The “flying elevator” conception

 

  Corner aspects of the liftoplane were originated from following thought experiment, which I imagined in one day.

  Consider an elevator (or lift), which going up on some wire, which is winding in elevator’s own drum by power of its own engine. And now consider also: other end of the wire is fixedly connected to some wing or lightweight glider, which is gliding down. Also consider horizontal components of speed of both: elevator and glider are equal, and also the movement of both is without acceleration. Additionally consider: let aerodynamic drags of the elevator and of the wire are negligible. So this system will be in the presented movement until exists free length of the wire. But let stay away now from the problem of limited time of the movement and look on instant characteristics of the system.

 

  We can simple find, the system possess a some center of gravity (CG), which moves forward with same horizontal speed as both components of the system and will move up in case of the elevator is going up with a speed higher than the glider gliding down. And so potential energy of entire system will be increasing due to a work performing by engine of elevator. Now the system can be considered, from point of view the increasing energy, like as some aircraft in ascent, where powering is on 100 percents mechanical. But this assuming can be not OK sound for some people acquainted with realm of aircrafts. Indeed, we know a powered aircraft should have a something for propulsion its forward, like propeller, turbojet engine or rotor of helicopter articulated to forward flight. On other side it wouldn’t such surprisingly sound for people more acquainted with aspects of non-powered flight, for example for people having experience in gliding, hang gliding or paragliding. They know: any non-powered glider is being propelled forward by gravity force due to spending energy from decreasing its altitude. More than, they have experience of ascent in raising air of dynamical or thermal nature. The raising air acts as the elevator in considered thought experiment in pure mechanical manner. And when the glider is going up in the raising air, it still continues gliding down relative the air itself under propulsion force of gravity, having some gliding angle. Also such people know how to switch direction of the propulsion force for deceleration the glider upon landing.

 

  So considered system possess some equivalence with a glider placed into raising air, and power of elevator acts there as power of the raising air. And now we can find: the system possesses a powered lift instead of the powered propulsion of an airplane. And propulsion gravitic component of the system is powered by increasing altitude of CG from the lift powering. Also now we can find: a correct particular implementation of the "flying elevator" abstract conception will have great advantage over conventional airplane. It is very high propulsion efficiency, since the powered propulsion will be excluded from its scope as much as possible with related loss of power on it.

 

  Now before go forward, lets look on diagram below, which explains the conception in details. There and in other places I use arrow sign for designate a vector. Also I use the "^" sign for designate a normalized vector or vector of unitary length, which dot product with some other vector is simple a projection scale a one vector on direction of other.

"Flying elevator" conception's diagram

  There we can see the glider connected by the wire with the elevator. The glider has a speed vector VG and undergoes gravity force GF, which value is formulated in the first upper equation, where vector G is gravitic acceleration, and masses of elevator and glider are referenced as ML and MG respectively. The gravity force is full compensated by full aerodynamic force AF, as it formulated by the second upper equation. The third equation presents strain force of wire SF, which is opposed to gravity force of elevator only. The aerodynamic force can be decomposed to two components: a component perpendicular to airflow direction LF, which is lifting force, and component in direction opposed to source of airflow DF, which is drag force. The gravity force GF has a projection on gliding direction GP0, which value is formulated in the fourth upper equation. The GP0 force exactly compensates the drag force DF and so it acts as a propulsion force, which is formulated in the fifth equation. I will reference the GP0 force as primary gravitic propulsion force. The sixth upper equation represents other side of using the lifting force LF as a thrust force TF, which is useable in realm of helicopter aircrafts and also in some explanations of presented invention. And the equation presents a simple way to calculate it by subtracting the drag force from the full aerodynamic force vectorially.

