Practical Training Report Submitted by Kailash Kotwani Under guidance of Professor S K Sane and Dr. Hemendra Arya

Transcription

1 Propeller Characterization Practical Training Report Submitted by Kailash Kotwani Under guidance of Professor S K Sane and Dr. Hemendra Arya Center for Aerospace System and Design Engineering Department of Aerospace Engineering Indian Institute of Technology, Bombay August,

2 Abstract Selecting correct combination of engine and propeller is very crucial step in design of any airworthy vehicle. Whether the output power produced by selected engine propeller combination will be sufficient enough to provide esteemed mission requirements, is the chief question in front of any design engineer. Power vs Velocity and Thrust vs Velocity characteristics are very important for the design purpose. The information regarding these characteristics is not available in open literature for small propellers and engines used for MAVs. The objective of present study is to establish a measurement system and obtain performance maps for mini propellers and small engines. To reduce the efforts involved and widen the range of analysis, the characteristics are studied using non-dimensional parameters (C P, C T, J etc). Another important aspect is optimizing performance by selecting propeller of best efficiency in the required velocity ranges. These characteristics are determined experimentally using the wind tunnel system built for the MAV development purpose. Different engine-propeller combinations are tested in wind tunnel at different flow velocities. Required plots are generated using data obtained from experiments. Nomenclature A = Area (m 2 ) c = Chord Length (m) C P = Coefficient of Power C T = Coefficient of Thrust C Q = Coefficient of Torque d = Diameter (inch/m) D = Drag (N)/Diameter (inch/m) E b = Back EMF (V) I = Current Supplied (A) J = Advance Ratio K = DC motor constant L = Lift (N) N = RPM (1/min) n = RPS or Rotational frequency (1/s) P = Power (W) p = pitch (inch) P I = Input Power (W) P o = Output Power (W) P A = Net or Useful power for thrust production (W) Q = Torque (N.m) r = radius (inch/m) R a = Armature Resistance (Ω) T = Thrust (N) T A = Thrust Available (N) 2

3 V = Voltage Across motor (V)/Flow Velocity (m/s) V R = Resultant flow Velocity (m/s) V = Translational Velocity Component (Upstream flow velocity) (m/s) V r = Rotational Velocity Component (m/s) η x = Efficiency of x ϕ = DC motor flux β = Pitch angle or angle of airfoil with plane of rotation (radian/degree) ω = Rotational Velocity (rad/s) φ = Angle to direction of motion to which V R acts (radian/degree) α = Angle of attack of airfoil (radian/degree) Contents Abstract Nomenclature Contents 1. Introduction 2. Theory and background 3. Operation Limitations 3.1 Motor Operating Limiations 3.2 Propeller Operating Limitations 4. Experiment to determine NO LOAD characteristics of Motor 4.1 Apparatus 4.2 Theory 4.3 Set Up Description and Measurements4.4 Observation: 4.5 Calculations and Analysis 4.6 Conclusions 5. Experiment to predict the shaft power of DC motor 5.1 Apparatus 5.2 Theory 5.3 Experimental Set-up and description 5.4 Observations 5.5 Calculation and Analysis 6. Discussion and Further work References Appendix A) Motor Specifications B) Observation and Calculation tables C) Matlab Codes Acknowledgement 3

4 1. Introduction Because of Simplicity, efficiency and cost effectiveness, propeller based IC engines are the best choice as means for thrust production at the first stage of developing a MAV (Mini aerial Vehicle). Thrust and Power generated by a propeller is function of propeller geometry (This include pitch, diameter, airfoil sections at different crossections, weight, no. of blades etc.), flow velocity, RPM and torque applied by the shaft of engine. The MAV being developed will encounter flow velocities in the range of 20 m/s. A wind tunnel system (test section of crossection 1mX1m) has been developed which can generate flow velocities up to 10 m/s (Image 1). In future it will be upgraded to generate velocities in the range of 20 to 25 m/s. So with present system experiments have been conducted upto the velocity of 10 m/s only. Image 1: Wind Tunnel for experimentation on MAV As running an IC engine inside the tunnel involves many complexities e.g. starting trouble, oil in exhaust, variable RPM at constant fuel supply etc. So it was decided to use an electric DC motor for experimentation purpose which is very easy to handle though an IC engine will be used for onboard flights. Here an Astro 15 Cobalt Geared Motor (Model no. p/n 615G) was used for experimentation. Motor is shown in Image 2 and its specifications are given in appendix (A). 4

