Propeller aircraft polar curve determination method

Abstract

The application provides a propeller aircraft polar curve determination method, introduces a tension coefficient term in a general propeller aircraft polar curve model, represents the influence of propeller slipstream on the resistance coefficient, establishes a general polar curve model which can be simultaneously applied to the cruising, climbing and descending states of the propeller aircraft, and then determines the expression of the general polar curve model by using the cruising, climbing and descending test flight data of the propeller aircraft, so that the same configuration can be simultaneously applied to the flight performance expansion calculation of the propeller aircraft in different flight states, the efficiency and accuracy of the propeller flight performance calculation can be improved, and effective guidance can be provided for the rapid iteration of the design and improvement of the propeller aircraft.

Description

A method for determining the polar curve of a propeller aircraft Technical Field

[0001] This application belongs to the technical field of polar curve determination for propeller aircraft, and specifically relates to a method for determining the polar curve of a propeller aircraft. Background Technology

[0002] The power of a propeller-driven aircraft engine varies during climb, cruise, and descent, resulting in significant differences in the intensity of the slipstream generated by the propeller and its impact on the aerodynamics of the aircraft. Consequently, the polar curves of a propeller-driven aircraft differ considerably during these three flight states.

[0003] Currently, polar curves of propeller aircraft under a certain flight state are mostly used to calculate and evaluate the flight performance of propeller aircraft under different flight states. The calculation results will have large deviations, making it difficult to provide effective guidance for the design and improvement of propeller aircraft.

[0004] This application is made in view of the aforementioned technical deficiencies.

[0005] It should be noted that the above background information is only used to assist in understanding the inventive concept and technical solution of this invention, and it does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed on the filing date of this application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0006] The purpose of this application is to provide a method for determining the polar curve of a propeller aircraft, so as to overcome or mitigate at least one of the known technical defects.

[0007] The technical solution of this application is:

[0008] A method for determining the polar curve of a propeller-driven aircraft includes:

[0009] Step 1: In the polar curve model of the propeller aircraft before stall, a thrust coefficient term is introduced to characterize the influence of the propeller slipstream on the drag coefficient, and a polar curve model considering the influence of the slipstream is established.

[0010] Step 2: Based on the dynamic equilibrium equations of propeller aircraft during steady level flight, establish a general polar curve model applicable to trim in cruise, climb, and descent states.

[0011] Step 3: Based on the equation of motion of the center of mass of the propeller aircraft in the vertical plane, the least squares method is used to fit the experimental data of the propeller aircraft in stable level flight during cruise to obtain the polar curve expression of the cruise state.

[0012] Step 4: Based on the dynamic equations of steady climb / descent of propeller aircraft, the polar curve expressions of the climb / descent states are obtained by fitting the data from the steady climb / descent test flights of propeller aircraft using the least squares method.

[0013] Step 5: Based on the polar curve expressions for cruise, climb / descent states, perform parameter calculations for the general polar curve model to obtain the general polar curve model expressions for propeller aircraft with the same configuration in cruise, climb, and descent states.

[0014] Based on at least one embodiment of this application, in the above-described method for determining the polar curve of a propeller aircraft, step one specifically comprises:

[0015] Establish a polar curve model of a propeller-driven aircraft before stall:

[0016] C D =C Dmin +K×(C L -C L0 ) 2 ;

[0017] Among them, C D C is the drag coefficient; Dmin K is the minimum drag coefficient; C is the induced drag factor; L C is the lift coefficient; L0 The initial lift coefficient;

[0018] In the polar curve model of a propeller-driven aircraft before stall, a thrust coefficient term is introduced to characterize the influence of the propeller slipstream on the drag coefficient, resulting in a polar curve model that considers the slipstream effect:

[0019] C D =C Dmin +K×(C L -C L0 ) 2 +K Tc Tc;

[0020] Where Tc is the propeller thrust coefficient; K Tc This is the factor affecting the tensile strength coefficient.

[0021] Based on at least one embodiment of this application, in the above-described method for determining the polar curve of a propeller aircraft, step two specifically comprises:

[0022] Based on the dynamic equilibrium equations of a propeller-driven aircraft during steady level flight, a model is established to represent the relationship between the drag coefficient and thrust coefficient of a propeller-driven aircraft.

[0023] C D =nTc;

[0024] Where n is the number of engines in the propeller aircraft;

[0025] Substituting the model of the relationship between the drag coefficient and thrust coefficient of a propeller-driven aircraft into the polar curve model that considers the slipstream effect, we obtain the polar curve model of the propeller-driven aircraft in cruise state:

[0026] C D =C Dmin_cruise +K cruise (C L -C L0 ) 2 ;

[0027] C Dmin_cruise =C Dmin / (1-K Tc / n);

[0028] K cruise =K / (1-K) Tc / n);

[0029] Among them, C Dmin_cruise K represents the minimum drag coefficient for a propeller-driven aircraft during cruise. cruise This is the induced drag factor for a propeller-driven aircraft during cruise.

