VTOL aircraft with a thrust-to-weight ratio smaller than 0.1

Abstract

VTOL aircraft with a thrust-to-weight ratio smaller than 0.1, during vertical take-off/landing, obtains an another lift, besides a lift generated by low-temp bypass duct (15) directing the low-temp air (18) from the turbofan engine (3) to flow, through its outlet (19) in form of low-temp planar jet (20), over the upper surface of the wing and in the direction of the wingspan, by high-temp bypass duct (15) directing the high-temp air (18) from the turbofan engine (3) to flow, through its outlet (12) in form of high-temp planar jet (13), above the low-temp planar jet (20) in the direction of the wingspan but not burn up the wing and enables the ailerons (1, 2) to control the balances of the aircraft more efficiently.

Claims

1. An aircraft capable of vertical take-off/landing, comprising: ailerons (1, 2); a turbofan engine (3) including a low-temp duct (6) with an openable and closable propelling nozzle (7) and a high-temp duct (4) with an openable and closable propelling nozzle (5); a low-temp bypass duct (15) including an openable and closable inlet (14) connected to the low-temp duct (6), an outer wall (16), an inner wall (17) and a thin slot outlet (19) set on the upper surface of the wing and in the direction of the wingspan; and a high-temp bypass duct (9) including an openable and closable inlet (8) connected to the high-temp duct (4), an outer wall (10) and a thin slot outlet (12) set above the thin slot outlet (19) of the low-temp bypass duct (15) in the direction of the wingspan.

2. The aircraft according to claim 1 wherein the low-temp duct (6) spouts directly low-temp air (18) into the atmosphere to generate a thrust during forward flight when the propelling nozzle (7) of low-temp duct (6) is opened and the inlet (14) of the low-temp bypass duct (15) is closed.

3. The aircraft according to claim 1 wherein the high-temp duct (4) spouts directly high-temp air (11) into the atmosphere to generate another thrust during forward flight when the propelling nozzle (5) of high-temp duct (4) is opened and the inlet (8) of the high-temp bypass duct (9) is closed.

4. The aircraft according to claim 1 wherein the low-temp bypass duct (15) directs the low-temp air (18) from the low-temp duct (6) to flow, in form of low-temp planar jet (20), over the upper surface of the wing and in the direction of the wingspan, thereby generating a vertical lift and enabling the ailerons (1, 2) to control horizontal and vertical balances of the aircraft during vertical take-off/landing when the propelling nozzle (7) of low-temp duct (6) is closed and the inlet (14) of the low-temp bypass duct (15) is opened.

5. The aircraft according to claim 1 wherein the high-temp bypass duct (9) directs the high-temp air (18) from the high-temp duct (4) to flow, in form of high-temp planar jet (13), above the low-temp planar jet (20) in the direction of the wingspan, thereby generating another vertical lift and enabling the ailerons (1, 2) to control horizontal and vertical balances of the aircraft more efficiently during vertical take-off/landing when the propelling nozzle (5) of high-temp duct (4) is closed and the inlet (8) of the high-temp bypass duct (9) is opened.

6. The aircraft according to one of claims 1-5 wherein the thin slot outlet (12) of the high-temp bypass duct (9), set above the thin slot outlet (19) of the low-temp bypass duct (15), enables the high-temp planar jet (13) not to burn the upper surface of the aircraft during vertical take-off/landing.

Description

BRIEF DESCRIPTION OF THE DRAWING

(1) The attached drawings illustrate the invention:

(2) FIG. 1 is a side view of an aircraft with this invention during vertical take-off and landing.

(3) FIG. 2 is a top view of an aircraft with this invention during vertical take-off and landing.

(4) FIG. 3 is a rear view of an aircraft with this invention during vertical take-off and landing.

(5) FIG. 4 is J local view for FIG. 3.

(6) FIG. 5 is A-A Section for FIG. 4

(7) FIG. 6 is B-B Section for FIG. 4.

(8) FIG. 7 is part Section for FIG. 4.

(9) FIG. 8 is K local view for FIG. 3.

(10) FIG. 9 is C-C Section for FIG. 8.

(11) FIG. 10 is a side view of an aircraft with this invention during forward flight.

