micro air vehicle lifted by a magnus rotor a proof of · pdf filemeasured by magnus at that...

American Institute of Aeronautics and Astronautics

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Micro Air Vehicle lifted by a Magnus Rotor A Proof of Concept

Jost Seifert* 85077 Manching, Germany

The application of a Magnus rotor as lifting device has been investigated and tested with a Micro Air Vehicle (MAV). The main focus was put on the efficiency of the rotor system and on the impact of gyroscopic forces on the flight dynamics. Successful flights were demonstrated, and the findings showed that the design and operation of such a rotor airplane is rather different to airplanes with wings. The Magnus effect generates significantly higher lift forces than an ordinary wing with the same reference area. The rotor system, however, will be heavier than a comparable wing, and will consequently diminish the effectiveness of a Magnus rotor. Flight tests revealed that the flight characteristic of the rotor airplane is dominated by precession. For the few tests performed, the handling qualities are rated to be satisfactory. For future applications there is an opportunity to take advantage of the gyroscopic forces, using an appropriate flight control system.

Nomenclature A = aspect ratio CL = lift coefficient CD = drag coefficient CT = torque coefficient D = drag d = cylinder diameter de = endplate diameter ds = disk spacing Izz = moment of inertia L = lift l = cylinder length M = pitching moment n = revolutions per second nz = load factor P = power consumption p = roll rate Re = Reynolds number Sref = reference area T = torque u = circumferential velocity V = airspeed α = velocity ratio, α = u/V ρ = air density ω = angular velocity


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I. Introduction

USTAV Magnus was a Professor of Physics at the University of Berlin during the years 1834 to 1869. His prominent experiment was conducted in 1852. It consisted of a brass cylinder held between two conical

bearings to which he could impart a high speed of rotation by means of a string. He mounted the cylinder upon a freely rotatable arm and directed a current of air from a blower towards it. When the cylinder revolved, he noticed a strong lateral deviation. The spinning body always tended to deflect towards the side of the rotor that was traveling in the same direction as the wind coming from the blower. However, the magnitude of the deflecting forces was not measured by Magnus at that time.1 This aerodynamic characteristic is called Magnus effect and today is well known for its influence on the flight path of a spinning ball. Besides ball games, the method of producing a lift force by spinning a body of revolution in cross-flow was not used in any kind of commercial application until the year 1924. Anton Flettner made the most notable attempt to use the high lift forces obtainable on a spinning cylinder in an airstream. Flettner consulted with Ludwig Prandtl and the Göttingen research group (Jakob Ackeret, Albert Betz, Carl Wieselsberger et al.) on the idea of replacing the sail of a vessel with rotors. The power to drive these rotors was a small fraction of the power required for the conventional screw propulsion, in order to achieve the same sailing speed. And in cross wind, the Magnus effect would produce a thrust many times that for an equivalent sail surface. Ackeret2 conducted a series of wind tunnel tests on cylinders with endplates. These tests indicated that the method was feasible. The idea of applying endplates to the rotors was born by Prandtl.3 The effect of endplates resulted in a lift force twice as strong. Flettner built a full size rotor ship, which was tested in adverse weather without breakdown. Moreover, a comparatively small heeling was reported, affirming Flettner’s assumption that the magnitude of the aerodynamic forces will level off above a critical wind speed (Fig. 1).4 The reason for this

phenomenon is found in the dependence of the aerodynamic coefficients on the airspeed. With increasing airspeed, the velocity ratio α between circumferential velocity und airspeed decreases and hence the coefficients accordingly, in particular the lift coefficient. Although this propulsion system was quite inexpensive for ships, the speed and reliability of the conventional screw propulsion was more than competitive. The Flettner rotor technology disappeared after a few years of operation. Newspapers reported on a rotor plane, which was developed in secrecy in New York in 1930.5-7 The owner of this airplane with the registration number 921-V was Edward F. Zaparka. He is the inventor of Magnus effect related devices and their application in airplanes, which were granted several patents. This rotor plane was manufactured by the Plymouth Development Corporation in New York. It was powered by a 165 hp Wright motor and equipped with an additional 90 hp American Cirrus motor to drive the cylinders.

