Method for determining maximum take-off weight and battery weight of an electric aircraft

Abstract

The application discloses a kind of determination methods of maximum take-off weight and battery weight of electric aircraft, wherein the maximum take-off weight determination method of electric aircraft includes: establishing the maximum take-off weight equation of electric aircraft;Solving the maximum take-off weight equation of electric aircraft, obtain the maximum take-off weight of electric aircraft.The determination method of the battery weight of electric aircraft includes: determining the maximum take-off weight of electric aircraft;Maximum take-off weight is used to calculate the battery weight of electric aircraft.The determination method of the maximum take-off weight and battery weight of electric aircraft, the energy consumed by aircraft mission profile is used to estimate the battery weight, the estimation result is more accurate, the reliability is higher, the calculation process is simpler, and the calculation parameter is more simplified.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electric aircraft, and particularly provides a method for determining the maximum take-off weight and battery weight of an electric aircraft. BACKGROUND

[0002] From an economic point of view, the price of aviation fuel continues to rise as fossil fuels are depleted, leading to a corresponding increase in the operating cost of aviation; from an environmental point of view, the consumption of aviation fuel is increasingly contributing to air pollution and global warming, so aircraft manufacturers are actively exploring alternatives to fuel-powered systems. Electric aircraft stand out with their zero carbon emissions, low noise, low operating costs, high energy utilization efficiency, and other advantages, providing a new technical path for the green transformation of the aviation industry.

[0003] As one of the important parameters of an aircraft, the maximum take-off weight directly affects the overall arrangement of the aircraft, the performance, load and cost of the aircraft, and is one of the important work contents in the conceptual design stage of the aircraft. Compared with traditional fuel-powered aircraft, the energy source of a lithium battery electric aircraft is lithium batteries, and the weight of the aircraft remains unchanged during flight, resulting in different parameter selection and use methods in the calculation of the take-off weight of the electric aircraft. Therefore, the fuel coefficient method for estimating the take-off weight of the traditional fuel-powered aircraft is not applicable to the electric aircraft. If the method traditionally applied to fuel-powered aircraft is used to calculate the take-off weight of the electric aircraft, the result will be inaccurate, affecting the rationality of the aircraft design scheme, and thus increasing the number of iterations of the aircraft design and affecting the aircraft development cycle.

[0004] Therefore, it is an urgent problem to propose a reasonable method for determining the take-off weight of an electric aircraft. SUMMARY

[0005] In view of this, the purpose of the present application is to provide a method for determining the maximum take-off weight and battery weight of an electric aircraft, to solve the problem that the traditional take-off weight calculation method applied to fuel-powered aircraft is not applicable to the estimation of the take-off weight of an electric aircraft.

[0006] In one aspect, the present application provides a method for determining the maximum take-off weight of an electric aircraft, comprising:

[0007] S1: establishing a maximum take-off weight equation of the electric aircraft, the maximum take-off weight equation of the electric aircraft being as follows:

[0008] W TO = W E +W PL +W B ;

[0009] In the formula, W TO is the maximum take-off weight of the electric aircraft; W EW PL W B W

[0010] where,

[0011] where, E is the total energy required for the electric aircraft flight; e b is the battery energy density;

[0012] where, E = E warm-up + E roll + E climb + E cruise + E loiter + E descent + E landing ;

[0013] where, E warm-up is the energy consumed during the warm-up taxi phase; E roll is the energy consumed during the take-off roll phase; E climb is the energy consumed during the climb phase; E cruise is the energy consumed during the cruise phase; E loiter is the energy consumed during the hover phase; E descent is the energy consumed during the descent phase; E landing is the energy consumed during the landing taxi and stop phase;

[0014] where,

[0015] where, P warm-up is the required power during taxi; t warm-up is the time consumed during taxi; η warm-up is the electric propulsion system efficiency during taxi;

[0016]

[0017] where, F static_thrust is the static thrust of the electric motor; C D0 is the zero-lift drag coefficient; k is the induced drag factor; p roll is the air density during the take-off roll; S is the wing area; g is the gravitational acceleration; a is the runway slope angle; η roll is the electric propulsion system efficiency during the take-off roll; m is the friction coefficient; V TO is the take-off speed; W TO is the maximum take-off weight;

[0018]

[0019] where, q is the climb angle; p climb is the air density during the climb; ROC is the rate of climb; CD0 zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R climb efficiency of the electric propulsion system during climb; H cruise cruise altitude of the aircraft; V climb climb speed; W TO maximum take-off weight;

[0020]

[0021] where C D0 zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise range of the aircraft during cruise; p cruise air density during cruise; η cruise efficiency of the electric propulsion system during cruise; V cruise cruise speed; W TO maximum take-off weight.

[0022]

[0023] where p loiter efficiency of the electric propulsion system during hover; V loiter hover speed; p loiter air density during hover; t loiter time consumed during hover; C D0 zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO maximum take-off weight;

[0024]

[0025] where p descent air density at glide altitude; V descent glide speed; R descent glide ratio; η descent efficiency of the electric propulsion system during glide; glide angle; H cruise cruise altitude of the aircraft; C D0 zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO maximum take-off weight;

[0026]

[0027] where P landing electric motor power at stand; t landing time consumed at stand; η landing efficiency of the electric propulsion system at stand;

[0028] S2: solving the maximum take-off weight equation of the electric aircraft to obtain the maximum take-off weight of the electric aircraft.