[0030] The minimum drag coefficient C of a propeller aircraft during cruise. Dmin_cruise Induced resistance factor K cruise Substituting these values ​​into the polar curve model that considers the slipstream effect, we obtain a general polar curve model applicable to trimming during cruise, climb, and descent:

[0031] C D =C Dmin_cruise (1-K Tc / n)+K cruise (1-K Tc / n)(C L -C L0 ) 2 +K Tc Tc.

[0032] Based on at least one embodiment of this application, in the above-described method for determining the polar curve of a propeller aircraft, step three specifically comprises:

[0033] Through stable level flight tests of a propeller-driven aircraft in cruise mode, the engine speed of the propeller-driven aircraft during stable level flight was measured under different combinations of altitude, weight, and speed. Based on the engine power characteristic curve, the thrust value under the corresponding flight conditions was obtained. According to the equation of motion of the center of mass in the vertical plane during stable level flight of the propeller-driven aircraft, the lift coefficient C under each combination of altitude, weight, and speed was calculated. L Drag coefficient C D ;

[0034] Based on the engine power of the propeller aircraft at different level flight speeds, the cruise state extreme curve test flight values ​​were obtained. The least squares method was used to fit and obtain the model expression of the propeller aircraft cruise state extreme curve:

[0035] C D =AC L 2 +BC L +C;

[0036] Where A, B, and C are the coefficients of the polar curve model obtained by least squares fitting.

[0037] Based on at least one embodiment of this application, in the above-described method for determining the polar curve of a propeller aircraft, the specific process of step four is as follows:

[0038] Based on the dynamic equations of steady climb / descent of a propeller-driven aircraft, a calculation model for the lift coefficient and drag coefficient during steady climb / descent of a propeller-driven aircraft is obtained:

[0039]

[0040]

[0041] Where θ is the track angle; α is the angle of attack; qS is the rate of change of flight speed with flight altitude; W is the flight mass; qS is the product of flight kinetic pressure and wing area.

[0042] Steady climb / descent tests were conducted on a propeller-driven aircraft in cruise configuration to obtain the climb / descent rate and dV / dh under different combinations of flight conditions. Based on the engine speed during climb / descent and combined with the engine power characteristic curve, the thrust value under the corresponding flight conditions was obtained, and thus the lift coefficient C under each combination of altitude, weight, and speed was obtained. L and drag coefficient C D ;

[0043] The least squares method was used to fit the model expression of the climb / descent polar curve of the propeller aircraft:

[0044] C D =A1C L 2 +B1C L +C1;

[0045] Based on at least one embodiment of this application, in the above-described method for determining the polar curve of a propeller aircraft, step five specifically comprises:

[0046] Based on the fitting, the polar curve model expressions for the cruise, climb / descent states of a propeller aircraft are obtained. The relevant parameters in the general polar curve model for propeller aircraft are then calculated, leading to the general polar curve model expressions for propeller aircraft with the same configuration in cruise, climb, and descent states.

[0047]

[0048] K cruise =A;

[0049]

[0050]

[0051]

[0052] This application has at least the following beneficial technical effects:

[0053] This paper presents a method for determining the polar curve of a propeller aircraft. The method introduces a thrust coefficient term into a general propeller aircraft polar curve model to characterize the influence of propeller slipflow on the drag coefficient. A universal polar curve model is established that is applicable to the cruise, climb, and descent states of propeller aircraft. The expression of this universal polar curve model is then determined using cruise and climb / descent test flight data of the propeller aircraft. With the same configuration, it can be applied to extended calculations of the flight performance of propeller aircraft under different flight states, improving the efficiency and accuracy of propeller flight performance calculations. This provides effective guidance for the rapid iteration of propeller aircraft design and improvement. Attached Figure Description

[0054] Figure 1 is a schematic diagram of the method for determining the polar curve of a propeller aircraft provided in an embodiment of this application;

[0055] Figure 2 is a schematic diagram of the expression of the fitting polar curve model of the cruise state of a propeller aircraft provided in the embodiment of this application.

[0056] Figure 3 is a schematic diagram of the expression of the pitch curve model of the propeller aircraft climb / descent provided in the embodiment of this application. Detailed Implementation

[0057] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings. Other related parts can be referred to the general design. In the absence of conflict, the embodiments and technical features in the embodiments of this application can be combined with each other to obtain new embodiments.