II. Background information The analysis of existing small UAV and MAV designs reveals a trend of rapidly decreasing payload weight with

decreasing size.8 Power and propulsion begin to dominate the weight budget for smaller vehicles. Mission capabilities are generally proportional to payload carrying capacity. One of the ideas to enhance payload weight is to generate lift by a rotating cylinder (CL > 10 have been measured in wind tunnel tests). However, a rotating cylinder or a Magnus rotor in general requires additional power to drive. Such a driving mechanism always comes along with additional weight, compared to a conventional wing. Conceptual design studies and extensive wind tunnel tests have been performed recently by Badalamenti, which reveal the specific challenges in rotor airplane design.9 This contribution provides evidence that the design, development, and operation of a Micro Air Vehicle lifted by a Magnus rotor is feasible.

G

5000

3000

4000

2000

1000

tota

l for

ce, k

g

0 10 20 30 wind speed, m/s

Figure 1. Characteristic of a Magnus rotor as predicted and reported by Flettner.4 The increase of the aerodynamic total force with increasing dynamic pressure at a constant rotor speed will diminish above a critical wind speed.


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The aerodynamic fundamentals of a Magnus rotor are different from those of an airfoil. First of all, the

magnitude of the lift and drag coefficients is dependent on the velocity ratio α, which is the fraction of the circumferential speed u of the rotor to the airspeed V (see Fig. 2). Furthermore, there exists no stall which is typical for wings, but there is a similar phenomenon, called the Negative Magnus Force, which is explained in detail in Swanson's review paper.10 At low Reynolds numbers and velocity ratios, the lift vector is opposed to the usual direction, i.e. downwards. This condition is met for MAV at high-speed flight.

The aerodynamic forces and torque can be calculated according to Eq. (1-3). The torque equation and the torque coefficient (CT = 1.2) are derived by Thom.11,12

refL SVcL ⋅⋅⋅= 2

2ρ

(1)

refD SVcD ⋅⋅⋅= 2

2ρ

(2)

3dlVncT T ⋅⋅⋅⋅⋅= ρ (3)

Depending on its design, the Magnus rotor must revolve at high speed to produce sufficient lift. Therefore the gyroscopic effects such as precession and nutation have to be taken into account. Potts' review13 on air vehicles with circular planform (disk-wings) provides an analysis of the effect of gyroscopic forces on the flight dynamics of a spinning disc-wing. Such Frisbee-like air vehicles are typically unstable in the pitch axis and must be inertially stabilized by spinning. If the disk is rotating, gyroscopic effects dictate that this pitching moment results in a rolling rate. For a disk rotating in the direction of positive yaw, a positive pitching moment will generate a negative roll rate (see Eq. (4) and Fig. 3).

zzzIMpω

−= (4)

Figure 2. Lift and Drag coefficients of a Magnus rotor with spanwise disks (Thom-Rotor). Data from Thom11 measured at Re = 10,000 for a rotor with a diameter ratio de/d = 3. Maximum L/D is assumed in the range α = 3.5-4.5.


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Izz, ωz

p

M flight direction

Figure 3. Definition of the body fixed axis system of a disk-wing.

0 5 10 15 20 25 30

1

2

3

4

5

Mass, gram

Rotor model Wing model

propulsion

avionics

landing gear

fuselage

lifting device

Figure 6. Mass distribution of both airplane models, the Wing model Ember and Rotor model Spicy.

The induced roll rate p, as given in Eq. (4), is proportional to the magnitude of the aerodynamic pitching moment M, but it is inversely proportional to the angular momentum of the rotating disk Izz ωz. This knowledge on precession translated to the flight dynamics of an air vehicle equipped with rotating cylinders leads for example to a yawing motion, if a rolling moment was induced. At fast rotation this precession occurs very slowly. An example for a successful usage of gyroscopic forces is the VTOL concept proposed by Gress,14 which already uses precession for flight control.