(12) FIG. 11 is a top view of an aircraft with this invention during forward flight.

(13) FIG. 12 is a rear view of an aircraft with this invention during forward flight.

(14) FIG. 13 is M local view for FIG. 12.

(15) FIG. 14 is D-D Section for FIG. 13.

(16) FIG. 15 is E-E Section for FIG. 13.

(17) FIG. 16 is part Section for FIG. 13.

(18) FIG. 17 is N local view for FIG. 12.

(19) FIG. 18 is F-F Section for FIG. 17.

DETAILED DESCRIPTION OF THE INVENTION

(20) Referring to above drawings, an aircraft with this invention comprises: ailerons (1, 2); a turbofan engine (3) including a low-temp duct (6) with an openable and closable propelling nozzle (7) and a high-temp duct (4) with an openable and closable propelling nozzle (5); a low-temp bypass duct (15) including an openable and closable inlet (14) connected to the low-temp duct 6), an outer wall (16), an inner wall (17) and a thin slot outlet (19) set on the upper surface of the wing and in the direction of the wingspan; a high-temp bypass duct (9) including an openable and closable inlet (8) connected to the high-temp duct (4), an outer wall (10) and a thin slot outlet (12) set above a thin slot outlet (19) of the low-temp bypass duct (15) and in the direction of the wingspan.

(21) Referring to FIG. (1-9), during vertical take-off/lading, the propelling nozzles (5, 7) of the low-temp duct (6) and the high-temp duct (4) of the turbofan engine (3) are closed. At same time, the inlets (8, 14) of the low-temp bypass duct (15) and the high-temp bypass duct (9) are opened. Then, the turbofan engine (3) starts to supply the low-temp air (18) to the low-temp duct (6) and the high-temp air (11) to the high-temp duct (4). Now, the low-temp bypass duct (15) directs the low-temp air (18) from the low-temp duct (6) and enables it, in form of low-temp planar jet (20), to flow over the upper surface of the wing and in the direction of wingspan. Because the velocity of the air flowing over the upper surface of the wing is higher than that over the lower surface of the wing, and according to Principle of Bernoulli stating an increase in the speed occurs simultaneously with a decrease in pressure, a vertical lift is generated on the wing due to the lower pressure on the upper surface of the wing than that on the lower surface of the wing and the low-temp planar jet (20) enables the ailerons to control horizontal and vertical balances of the aircraft. Similarly, the high-temp bypass duct (9) directs the high-temp air (11) from the high-temp duct (4) and enables it, in form of the high-temp planar jet (13), to flow above the low-temp planar jet (20) in the direction of wingspan, thereby generating another vertical lift and enabling the ailerons to control horizontal and vertical balances of the aircraft more efficiently. The thin slot outlet (12) of the high-temp bypass duct (9), set above the thin slot outlet (19) of the low-temp bypass duct (15), enables the high-temp planar jet (13) not to burn up the upper surface of the wing.

(22) Referring to FIG. (10-18), during forward flight, the propelling nozzles (5, 7) of the low-temp duct (6) and high-temp duct (4) of the turbofan engine (3) are opened. At same time, the inlets (8, 14) of the low-temp bypass duct (15) and the high-temp bypass duct (9) are closed. Then, the low-temp air (18) and the high-temp air (11) spout directly from the propelling nozzles (5, 7) of the low-temp duct (6) and the high-temp duct (4) into atmosphere to generate thrusts.

(23) All the formulas and calculations for this invention are listed in Annex 1.

(24) All the formulas and calculations used to retrofit an Airbus A-380 based on this invention are listed in Annex 2.

(25) This invention can be used to retrofit an existing aircraft to achieve VTOL or manufacture a VTOL aircraft with a thrust-to-weight ratio smaller than 0.1.