 

  Full speed of elevator is a simple algebraic vectorial sum of the gliding VG vector and the winding lifting speed vector VL. The CG point on the wire represents the center of gravity of entire system itself. The point has its own speed vector V, which value is formulated by the weighting equation on center of the diagram. In current example the CG point is placed on the wire, but in more complex cases it can be placed simple in space. And so it isn't attributed to some element of system, it is attributed to entire system. The CG point possesses a mass of the entire system, so the balance of AF force and GF force can be considered there also. But the AF force is referenced there by other name as a power lifting force PLF, which means the CG point is subject of some lifting. It is reflected in the first equation of the bottom group. We will encounter duality of actuation of the lifting force PLF, by projection it on the vector V. It brings a lift propulsion LP, which represented in the second equation. Also projection of the primary gravitic propulsion GP0 on the vector V brings entire gravitic propulsion GP, which is represented in the third bottom equation. The fourth equation represents a consumed power as dot product of the strain force on elevator’s winding speed. Having the power we can calculate two vectors. The first is a power-lifting speed PLS, which is represented in the fifth equation. And second is a consumed thrust CT, which is represented in the sixth equation. Also we can see, a sum of both kinds of propulsion is equal to the consumed thrust, which is represented in the seventh equation. These PLS and CT represent a duality of powering the system. By first we can say as lift powering and by second we can say as thrust or propulsion powering. But we should understand, they are connected by the common power value, which is a scalar quantity, and so it isn't represents particular force doing the work. There is simple exchange of power between the elevator and gravitational field by increasing or compensating the altitude of CG.

 

  Let look now for a particular case, when CG has only horizontal motion. It will be correspond to aircraft on cruise. We can simple see that LP for the case is equal to zero. And system goes forward only by the gravitic propulsion GP, but a power for this propulsion is providing by the elevator. For the case absolute propulsion efficiency will be defined by a loss of moment through a downwash of the glider. But the loss is already included in balance of the drag as an inductive drag. So the propulsion efficiency relative to non-powered wing will be equal to 100 percents.

 

  Now let look for a case when the elevator doesn't work. It will be simple gliding. We can simple see that LP will be exactly compensated by GP, and so the CT will be equal to zero in full accordance with the non-powered flight.

 

  Also there exists other interesting variant of applying the "flying elevator" conception: now to analyze the induced drag itself upon a gliding. From the lifting line theory is known, the induced drag is created by a vortex connected with wings of finite span. It is known as "horseshoe" vortex. The vortex creates some complex induced deviation of a base flow. This component on near infinity in downstream direction has vertical direction and is known as a downwash. Also this component in vicinity of wing itself is known as inwash or inflow. That inflow also points down in counter- direction of lift but is two times small than the downwash. Since the component represents a loss, it is mapped for practical use to those induced drag by a reposition of actual aerodynamic force to reference frame of non-disturbed stream in far infinity. But on other side it can be considered as kind of continuously sinking air. This sinking air can be considered as a negative powering, where potential energy is going back to power source. But power source there is the gravitational field itself, which provides propulsion for compensating the airfoil section drag. But powering the "horseshoe" vortex also needs energy. And so we can see that gravitic power there is split on two ways. The first is the simple compensation of the airfoil section drag, such as profile drag. And second is a powering the "horseshoe" vortex, which performs self-servicing for the powering by placing the glider inside of sinking air of the inflow. It looks interesting, but what useful thing we can get from it? It is a horizontal acceleration. The horizontal acceleration of the glider will be powered only by the first component of the gravitic propulsion, since the "horseshoe" vortex steals the second for its own servicing. For using this feature we should consider a gliding of the glider inside its own inflow. For such gliding a correspondent gliding angle exists. I will reference it as a local gliding angle (LGA) of glider. Now consider we have some implementation of the "flying elevator" conception in some aircraft. We can decompose particular flight of the aircraft to a "glider" component and a "lift" component. Let name the "glider" component as embedded virtual glider or simple virtual glider. So said LGA can be obtained from the virtual glider. Knowing of it is useable for understanding when the aircraft will accelerate or decelerate for any particular flight operation. A real glider cannot change its LGA instantly for correcting its acceleration, since it’s changing is linked to changing flight path by entire mass of the glider. But the virtual glider can do it upon simple changing articulation of its actuator.

 

  Other interesting thing, which can provide the conception, it is ability for recuperation energy with same level of efficiency as spending it for flight. For it, we need only to switch direction of the winding lift speed and the aircraft will enter in a recuperative descent. More than, the "glider" can simple exchange exceptional speed on additional altitude and that altitude can be wound back for gaining energy. By doing both these actions simultaneously we can perform a recuperative deceleration too.

