Engineering Flettner Rotors to Increase Propulsion Author: Chance D. Messer Mentor: Jeffery R. Wehr Date: April 11, 2016 Advanced STEM Research Laboratory, Odessa High School, 107 E 4 th Avenue, Odessa WA 99159 Email: messerchance@gmail.com School Phone: 509-982-2111 ext. 214 Key Words: Flettner rotors, Magnus effect, Propulsion ABSTRACT Flettner rotors use the Magnus effect to propel objects forward by creating a vortex of rotating air about itself. The air gets pulled along the rotating cylinder creating low pressure, and on the opposite side, a higher pressure is created, thus propelling the boat forward. This effect is also the lateral force that acts on a rotating circular cylinder, the axis of which is perpendicular to the flow. Two Flettner rotors, 21.0 cm by 3.0 cm, were 3-D printed and attached to a boat 27.8 cm by 23.0 cm. Attached to the boat, a motor was used to acquire a control velocity. Two control groups were created. One control group had no wind and the other had wind blowing on the nonrotating rotors. The experimental group had wind blowing on the rotating rotors. The average velocity of the control group with wind was 8.7 cm/s (±1.01 cm/s) and without wind was 12.35 cm/s (±0.77 cm/s). The average velocity of the experimental group was 14.97 cm/s (±0.98 cm/s). The results revealed an increase in velocity of 42% from the control group to the experimental group when the engineering goal only required a 15% velocity increase. Both control groups were compared to the experimental group and were found to be statistically different. Future plans for this project include a rotating platform for the rotors to utilize every wind direction. INTRODUCTION Flettner rotors use the Magnus effect to propel objects forward by creating a vortex of rotating air about itself. The air gets pulled along the rotating cylinder creating low pressure, and on the opposite side, a higher pressure is created, thus propelling the boat forward. On the opposite side, where the motions are opposed, the velocity is increased [1] (Figure 1a). This effect is also the lateral force that acts on a rotating circular cylinder, the axis of which is perpendicular to the flow [2]. The Magnus effect provides a moving wall on its body to influence the boundary layer around the device, in order to produce a lifting force perpendicular to the flow direction. Flow control is also possible by placing rotating cylinders, spinning at constant rate, at appropriate locations in the flow [3].
Anton Flettner invented the Flettner Rotor in the 1920s as an extremely effective method of reducing fuel cost while increasing ship stability and passage times for commercial blue water shipping [4]. The effect of the Flettner rotor cannot be explained in accordance with the prevailing views on wind pressure, although it is claimed to exert as much force as a sail having 10-15 times as large a frontal area [5]. The rotors also have numerous advantages over conventional wind-driven propulsion, being only one quarter of the weight of the masts, sails and rigging they replaced and permitting the vessel to make more rapid progress over a wide range of wind speeds and directions than conventional sails [6] (Figure 1b) A sail would have to be moved to accommodate for the wind angle while the Flettner rotor would not have to be moved. Since the 1980s, CO 2 international shipping emissions have more than doubled between 1979 and 2009 [7]. The velocities of the trade winds at the earth surface amount to 5-8 m/s on the average [8]. Applying Flettner rotors to a typical bulk carrier equipped with three Flettner rotors making a round voyage on the route suggests possible fuel savings of 16% [9]. Faster air creates a lower pressure Crosswind Direction of lift Spinning Cylinder Direction of the flow Boat Flettner Rotor Direction of lift Turbulence Direction of rotation Slower air creates a higher pressure Figure 1a The Magnus effect occurs when airflow is pulled around a rotating cylinder creating lift perpendicular to the flow. Figure 1b Flettner rotors use the Magnus effect for propulsion. The direction of the lift is perpendicular to the wind direction.
The engineering goal of this experiment was to create Flettner rotors that would be placed on a boat to increase its propulsion by 15%. If the propulsion is increased, travel times would be decreased, therefore decreasing fuel emissions. The analysis included comparing the velocity of the ship before and after adding the Flettner rotor equipment, the velocity of each group with and without wind, the electrical efficiency of the rotors, and the force lift of each rotor. MATERIALS AND METHODS Two Flettner rotors were designed and engineered using 3-D modeling software to create two ABS plastic cylinders 21 cm tall x 3 cm wide (Figure 2). The cylinders were attached to a 12 volt motor that spun at 12,796 rpm. This process was repeated to make a second Flettner rotor. The rpm of the Flettner rotors was found using a photogate and a laser. Figure 2 The design of one Flettner rotor using a 3-D modeling program.
Both of the rotors were attached to a boat 23 cm wide x 28 cm long on a platform 4.5 cm tall. The rotors were placed 6 cm apart using a DC motor and a gear system to spin both of the rotors at 12,796 rpm (Figure 3). The two Flettner rotors were attached 6 cm apart in the center of the boat. An additional 1.5 volt motor with a plastic propeller was attached to the back of the boat like a standard boat. With the Flettner rotor equipment, the boat weighed 991 grams. Without the Flettner rotor equipment, the boat weighed 538 grams. Figure 3 The gear system with a DC motor to spin the Flettner rotors. The boat was then placed in a pool of water 80 cm long 36.5 cm wide and 4 cm deep to simulate a large body of water (Figure 4). Eighteen ceramic ring magnets 3.2 cm in diameter were placed on both sides of the pool of water 2.7 cm apart (Figure 5). Eight of the same magnets were attached to both sides of the boat with the same poles facing each other, to repel the boat away from the sides of the pool to reduce friction. Figure 4 Pool of water used to obtain each trial. Figure 5 Ceramic ring magnets that were screwed onto the sides of the pool of water and the sides of the boat.