ANNEX 1

(26) TABLE-US-00001 P Atmospheric pressure (Unit: Pa) R Ideal gas constant (Unit: J. K .sup.1. mol .sup.1) .sub.0 Low-temp jet density at the outlet (Unit:kg/m.sup.3) .sub.1 Atmospheric density (Unit:kg/m.sup.3) Jet density on the cross-section (Unit: kg/m.sup.3) .sub.m Jet density of the shaft (Unit: kg/m.sup.3) T.sub.0 Jet temp at the low-temp outlet (Unit: K) T.sub.1 Atmospheric temp (Unit: K) T Jet temp on the cross-section (Unit: K) V.sub.0 Jet speed at the outlet of low-temp (Unit: m/s) bypass duct V{acute over (.sub.0)} Jet speed at the outlet of high-temp (Unit: m/s) bypass duct V Jet speed on the cross-section (Unit: m/s) V.sub.m Jet speed of shaft (Unit: m/s) h.sub.0 Jet height of the outlet (Unit: m) h.sub.m Jet height of the cross-section (Unit: m) h Jet height on the cross-section (Unit: m) L Width of the outlet (Unit: m) C Gas specific volume (Unit: m.sup.3/kg) M Molar mass (Unit: kg/mol) Q Air inflow of turbofan engine (Unit: kg/s) B Bypass ratio of turbofan engine (Dimensionless unit) G Maximum take-off weight (Unit: T) X Distance between any point and outlet (Unit: m) of low-temp bypass duct in jet direction X.sub.1 Distance between wing root and low- (Unit: m) temp outlet in jet direction X.sub.2 Distance between low-temp outlet (Unit: m) and crossover point at which jet boundary intersects with trailing edge of wing in jet direction X.sub.3 Distance between wingtip and (Unit: m) low-temp outlet in jet direction Angle between jet boundary and (Unit: ) trailing edge of wing Angle between chord line of wing (Unit: ) and long side of outlet Dihedral angle of wing (Unit: ) Sweep forward angle of jet (Unit: ) Included angle between axis of low- (Unit: ) temp jet and one of the high-temp jet Sweep back angle of jet (Unit: ) F Total vertical lift (Unit: T) F.sub.1 Lift between wing root and low-temp outlet (Unit: T) F.sub.2 Lift between low-temp outlet and crossover (Unit: T) point at which jet boundary intersects with trailing edge of wing F.sub.3 Lift between wingtip and low-temp outlet (Unit: T) F.sub.4 Downward pressure generated (Unit: T) by slant upward deflected jet F.sub.5 Thrust generated by jet of low-temp outlet (Unit: T) F.sub.6 Thrust generated by jet of high-temp outlet (Unit: T) b Constant (Dimensionless unit) d Constant (Dimensionless unit) C Constant (Dimensionless unit) n.sub.1 S/N of turbofan engine (Dimensionless unit) n.sub.2 S/N of turbofan engine used in vertical (Dimensionless Take-off/landing unit) n.sub.3 S/N of outlet of low-temp bypass duct (Dimensionless unit) TW R Thrust-to-weight ratio of aircraft (Dimensionless unit)

(27) According to thermodynamic, relative values of the enthalpy of various jet cross-sections are same each other when pressures of these jet cross-sections are equal and the value of surrounding gas is starting value.

(28) And according to the feature of planar jet, it just spread on the flat which is perpendicular to the outlet section.

(29) $P=\frac{{}_0}{M}{\mathrm{RT}}_0=\frac{{}_1}{M}{\mathrm{RT}}_1=\frac{}{M}\mathrm{RT}$${}_0{V}_0{h}_0\mathrm{LC}\left(T_0-T_1\right)=\mathrm{VL}C\left(T-T_1\right)h$${}_0{V}_0{h}_0\left(\frac{1}{{}_0}-\frac{1}{{}_1}\right)=V\left(\frac{1}{}-\frac{1}{{}_1}\right)h$

(30) And according to the similarity of velocity and density distribution on the various jet sections,

(31) $\begin{array}{cc}\sqrt{\frac{V}{V_m}}=\frac{-{}_1}{{}_m-{}_1}=1-{\left(\frac{h}{h_m}\right)}^{1.5}{h}_0{V}_0\left({}_0-{}_1\right)=\left(-{}_1\right)Vh\frac{h_0{V}_0\left({}_0-{}_1\right)}{\left({}_m-{}_1\right)V_m{h}_m}=\frac{\left(-{}_1\right)V}{\left({}_m-{}_1\right)V_m{h}_m}h={}_0^{h_m}{\left[1-{\left(\frac{h}{h_m}\right)}^{1.5}\right]}^3.Math.\frac{1}{h_m}h={}_0^1{\left[1-{\left(\frac{h}{h_m}\right)}^{1.5}\right]}^3\left(\frac{h}{h_m}\right)=0.3682\left({}_m-{}_1\right)=\frac{h_0{V}_0\left({}_0-{}_1\right)}{0.3682.Math.V_m{h}_m}& \left(1\right)\end{array}$

(32) According to dynamic characteristic of jet, momentums of the various sections are same each other in case of equal pressures.