5 Image 2: Cobalt Geared DC Motor There are two methods by which power at the shaft of motor can be estimated 1) Determining No load characteristics then assuming that Back EMF vs RPM characteristics and Mechanical Losses at No Load and Loaded conditions are same. 2) Directly measuring torque at the shaft using torque sensor The task of power measurement using first method has been completed till now (With an 11X7 Masterscrew glass filled nylon propeller) and is discussed in this section. In this method first armature resistance of motor is measured by short-circuiting it at the supply of very low current and voltage (Armature Resistance is measured at beginning and at the end of experiment because it is sensitive to temperature of motor which varies during the operation). Motor is run under No Load condition (No propeller at the shaft) and input power consumption at different RPM is measured. Hence back EMF and mechanical losses are calculated using theoretical relationship. Again motor is run at loaded condition and Input power consumption is measured at different RPM. Using no load characteristics of back EMF and mechanical losses, shaft power is calculated. This way we obtain Shaft Power vs RPM characteristics. Experiment under Loaded condition is repeated for different flow velocities in wind tunnel and corresponding C P vs J plot is obtained. Shaft Power vs RPM plot at different flow velocities is cross-plotted to obtain Shaft power vs flow velocity plot at different RPM. All these characteristics are analyzed carefully and compared with ones available in literature for larger propeller. 5

6 2. Theory and Background Similar to wings propellers are made up of airfoil sections designed to generate an aerodynamic force. The wing force provides lift to sustain the airplane in the air; the propeller force provides thrust to push the airplane through the air. A sketch of a simple three-blade propeller is given in Fig 1, illustrating that a cross section is indeed an airfoil shape. However, unlike a wing, where the chord lines of the airfoil sections are essentially all in the same direction, a propeller is twisted such that the chord line changes angle from root at prop-hub to tip. This is illustrated in Fig 2, which shows a side view of the propeller, as well as two sectional views, one at the tip and the other at the root. The angle between the chord line and the propeller s plane of rotation is defined as the pitch angle β. The distance from root to given section is r. Note that β = β(r). 1 Fig 1: Crossection of a three bladed propeller 1 Fig. 2: Varying pitch angle along the span of propeller 1 6

7 2 2 R V V r V = + (1) Where V is the translational velocity component and V r is the rotational component. This resultant V R acts at a certain angle φ to the plane of rotation, and this angle is defined as V V V tanφ = = = (2) Vr rω 2πrn The airflow seen by a given propeller is combination of the airplane s forward motion and the rotation of the propeller itself. This is sketched in Fig. 3a, where the airplane s relative wind is V and the speed of the blade section due to rotation of the propeller is rω. Here, ω denotes the angular velocity of the propeller in radians per second. Hence, the relative wind seen by the propeller section is the vector sum of V and rω, as shown in Fig 3b. Fig 3: Resultant local velocity seen by a section of propeller 1 If the chord line of the airfoil section is at an angle of attack α with respect to the local relative wind V R, then lift and drag (Perpendicular and parallel to V R, respectively) are generated. In turn, as shown in Fig. 4, the components of L and D in the direction of V produce a net thrust T: Fig 4: Lift and drag force on an airfoil of a propeller 1 T = L cosφ - D sinφ (3) Where φ = β - α (4) This thrust, when summed over the entire length of the propeller blades, yields the net thrust available. (T A ) which drives the airplane forward. 7

