CN112347553A - Design method for variation of longitudinal static stability margin of airplane along with attack angle - Google Patents

Design method for variation of longitudinal static stability margin of airplane along with attack angle Download PDF

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CN112347553A
CN112347553A CN202011065195.XA CN202011065195A CN112347553A CN 112347553 A CN112347553 A CN 112347553A CN 202011065195 A CN202011065195 A CN 202011065195A CN 112347553 A CN112347553 A CN 112347553A
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肖良华
赵艳平
陈斌
闫林明
徐良
温俊杰
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Chengdu Aircraft Industrial Group Co Ltd
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Abstract

The invention discloses a design method of airplane longitudinal static stability margin changing with an attack angle,
Figure DDA0002713553050000011
is in linear relation with alpha, and the sign of B term determines
Figure DDA0002713553050000012
Increase and decrease of (2), positive and negative of item B
Figure DDA0002713553050000013
And (6) determining. If Δ z < 0, i.e. the focal point z coordinate is higher than the center of gravity, B<0，
Figure DDA0002713553050000014
With the increase and decrease of the attack angle, the longitudinal static stability of the aircraft develops towards the more and more stable direction; if Δ z > 0, i.e. the focal point z-coordinate is lower than the center of gravity, B>0，
Figure DDA0002713553050000015
With increasing angle of attack, the longitudinal static stability of the aircraft is developing towards becoming more and more unstable. The invention can design the change relation of the longitudinal static stability of the aircraft along with the attack angle according to the requirement, thereby meeting the requirements of different design points of the aircraft on aerodynamics. The invention has the characteristics of simplicity, convenience, rapidness, accuracy and the like, is suitable for the design of various airplanes such as light airplanes and transport planes, can greatly save the design cost, and can obtain good economic benefit in prediction.

Description

Design method for variation of longitudinal static stability margin of airplane along with attack angle
Technical Field
The invention belongs to the technical field of airplane design, and particularly relates to a design method for changing a longitudinal static stability margin of an airplane along with an attack angle.
Background
In aircraft design, longitudinal static stability margin design is a very critical ring, and relates to aircraft flight stability and maneuverability. If the static stability margin is too small, the stability is insufficient, and the flight safety is influenced; if the static stability margin is too large, the controllability is not strong, resulting in a decrease in the controllability. For civil transport aircraft, for example, the longitudinal static stability margin is generally designed to ensure flight safety
Figure BDA0002713553030000013
Left and right.
The conventional approach to longitudinal static margin design is to adjust by the longitudinal position of the wing and tailplane on the body axis. The longitudinal static margin designed by the method is generally kept constant in the use attack angle range. For some aircraft, the designer may wish that its longitudinal static margin may vary with angle of attack over the range of angles of attack in use. For light aircraft, the longitudinal static stability margin of the aircraft is required to be smaller in a small attack angle range, so that the aircraft has enough head raising control capability in the take-off process, and the take-off of the aircraft is enabled to be quick enough; and the range of the attack angle is larger so as to ensure the flight safety of the airplane. Therefore, it is desirable that its longitudinal static margin increases with increasing angle of attack.
Disclosure of Invention
The invention aims to provide a design method for changing a longitudinal static stability margin of an airplane along with an attack angle, and aims to realize that the longitudinal static stability margin of the airplane increases or decreases along with the increase of the attack angle when the airplane flies.
When the full-machine focus position is higher than the reference gravity center:
if the aircraft is originally designed for longitudinal net stability, the longitudinal static stability margin is increased as the angle of attack increases,
if the aircraft is originally designed according to longitudinal static instability, the longitudinal static instability margin is reduced along with the increase of the attack angle.
When the full-machine focus position is lower than the reference gravity center:
if the aircraft is originally designed for net longitudinal stability, the longitudinal static margin is reduced as the angle of attack increases,
if the aircraft is originally designed according to longitudinal static instability, the longitudinal static instability margin is increased along with the increase of the attack angle.