(33) $\begin{array}{cc}{}_0{\mathrm{Lh}}_0{V}_0^2={\mathrm{LV}}^{2}h{}_0{h}_0{V}_0^2=V^{2}h=\left(-{}_1\right)V^{2}h+{}_1{V}^{2}h\frac{{}_0{h}_0{V}_0^2}{\left({}_m-{}_1\right)V_m^2{h}_m}={}_0^1\frac{\left(-{}_1\right)V^2}{\left({}_m-{}_1\right)V_m^2}\left(\frac{h}{h_m}\right)+{}_0^1\frac{{}_1{V}^2}{\left({}_m-{}_1\right)V_m^2}\left(\frac{h}{h_m}\right)={}_0^1{\left[1-{\left(\frac{h}{h_m}\right)}^{1.5}\right]}^5\left(\frac{h}{h_m}\right)+\frac{{}_1}{\left({}_m-{}_1\right)}{}_0^1{\left[1-{\left(\frac{h}{h_m}\right)}^{1.5}\right]}^4\left(\frac{h}{h_m}\right)=0.2786+\frac{0.3156{}_1}{\left({}_m-{}_1\right)}\frac{0.3682V_0{}_0}{V_m\left({}_0-{}_1\right)}=0.2786+\frac{0.1162h_m{V}_m{}_1}{h_0{V}_0\left({}_0-{}_1\right)}& \left(2\right)\end{array}$

(34) Substitute (1) into (2):

(35) $\begin{array}{cc}\frac{0.1162h_m{}_1}{h_0{}_0}.Math.{\left(\frac{V_m}{V_0}\right)}^2+0.2786\frac{\left({}_0-{}_1\right)}{{}_0}.Math.\left(\frac{V_m}{V_0}\right)-0.3682=0\frac{V_m}{V_0}=\frac{\frac{0.2786\left({}_1-{}_0\right)}{{}_0}+\sqrt{{\left[\frac{0.2786\left({}_0-{}_1\right)}{{}_0}\right]}^2+\frac{0.1711h_m{}_1}{h_0{}_0}}}{\frac{0.2324h_m{}_1}{h_0{}_0}}{V}_m=\frac{1+\sqrt{1+\frac{0.1711h_m{}_0{}_1}{{0.2786}^2{h_0\left({}_0-{}_1\right)}^2}}}{\frac{0.2324h_m{}_1}{0.2786h_0\left({}_0-{}_1\right)}}{V}_0& \left(3\right)\end{array}$

(36) Substitute (3) into (1)

(37) $\begin{array}{cc}\left({}_m-{}_1\right)=\frac{h_0{V}_0\left({}_0-{}_1\right)}{0.3682.Math.V_m{h}_m}{}_m={}_1-\frac{\frac{0.2324}{0.36820.2786}{}_1}{1+\sqrt{1+\frac{0.1711h_m{}_0{}_1}{{0.2786}^2{h_0\left({}_0-{}_1\right)}^2}}}& \left(4\right)\end{array}$

(38) When XX.sub.1 or XX.sub.2

(39) $F=P-\left[P-\left(P-\frac{1}{2}{}_m{V}_m^2\right)\right]Lx=\frac{1}{2}{}_m{V}_m^{2}Lx$

(40) Substitute (3), (4) into (2)