The force lift on a rotating cylinder formula was used to calculate the force lift (F) per unit length (L): F L = pgv [1] where G represents the strength of the vortex in m 2 /s, p represents the air density in kg/m 3, and v represents the velocity of the wind in m/s. The strength of the vortex was calculated using equation 2: [2] G = (2πr) 2 S where r equals the radius of the cylinder in centimeters and S equals the rotations of the Flettner rotors per second. The electrical efficiency of the Flettner rotors was also calculated using the formula: n = ( P out P in ) 100% [3] where n equals the electrical efficiency, P out equals the useful power output in watts, and P in equals the power input in watts. The power input was calculated using the formula: P in = VI [4] where V is the voltage in volts and I is the current in amps. To calculate the power output, the formula was used: P out = ( 2π 60 )Ta [5] where T is torque in Newton meters and a is the angular acceleration in RPM/second. To find the torque, the formula was used: T Ia [6]
where I equals the moment of inertia in kg*m 2 and a equals the angular acceleration in RPM/second. The moment of inertia is found using this formula: I = 1 2 MR2 [7] where M equals the mass of the Flettner rotor in kg and R equals its radius in meters. The average angular acceleration was calculated using the formula: a = W t [8] Where W equals the angular velocity of the Flettner rotor and t equals the change in time it took for the boat to reach the end of the pool of water. Each of the Flettner rotors created 1.652 N of lift for a total of 3.304 N of lift for both rotors. The rotors spun at an 89.2% electrical efficiency. To collect the experimental group data, a fan was placed on a cart 30 cm away from the boat set on high at 3.5 m/s after the Flettner rotors started spinning. A timer was started when the fan and back motor were turned on and stopped when the boat hit the end of the pool of water. This process was repeated 29 times for a total of 30 trials. An additional 30 trials were ran without the Flettner rotors, with wind, and without wind to get two control times. With the distance and the time it took to travel the pool, the velocity was found and all groups were compared using a two-tailed t-test. RESULTS The average velocity of the control group (with motor and no wind) was 12.35 cm/s (±0.77 cm/s) while the average velocity of the experimental group (with rotors, motor, and wind) was 14.97 cm/s (±1.01 cm/s). The average velocity of the second control group (with motor and
wind) was 8.7 cm/s (±0.98 cm/s). The average velocity of the boat without Flettner rotors attached was 6.48 cm/s (± 0.60 cm/s) (Table 1). The standard deviation of the control group (with motor and no wind) was ±0.77 cm/s. The standard deviation of the second control group (with motor and wind) was ±0.98 cm/s. The standard deviation of the experimental group (with rotors, motor, and wind) was ±1.01 cm/s. When running a velocity-weight analysis by using the ratio between the weight and the velocity of the boat, the control group had a 0.24 m/s per kg ratio while the experimental group had a 0.15 m/s per kg ratio. Table 1 Motor No Rotor- No Wind Motor No Rotor Wind (350 cm/s) Motor Rotor Assist Wind (350 cm/s) Average Velocity (cm/s) Standard Deviation (±cm/s) # Trials 12.35 0.77 30 8.70 0.98 30 14.97 1.01 30 DISCUSSION The velocity from both of the control groups (motor, with and without wind) and the experimental group (rotors, motor, and wind) was compared using a two-tailed t-test, and there was a statistical difference between them (t=±2.00;p<0.001; df=58). The engineering goal of this project was accepted, the experimental group s velocity Figure 6 The comparison between the average velocities of the control group (with wind) and the experimental group (with wind and rotors) with standard deviation. Figure 7 The comparison between the average velocities of the control group (no wind) and the experimental group (with wind and rotors) with standard deviation.
was greater than both of the control groups, without wind, and with wind, by 17% and 42% respectively (Figure 6 and 7). When comparing velocity of the control group to the boat without Flettner rotors attached, there was no statistical difference between them. The added mass did not impede the velocity of the boat when compared to the boat s velocity with no Flettner rotor equipment. In the next phase of research, the design of the boat will be altered to find the ideal design to achieve the highest velocity possible. More rotors will be added to find the amount of velocity increase per rotor. The rotation speed of the rotors will be increased to calculate the increased lift produced by the rotors. The amount of space in between each rotor will be widened and slimmed down to determine the optimal distance between them that creates the maximum lift.
REFERENCES & LITERATURE CITED 1. Nuttall P, and Kaitu u J. (2013) The Magnus Effect and the Flettner Rotor: potential application for future oceanic shipping. Journal of Pacific Studies, pp 1. 2. Briggs LJ. (1959) Effect of spin and speed on the lateral deflection (curve) of a baseball; and the Magnus effect for smooth spheres. Am. J. Phys 27, 8, pp 1. 3. Tanaka H, and Nagano S. (1973) Study of flow around a rotating circular cylinder. Bulletin of JSME 16, 92: pp 234-243. 4. Seifert J. (2012) A review of the Magnus effect in aeronautics. Progress in Aerospace Sciences, 55: pp 17-45. 5. Mittal S, Kumar B. (2003) Flow past a rotating cylinder. Journal of Fluid Mechanics, 476: pp 303-334. 6. Prandtl L. (1926) Application of the Magnus Effect to the wind propulsion of ships. National Advisory Committee for Aeronautics. Technical Memorandum, 367, pp 2. 7. Craft TJ, Iacovides H, and Launder BE. (2011) Dynamic performance of Flettner rotors with and without Thom discs. In Proc. 7 th Symp. on Turbulence & Shear Flow Phenomena, pp 1. 8. Traut M, et al.(2014) Propulsive power contribution of a kite and a Flettner rotor on selected shipping routes. Applied Energy, 113, pp 2. 9. Zeńczak W. (2012) The selected methods of utilizing the wind power as the auxiliary source of energy on diesel engine powered ships. Journal of Polish CIMAC, 7, 1: pp 305-314.