8 as There is one more important parameter, propeller efficiency (η) which is defined PA TA V CT? P = = = J (5) P P CP Where P is power at the shaft of engine, J is advance ratio, C T is thrust coefficient and C P is power coefficient. The advance ratio J, which is a measure of how far the propeller moves forward through the medium per rotation of the propeller, is defined as V J = (6) nd For a propeller the non dimensional thrust coefficient is defined as T C T = (7) ρn 2 D 4 Similarly, Power coefficient is defined as P C P = (8) ρn 3 D 5 A propeller is nomenclatured in terms of two parameters, pitch and diameter. Pitch is defined as the horizontal distance moved by propeller in one complete rotation at 100 % efficiency and zero slipping. So airfoil at particular section of propeller performs motion in helical direction as shown in Fig. 5. If the helix is unwrapped onto a two dimensional plane, the length p is defined geometrically as p = 2πr. tan β (9) Fig. 5: Measuring Pitch of a propeller 4 It should be noted that industry standards are that pitch is measured at 75% of radius that is value of r and β in eqn (9) is what at 75% of radius. 8

9 3 Operation Limitations 3.1 DC Motor Operating Limitation 1) Voltage, Current and Power Limitations Normal voltage range specified = 8 to 12 Volt (Appendix A) Though 12 volt is not maximum upper limit because the same motor has been used with 12 Nicads battery (Expected performance mapping Appendix A) Maximum Applied voltage = 1.2*12=14.4 Volt. For performance mapping manufacturer has crossed 12 Volt, is confirmed from the fact that with 12 Nicads batteries power consumption was 325 Watt at 24 A current supply Applied voltage at that time = 325/24=13.54 Volt Another way to obtain maximum voltage across the motor is through maximum continuous current and power specified by manufacturer Maximum Continuous current = 25 A Maximum Continuous power= 400 W Maximum applied voltage = 400/25 = 16 V This analysis shows that it is not unsafe to run motor between 12 to 16 Volt range. One thing should be kept in mind that in high voltage ranges motor should not be run for longer time as motor becomes too hot. Secondly armature resistance is sensible to temperature of motor. Analysis of manufacturer s specification from three different perspectives is giving three different values of Maximum voltage. This confirms that specification provided by manufacturer is not suitable for engineering analysis and one should develop one s own safeguards and measuring systems for engineering and research analysis. 2) RPM and Torque Limitations This cobalt motor uses a gear for reducing the final RPM at the shaft. Gear Ratio = 2.38 to 1 (Appendix A) Motor Speed/volt = 1488 rpm/volt Geared motor speed/volt = 652 rpm/volt Lets say maximum applied voltage across the motor = 15 V Geared motor speed = 652*15= 9780 rpm Ungeared motor speed = rpm This large ungeared speed can be utilized by taking out gear and using motor directly. Even with gear motor provides decent rpm which is in the range of Similarly, Motor torque/amp = 0.91 in-oz/amp Geared torque/amp = 2.17 in-oz/amp At maximum current = 25 A Geared torque = 0.91*25=22.75 in-oz Ungeared torque = 2.17*25 = in-oz 9

10 3.2 Propeller operating limitations 1) Noise Considerations The prop tip speed should not exceed 600 to 650 feet per second (180 to 200 m/s) to keep it within the noise limit (For a master airscrew nylon prop). 6 Tip Speed = V r (ft/s) = rω = *RPM*(Diameter in Inches) Vr RPM = (10) D Lets Say we take limiting propeller tip speed as 600 ft/s For 11X7 master-airscrew propeller, limiting RPM can be calculated Limiting RPM = 600/( *11) =12510 rpm 2) Mechanical Considerations One of the differences between wood and glass-filled nylon propellers is that glass-filled nylon props have suggested RPM limits for mechanical considerations. This varies according to Diameter of prop. For a Master Airscrew prop RPM limit recommended by manufacturer is calculated as follows. 6 RPM operating limit = 160,000/(Diameter in inches) (11) For a 11X7 prop, RPM operating limit = 160,000/11 = 14,545 rpm Minimum of the above two operating limits will be taken into consideration that is rpm. 10