[0029] Preferably, in S2, the maximum take-off weight equation of the electric aircraft is solved by using an iterative method, and the specific steps are as follows:

[0030] S21: presetting an initial value of the maximum take-off weight of the electric aircraft;

[0031] S22: bringing the initial value of the maximum take-off weight of the electric aircraft into the right side of the maximum take-off weight equation of the electric aircraft to obtain a calculated value of the maximum take-off weight of the electric aircraft;

[0032] S23: subtracting the calculated value of the maximum take-off weight of the electric aircraft obtained in S22 from the preset initial value of the maximum take-off weight of the electric aircraft, if the calculated difference value is less than a preset iteration termination difference value, then the iteration is terminated, and the calculated value of the maximum take-off weight of the electric aircraft is taken as the maximum take-off weight of the electric aircraft, otherwise, returning to S21 and taking the calculated value of the maximum take-off weight of the electric aircraft obtained in the previous step as the initial value of the maximum take-off weight of the electric aircraft for the next iteration, and continuing to execute S22 and S23 until the iteration termination condition is met.

[0033] The application also provides a method for determining the battery weight of an electric aircraft, comprising:

[0034] determining the maximum take-off weight of the electric aircraft according to the method for determining the maximum take-off weight of the electric aircraft;

[0035] calculating the battery weight W of the electric aircraft by using the following formula B :

[0036]

[0037] In the formula, E is the total energy required for the flight of the electric aircraft; e b is the energy density of the battery;

[0038] wherein E=E warm-up +E roll +E climb +E cruise +E loiter +E descent +E landing ;

[0039] In the formula, E warm-up is the energy consumed in the warm-up taxiing phase; E roll is the energy consumed in the take-off taxiing phase; E climb is the energy consumed in the climbing phase; E cruise is the energy consumed in the cruising phase; Eloiter Energy consumed for the spiral phase; E descent Energy consumed for the glide phase; E landing Energy consumed for the landing taxi phase; E

[0040] where,

[0041] where, P warm-up Required power during taxi; t warm-up Time consumed during taxi; η warm-up Efficiency of the electric propulsion system during taxi;

[0042]

[0043] where, F static_thrust Static thrust of the electric motor; C D0 Zero-lift drag coefficient; k is the induced drag factor; p roll Air density during the take-off run; S is the wing area; g is the gravitational acceleration; a is the runway slope angle; η roll Efficiency of the electric propulsion system during the take-off run; m is the friction coefficient; V TO Take-off speed; W TO Maximum take-off weight;

[0044]

[0045] where, q is the climb angle; p climb Air density during the climb; ROC is the rate of climb; C D0 Zero-lift drag coefficient; k is the induced drag factor; S is the wing area; η climb Efficiency of the electric propulsion system during the climb; H cruise Cruising altitude of the aircraft; V climb Climb speed; W TO Maximum take-off weight;

[0046]

[0047] where, C D0 Zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise Range of the cruising segment of the aircraft; p cruise Air density during the cruise; η cruise Efficiency of the electric propulsion system during the cruise; V cruise Cruise speed; W TO Maximum take-off weight.

[0048]

[0049] where, ηloiter For the efficiency of the electric propulsion system during the hovering phase; V loiter ρ is the rotational speed; loiter t is the air density during hovering; loiter The time consumed during the hovering phase; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO Maximum takeoff weight;

[0050]

[0051] In the formula, ρ descent V is the air density at the descent altitude; descent R represents the descent speed. descent The rate of decline; η descent For the efficiency of the electric propulsion system during the descent phase; For glide slope; H cruise C is the aircraft's cruising altitude. D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO Maximum takeoff weight;

[0052]

[0053] In the formula, P landing The motor power when the machine is stopped at the designated position; t landing η is the time consumed when the machine stops at its designated position. landing The efficiency of the electric propulsion system when the machine is stopped at its designated position.

[0054] The present invention provides a method for determining the maximum takeoff weight and battery weight of an electric aircraft. The maximum takeoff weight of the electric aircraft can be determined using the equation for the maximum takeoff weight of the electric aircraft. The maximum takeoff weight of the electric aircraft is composed of multiple parts. The present invention uses the energy consumed by the aircraft mission profile to estimate the battery weight, resulting in a more accurate and reliable estimation. The calculation process is also simpler and the calculation parameters are further simplified. Attached Figure Description

[0055] The invention will be further explained below with reference to the accompanying drawings.

[0056] Figure 1 A flowchart illustrating the method for determining the maximum takeoff weight of an electric aircraft provided by this invention;

[0057] Figure 2 A graph showing the relationship between the empty weight and maximum takeoff weight of electric aircraft with four or fewer seats;

[0058] Figure 3 This is a cross-sectional view of the flight mission of an electric aircraft. Detailed Implementation

[0059] The application will be further explained in connection with specific embodiments, but is not limited to them.