(41) $=\frac{1}{2}{}_0^X\left[{}_1-\frac{\frac{0.2324}{0.36820.2786}{}_1}{1+\sqrt{1+\frac{0.1711h_m{}_0{}_1}{{0.2786}^2{h_0\left({}_0-{}_1\right)}^2}}}\right].Math.{\left[\frac{1+\sqrt{1+\frac{0.1711h_m{}_0{}_1}{{0.2786}^2{h_0\left({}_0-{}_1\right)}^2}}}{\frac{0.2324h_m{}_1}{0.2786h_0\left({}_0-{}_1\right)}}\right]}^2.Math.V_0^{2}Lx=\frac{1}{2}{}_0^X\left\{{{}_1\left[\frac{1+\sqrt{1+\frac{0.1711h_m{}_0{}_1}{{0.2786}^2{h_0\left({}_0-{}_1\right)}^2}}}{\frac{0.2324h_m{}_1}{0.2786h_0\left({}_0-{}_1\right)}}\right]}^2-\frac{0.2324}{0.36820.2786}{}_1.Math.\left[\frac{1+\sqrt{1+\frac{0.1711h_m{}_1{}_0}{{0.2786}^2{h_0\left({}_1-{}_0\right)}^2}}}{\frac{0.2324h_m{}_1}{0.2786h_0\left({}_1-{}_0\right)}}\right]\right\}.Math.V_0^{2}Lx=\frac{1}{2}{}_0^x{}_1\left\{\frac{2+\frac{0.1711h_m{}_1{}_0}{{0.2786}^2{h_0\left({}_1-{}_0\right)}^2}+2\sqrt{1+\frac{0.1711h_m{}_1{}_0}{{0.2786}^2{h_0\left({}_1-{}_0\right)}^2}}}{{\left[\frac{0.2324h_m{}_1}{0.2786h_0\left({}_1-{}_0\right)}\right]}^2}-\frac{\left(\frac{0.2324}{0.36820.2786}+\frac{0.2324}{0.36830.2786}\sqrt{1+\frac{0.1711h_m{}_1{}_0}{{0.2786}^2{h_0\left({}_1-{}_0\right)}^2}}\right)}{\left({\left[\frac{0.2324h_m{}_1}{0.2786h_0\left({}_1-{}_0\right)}\right]}^2\right)}\right\}.Math.V_0^{2}x=\frac{1}{2}\stackrel{X}{\underset{0}{}}\left\{\frac{0.1711{}_0}{{0.2324}^2\left(\frac{h_m}{h_0}\right)}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{\left(\frac{h_m}{h_0}\right)}^2}-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.\left(\frac{h_m}{h_0}\right)}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}.Math.\left(\frac{h_m}{h_0}\right)\right]}^2}\right\}.Math.V_0^{2}Lx$

(42) Because of

(43) $\frac{h_m}{h_0}=2.44\left(\frac{0.12x}{h_0}+0.41\right)$

(44) When XX.sub.2 or XX.sub.3

(45) $F_1=\frac{1}{2}{}_{1.0004}^{2.44\left(\frac{0.12X_1}{h_0}+0.41\right)}\left\{\frac{0.1711{}_0}{{0.2324}^2\left(\frac{h_m}{h_0}\right)}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{\left(\frac{h_m}{h_0}\right)}^2}-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.\left(\frac{h_m}{h_0}\right)}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}.Math.\left(\frac{h_m}{h_0}\right)\right]}^2}\right\}.Math.\frac{h_0{V}_0^{2}L}{2.440.12}\left(\frac{h_m}{h_0}\right)=\frac{1}{2}{}_{1.0004}^{2.44\left(\frac{0.12X_1}{h_0}+0.41\right)}\left\{\frac{0.1711{}_0}{{0.2324}^{2}x}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{x}^2}-\frac{0.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2}.Math.\frac{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}}{.Math.x^2}\right\}.Math.\frac{h_0{V}_0^{2}L}{2.440.12}x$$\frac{\sqrt{1+\mathrm{bx}}}{x^2}x=-\left(\frac{\sqrt{1+\mathrm{bx}}}{x}-\frac{b}{2}\ln \frac{\sqrt{1+\mathrm{bx}}-1}{\sqrt{1+\mathrm{bx}}+1}+C\right)$