11 4. Experiment to determine NO LOAD characteristics of Motor The objective of this experiment was 1) To measure the armature resistance of the motor 2) To determine the No Load characteristics of the motor that is obtaining Back EMF vs RPM and Mechanical losses vs RPM characteristics. The above data will be used to predict the shaft power of DC motor. 4.1 Apparatus DC Regulated power supply, DM 20 Multimeter, DC Motor, Optical tachometer. 4.2 Theory Voltage eqn of Motor is given as 2 V = E b + I*R a (12) Multiplying (1) by I V*I = I* E b + I 2 *R a (13) Where, V*I = Input Power I 2 *R a = Electrical losses in armature I* E b = Mechanical power developed Hence eqn (13) can be interpreted as Input power = Mechanical power developed + electrical losses in armature Certain percentage of mechanical power developed is required for supplying iron and friction losses in the motor and rest is available as output to drive the shaft of motor Hence one can write eqn as Input power = V*I= mechanical losses + Electrical losses + output (or net available power at the shaft) (14) Under no load conditions, torque applied at the shaft is zero hence output of motor is zero. That is the total power supplied is used to overcome mechanical and electrical losses only. Output = 0 (under no load conditions) (15) Relationship between speed and back emf of motor is given as 2 E b = N*ϕ/K (16) When RPM is zero back emf is also zero (from (16)). So eqn (13) will become Ra = V/I (17) Using this Ra to calculate back emf for all values of current and voltage. This will enable us to determine characteristic of mechanical losses Vs RPM using eqns (13), (14) and (15). For a constant flux motor back emf is directly proportional to speed of motor (from (16)) 11

12 Hence, E b α RPM This will provide linear relationship between back emf and RPM, which will be used to evaluate back emf under loaded conditions and hence mechanical power developed. Fig. 6: Experiment Set up Image 3: No Load experiment set up 12

13 4.3 Set Up Description and Measurements: Set up is arranged as shown in Fig. 6 and Image 3. Motor at no load is mounted on rigid stand and connected to power supply. Voltmeter is connected to measure the voltage across the motor. A white patch is marked on shaft of motor of measuring RPM using Tachometer. Before switching on power supply it is ensured that voltage and current knobs of supply are at zero. Supply is switched on and voltage and current are increased gradually. For measuring Ra, one has to ensure that motor shaft should not rotate and current is brought in the range of 1 amp. After that voltage is measured in steps of 1 volt and readings of current and RPM are noted down. This is done upto 10 volts. At the end of experiment readings are taken again for measuring Ra. Precautions: 1) Select the proper measurement range of voltmeter for accuracy in results. Select smaller range (i.e. 200 mv or 2 V) for measuring Ra and higher range (20 V) for measuring voltage across the motor. 2) While measuring Ra ensure that shaft of motor is not rotating. Circuit should behave like a short circuit. 3) All electrical devices have transition time for warming up, so after changing any parameter one should wait for sometime to stabilize readings that is steady state. 4) Measure armature resistance at the start and again at the end because of high heating due to long run-time of motor there is enormous difference in both the readings. 4.4 Observation: I set of readings Date: 28 th July 2003 Experiment begins at: 11:21 Experiment Ends at: 12:24 Temperature at the start/end: 28.5/29 deg C Pressure at the start/end: 995/996 mbar Humidity at the start/end: 81/80 % Armature Resistance Measurement (Ra): (Measurements were taken when motor shaft was not rotating.) Voltage across motor (V) Current Supplied (A) Starting End Table 1: Armature resistance measurement 13