[0060] Among the existing aircraft maximum take-off weight estimation methods, the estimation method mainly given for oil-driven aircraft is not applicable to electric aircraft, therefore, the application provides a determination method for maximum take-off weight of electric aircraft, as shown in the figure, comprising: Figure 1

[0061] S1: establishing the maximum take-off weight equation of the electric aircraft, the maximum take-off weight equation of the electric aircraft is as follows:

[0062] W TO =W E +W PL +W B ;

[0063] In the formula, W TO is the maximum take-off weight of the electric aircraft; W E is the empty weight; W PL is the payload; W B is the battery weight;

[0064] Among them,

[0065] In the formula, E is the total energy required for the flight of the electric aircraft; e b is the battery energy density;

[0066] Among them, E=E warm-up +E roll +E climb +E cruise +E loiter +E descent +E landing ;

[0067] In the formula, E warm-up is the energy consumed in the warm-up taxiing stage; E roll is the energy consumed in the take-off taxiing stage; E climb is the energy consumed in the climbing stage; E cruise is the energy consumed in the cruising stage; E loiter is the energy consumed in the hovering stage; E descent is the energy consumed in the descending stage; E landing is the energy consumed in the landing taxiing and parking stage;

[0068] Among them,

[0069] In the formula, P warm-up is the required power when taxiing; t warm-up is the time consumed when taxiing; η​warm-up Efficiency of the electric propulsion system for taxiing phase;

[0070]

[0071] where F is the force of the air; F static_thrust is the static thrust of the electric motor; C D0 is the zero-lift drag coefficient; k is the induced drag factor; p roll is the air density during taxiing; S is the wing area; g is the gravitational acceleration; a is the runway slope angle; η roll is the efficiency of the electric propulsion system for the take-off taxiing phase; m is the friction coefficient; V TO is the take-off velocity; W TO is the maximum take-off weight;

[0072]

[0073] where q is the climb angle; p climb is the air density during climbing; ROC is the rate of climb; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; η climb is the efficiency of the electric propulsion system for the climbing phase; H cruise is the cruising altitude of the aircraft; V climb is the climbing velocity; W TO is the maximum take-off weight;

[0074]

[0075] where C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise is the range of the cruising phase of the aircraft; p cruise is the air density during cruising; η cruise is the efficiency of the electric propulsion system for the cruising phase; V cruise is the cruising velocity; W TO is the maximum take-off weight.

[0076]

[0077] where η loiter is the efficiency of the electric propulsion system for the circling phase; V loiter is the circling velocity; p loiter is the air density during circling; t loiter is the time consumed during the circling phase; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum take-off weight;

[0078]

[0079] where p descent is the air density at glide height; V descent is the glide speed; R descent is the glide rate; η descent is the electric propulsion system efficiency during glide; a is the glide angle; H cruise is the cruise altitude of the aircraft; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum take-off weight;

[0080]

[0081] where P landing is the electric motor power when stopping on the runway; t landing is the time consumed when stopping on the runway; η landing is the electric propulsion system efficiency when stopping on the runway;

[0082] S2: solving the maximum take-off weight equation of the electric aircraft to obtain the maximum take-off weight of the electric aircraft.

[0083] As an improvement of the technical scheme, in S2, the maximum take-off weight equation of the electric aircraft is solved by using an iterative method, and the specific steps are as follows:

[0084] S21: presetting an initial value of the maximum take-off weight of the electric aircraft;

[0085] S22: bringing the initial value of the maximum take-off weight of the electric aircraft into the right side of the maximum take-off weight equation of the electric aircraft to obtain a calculated value of the maximum take-off weight of the electric aircraft;

[0086] S23: subtracting the calculated value of the maximum take-off weight of the electric aircraft obtained in S22 from the preset initial value of the maximum take-off weight of the electric aircraft, if the calculated difference value is less than a preset iteration termination difference value, then the iteration is terminated, and the calculated value of the maximum take-off weight of the electric aircraft is taken as the maximum take-off weight of the electric aircraft, otherwise, returning to S21 and taking the calculated value of the maximum take-off weight of the electric aircraft obtained in the last step as the initial value of the maximum take-off weight of the electric aircraft for the next iteration, and continuing to execute S22 and S23 until the iteration termination condition is met.

[0087] The application further provides a method for determining the battery weight of an electric aircraft, comprising:

[0088] determining the maximum take-off weight of the electric aircraft according to the method for determining the maximum take-off weight of the electric aircraft;

[0089] calculating the battery weight W B of the electric aircraft by using the following formula:

[0090]

[0091] where E is the total energy required for the electric aircraft flight; e b is the battery energy density;

[0092] where E = E warm-up + E roll + E climb + E cruise + E loiter + E descent + E landing ;

[0093] where E warm-up is the energy consumed during the warm-up taxi phase; E roll is the energy consumed during the take-off roll phase; E climb is the energy consumed during the climb phase; E cruise is the energy consumed during the cruise phase; E loiter is the energy consumed during the hover phase; E descent is the energy consumed during the descent phase; E landing is the energy consumed during the landing taxi and parking phase;

[0094] where,

[0095] where P warm-up is the required power during taxi; t warm-up is the time consumed during taxi; η warm-up is the electric propulsion system efficiency during taxi;

[0096]