[0058] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "upper," "lower," "left," "right," "center," "vertical," "horizontal," "inner," and "outer," etc., used in this application description to indicate relative direction or positional relationship are used only to indicate relative orientation or positional relationship, and do not imply that the device or component must have a specific orientation, or be constructed and operated in a specific orientation. When the absolute position of the described object changes, its relative positional relationship may also change accordingly, and therefore should not be construed as a limitation on this application. The terms "first," "second," "third," and similar terms used in this application description are used only for descriptive purposes to distinguish different components, and should not be construed as indicating or implying relative importance. The terms "a," "one," or "the," etc., used in this application description should not be construed as an absolute limitation on quantity, but should be construed as indicating the existence of at least one. The terms "including," "comprising," etc., used in this application description mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, without excluding other elements or objects.

[0059] Furthermore, it should be noted that, unless otherwise explicitly specified and limited, terms such as “installation,” “connection,” and “linkage” used in the description of this application should be interpreted broadly. For example, a connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; or it can be a connection within two components. Those skilled in the art can understand its specific meaning in this application based on the specific circumstances.

[0060] The present application will now be described in further detail with reference to Figures 1-3.

[0061] In a specific embodiment, given the known flight test data for the cruise and climb states of a propeller-driven aircraft, which is a twin-engine aircraft, the process for determining the polar profile of this propeller-driven aircraft is as follows:

[0062] Step 1. Introduce a thrust coefficient term into the polar curve model of a propeller aircraft before stall to characterize the influence of the propeller slipstream on the drag coefficient, thus obtaining a polar curve model of a propeller aircraft considering the slipstream effect:

[0063] C D =C Dmin +K×(C L -C L0 ) 2 +K Tc Tc;

[0064] Step 2. Establish a polar curve model for the cruise state of a propeller-driven aircraft. The specific steps are as follows:

[0065] 1) Based on the dynamic equilibrium equations of a propeller-driven aircraft during steady level flight, i.e., drag equals thrust, the following model is established to establish the relationship between the drag coefficient and thrust coefficient of a propeller-driven aircraft:

[0066] C D =2Tc;

[0067] 2) Substituting the relationship model between the drag coefficient and thrust coefficient of the propeller aircraft into the polar curve model of the propeller aircraft considering the slipstream effect established in step 1, the following polar curve model of the propeller aircraft in cruise state is obtained:

[0068] C D =C Dmin_cruise +K cruise (C L -C L0 ) 2 ;

[0069] C Dmin_cruise =C Dmin / (1-K Tc / 2);

[0070] K cruise =K / (1-K) Tc / 2);

[0071] 3) Substituting the minimum drag coefficient and induced drag factor of the propeller aircraft during cruise into the propeller aircraft polar curve model considering slipstream effects established in step 1, the following general polar curve expression for trim, applicable to cruise, climb, and descent, is obtained:

[0072] C D =C Dmin_cruise (1-K Tc 2)+K cruise (1-K Tc 2)(C L -C L0 ) 2 +K Tc Tc;

[0073] Step 3. Establish a cruise state polar curve model for the actual flight test of the propeller aircraft. The specific steps are as follows:

[0074] 1) Using stable level flight test data of propeller-driven aircraft in cruise mode, the lift coefficient C under different combinations of altitude, weight, and speed was calculated. L and drag coefficient C D The value of is shown in Figure 2.

[0075] 2) Based on the test flight values ​​of the cruise state polar curves obtained from the engine power state at different level flight speeds, the cruise state polar curve model of the propeller aircraft was obtained by fitting using the least squares method, as follows:

[0076] C D =0.0745C L 2 -0.0032C L +0.0297;

[0077] Step 4. Establish a climb state polar curve model for the actual flight test of the propeller aircraft. The specific steps are as follows:

[0078] 1) Based on the dynamic equations of steady climb / descent of a propeller-driven aircraft, the calculation models for the lift coefficient and drag coefficient during steady climb / descent of a propeller-driven aircraft are obtained as follows:

[0079]

[0080]

[0081] 2) By conducting steady climb / descent tests on propeller-driven aircraft in cruise configuration, the lift coefficient C under each combination of altitude, weight, and speed was obtained. L and drag coefficient C D The value of is shown in Figure 3;

[0082] 3) The following is a model of the climb state polar curve of a propeller aircraft obtained by fitting using the least squares method:

[0083] C D =0.0607C L 2 +0.0659C L +0.0022;

[0084] Step 5. By fitting the actual cruise and climb / descent state polar curve models of the propeller aircraft during test flights, the relevant parameters and model expressions in the general polar curve model of the propeller aircraft are further obtained as follows:

[0085] CDmin_cruise =0.0297;

[0086] K cruise =0.0745;

[0087] C L0 =0.0215;

[0088] K Tc =0.3705;

[0089] C D =0.0607*(C L -0.0215) 2 +0.3705*Tc+0.0242.