14 Obs. Voltage Across Current Supplied Speed (RPM) no. Motor (V) (A) Table 2: Measuring Voltage, current and speed During this experiment range of voltmeter selected was higher (20 V). Hence it was decided to repeat the experiment for measuring R a at lower voltage ranges. Accordingly in the second set of readings, R a was measured at all possible ranges of voltmeter. II set of readings Date: 2/8/03 Experiment starts at: 11:02 am Temp: 29 o C Pressure: 1001 mbar Humidity: 80% Ends at: pm Armature Resistance Measurement (Ra): (Measurements were taken when motor shaft was not rotating.) Sr. No. Voltage (V) Current (A) Voltage Range used (V) A) Before starting the experiment V D.C V D.C V D.C mv D.C. B) At the end of the experiment V D.C V D.C V D.C. Table 3: Armature resistance measurement Readings obtained at 2 V DC were coming close to the values provided by manufacturer. So it was decided to consider these values only. 14

15 Obs. no. Voltage Across Current Supplied Speed (RPM) Motor (V) (A) Table 4: Measuring Voltage, current and speed 4.5 Calculations and Analysis Estimating value of armature resistance For I set of observations: From eqn (17), Ra = V/I At the start of experiment: Ra = Ω At the end of experiment: Ra = Ω Hence Ra Ω For II set of observations: From eqn (17), R a = V/I We use the value of R a as calculated from the 2 V D.C. range of the Multimeter. This range has been selected due to the inherently small value of R a estimated At the start of experiment: R a = V/I = /1 = Ω. At the end of experiment: R a = V/I =0.188/2 = 0.094Ω. Hence Average R a ( )/2 = Ω. Average Ra (from set 1 and 2) = W [Note: Manufacture s manual provide value of Ra = Ω (Appendix A)] Using eqns 12, 13, 14 and 15 back emf, mechanical losses and electrical losses are calculated in table 5. 15

16 Speed (RPM) Input Power V*I (Watt) Back EMF V- I*Ra (V) Mechanical Losses I* Eb (Watt) Electrical Losses I^2*Ra (Watt) Table 5: Calculating Back EMF and Mechanical Losses at different RPM 16

17 The values of back emf are plotted against those of motor speeds for both the sets of readings, on the same scale to yield an approximately straight line Back EMF (V) Motor Speed (RPM) Graph 1: Back EMF vs Motor Speed Losses (Watt) Speed (RPM) Mechanical Losses Electrical Losses Graph 2: Mechanical and Electrical Losses Vs RPM 17

18 4.6 Conclusions 1) Value of R a = Ω which is closer to the value provided in manufacturer s manual (Ra= 0.069Ω). 2) Relationship between back emf and speed is determined as linear experimentally, this matches with theoretical formula. Determined mathematically relationship can be given as Back emf = *RPM (18) 3) Mechanical losses (Iron and friction) are calculated at various speeds and mathematical relationship between them is obtained Mechanical Losses = *E-10*(speed) *E-6*(speed) *E-3*(speed) (19) (Matlab code for obtaining eqn (18) and (19) is given in Appendix C (1)) 18

19 5. Experiment to predict the shaft power of DC motor In this experiment, motor loaded with propeller is tested in wind tunnel at different flow velocities. For a particular flow velocity, Power consumption is measured at all RPM values. Using the back emf measured at NO Load conditions, Mechanical power developed by motor is calculated. Shaft power is obtained by subtracting mechanical losses from mechanical power. First this experiment was conducted with 11X7 propeller. Later this will be repeated with propeller of other sizes too. 5.1 Apparatus Regulated DC Power Supply, Micro-Manometer, Pitot Static tube, Voltmeter, Tachometer, Tunnel system with Regulated power supply, set up for mounting motor inside the tunnel. 5.2 Theory Relationship of Back EMF (E b ) with RPM was established in previous experiment. From eqn (18) Back emf = *RPM (18) Mechanical Power developed = Mechanical Losses + Shaft power = E b *I Shaft Power = E b *I- Mechanical Losses (20) Mechanical Losses are determined using eqn (19) which was established in no load experiment. Mechanical Losses = *E-10*(speed) *E-6*(speed) *E-3*(speed) (19) So shaft power is calculated using eqn (20). Once Shaft power is known we can estimate value of C p using eqn (8) Equation 1 P C P = (8) ρn 3 D 5 J is calculated using eqn (6) V J = (6) nd Plot of C p vs J is obtained for all flow velocities between 0 to 10 m/s. Shaft power is estimated using eqn (20) at all values of RPM for a particular flow velocities. In this way Plot of Shaft power vs RPM is obtained at all flow velocities. This power vs rpm plot is cross plotted to obtain power vs velocity plot for different values of RPM. Voltage across motor was being measure at every step. So another plot of power vs voltage is obtained for all flow velocities. [Note: In this experiment it is assumed that flow velocity induced by DC motor is negligible so we will talk in terms of wind tunnel velocity only] 19