[0097] where F static_thrust is the static thrust of the electric motor; C D0 is the zero-lift drag coefficient; k is the induced drag factor; p roll is the air density during the roll; S is the wing area; g is the gravitational acceleration; a is the runway slope angle; η roll is the electric propulsion system efficiency during the take-off roll phase; m is the friction coefficient; V TO is the take-off speed; W TO is the maximum take-off weight;

[0098]

[0099] where q is the climb angle; p climb is the air density during the climb; ROC is the rate of climb; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; η climbVc= Vc- Vc- Vc cruise Vc= Vc- Vc- Vc climb Vc= Vc- Vc- Vc TO MTO = MTO = MTO

[0100]

[0101] where C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise is the range of the aircraft during the cruise segment; p cruise is the air density during the cruise; η cruise is the electric propulsion system efficiency during the cruise; V cruise is the cruise speed; W TO is the maximum takeoff weight.

[0102]

[0103] where p loiter is the electric propulsion system efficiency during the hover; V loiter is the hover speed; p loiter is the air density during the hover; t loiter is the time consumed during the hover; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum takeoff weight;

[0104]

[0105] where p descent is the air density at the glide altitude; V descent is the glide speed; R descent is the rate of descent; η descent is the electric propulsion system efficiency during the glide; is the glide angle; H cruise is the cruise altitude of the aircraft; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum takeoff weight;

[0106]

[0107] where P landing is the electric motor power when the aircraft is on the ground; t landing is the time consumed when the aircraft is on the ground; η landing is the electric propulsion system efficiency when the aircraft is on the ground.

[0108] The method for determining the maximum take-off weight and the battery weight of the electric aircraft can determine the maximum take-off weight of the electric aircraft by solving the equation of the maximum take-off weight of the electric aircraft, wherein the maximum take-off weight of the electric aircraft is composed of multiple parts, the battery weight is estimated by the energy consumed by the aircraft mission profile, the estimation result is more accurate, the reliability is higher, the calculation process is simpler, and the calculation parameters are more simplified.

[0109] The maximum take-off weight of the electric aircraft is estimated according to the consumed energy in the flight mission profile, and is used for calculating the maximum take-off weight in the scheme design stage of the electric aircraft, so as to provide basic parameters for further aircraft design.

[0110] Taking a lithium battery electric aircraft as an example, the derivation process of the maximum take-off weight equation of the electric aircraft established by the application is given below:

[0111] Compared with the traditional oil-driven aircraft, the lithium battery electric aircraft is provided with energy by lithium batteries instead of fuel, therefore, the maximum take-off weight of the electric aircraft is composed of three parts of the airframe weight, the payload and the battery weight:

[0112] W TO =W E +W PL +W B ;

[0113] In the formula, W E is the airframe weight; W PL is the payload; and W B is the battery weight.

[0114] Among them, the fitting expression between the airframe weight and the maximum take-off weight of the commonly used civil aircraft is:

[0115] lgW E =(lgW TO -A) / B;

[0116] In the formula, W E is the airframe weight, and W TO is the maximum take-off weight, and for the civil aircraft, A=0.08330 and B=1.0383. The above formula is obtained according to the data accumulation and statistics of aircraft design in foreign countries for decades, and has very wide applicability for the traditional oil-driven aircraft. However, the maximum take-off weight of the electric aircraft is different from the maximum take-off weight of the oil-driven aircraft, so the coefficient needs to be corrected and re-fitted.

[0117] The future development of four-seat or less electric aircraft should be estimated according to the data of the electric aircraft developed in recent years. Table 1 is the statistical data of the maximum take-off weight and the empty weight of the four-seat or less electric aircraft developed in recent years at home and abroad, which can more accurately reflect the current development level of the four-seat or less electric aircraft.

[0118] Table 1 Weight data of four-seat or less electric aircraft developed in recent years at home and abroad

[0119] Serial number Aircraft name Take-off weight / kg Empty weight / kg 1 RX1E-A 600 280 2 E430 470 218 3 Alpha Electro 570 251 4 Velis Electro 600 290 5 e-Flyer 2 862 409 6 Aura Aero Era 750 290 7 e-Flyer 4 1360 470 8 eDA40 1310 880 9 Sun Flyer 2 1134 680 10 Taurus Electro G2.5 550 308 11 Taurus Electro G4 1500 632 12 ElectraFlyer-C 283 130 13 ElectraFlyer-ULS 238 111 14 Elektra Trainer 600 240

[0120] According to the weight data in Table 1, the actual fitting curve is shown in FIG. 1, and the fitting results are A = 0.37140 and B = 0.98357. Figure 2

[0121] Therefore, the empty weight and the maximum take-off weight of the four-seat or less electric aircraft can be fitted as follows:

[0122] lgW E =(lgW TO -0.37140) / 0.98357;

[0123] Through the above formula, the relationship between the empty weight and the maximum take-off weight can be obtained as follows:

[0124]

[0125] Similarly, the fitting expression of the empty weight and the maximum take-off weight of other types of electric aircraft can also be obtained according to the statistical data of the maximum take-off weight and the empty weight, and then the relationship between the empty weight and the maximum take-off weight can be obtained, which is not described here;

[0126] Among them, the payload can be determined according to the design requirements of the aircraft. For a four-seat aircraft, the payload includes the weight of the crew, passengers and their luggage, which can be expressed as:

[0127] W PL =W CRE +W PAS +W BAG ;

[0128] In the formula, W CRE is the weight of the crew; W PAS is the weight of the passengers; and W BAG is the weight of the luggage.