[0090] The technical solution of this application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of this application is obviously not limited to these specific embodiments. Without departing from the principles of this application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of this application.

Claims

1. A method for determining the polar curve of a propeller-driven aircraft, characterized in that, include: Step 1: In the polar curve model of a propeller aircraft before stall, a thrust coefficient term is introduced to characterize the influence of the propeller slipstream on the drag coefficient, establishing a polar curve model considering the slipstream effect. Step 2: Based on the dynamic equilibrium equations of a propeller aircraft in steady level flight, a universal polar curve model applicable to cruise, climb, and descent trim is established. Step 3: Based on the equations of motion of the propeller aircraft's center of mass in the vertical plane, the least squares method is used to fit the polar curve expression for cruise state using experimental data from stable level flight in cruise state. Step 4: Based on the dynamic equations of a propeller aircraft in steady climb / descent, the least squares method is used to fit the polar curve expression for climb / descent state using experimental data from steady climb / descent flight of the propeller aircraft. Step 5: Based on the polar curve expressions for cruise and climb / descent states, the parameters of the universal polar curve model are solved to obtain the universal polar curve model expression for a propeller aircraft with the same configuration in cruise, climb, and descent states. Step 1 specifically involves: establishing a polar curve model of a propeller aircraft before stall. ;in, This is the drag coefficient; It is the minimum drag coefficient; It is the induced resistance factor; The lift coefficient; The initial lift coefficient is used. In the polar curve model of a propeller-driven aircraft before stall, a thrust coefficient term is introduced to characterize the influence of the propeller slipstream on the drag coefficient, resulting in a polar curve model that considers the slipstream effect. ;in, This is the propeller thrust coefficient; The thrust coefficient is an influencing factor; Step two specifically involves: establishing a model relating the drag coefficient and thrust coefficient of a propeller-driven aircraft based on the dynamic equilibrium equations for steady level flight. Where n is the number of engines in the propeller aircraft; substituting the propeller aircraft drag coefficient versus thrust coefficient relationship model into a polar curve model that neglects slipstream effects, we obtain the polar curve model for the propeller aircraft's cruise state: ； ； ;in, This is the minimum drag coefficient for a propeller-driven aircraft during cruise. The induced drag factor of a propeller-driven aircraft during cruise; the minimum drag coefficient of a propeller-driven aircraft during cruise. Induced resistance factor Substituting these values ​​into the polar curve model that considers the slipstream effect, we obtain a general polar curve model applicable to trimming during cruise, climb, and descent: 。 2. The method for determining the polar curve of a propeller-driven aircraft according to claim 1, characterized in that, Step three specifically involves: conducting stable level flight tests of the propeller aircraft during cruise, measuring the engine speed of the propeller aircraft under different combinations of altitude, weight, and speed during stable level flight, obtaining the thrust value under the corresponding flight conditions based on the engine power characteristic curve, and calculating the lift coefficient for each combination of altitude, weight, and speed based on the equation of motion of the center of mass in the vertical plane during stable level flight of the propeller aircraft. drag coefficient ； Based on the engine power of the propeller aircraft at different level flight speeds, the cruise state extreme curve test flight values ​​were obtained. The least squares method was used to fit and obtain the model expression of the propeller aircraft cruise state extreme curve: Where A, B, and C are the coefficients of the polar curve model obtained by least squares fitting.

3. The method for determining the polar curve of a propeller-driven aircraft based on claim 2, characterized in that, Step four involves the following process: Based on the dynamic equations of steady climb / descent for propeller-driven aircraft, calculation models for the lift coefficient and drag coefficient during steady climb / descent are obtained: ； ;in, The track angle; Angle of attack; Let be the rate of change of flight speed with altitude; W be the flight mass; and qS be the product of flight pressure and wing area. Steady climb / descent tests were conducted on a propeller-driven aircraft in cruise configuration to obtain the climb / descent rates and dV / dh under different flight condition combinations. Based on the engine speed during climb / descent and combined with the engine power characteristic curve, the thrust values ​​under corresponding flight conditions were obtained, thus yielding the lift coefficient for each combination of altitude, weight, and speed. and drag coefficient The least squares method was used to fit the equations to obtain the model expression for the climb / descent polar curves of a propeller-driven aircraft: 。 4. The method for determining the polar curve of a propeller-driven aircraft based on claim 3, characterized in that, Step five specifically involves: obtaining the polar curve model expressions for the cruise, climb / descent states of a propeller aircraft based on the fitted data; solving for the relevant parameters in the general polar curve model of the propeller aircraft; and then obtaining the general polar curve model expressions for the propeller aircraft with the same configuration in the cruise, climb, and descent states. ； ； ； ； 。

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