20 5.3 Experime ntal Set-up and description Experimental set-up is shown in (Image 4). Motor with a mount is rigidly clamped on a stand and this stand is fixed on the base of tunnel in test-section. Height of stand is such that propeller is at the center of tunnel. A white patch of paint is coated on back side of each blade of propeller. This white patch is for the purpose of reflecting light emanating from optical tachometer fixed at the back of propeller on stand for measuring RPM of propeller. Motor is supplied current from a DC regulated power supply. A voltmeter is connected across motor to measure the voltage. Flow velocity inside the tunnel is controlled using Dimmer stat. A pitot static tube mounted at 78 cm from tunnel inlet is connected to micro-manometer for measuring tunnel flow velocity. Image 4: Set up inside the tunnel for predicting output power 20

21 5.4 Observations First this experiment was conducted when there was no flow inside the tunnel. Later on this experiment was repeated with V=2, 3 m/s. Observation and Calculation tables for rest of the flow velocities are given in Appendix B. Date : 04/08/03 Obs. No. Parameter At beginning of the expt. 1 Time 16:55 17:20 2 Temperature (ºC) Pressure (mbar) Relative Humidity 79% 80% 5 Voltage across motor at static condition (for measuring R a ) (V) Current through motor at static condition (for measuring R a ) (A) Table 6: Measuring Experiment Parameters Obs. No. Flow Velocity=0 m/s with a 11X7 propeller Voltage across DC Current through motor DC Motor (V) (A) At end of the experiment 2 Propeller Speed (RPM) Table 7: Observation table for power consumption and RPM 21

22 5.5 Calculation and Analysis All the parameters as explained in section 5.2 theory are calculated and their plots are obtained for all flow velocities. (Note: Observation and Calculation tables for velocities other than 0 m/s are given in Appendix B) Voltage across DC Motor Motor RPM Input Power Mechanical Back emf Losses Shaft power Efficiency of Motor Table 8: Calculating Cp and shaft power at zero flow velocity. For obtaining correct plot of Cp Vs J, all those points which have values of J greater than 0.8 were ignored because J is ratio of forward velocity to rotational velocity at tip of prop. For a MAV in flight Values of RPM are much higher and therefore forward velocity is much lesser than rotational velocity at the tip of prop. Also those first few values of Cp which were obtained at very low power supply giving enormously high values, were ignored. Cp 22

23 Cp Vs J Cp (power coefficient) V=2.25 m/s V=3.19 m/s V = 3.9 m/s V = 5.04 m/s v = 6.36 m/s V = 7.34 m/s V = 8.11 m/s V = 9.18 m/s V = 9.63 m/s J (advancd ratio) Graph 3: Cp Vs J plot for velocities 2.25 to 9.63 m/s Shaft Power Vs RPM Power Watts Motor Speed (RPM) V = 0 m/s V=2.25 m/s V=3.19 m/s V=3.90 m/s V = 5.04 m/s V = 6.36 m/s V = 7.34 m/s V = 8.11 m/s V = 9.18 m/s V = 9.63 m/s Graph 4: Shaft Power vs RPM at different flow velocities Power vs RPM plot was crossploted using Matlab code (given in Appendix C) to obtain power vs Velocity plot shown in Graph 5. 23