[0129] ​Battery weight is the energy source of electric aircraft. Since the weight of electric aircraft remains unchanged during flight, the traditional method of calculating fuel coefficient according to flight mission profile is not applicable to the estimation of battery weight coefficient of electric aircraft. The energy source of electric aircraft during the entire flight process is provided by the power battery, therefore, the battery weight can be determined according to the total energy required for the entire flight and the energy density of the battery, which can be expressed as:

[0130]

[0131] In the formula, E is the total energy required for flight; e b is the energy density of the battery.

[0132] The total energy E can be estimated according to the flight mission profile of the aircraft. According to the flight profile requirements for aircraft in CCAR-121, the flight mission profile of civil aircraft is usually composed of engine starting warm-up taxi, take-off, climb, cruise, hover, glide, taxi climb, taxi cruise, descent, landing taxi, and parking. Considering the influence of battery energy density on four-seat electric aircraft, it is currently only used for intra-field flight, therefore, for four-seat electric aircraft, the flight mission profile is simplified to warm-up taxi, take-off, climb, cruise, hover, glide, and landing taxi, which can be defined as shown in Figure 3 .

[0133] (1) Warm-up taxi phase

[0134] For the warm-up taxi phase, warm-up is mainly to preheat the battery and electronic equipment to ensure normal operation of the system in low temperature environment, the battery heating power requirement is usually between 1kW-5kW, the electronic equipment startup is usually between 0.5kW-2kW, the total power requirement of the warm-up phase is between 1.5kW-7kW, and the power requirement is usually low and can be ignored. The taxi phase requires driving the motor to make the aircraft taxi on the ground at low speed to the aircraft runway, the taxi power of light electric aircraft is about 10kW-20kW, and the time consumed in the taxi phase is usually controlled between 3-10min, the specific time needs to be evaluated in combination with the aircraft model and airport operation conditions.

[0135] The energy consumed in the warm-up taxi phase can be expressed as:

[0136]

[0137] In the formula, P warm-up is the power required during taxi; t warm-up is the time consumed during taxi; η warm-up is the efficiency of the electric propulsion system in the taxi phase.

[0138] (2) Take-off taxi phase

[0139] For the take-off run, the power required for the run can be expressed as:

[0140] P roll = F roll · V roll ;

[0141] where F roll is the average thrust of the aircraft during the run, which can be taken as 0.8 times the static thrust of the electric motor.

[0142] F roll = 0.8 F static_thrust ;

[0143] where F static_thrust is the static thrust of the electric motor.

[0144] The run speed is usually taken as the average of the take-off speed, which is generally 1.1 to 1.2 times the stall speed, i.e.

[0145] V TO = (1.1-1.2) · V stall ;

[0146] where V stall is the stall speed.

[0147] The run speed can be approximated as:

[0148]

[0149] During the run, the aircraft mainly overcomes the component of gravity, air resistance and ground friction to accelerate the aircraft to the take-off speed. Therefore, the time required for the run is:

[0150]

[0151] where a roll is the acceleration of the aircraft during the run.

[0152]

[0153] where W roll is the component of gravity in the direction of the run that the aircraft overcomes; D roll is the air resistance that the aircraft overcomes; F friction is the friction between the tires and the runway that the aircraft overcomes; and g is the acceleration due to gravity.

[0154] During the take-off run, the component of gravity in the direction of the run that the aircraft overcomes is usually related to the slope of the runway and can be expressed as:

[0155] W roll = W TO · sin(α);

[0156] where a is the runway slope angle.

[0157] The air resistance that the aircraft overcomes during the takeoff run is:

[0158]

[0159] where p is the air density during the takeoff run; C is the air resistance coefficient during the takeoff run; and S is the wing area. roll D_roll

[0160] During the aircraft conceptual design phase, the air resistance coefficient can be estimated by the polar curve equation, which is specifically expressed as:

[0161]

[0162] where C is the zero-lift air resistance coefficient, which can be matched and selected by the empirical equation of different types of aircraft; k is the induced resistance factor; and C is the takeoff air lift coefficient. D0 L_roll

[0163] The induced resistance factor k can be determined by the following equation:

[0164]

[0165] where AR is the aspect ratio of the aircraft wing; and e is the Oswald efficiency factor, which can be selected according to the different shapes of the aircraft.

[0166] The takeoff air lift coefficient of the aircraft is much smaller than the aircraft lift-off air lift coefficient, and is approximately expressed as:

[0167] L_roll L_TO

[0168] The aircraft lift-off air lift coefficient is:

[0169]

[0170] The friction between the tire and the runway that the aircraft overcomes during the takeoff run is:

[0171] friction TO roll

[0172] where m is the friction coefficient; and L is the takeoff air lift of the aircraft. roll

[0173] The takeoff air lift of the aircraft during the takeoff run can be expressed as:

[0174] ​​​​​​​​​​​​

[0175] where C L_roll is the lift coefficient of the aircraft during the takeoff roll.