III. Aircraft Design

Selection of the configuration The only design objective of the MAV was to make it fly. It was decided to modify a commercial Slow Flyer

(Parkzone Ember, Fig. 4) instead of building a new model from scratch. The design goal was to keep all existing parts of the Slow Flyer, except the wing.

It was obvious that all

modifications would result in increased total weight. So it was decided to moderately reduce the wing reference area, even if the Magnus effect was expected to provide much more lift than necessary. The reference area for the rotors was defined as 75% of the wing area. The rotor dimensions were defined accordingly, leading to a length of 25 cm for each cylinder, resulting in a span of 58 cm, and a rotor diameter of 6 cm (Fig. 5). A test series of different Magnus rotors and different plate sizes was performed, in order to optimize the rotor for minimum drag. The best solution was a Thom rotor with multiple disks.

Figure 4. The reference model Parkzone Ember. Courtesy of Parkzone

Figure 5. The Author's Remotely Piloted Aircraft Spicy (Spinning cylinder). This model is based on a Magnus rotor with spanwise disks (Thom rotor)


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1 10 100 1000

critical Reynolds number

airspeed [m/s]

cylin

der d

iam

eter

[m]

10

1

0.1

0.01

laminar flow

turbulent flow

MAV

Figure 7. Diagram showing the critical Reynolds number area for different cylinder diameters and airspeeds (at sea level).

Modifications Some structural modifications had to be made to mount the rotor system and to deal with the increased weight.

The two rotors are mounted on a cantilever attachment and connected to the gearbox, which increases the torque of the electric motor and adjusts the rotor speed as required. The mass distribution is given in Fig. 6, showing the weight increments of all components. The weight of the rotor system turned out to be four times higher than the wing, requiring a more robust landing gear. A more powerful electric motor was installed for propulsion because of the higher drag of the rotors. A little increment of the fuselage weight resulted from a larger vertical tail, which was necessary for controllability. This mass breakdown clearly demonstrates that the design goal of replacing a wing merely by a Magnus rotor could not be achieved.

Rotor related considerations At first, the aspect ratio for each rotor was selected to A = 4. In order to fly at minimum drag, the design point

was set to a velocity ratio α = 3.5. The final rotor model weight was estimated at 0.05 kg. Based on the desired airspeed of 2.2 m/s, the peripheral speed was calculated to u = 8 m/s. The reference area of both rotors was calculated with Eq. (5) for a lift coefficient CL = 5.1, which corresponds to α = 3.5 (see Fig. 2.). Following this, the dimensions of each rotor were set to a diameter of 0.06 m and a length of 0.25 m.

2

2VC

gWSL

ref

⋅⋅

⋅=

ρ (5)

For a rotor speed of 2300 rpm and a cruise speed of 2.2 m/s the power consumption of the rotor was calculated to P = 4 W, according to Eq. (3) and (6).

nTP ⋅⋅= π2 (6)

Each rotor was equipped with disks of the size de/d = 3 and a disk spacing of ds/d = 1.5. In 1934, Thom11 conducted experiments with a rotor of the same characteristics and achieved a maximum aerodynamic efficiency of

L/D = 22. Finally, the wing loading of the Author's rotor model Spicy was three times higher than that of Ember (1.5 instead of 0.5 kg/m²).

The center of gravity position should be selected close to the rotor axis. A position slightly aft is recommended to compensate the pitch down moment resulting from the rotor’s aerodynamic torque. A rotor airplane is very sensitive to a lateral displacement of the center of gravity position, which would result in a yawing motion, due to the gyroscopic forces of a fast spinning rotor.