(46) 0$\begin{array}{cc}{F}_1={\left\{\frac{0.1711{}_0}{{0.2324}^2}\ln x+\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^{2}x}+\frac{0.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2}.Math.\left[\frac{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}}{x}-\frac{0.1711{}_1{}_0}{2{0.2786}^2{\left({}_1-{}_0\right)}^2}\ln \frac{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}-1}{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}+1}\right]\right\}}_{2.440.41}^{2.44\left(\frac{0.12X_1}{h_0}+0.41\right)}\frac{1}{2}\frac{h_o{V}_0^{2}L}{2.440.12}& \left(5\right)\end{array}$

(47) $\begin{array}{cc}{F}_2={\left\{\frac{0.1711{}_0}{{0.2324}^2}\ln x+\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^{2}x}+\frac{0.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2}.Math.\left[\frac{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}}{x}-\frac{0.1711{}_1{}_0}{2{0.2786}^2{\left({}_1-{}_0\right)}^2}\ln \frac{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}-1}{\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x+1}}\right]\right\}}_{2.440.41}^{2.44\left(\frac{0.12X_2}{h_0}+0.41\right)}\frac{1}{2}\frac{h_0{V}_0^{2}L}{2.440.12}& \left(6\right)\end{array}$

ANNEX 2

(48) When X.sub.2XX.sub.3

(49) $\begin{array}{cc}{F}_3=\frac{1}{2}{}_{X_2}^{X_3}\left\{\frac{0.1711{}_0}{{0.2324}^2\left(\frac{h_m}{h_0}\right)}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{\left(\frac{h_m}{h_0}\right)}^2}-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.\left(\frac{h_m}{h_0}\right)}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}.Math.\left(\frac{h_m}{h_0}\right)\right]}^2}\right\}{V}_0^2\left[L-\left(x-X_2\right)\tan \right]x& \left(7\right)\end{array}$

(50) When force is zero in body axis direction,

(51) $\begin{array}{cc}{F}_4=F_5+F_6\left(F_4+F_5+F_6\right)\sin =\left(F_5+F_6\right)\sin ={\sin }^{-1}\frac{1}{2}\sin & \left(8\right)\\ F=n_2\left(F_1+F_2+F_3\right)\cos \cos -n_2\left[F_4\cos +F_6\sin \left(+\right)-F_6\sin \left(-\right)\right]& \left(9\right)\end{array}$

(52) VTOL can be achieved once: F>G

ANNEX 2

(53) n.sub.1=14

(54) n.sub.2=12

(55) n.sub.3=14

(56) M=29 kg/mol

(57) Q(Air inflow of Trent 900 turbofan engine)=1204 kg/s

(58) B(Bypass ratio of Trent 900 turbo fan engine)=8.5:1

(59) G(Maximum take-off weight of A380)=560T

(60) T.sub.0=383K

(61) .sub.1=1.293 kg/m.sup.2

(62) Assuming:

(63) $=36.5$$F_4=\frac{1}{n_2}{\mathrm{QV}}_0=\frac{1}{2}1204211=127002N=13T$${}_0=\frac{{\mathrm{MP}}_0}{{\mathrm{RT}}_0}=\frac{101325290.001}{8.31383}=0.9232\mathrm{kg}\text{/}{m}^3$$h_0=0.46m$$L=6m$$V_0=\frac{\frac{1}{n_2}Q\frac{8.5}{8.5+1}}{{}_{0}L{h}_0}=\frac{\frac{1}{2}1204\frac{8.5}{8.5+1}}{0.923260.46}=211m\text{/}s$$V_0^{}=V_0=211m\text{/}s$$F_6=\frac{1}{n_2}Q\frac{1}{8.5+1}{V}_0^{}=11370.7368N=1.4T$$X_1=11m$$X_2=18m$$X_3=32m$$=14$$=5$$=5$$=36.5$$=216.3$

