle of attack is around 20 percent of the quasi-steady one. The results for flow deflection angles of ten degrees and twenty degrees show a different trend. When we compare the results of the damping derivatives for a fixed pivot position, it is seen that the damping derivatives show different behavior for two different values of the flow deflection angle δ. The steady-state varies for two values of δ. When we look at the damping derivatives at hinge point k = 0.6, the magnitude is small. The steady-state is attained early for quasi-steady in comparison to the unsteady damping derivatives

Computation of damping derivative of an Ogive at highspeed flow

This paper aims to derive an expression for the damping derivative of an ogive in pitch. The Ogive shape is achieved by superposing an arch on the cone. The inertia levels considered are M = 5, 7, 9, 10, and 15. The contemporary theory applies to the connected shock case & the Mach M2 behind the shock M2 ≥ 2.5. Damping derivatives are examined for ogive for γ = 1.4 at various semi angles for differing pivot positions and Mach numbers and λ = ± 5, 10. Results indicate a continued decrease in stability derivatives. However, the damping derivatives turn independent of Mach M for Mach more than ten— with a surge in the cone angle, a continued rise in the damping derivatives attained

Analytical and numerical simulation of surface pressure of an oscillating wedge at hypersonic Mach numbers and application of Taguchi's method

This paper aims to estimate the surface pressure of a wedge at hypersonic Mach numbers at a considerable angle of incidence. The Ghosh similitude, corresponding strip theory, and piston theory are used to determine the pressure distribution analytically, and the results are compared to those of the CFD analysis. The theory is valid when the shock wave is attached to the leading edge of the nose of the wedge. Pressure on the windward surface was considered in the analysis. The pressure on the Lee surface is neglected. The condition for the validity of the theory is that the Mach number M2 behind the shock wave is greater than 2.5. The parameters taken into account for the study are the wedge angle and Mach number. The range of wedge angle considered is from 5 to 25 degrees and the Mach number considered is from 5 to 15. The analytical and the CFD results are in good agreement. The findings indicate that the parameters like wedge angle and Mach number are influential parameters that influence the wedge surface static pressur