The invention is mainly realized by the following technical scheme: a design method for variation of longitudinal static stability margin of airplane with attack angle includes creating the coordinate system of aircraft, defining the coordinate of reference barycenter as (x)g,yg,zg) The focal point coordinate of the whole machine is (x)f,yf,zf) Average aerodynamic chord length of the aircraft is cA，Δx＝xf-xg，
Figure BDA0002713553030000011
Δz＝zf-zg，
Figure BDA0002713553030000012
Figure BDA0002713553030000021
Figure BDA0002713553030000022
Wherein alpha is the incident angle of incoming flow,
Figure BDA0002713553030000023
is in linear relation with alpha, and the sign of B term determines
Figure BDA0002713553030000024
Increase and decrease of (2), positive and negative of item B
Figure BDA0002713553030000025
Determining;
if Δ z < 0, i.e. the focal point z coordinate is higher than the center of gravity, B<0，
Figure BDA0002713553030000026
With the increase and decrease of the attack angle, the longitudinal static stability of the aircraft develops towards the more and more stable direction;
if Δ z > 0, i.e. the focal point z-coordinate is lower than the center of gravity, B>0，
Figure BDA0002713553030000027
With increasing angle of attack, the longitudinal static stability of the aircraft is developing towards becoming more and more unstable.
In order to better implement the invention, further, the focus of the aircraft with longitudinal static stability is located at a point F, the reference gravity center is located at a point O, the incoming flow attack angle is alpha, and the incoming flow speed is V∞(ii) a When the longitudinal aerodynamic force borne by the aircraft is translated to the focus F, the aircraft is subjected to a lift force L perpendicular to the incoming flow direction, a resistance D parallel to the incoming flow direction and a moment M0(ii) a The gravity center O is subjected to engine thrust T and the gravity G of the whole engine; moment is taken for the center of gravity O, and the following are:
M＝M0+Δx·Lcosα+Δz·Lsinα+Δx·Dsinα-Δz·Dcosα (1)
two sides of the pair formula (1) are divided by
Figure BDA0002713553030000028
Can be converted into coefficients, having:
Figure BDA0002713553030000029
the common airplane uses an attack angle smaller than 15 degrees, and in the attack angle range, the lift coefficient is larger than the drag coefficient by more than one order of magnitude; therefore, the resistance C is neglected in the formula (2)DItem, and pair CLThe derivation is as follows:
Figure BDA00027135530300000210
since α is a small amount, sin α and cos α can be approximated as α and 1, respectively; by using the linear relationship of the lift coefficient,
Figure BDA00027135530300000211
equation (3) can be further rewritten as:
Figure BDA00027135530300000212
neglect of alpha content2The second order fractional term of (a) finally yields:
Figure BDA00027135530300000213
in the formula (5)
Figure BDA0002713553030000031
Equation (6) is obtained.
To better implement the invention, further, the origin of the coordinate system is located at the reference center of gravity of the aircraft; the axis Ox is in the symmetrical plane of the aircraft, is parallel to the axis of the fuselage or the average aerodynamic chord line of the wing, and points forward; the Oz axis is also in the symmetrical plane, is vertical to the Ox axis and points downwards; the Oy axis is perpendicular to the plane of symmetry and points to the right.
To better implement the invention, further, B is provided if Δ z < 0, i.e. the focus z coordinate is higher than the center of gravity<0，
Figure BDA0002713553030000032
With increasing angle of attack decreasing, the longitudinal static stability of an aircraft designed according to longitudinal static stability increases with increasing angle of attack, and with an aircraft designed according to longitudinal static instability, the longitudinal static instability decreases with increasing angle of attack.
To better implement the invention, further, if Δ z > 0, i.e. the focus z-coordinate is below the center of gravity, B>0，
Figure BDA0002713553030000033
With increasing angle of attack, the longitudinal static stability of an aircraft designed according to longitudinal static stability decreases with increasing angle of attack, and with increasing angle of attack, the longitudinal static instability of an aircraft designed according to longitudinal static instability increases.
The invention has the following beneficial effects:
(1) according to the design method provided by the invention, the change relation of the longitudinal static stability of the aircraft along with the attack angle can be designed according to the requirement, so that the requirements of different design points of the aircraft on aerodynamics can be met.
(2) The design method has the characteristics of simplicity, convenience, rapidness, accuracy and the like, is suitable for designing various airplanes such as light airplanes and transport planes, can greatly save the design cost, and can obtain good economic benefit in prediction.
(3) The aircraft designed according to the scheme has the characteristic that the longitudinal static stability is changed along with the change of the attack angle, so that the flight performance and the flight safety can be considered at the same time.