[0176] Therefore, the energy consumed during the takeoff roll phase can be represented as:

[0177]

[0178] where η roll is the efficiency of the electric propulsion system during the takeoff roll phase.

[0179] (3) Climb Phase

[0180] For the climb phase, the power required by the electric aircraft is mainly related to factors such as the weight of the aircraft, the climb rate, air density, aerodynamic drag, etc., and can be represented as:

[0181] P climb = F climb · V climb ;

[0182] where F climb is the required thrust during the climb; V climb is the climb speed.

[0183] The required thrust F climb during the climb can be decomposed into two parts, which are the component of the climb to overcome gravity and the component of the climb to overcome aerodynamic drag, and can be represented as:

[0184] F climb = W TO · sin(θ) + D climb ;

[0185] where W TO is the maximum takeoff weight of the aircraft; θ is the climb angle; D climb is the aerodynamic drag.

[0186] The aerodynamic drag can be calculated by the following formula:

[0187]

[0188] where ρ climb is the air density during the climb; C D_climb is the drag coefficient of the aircraft during the climb.

[0189] The expression of the drag coefficient during the climb is:

[0190]

[0191] The lift coefficient of the aircraft during the climb is:

[0192]

[0193] The climb angle can be expressed in terms of the climb rate and the flight speed:

[0194]

[0195] where ROC is the climb rate.

[0196] Substituting the formula, the power required in the climb phase is:

[0197]

[0198] The time consumed in the climb phase is:

[0199]

[0200] where H cruise is the cruising altitude of the aircraft.

[0201] Therefore, the energy consumed in the climb phase is:

[0202]

[0203] where η climb is the efficiency of the electric propulsion system in the climb phase.

[0204] (4) Cruise phase

[0205] For the cruise phase, the power of the aircraft is:

[0206] P cruise = F cruise · V cruise ;

[0207] where F cruise is the required thrust in the cruise; V cruise is the cruise speed.

[0208] In the cruise, the aircraft is in equilibrium, at which time the lift of the aircraft is equal to the gravity, and the thrust is equal to the drag, and the required thrust F cruise can be expressed as:

[0209]

[0210] where p cruise is the air density in the cruise; C D_cruice is the drag coefficient in the cruise.

[0211] The drag coefficient of the aircraft in the cruise phase can be expressed as:

[0212]

[0213] The lift coefficient of the aircraft in the cruise phase can be expressed as:

[0214]

[0215] Substitute the C L_cruise into the drag equation to obtain the total power:

[0216]

[0217] The time consumed in the cruise phase is:

[0218]

[0219] where R cruise is the range of the aircraft in the cruise phase.

[0220] Therefore, the energy consumed in the cruise phase is:

[0221]

[0222] where η cruise is the efficiency of the electric propulsion system in the cruise phase.

[0223] (5) Hover phase

[0224] For the hover phase, the total power required for the aircraft includes the induced power and the zero-lift power. The induced power required during hovering is:

[0225]

[0226] where V loiter is the hover speed; and p loiter is the air density during hovering.

[0227] The zero-lift power required during hovering can be expressed as:

[0228]

[0229] The total power required during hovering is:

[0230]

[0231] The time consumed in the hover phase t loiter is determined according to the mission requirements.

[0232] Therefore, the energy consumed in the hover phase is:

[0233]

[0234] where η loiter is the efficiency of the electric propulsion system in the hover phase.

[0235] (6) Descent phase

[0236] For the descent phase, the required power is similar to the climb phase, the aircraft gravity and the aircraft thrust together overcome the aerodynamic drag, which can be expressed as:

[0237]

[0238] where ρ descent is the air density at the descent altitude; V descent is the descent speed; C D_descent is the aircraft drag coefficient during descent; R descent is the descent rate.

[0239] The aircraft drag coefficient during the descent phase can be expressed as:

[0240]

[0241] The aircraft lift coefficient during the descent phase can be expressed as:

[0242]

[0243] where θ is the descent angle.

[0244] The time consumed during the descent phase is:

[0245]

[0246] Therefore, the energy consumed during the descent phase is:

[0247]

[0248] where η descent is the electric propulsion system efficiency during the descent phase.

[0249] (7) Landing taxi to parking phase

[0250] For the landing taxi to parking phase, the electric aircraft usually shut down the electric motor to taxi, and no battery energy is consumed. When the aircraft needs to maintain low-speed movement to taxi to the parking stand, the electric motor provides positive thrust, which consumes battery energy, but the power is low, usually 1-10 kW, and the taxi time needs to be evaluated in combination with the aircraft model and airport operating conditions.

[0251] The energy consumed during the landing taxi to parking phase is:

[0252]

[0253] where P landing is the electric motor power when parking at the stand; t landing is the time consumed when parking at the stand; η landing is the electric propulsion system efficiency when parking at the stand.

[0254] Therefore, the total energy consumed by the aircraft mission profile is:

[0255] E = E warm-up + E roll + E climb + E cruise + E loiter + E descent + E landing ;

[0256] By sorting, the energy of each stage is a function of the maximum take-off weight, and the energy of each stage can be expressed as:

[0257]

[0258] where P warm-up is the required power during taxiing; t warm-up is the time consumed during taxiing; η warm-up is the efficiency of the electric propulsion system during taxiing.