Today, there are no specific methods

available on how to design the lifting device of a rotor airplane or its airframe according to the requirements. Therefore, the fundamentals of aircraft conceptual design have to be tailored for rotor airplanes. New design methods and charts, which show for example the operating points of a rotor airplane during a flight mission, were required. They are presented here.


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Figure 8. Design chart. This chart presents operating points at two different load factors nz.

One critical issue the designer has to take into account is the Negative Magnus Force, especially in the case of

Micro Aerial Vehicles. This effect originates in the boundary layer of the rotor, and develops when the separation point on the upper side moves forward, resulting in an upward deflection of the air stream.

With increasing airspeed, the rotational speed is typically reduced to adjust the lift produced at higher dynamic pressure. Below a velocity ratio α < 0.2, the Negative Magnus Force may appear, if the Reynolds number is in the critical range between 99k < Re < 501k. In Fig. 7, the critical flight condition is presented for the MAV, whose Magnus rotor has a diameter of d = 0.06 m. The MAV takes off at an airspeed of V = 2 m/s and theoretically enters the critical range at approximately 20 m/s with a velocity ratio α < 0.2. The MAV investigated here, however, is not capable to fly this fast.

A design chart is given in Fig. 8, where the rotational speed u and n of a Magnus rotor is plotted over airspeed V. The rotational speed is given in m/s (left ordinate) and rpm (right ordinate). The design chart can be interpreted as follows: The rotor airplane accelerates from standstill (0) to take off speed with a constant spinning rate of 3000 rpm. It takes off with a load factor nz > 1 (1). After a short climb segment the flight path levels off with nz = 1. The flight speed increases further from 2 m/s to 6 m/s in horizontal flight, so that the velocity ratio has to be decreased in order to keep the lift constant (2). The rotor airplane then makes a turn at constant nz = 2 (which translates to a bank angle of 60 deg) and increases the rotational speed and therefore the velocity ratio to attain more lift (3). Having completed the turn, the rotor airplane levels off at nz = 1 (4). In this way the operating points of the rest of the flight can be interpreted accordingly.

Different velocity ratios α = 0.1 to α = 3.5 are additionally marked in the design chart. These lines of constant α are useful for selecting the design point of a rotor airplane. As example, the design point at maximum lift to drag ratio (in this example at α = 3.5) is given in Fig. 8.


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Figure 9. State space model of lateral directional motion. The derivates Nr, Np, Lr, and Lp had to be adapted to account for gyroscopic forces.

IV. Results

A. Flight Mechanical Analysis (lateral directional motion) The equations of lateral directional motion have been developed for a MAV comprising a Magnus rotor to take

the gyroscopic forces into account. A flight mechanical analysis was made on the basis of a standard state space model of lateral motion, which is given in Fig. 9. All modified derivatives are highlighted.

As there was no aerodynamic dataset for the entire airplane available, this analysis was limited to a Magnus rotor

alone. The extended rolling and yawing moment derivatives are given in Fig. 10. All parameters describing the gyroscopic effects are listed in the second term. The rotational speed of a Magnus rotor is named ωy,zyl. The first term, which describes the aerodynamic influence on the airplane motion, was disregarded at first.

The results of a 3-degree-of-freedom simulation of a Magnus rotor spinning at 2500 rpm are given in Fig. 11. The response of a theoretical aileron step input is printed in the left column and the response of a rudder step input is given in the right column. The diagrams show that the aileron input has a major influence on the yawing motion, and the rudder has a major influence on the rolling motion at high spinning velocities. Further investigations on the flight dynamics of a rotor airplane were performed recently by de Vautibault,15 who provides a broader insight to controllability and stability in lateral motion.

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Figure 10. Lateral directional derivatives


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B. Flight Test Flight experiments were conducted with the rotor model Spicy (see Fig. 5). Two rotating cylinders made of paper sheets with spanwise disks were mounted on a commercial slow flyer model (see Fig. 4), replacing the conventional wings.