Drawings
FIG. 1 is a schematic view of an aircraft under longitudinal force;
fig. 2 is a schematic diagram of the gravity center positions of three solutions of the NACA0012 airfoil provided in embodiment 2 of the present invention;
FIG. 3 shows three solutions C of the NACA0012 airfoil profile provided by embodiment 2 of the present inventionm-CLA curve;
FIG. 4 shows three embodiments of the present invention provided in example 2
Figure BDA0002713553030000034
Curve with angle of attack.
Detailed Description
Example 1:
a design method for variation of an aircraft longitudinal static stability margin with an attack angle is disclosed, as shown in FIG. 1, firstly, a coordinate system of an aircraft is defined according to a body coordinate system, namely: the origin is located at the reference center of gravity of the aircraft; the axis Ox is in the symmetrical plane of the aircraft, is parallel to the axis of the fuselage or the average aerodynamic chord line of the wing, and points forward; the Oz axis is also in the symmetrical plane, is vertical to the Ox axis and points downwards; the Oy axis is perpendicular to the plane of symmetry and points to the right. Defining a reference barycentric coordinate as (x)g,yg,zg) The coordinate of the focus of the whole machine (hereinafter referred to as focus) is (x)f,yf,zf) The incoming flow velocity is V∞The atmospheric density is rho, the reference area of the aircraft is S, and the average aerodynamic chord length of the aircraft is cA，Δx＝xf-xg，
Figure BDA0002713553030000041
Δz＝zf-zg，
Figure BDA0002713553030000042
The aircraft of the conventional layout has wings and a horizontal tail, and the longitudinal static stability of the aircraft is mainly determined by the wings and the horizontal tail. The focal point of an aircraft with longitudinal static stability, viewed from the longitudinal axis of the body (Ox axis), is behind the reference center of gravity, i.e., Δ x > 0. The focal point is generally not coincident with the z-coordinate of the center of gravity as viewed on the Oz-axis. According to the coordinate system shown in FIG. 1, if the z coordinate of the focus is higher than the center of gravity, Δ z is less than 0; if the focus z coordinate is below the center of gravity, Δ z > 0.
The research of the invention shows that if delta z is less than 0, the longitudinal static stability of the aircraft can be developed towards the direction of more and more stability along with the increase of the attack angle, so that the longitudinal static stability of the aircraft designed according to the longitudinal static stability can be stronger and stronger, and the longitudinal static instability of the aircraft designed according to the longitudinal static instability can be weaker and weaker; if Δ z > 0, the longitudinal static stability of the aircraft develops in an increasingly unstable manner with increasing angle of attack, i.e. the longitudinal static stability becomes increasingly weaker for an aircraft designed for longitudinal static stability and increasingly stronger for an aircraft designed for longitudinal static instability. In conclusion, the change of the longitudinal static stability of the aircraft along with the change of the attack angle is closely related to the delta z, and the invention can be realized through the design of the delta z. The longitudinal static stability as a function of the angle of attack is explained in more detail below.
As shown in FIG. 1, the focal point of a longitudinal statically stable aircraft is located at point F, the reference center of gravity is located at point O, the incoming flow incidence angle is alpha (radian), and the incoming flow velocity is V∞. When the longitudinal aerodynamic force borne by the aircraft is translated to the focus F, the aircraft is subjected to a lift force L (vertical to the incoming flow direction), a resistance force D (parallel to the incoming flow direction) and a moment M0(ii) a The gravity center O is subjected to engine thrust T and the gravity G of the whole engine; moment is taken for the center of gravity O, and the following are:
M＝M0+Δx·Lcosα+Δz·Lsinα+Δx·Dsinα-Δz·Dcosα (1)
two sides of the pair formula (1) are divided by
Figure BDA0002713553030000046
Can be converted into coefficients, having:
Figure BDA0002713553030000043
in general, a typical aircraft uses an angle of attack less than 15 °, over which range the lift coefficient is more than an order of magnitude greater than the drag coefficient. Therefore, the resistance C is neglected in the formula (2)DItem, and pair CLThe derivation is as follows:
Figure BDA0002713553030000044
since α is a small quantity, sin α and cos α can be approximated as α and 1, respectively. By using the linear relationship of the lift coefficient,
Figure BDA0002713553030000045
equation (3) can be further rewritten as:
Figure BDA0002713553030000051
neglect of alpha content2The second order fractional term of (a) finally yields:
Figure BDA0002713553030000052
in the formula (5)
Figure BDA00027135530300000514
Then there are:
Figure BDA0002713553030000053
as can be seen from equation (6), for an aircraft, the term A, B is determined accordingly, and then
Figure BDA0002713553030000054
Is in linear relation with alpha, and the sign of B term determines
Figure BDA0002713553030000055
The increase or decrease of (2).