[0259]

[0260] where F static_thrust is the static thrust of the electric motor; C D0 is the zero-lift drag coefficient; k is the induced drag factor; ρ roll is the air density during the take-off run; S is the wing area; g is the acceleration due to gravity; α is the runway slope angle; η roll is the efficiency of the electric propulsion system during the take-off run; μ is the friction coefficient; V TO is the take-off speed; W TO is the maximum take-off weight.

[0261]

[0262] where θ is the climb angle; ρ climb is the air density during climbing; ROC is the rate of climb; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; η climb is the efficiency of the electric propulsion system during climbing; H cruise is the cruising altitude of the aircraft; V climb is the climbing speed; W TO is the maximum take-off weight.

[0263]

[0264] where C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise is the range of the cruising segment of the aircraft; ρ cruiseη is the air density during cruising. cruise For the efficiency of the electric propulsion system during the cruise phase; V cruise For cruising speed; W TO This is the maximum takeoff weight.

[0265]

[0266] In the formula, η loiter For the efficiency of the electric propulsion system during the hovering phase; V loiter ρ is the rotational speed; loiter t represents the air density during hovering. loiter The time consumed during the hovering phase; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO This is the maximum takeoff weight.

[0267]

[0268] In the formula, ρ descent V is the air density at the descent altitude; descent R represents the descent speed. descent The rate of decline; η descent For the efficiency of the electric propulsion system during the descent phase; For glide slope; H cruise C is the aircraft's cruising altitude. D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO This is the maximum takeoff weight.

[0269]

[0270] In the formula, P landing The motor power when the machine is stopped at the designated position; t landing η is the time consumed when the machine stops at its designated position. landing The efficiency of the electric propulsion system when the machine is stopped at its designated position.

[0271] Therefore, the battery weight can be expressed in terms of the maximum takeoff weight as:

[0272]

[0273] In the formula, e b This refers to the battery energy density.

[0274] Therefore, the maximum takeoff weight can be expressed as:

[0275]

[0276] In the formula, E warm-up Energy consumed during the warm-up and coasting phase; E rollEnergy consumed for take-off phase; E climb Energy consumed for climb phase; E cruise Energy consumed for cruise phase; E loiter Energy consumed for loiter phase; E descent Energy consumed for descent phase; E landing Energy consumed for taxi-in and parking phase; e b Battery energy density; W CRE Crew weight; W PAS Passenger weight; W BAG Luggage weight.

[0277] The right side of the above equation (maximum take-off weight equation) is a function of the maximum take-off weight W TO , so the equation can be solved by iteration to obtain the maximum take-off weight W TO . The specific process of constructing and solving the equation is as follows: constructing the equation: obtain the calculation formula of the empty weight, payload and energy consumed by each phase of the aircraft mission profile according to the aircraft design parameters, obtain the battery weight formula through the energy consumed formula, and then combine the above formulas to obtain a maximum take-off weight equation; solving the equation: preset an initial value W TO1 for the maximum take-off weight, substitute this value into the maximum take-off weight function on the right side of the maximum take-off weight equation to obtain a calculated value W TO2 for the maximum take-off weight, usually the difference between the two values is large, which does not meet the requirements, at this time, update the initial value W TO2 using the calculated value W TO1 and continue to substitute it into the maximum take-off weight function, iteratively calculate W TO2 , after several iterations, when the difference between the take-off weights calculated by two iterations (i.e. the latest W TO2 and W TO1 ) is small enough, the iteration is ended, and the weight value obtained at this time is the maximum take-off weight W TO of the four-seat electric aircraft.

[0278] Based on the take-off weight estimation method of the oil-powered aircraft, the relationship between the energy consumption and the take-off weight of the electric aircraft is introduced, and the take-off weight estimation method of the electric aircraft is established. The energy consumed by the aircraft mission profile is introduced, and the energy consumed by the traditional aircraft is replaced by the fuel weight, the expression of the energy consumed by the aircraft mission in different phases is obtained, the relationship between the lithium battery weight and the take-off weight of the aircraft is obtained, and then the equation for estimating the take-off weight of the aircraft is obtained.

[0279] The embodiments of the present application are described in detail above with reference to the accompanying drawings, but the present application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present application.