 

  Now let look how the "flying elevator" conception applies on known types of aircrafts. Let look on an airplane on the cruise flight. The airplane will have zero flight path-angle due to the cruise operation. And so projection of gravity force on drag direction is also zero, which disables actuation of the gravitic propulsion. The airplane compensates the drag using a separated actuator such as propeller, turbojet or turbofan engine. The separated actuator has significantly low thrust specific area than wings of the airplane. From the lifting line theory is known, the thrust specific area of wings itself, which creates the downwash, is almost equal to area of a circle, which diameter is based on the wingspan. The separated actuator of airplane has high outflow speed, which limits its propulsion efficiency. The efficiency for propeller practically lays in range 0.5 - 0.8. Also propellers perform badly for speed near of subsonic. Turbojet engines perform well for subsonic speed, but their propulsion efficiency lays in range 0.2 - 0.3. Turbofan engines on subsonic flight have propulsion efficiency of the fan itself about 0.7, for the nozzle only about 0.25 and overall about 0.5. But the low nozzle efficiency is particularly compensated by high thermal efficiency of the nozzle stage itself, which is about 0.65. So overall efficiency relative to fuel energy is about 0.37. Now we can see, having the propulsion efficiency near to 100 percents can elevate the overall efficiency up to 0.4-0.45.

 

  Next we can analyze an autogiro aircraft. Projection of gravity force on blades of its rotor is not zero, which is used for actuation its rotor. But nevertheless, when the autogiro is on a cruise, it performs as wing of airplane, having overall zero-action of gravity force, because a separated additional actuator also used there for propulsion.

 

  Now let look on a helicopter on the cruise flight. There is different picture. Its rotor is actuated on such manner that blades are in flapping motion over entire turn. Their wingtips are laid in a common surface inclined on some angle toward direction of flight. So part of entire thrust is horizontal and performs a horizontal propulsion. But we can see difference in gliding blades on different phases of rotation. A wing begins gliding down toward direction of flight. It undergoes gravitic propulsion with increased magnitude of aerodynamic force. And the helicopter itself is going up like elevator, powered by rotors' engine. After it, direction is switched and wing is flaring up with decreased magnitude of aerodynamic force. And helicopter going down like elevator returning some power back to rotor. A difference in powering on both considered phases based on the vertical component of the rotor's thrust can be considered as lifting with PLS, compensating a sink rate of the embedded glider upon gravitic propulsion. Also for duality representation we can consider the horizontal component of entire thrust as a consumed trust CT. And core feature of helicopter, which permits it, is the common actuation area for those actions, due to using common actuator. So helicopter is kind of aircraft, which can be referenced as a self-actuating aircraft (SAA), because it doesn’t need a separate actuator for its propulsion. It uses for that the same actuator as for providing sustaining forces. And so propulsion feature of such aircraft has big thrust specific area, low outflow and high propulsion efficiency.

 

  We can see, helicopter is example of SAA aircraft, which reflects the "flying elevator" conception in its operation. But helicopter isn't optimal implementation of the conception, because it was designed for different target. It was designed for a vertical flight in first order and for a horizontal in second. But the conception itself was formulated for design an aircraft with ideal propulsion for the cruise flight. And particular drawback of helicopter in implementation of the conception is the pure gliding ability of its rotor.

 

  After understanding of existence of a SAA aircraft we can look for other examples of this kind. I suppose it can be understood that birds’ flight is an example of this kind. Indeed, birds have only one actuator for both sustain and propulsion actions: their wings. Also some birds can reach very high speed in horizontal flight. It is the gravitic propulsion of simple glider, which permits that. Never they can reach that only by flapping their wings in weightlessness environment. They use the flapping mainly for lifting themselves, compensating the glide-sinking rate. There were attempts for building ornithopters, which mimic this bird's flight. But I suppose the trend isn't correct. The bird's flight has a big drawback from point of view of people. It is high level of oscillating acceleration, mainly in vertical direction. Birds are well accustomed for that, but it would a variant of uncomfortable flight for people.

 

Copyright © 2018 Yuri Feldman - All Rights Reserved