For conventional aircraft, it is common
Figure BDA0002713553030000056
Ratio of
Figure BDA0002713553030000057
(α is in radians) is an order of magnitude smaller, and
Figure BDA0002713553030000058
and
Figure BDA0002713553030000059
generally within one order of magnitude, so the positive and negative of the B term
Figure BDA00027135530300000510
And determining, namely determining delta z. If Δ z < 0, i.e. the focal point z coordinate is higher than the center of gravity, B<0，
Figure BDA00027135530300000511
The longitudinal static stability of the aircraft can be developed towards an increasingly stable direction along with the increase and decrease of the attack angle, the longitudinal static stability of the aircraft originally designed according to the longitudinal static stability can be increasingly stronger, and the longitudinal static instability of the aircraft originally designed according to the longitudinal static instability can be increasingly weaker; if Δ z > 0, i.e. the focal point z-coordinate is lower than the center of gravity, B>0，
Figure BDA00027135530300000512
Along with the increase of the angle of attack, the longitudinal static stability of the aircraft can develop towards the direction of more and more instability, the longitudinal static stability of the aircraft originally designed according to the longitudinal static stability can be weaker and weaker, and the longitudinal static instability of the aircraft originally designed according to the longitudinal static instability can be stronger and stronger.
Example 2:
the invention discloses a design method for changing an aircraft longitudinal static stability margin along with an attack angle, which is implemented by calculating the aerodynamic characteristics of a NACA0012 two-dimensional airfoil profile, and simulating the change of the relative position relationship between an airfoil focal point and a reference focal point by selecting different reference focal point positions. Wherein the reference center of gravity of the scheme 1 is positioned at the chord length of the airfoil 1/4, so that the reference center of gravity is positioned at the chord length of the airfoil 1/4
Figure BDA00027135530300000513
Is approximately 0; keeping the longitudinal position of the center of gravity of reference constant, the z coordinate is changed to be above and below the airfoil focal point, respectively, resulting in solutions 2 and 3, as shown in fig. 2.
CFD simulation of this airfoil was performed using the commercial software FLUENT, with the calculation conditions Ma-0.2 and H-0 km, and the calculation scheme is shown in table 1. The calculation results are shown in table 2, because only the reference gravity center position is changed, the lift and drag coefficients of the three schemes are kept unchanged, but only the moment coefficients are different, and the change of the moment coefficients of the three schemes along with the lift coefficient is obtained through numerical simulation and is shown in fig. 3. It can be seen that for the scheme 1, because the reference gravity center coincides with the focal position, the moment coefficient is almost constant, and as the attack angle increases, the focal position of the airfoil profile slightly changes, so that the moment coefficient is not constant. For the scheme 2 and the scheme 3, the moment coefficient in a small attack angle range (corresponding to the lift coefficient less than 0.2) is close to that of the scheme 1, the moment coefficient is obviously changed along with the further increase of the attack angle, and the change trend of the moment coefficient is consistent with that of theoretical analysis.
For specific analysis
Figure BDA0002713553030000061
With the change of the attack angle, for the numerical simulation result, the calculation between two adjacent alpha is utilized
Figure BDA0002713553030000062
The results are shown in table 3 as stability reference values for the two α intermediate values. The theoretical value calculated using equation (6) can be used for comparison, as shown in fig. 4, where the dotted line is the theoretical value and the solid line is the actual simulation value. It can be seen that the theoretical value and the numerical simulation value are well matched in a small attack angle range; as the incidence angle increases, the practical simulation of scheme 1 is caused due to the change of the position of the airfoil focus
Figure BDA0002713553030000063
The results deviate from the theoretical 0 value. To exclude the effect of the change of the focal point position of the airfoil profile, the corresponding values of the solutions 2 and 3 can be respectively subtracted from the corresponding values of the solution 1, and further compared with the theoretical values, as shown in table 4. Therefore, after the influence caused by the change of the focal point position of the wing profile is eliminated, the relative deviation between the theoretical value and the numerical simulation value is not more than 3 percent, and the result shows that the design method has high precision and can be used for guiding the design of an aircraft.