Claims

1. A method of determining the maximum take-off weight of an electric aircraft, characterized in that, Comprising: S1: establishing a maximum take-off weight equation of the electric airplane, the maximum take-off weight equation of the electric airplane being as follows: W TO = W E + W PL + W B ; wherein W TO is the maximum takeoff weight of the electric aircraft; W E is the empty weight of the aircraft; W PL is the payload; and W B is the battery weight. wherein where E is the total energy required for the electrically powered aircraft to fly; e b is the energy density of the battery; wherein E = E warm-up +E roll +E climb +E cruise +E loiter +E descent +E landing ; wherein E warm-up is the energy consumed during the warm-up taxi phase; E roll is the energy consumed during the take-off roll phase; E climb is the energy consumed during the climb phase; E cruise is the energy consumed during the cruise phase; E loiter is the energy consumed during the holding pattern phase; E descent is the energy consumed during the descent phase; E landing is the energy consumed during the landing taxi and parking phase; wherein where P warm-up is the required power during the glide; t warm-up is the time consumed during the glide; η warm-up is the electric propulsion system efficiency during the glide phase; where F static_thrust is the motor static thrust; C D0 is the zero-lift drag coefficient; k is the induced drag factor; p roll is the air density during the ground run; S is the wing area; g is the gravitational acceleration; a is the runway slope angle; h roll is the electric propulsion system efficiency during the take-off ground run; m is the mass of the aircraft; m TO is the take-off speed; W TO is the maximum take-off weight; where θ is the climb angle; p climb is the air density during climb; ROC is the rate of climb; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; η climb is the electric propulsion system efficiency during climb; H cruise is the aircraft cruise altitude; V climb is the climb speed; W TO is the maximum takeoff weight; where C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise is the range of the aircraft in the cruise phase; p cruise is the air density at cruise; η cruise is the electric propulsion system efficiency in the cruise phase; V cruise is the cruise speed; W TO is the maximum takeoff weight; where η loiter is the efficiency of the electric propulsion system during the spiral phase; V loiter is the spiral velocity; p loiter is the air density during the spiral; t loiter is the time consumed during the spiral phase; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum take-off weight; where p descent is the air density at glide height; V descent is the glide speed; R descent is the rate of descent; η descent is the electric propulsion system efficiency during glide phase; is the glide angle; H cruise is the aircraft cruise altitude; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum take-off weight; where P landing is the electric motor power at the time of stopping at the stand; t landing is the time consumed at the time of stopping at the stand; η landing is the electric propulsion system efficiency at the time of stopping at the stand; S2: solving the maximum take-off weight equation of the electric airplane to obtain the maximum take-off weight of the electric airplane.

2. The method of determining the maximum takeoff weight of an electric aircraft of claim 1, wherein, In S2, the maximum take-off weight equation of the electric airplane is solved by using an iterative method, and the specific steps are as follows: S21: presetting an initial value of the maximum take-off weight of the electric airplane; S22: bringing the initial value of the maximum take-off weight of the electric airplane into the right side of the maximum take-off weight equation of the electric airplane to obtain a calculated value of the maximum take-off weight of the electric airplane; S23: subtracting the initial value of the maximum take-off weight of the electric airplane from the calculated value of the maximum take-off weight of the electric airplane obtained in S22, if the calculated difference is less than a preset iteration termination difference, then the iteration is terminated, and the calculated value of the maximum take-off weight of the electric airplane is taken as the maximum take-off weight of the electric airplane, otherwise, returning to S21 and taking the calculated value of the maximum take-off weight of the electric airplane obtained in the last step as the initial value of the maximum take-off weight of the electric airplane for the next iteration, and continuing to execute S22 and S23 until the iteration termination condition is met.

3. A method of determining the battery weight of an electric aircraft, characterized in that, Comprising: Determining the maximum take-off weight of the electric airplane according to the determination method of the maximum take-off weight of the electric airplane in claim 1 or 2; The electric aircraft battery weight W is calculated using the following formula B : where E is the total energy required for the electrically powered aircraft to fly; e b is the battery energy density; wherein E = E warm-up +E roll +E climb +E cruise +E loiter +E descent +E landing ; wherein E warm-up is the energy consumed during the warm-up taxi phase; E roll is the energy consumed during the take-off roll phase; E climb is the energy consumed during the climb phase; E cruise is the energy consumed during the cruise phase; E loiter is the energy consumed during the holding pattern phase; E descent is the energy consumed during the descent phase; E landing is the energy consumed during the landing taxi and parking phase; wherein where P warm-up is the required power during the glide; t warm-up is the time consumed during the glide; η warm-up is the electric propulsion system efficiency during the glide phase; where F static_thrust is the motor static thrust; C D0 is the zero-lift drag coefficient; k is the induced drag factor; p roll is the air density during the ground run; S is the wing area; g is the gravitational acceleration; a is the runway slope angle; h roll is the electric propulsion system efficiency during the take-off ground run; m is the mass of the aircraft; m TO is the take-off speed; W TO is the maximum take-off weight; where θ is the climb angle; p climb is the air density during climb; ROC is the rate of climb; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; η climb is the electric propulsion system efficiency during climb; H cruise is the aircraft cruise altitude; V climb is the climb speed; W TO is the maximum takeoff weight; where C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; R cruise is the range of the aircraft in the cruise phase; p cruise is the air density during cruise; η cruise is the electric propulsion system efficiency during cruise; V cruise is the cruise speed; W TO is the maximum takeoff weight; where η loiter is the efficiency of the electric propulsion system during the climb phase; V loiter is the climb speed; p loiter is the air density during the climb; t loiter is the time consumed during the climb phase; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum take-off weight; where p descent is the air density at glide height; V descent is the glide speed; R descent is the rate of descent; η descent is the electric propulsion system efficiency during the glide phase; is the glide angle; H cruise is the aircraft cruise altitude; C D0 is the zero-lift drag coefficient; k is the induced drag factor; S is the wing area; W TO is the maximum takeoff weight; where P landing is the electric motor power at the moment of stopping at the stand; t landing is the time consumed for stopping at the stand; η landing is the electric propulsion system efficiency at the moment of stopping at the stand.

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