The total weight of Spicy is 50 g and its reference area Sref = 0.03 m2, which is 25% less than the Sref = 0.04 m2 of Ember. More technical data is given in Table 1. A conventional rudder provides lateral control, and the variable cylinder speed provides longitudinal control. The flight envelope is within the laminar flow regime. Table 1. Technical data (Spicy) Weight 0.050 kg Total span 0.58 m Diameter 0.06 m Wing loading 1.5 kg/m² Rotor speed (max) 3000 rpm Propeller speed (max) 8500 rpm Rotor Power consumption 4 W (at 2300 rpm) Propulsive Power consumption 4 W (static)

The vehicle’s attitude is directly controlled by a conventional tail, which is providing a rudder and an elevator.

The size of the rudder had to be enlarged to achieve sufficient roll rates. The propulsion is of conventional type. An electric motor drives a two bladed propeller. The rotational speed is regulated with an electronic controller. The pilot is able to give yaw and pitch commands, as well as to adjust the rotary speed of the propeller and the two interconnected Magnus rotors.

The lifting force of the Magnus rotors is independent from the angle of attack, but can be changed with rotational speed of the rotor. The effect of a pitch command is in this case reduced to a pure thrust vector control without a change in the lifting force. A flare maneuver for landing has to be initiated by an increased rotor speed for a reduced glide path angle, in combination with a nose up command for attitude control.

The ground operation with the rudder turned out to be easy as long as the rotors were rotating at low speed, but became critical with increasing rotor speed, due to precession. In the worst case no yawing motion was achieved by a fully deflected rudder. Hence, the rotor model was hand launched. 19. M‰rz 2010 5

STEP PLOT

Figure 11. Simulation of the lateral motion of a rotating cylinder in forward flight. The response is given in rad/s after a step input from aileron or rudder.


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Multiple flights of this rotor model proved the applicability of rotating cylinders to small airplanes. However, many issues such as design optimization and flight control design require further research. A short video is available on the author’s website†, showing a controlled flight after hand launch.

One unique feature of every Magnus rotor was tested: The inability to stall. The rotor model was dropped with spinning cylinders but without any forward motion and instantly recovered flight within an altitude loss of 1 m.

As the rotor model lacks ailerons for roll and respectively yaw control, the precession effect of an induced rolling moment to a negative yawing motion could not be tested.

V. Conclusion and Outlook The aim of this study was to demonstrate the feasibility of using a rotating circular cylinder (Magnus rotor) as

the primary means of generating lift for flight, at a small scale on a miniature unmanned aircraft known as MAV. Successful application of rotating cylinders to MAV design can provide benefits by taking advantage of the large lift force generated by the rotating cylinder to increase the payload capacity of such a small airplane.

The key findings from the investigation of the design and test of a MAV lifted by a Magnus rotor are as follows: 1) A MAV of 50 g weight and 0.58 m span with a general configuration of twin cylinders about a central fuselage

was proven to be feasible. 2) A Magnus rotor with spanwise disks provides higher efficiency compared to a rotor with endplates only. 3) Gyroscopic forces have a major impact on the flying characteristics and hence must be accounted for in flight

control design. 4) Due to its lifting capabilities, a rotor airplane is well suited, if a heavy payload or small dimensions are required.

Recent research projects demonstrated a tethered flight of an unmanned air vehicle, propelled by a cycloidal blade system.16 Lightweight structures and high performance electric motors were used to hover in ground effect. The propulsive efficiency should be increased in the future to realize a fast forward flight and to carry additional payload. One favorable solution is presented by the author, which is able to provide thrust, lift and control power.17 It is a propulsion and lifting device with 360 degree thrust vector control. The Hybrid Rotor, as proposed by the author, is presented in Fig. 12.