Table 1 numerical simulation scheme
Figure BDA0002713553030000064
Table 2 numerical simulation results
Figure BDA0002713553030000065
TABLE 3 numerical simulation and theoretical calculation
Figure BDA0002713553030000071
Value of
Figure BDA0002713553030000072
TABLE 4 Pair of Z-positions of centers of gravity
Figure BDA0002713553030000073
Influence of (2)
Figure BDA0002713553030000074
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications and equivalent variations of the above embodiments according to the technical spirit of the present invention are included in the scope of the present invention.

Claims (5)

1. A design method for variation of longitudinal static stability margin of an airplane with an attack angle is characterized in that a coordinate system of an aircraft is established, and a reference barycentric coordinate is defined as (x)g,yg,zg) The focal point coordinate of the whole machine is (x)f,yf,zf) Average aerodynamic chord length of the aircraft is cA，
Figure FDA0002713553020000011
Wherein alpha is the incident angle of incoming flow,
Figure FDA0002713553020000012
is in linear relation with alpha, and the sign of B term determines
Figure FDA0002713553020000013
Increase and decrease of (2), positive and negative of item B
Figure FDA0002713553020000014
Determining;
if Δ z < 0, i.e. the focal point z coordinate is higher than the center of gravity, B<0，
Figure FDA0002713553020000015
With the increase and decrease of the attack angle, the longitudinal static stability of the aircraft develops towards the more and more stable direction;
if Δ z > 0, i.e. the focal point z-coordinate is lower than the center of gravity, B>0，
Figure FDA0002713553020000016
With increasing angle of attack, the longitudinal static stability of the aircraft is developing towards becoming more and more unstable.
2. The method as claimed in claim 1, wherein the longitudinal static margin of the aircraft is at F, the reference center of gravity is at O, the incoming flow angle of attack is α, and the incoming flow velocity is V∞(ii) a When the longitudinal aerodynamic force borne by the aircraft is translated to the focus F, the aircraft is subjected to a lift force L perpendicular to the incoming flow direction, a resistance D parallel to the incoming flow direction and a moment M0(ii) a The gravity center O is subjected to engine thrust T and the gravity G of the whole engine; moment is taken for the center of gravity O, and the following are:
M＝M0+Δx·Lcosα+Δz·Lsinα+Δx·Dsinα-Δz·Dcosα (1)
two sides of the pair formula (1) are divided by
Figure FDA0002713553020000017
Can be converted into coefficients, having:
Figure FDA0002713553020000018
the common airplane uses an attack angle smaller than 15 degrees, and in the attack angle range, the lift coefficient is larger than the drag coefficient by more than one order of magnitude; therefore, the resistance C is neglected in the formula (2)DItem, and pair CLThe derivation is as follows:
Figure FDA0002713553020000019
since α is a small amount, sin α and cos α can be approximated as α and 1, respectively; by using the linear relationship of the lift coefficient,
Figure FDA00027135530200000110
equation (3) can be further rewritten as:
Figure FDA0002713553020000021
neglect of alpha content2The second order fractional term of (a) finally yields:
Figure FDA0002713553020000022
in the formula (5)
Figure FDA0002713553020000023
Equation (6) is obtained.
3. A method of designing an aircraft longitudinal static margin as a function of angle of attack as claimed in claim 1 or claim 2 wherein the origin of the coordinate system is located at the centre of gravity of reference of the aircraft; the axis Ox is in the symmetrical plane of the aircraft, is parallel to the axis of the fuselage or the average aerodynamic chord line of the wing, and points forward; the Oz axis is also in the symmetrical plane, is vertical to the Ox axis and points downwards; the Oy axis is perpendicular to the plane of symmetry and points to the right.
4. The method as claimed in claim 1, wherein if Δ z < 0, i.e. the focus z coordinate is higher than the center of gravity, then B is<0，
Figure FDA0002713553020000024
With increasing angle of attack decreasing, the longitudinal static stability of an aircraft designed according to longitudinal static stability increases with increasing angle of attack, and with an aircraft designed according to longitudinal static instability, the longitudinal static instability decreases with increasing angle of attack.
5. The method as claimed in claim 1, wherein if Δ z > 0, i.e. the focus z coordinate is lower than the center of gravity, B is>0，
Figure FDA0002713553020000025
With increasing angle of attack, the longitudinal static stability of an aircraft designed according to longitudinal static stability decreases with increasing angle of attack, and with increasing angle of attack, the longitudinal static instability of an aircraft designed according to longitudinal static instability increases.
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