(64) $\begin{array}{cc}\begin{array}{c}{F}_1=209832.582[2.9246\ln x+\frac{0.1488}{x}+0.0312.Math.\\ {\left[\frac{\sqrt{1+19.2419x}}{x}-9.621\ln \frac{\sqrt{1+19.2419x}-1}{\sqrt{1+19.2419x}+1}\right]}_{2.440.41}^{2.44\left(\frac{0.12X_1}{h_0}+0.41\right)}\\ =209832.582\{2.9246\ln \frac{2.44\left(\frac{0.1211}{0.46}+0.41\right)}{2.440.41}+\\ 0.1488\left[\frac{1}{2.44\left(\frac{0.1211}{0.46}+0.41\right)}-\frac{1}{2.440.41}\right]+\\ 0.0312.Math.[\frac{\sqrt{1+19.24192.44\left(\frac{0.1211}{0.46}+0.41\right)}}{2.44\left(\frac{0.1211}{0.46}+0.41\right)}-\\ \frac{\sqrt{1+19.24192.440.41}}{2.440.41}-\\ 9.621\ln \frac{\sqrt{1+19.24192.44\left(\frac{0.1211}{0.46}+0.41\right)}-1}{\sqrt{1+19.24192.44\left(\frac{0.1211}{0.46}+0.41\right)}+1}+\\ 9.621\ln \frac{\sqrt{1+19.24192.440.41}-1}{\sqrt{1+19.24192.440.41}+1}]\}\\ =209832.582\left[6.0811-0.1301-0.0918-0.0873\right]\\ =1211132.68N\\ =124T\end{array}& \left(5\right)\end{array}$

(65) $\begin{array}{cc}{F}_2=209832.582\left\{2.9246\ln \frac{2.44\left(\frac{0.1218}{0.46}+0.41\right)}{2.440.41}+0.1488\left[\frac{1}{2.44\left(\frac{0.1218}{0.46}+0.41\right)}-\frac{1}{2.440.41}\right]+0.0312.Math.\left[\frac{\sqrt{1+19.24192.44\left(\frac{0.1218}{0.46}+0.41\right)}}{2.44\left(\frac{0.1218}{0.46}+0.41\right)}-\frac{\sqrt{1+19.24192.440.41}}{2.440.41}\right]-9.621\ln \frac{\sqrt{1+19.24192.44\left(\frac{0.1218}{0.46}+0.41\right)}-1}{\sqrt{1+19.24192.44\left(\frac{0.1218}{0.46}+0.41\right)}+1}+9.621\ln \frac{1\sqrt{+19.24192.440.41}-1}{\sqrt{1+19.24192.440.41}+1}\right]\}=209832.582\left[7.3757-0.1368-0.1015-0.0969\right]=1477326.2936N=151T& \left(6\right)\end{array}$

(66) $F_3=\frac{1}{2}{}_{2.44\left(\frac{0.12X_2}{h_0}+0.41\right)}^{2.44\left(\frac{0.12X_3}{h_0}+0.41\right)}\left\{\frac{0.1711{}_0}{{0.2324}^2\left(\frac{h_m}{h_0}\right)}-\frac{1.2655}{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]{\left(\frac{h_m}{h_0}\right)}^2}-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2\left({}_1-{}_0\right)}.Math.\left(\frac{h_m}{h_0}\right)}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}.Math.\left(\frac{h_m}{h_0}\right)\right]}^2}\right\}[L-\left(\frac{h_0}{2.440.12}\left(\frac{h_m}{h_0}\right)-\frac{0.41h_0}{0.12}-X_2\right)\tan ]\frac{h_0{V}_0^2}{2.440.12}\left(\frac{h_m}{h_0}\right)=\frac{1}{2}{}_{2.44\left(\frac{0.12X_2}{h_0}+0.41\right)}^{2.44\left(\frac{0.12X_3}{h_0}+0.41\right)}\left\{\frac{0.1711{}_0}{{0.2324}^{2}x}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{x}^2}-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.\left(\frac{h_m}{h_0}\right)}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}.Math.x\right]}^2}\right\}.Math.[L-\left(\frac{h_0}{2.440.12}x-\frac{0.41h_0}{0.12}-X_2\right)\tan ]\frac{h_0{V}_0^2}{2.440.12}x=\frac{1}{2}{}_{2.44\left(\frac{0.12X_2}{h_0}+0.41\right)}^{2.44\left(\frac{0.12X_3}{h_0}+0.41\right)}.Math.\frac{0.1711{}_0}{{0.2324}^{2}x}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{x}^2}$