It is a combination of two known devices for cruise flight – a propulsion system such as the cycloidal propeller

and an additional lift-generating device such as a rotating cylinder. A rotating cylinder is like a wing without control surfaces. For application in aeronautics, control devices are essential for flight. Aerodynamic analyses were performed to study the flow characteristics and to calculate forces and moments in cruise flight and hovering.18 A MAV design using the Hybrid Rotor is currently under investigation.19

† www.rotorflugzeug.de

Figure 12. Picture of a Hybrid Rotor model and a proposal for an adequate rotor airplane. The patent-registered Hybrid Rotor is a combination of a cycloidal propeller and a Magnus rotor.


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References

1Magnus, H. G., "Ueber die Abweichung der Geschosse, und: Ueber eine auffallende Erscheinung bei rotirenden Körpern" (On the deviation of projectiles, and: On a sinking phenomenon among rotating bodies), Annalen der Physik, vol. 164, no. 1, 1853, pp. 1-29.

2Ackeret J., "Neuere Untersuchungen der Aerodynamischen Versuchsanstalt," Zeitschrift für Flugtechnik und Motor-Luftschiffahrt, Göttingen, Vol.16, No.52, 1925.

3Wagner, C. D., Die Segelmaschine, Kabel Verlag, Hamburg, 1991. 4Flettner A., Mein Weg zum Rotor, Koehler & Amelang, Leipzig, 1926. 5Kieran, L. A., "Rotor Plane may open New Vista to Aircraft," The New York Times, August 24, 1930, p. 5. 6"Rotor Aircraft, wingless, is tested," The New York Times, August 20, 1930, p. 3. 7"Latest in Flying Ships - Plane Without Wings," The Washington Times, August 21, 1930. 8Coffey, T., and Montgomery, J. A., "The Emergence of Mini UAVs for Military Applications," Defense Horizons, Vol. 22,

2002, pp. 1-8. 9Badalamenti, C., "On the Application of Rotating Cylinders to Micro Air Vehicles," Ph. D. Dissertation, School of

Engineering and Mathematical Sciences, City University, London, 2010. 10Swanson, W. M., "The Magnus Effect: A summary of investigations to Date," Journal of Basic Engineering Transactions

of ASME, Vol. 83, No. 3, 1961, pp. 461-470. 11Thom A., "Effect of Discs on the Air Forces on a Rotating Cylinder," Aeronautical Research Committee, Reports and

Memoranda, 1934. 12Thom A., Sengupta SR., "Air Torque on a Cylinder Rotating in an Air Stream," Aeronautical Research Committee, Reports

and Memoranda No. 1520, 1932. 13Potts, J. R., and Crowther, W. J., "Flight Control of a spin stabilised axi-symmetric disc-wing," AIAA Aerospace Sciences

Meeting, AIAA, Reno, 2001. 14Gress, G. R., "Lift Fans as Gyroscopes for Controlling Compact VTOL Air Vehicles: Overview and Development Status of

Oblique Active Tilting," American Helicopter Society 63rd Annual Forum, American Helicopter Society International, Virginia Beach, 2007.

15de Vautibault, H., "Flight Dynamics Analysis of a Rotor-Plane," Diploma thesis, Lehrstuhl für Flugsystemdynamik, Technische Universität München, 2010.

16Hwang, I. S., Min, S. Y., Lee, C. H., and Kim, S. J., "Development of a Four-Rotor Cyclocopter," J Aircraft, Vol. 45, No. 6, 2008, pp. 2151-2157. doi: 10.2514/1.35575.

17Seifert, J., German Patent for "Fluggerät mit rotierenden Zylindern zur Erzeugung von Auftrieb und/oder Vortrieb," DE102007009951B3, filed 31.07.2008.

18Seifert, J., "Aerodynamic Analysis of a new Hybrid Rotor," Deutscher Luft- und Raumfahrt Kongress, DGLR, Aachen, 2009.

19Neppl, Ch., "Konstruktive Auslegung eines kurzstartfähigen unbemannten Luftfahrzeugs mit alternativem Rotorsystem", Master thesis, Technische Universität München, 2010.

micro air vehicle lifted by a magnus rotor a proof of · pdf filemeasured by magnus at that...

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