(67) $-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^2{x}^2}\}.Math.\left[1+\left(\frac{0.41h_0}{0.12L}+\frac{X_2}{L}\right).Math.\tan \right]-\left\{\frac{0.1711{}_0}{{0.2324}^2}-\frac{1.2655}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}\right]}^{2}x}-\frac{0.2655\sqrt{1+\frac{0.1711{}_1{}_0}{{0.2786}^2{\left({}_1-{}_0\right)}^2}.Math.x}}{{\left[\frac{0.2324{}_1}{0.2786\left({}_1-{}_0\right)}.Math.\right]}^{2}x}\right\}\frac{h_o\tan }{2.440.12L}.Math.\frac{h_0{V}_0^{2}L}{2.440.12}x\frac{\sqrt{1+x}}{x}x=2\sqrt{1+x}-\ln \frac{\sqrt{1+x}-1}{\sqrt{1+x}+1}+C$$F_3=209832.582\{1.8133\left[2.9246\ln x+\frac{0.1488}{x}+0.0312.Math.\left(\frac{\sqrt{1+19.2419x}}{x}-9.621\ln \frac{\sqrt{1+19.2419x}-1}{\sqrt{1+19.2419x}+1}\right)\right]-{0.0653\left[2.9246x-0.1488\ln x-0.0312\left(2\sqrt{1+19.2419x}-\ln \left(\frac{\sqrt{1+19.2419x}-1}{\sqrt{1+19.2419x}+1}\right)\right]\right\}}_{12.4578}^{21.3691}$

(68) $\begin{array}{cc}=209832.582\left\{1.8133\left[2.9246\ln \frac{21.3691}{12.4578}+0.1488\left(\frac{1}{21.3691}-\frac{1}{12.4578}\right)+0.0312\left(\frac{\sqrt{1+19.241921.3691}}{21.3691}-\frac{\sqrt{1+19.241912.4578}}{12.4578}-9.621\ln \frac{\sqrt{1+19.241921.3691}-1}{\sqrt{1+19.241921.3691}+1}+9.621\ln \frac{\sqrt{1+19.241912.4578}-1}{\sqrt{1+19.241912.4578}+1}\right)\right]-0.0653\left[2.9246\left(21.3691-12.4578\right)-0.1488\ln \frac{21.3691}{12.4578}-0.0312\left(2\sqrt{1+19.241921.3691}-2\sqrt{1+19.241912.4578}-\ln \frac{\sqrt{1+19.241921.3691}-1}{\sqrt{1+19.241921.3691}+1}+\ln \frac{\sqrt{1+19.241912.4578}-1}{\sqrt{1+19.241912.4578}+1}\right)\right]\right\}=209832.582\left\{1.8133\left[1.5781-0.005+0.0312\left(-0.2953-0.2934\right)\right]-0.0653\left[26.062-0.0803-0.0312\left(9.5748-0.0305\right)\right]\right\}=239636.5129N=24T& \left(7\right)\\ \begin{array}{c}={\sin }^{-1}\left(\frac{1}{2}\sin \right)\\ ={\sin }^{-1}\left(\frac{1}{2}\sin 36.5\right)\\ =17.3\end{array}& \left(8\right)\end{array}$

(69) According to this sweep forward angle, low-temp planar jet enables the aircraft to keep balances during vertical take-off/landing.

(70) 0$\begin{array}{cc}F=n_2\left(F_1+F_2+F_3\right)\cos \cos -n_2\left[F_4\cos +F_6\sin \left(+\right)-F_6\sin \left(-\right)\right]=2\left(124+151+24\right)\cos 5\cos 5-2\left[13\cos 17.3+1.4\sin \left(216.3+5\right)-1.4\sin \left(216.3-5\right)\right]=568TF-G=568-560=8T>0& \left(9\right)\\ \mathrm{TWR}=\frac{n_3\left(F_5+F_6\right)}{G}=\frac{n_3{F}_4}{G}=\frac{413}{560}=0.09<0.1& \left(10\right)\end{array}$

(71) It is clearly demonstrated above that VTOL is achievable on Airbus A380 once remodeled as shown, and more particularly, in case of using just two turbofan engines and thrust-to-weight ratio smaller than 0.1.