24 Power Vs Velocity Shaft Power (Watt) Power at RPM = 1000 Power at RPM=2000 Power at RPM=3000 Power at RPM=4000 Power at RPM=5000 Power at RPM=6000 Power at RPM = Velocity (m/s) Graph 5: Power vs Velocity at different RPM Plots of Shaft Power v/s Voltage across motor for different observed forward velocities 140 Shaft Power (Watt) Voltage across motor (Volt) Obs velocity v = 0 m/s Obs velocity v = 2.25 m/s Obs velocity v = 3.19 m/s Obs velocity v = 3.90 m/s Obs velocity v = 5.04 m/s obs velocity v = 6.36 m/s Obs velocity v = 7.34 m/s Obs velocity v = 8.11 m/s obs velocity v = 9.18 m/s Obs velocity v = 9.63 m/s Graph 6: Power Vs Voltage at different flow Velocities 24

25 6. Discussion and Further work 1) Upto this point sufficient technical information about the motor and different propellers has been collected and this will serve as an exhaustive matter of reference for further work in future. 2) Motor s No load characteristics have been determined which helped in predicting power generated at the shaft and obtaining other necessary plots. 3) A typical plot of Cp Vs J is shown in fig. 7 taken from reference no. 4 Fig7. Blade Performance Coefficients 4 The plot of Cp Vs J obtained in Graph 3 looks similar to that shown in Fig 7. Even the maximum value of Cp in both the plot is coming closer to same value of This confirms the validity of prediction of shaft power using no load characteristics. 4) From the plot of Power vs RPM (Graph 4), the relationship between power and rpm is coming cubic which again is in confirmation with physics. 5) Power Vs flow velocity plot (Graph 5) shows that shaft power required to rotate prop will decrease as flow velocity increases this again confirms physics of system because energy of flow will aid propeller to rotate hence lesser shaft power will be required. Following Tasks will be completed in future to finish this exercise of power plant measurement. 1) Uninstalled thrust measurement using load cell 2) Uninstalled toque measurement using torque sensors 3) Installed thrust and torque measurements 4) Repeating the whole exercise with different propeller-engine combinations 25

26 References 1. Anderson, J.D., Introduction to Flight, Mc Graw Hill publishing company, Fourth Edition, 2000, page no Thareja, B.L., Introduction to electrical engineering, S. Chand company and publisher limited, B B DALY, Woods Practical Guide to Fan Engineering, Woods of Colchester Limited publisher. 4. Von mises, R., Theory of flight, Dover Inc., New York, propeller instruction mannual) 7. (For DC motor instruction manual) 26

27 Appendix A Cobalt 15 Geared Motor 7 Cobalt 15 Geared Mtr 2.4 to 1 ratio, 10 to 12 cells, 300W Astro 15 Cobalt Geared Motor p/n 615G 7 Model No. Name p/n 615G 05 Geared Gear Ratio 2.38 to 1 Armature Winding Armature Resistance Magnet Type Bearings Motor Speed Geared Motor Speed Motor Torque/amp Geared Torque Voltage Range No Load Currrent Maximum Continuous Current Maximum Continuous Power Gear Motor Length Motor Diameter Motor Shaft Diameter Prop Shaft Diameter Gear Motor Weight 7 turns ohms Sm Cobalt Ball Bearings 1488 rpm/volt 652 rpm/volt 0.91 in-oz /amp 2.17 in-oz /amp 8 to 12 volts 2 amps 25 amps 400 watts 3.3 inches 1.3 inches 5/32 inch ¼ inch 9 oz Expected Performance of Cobalt 15 Geared Motor 7 27

28 Battery Prop Amps Watts Rpm 10 Nicads 11 x 7 14 amps 168 watts 6,400 rpm 10 Nicads 12 x 8 18 amps 206 watts 6,000 rpm 12 Nicads 11 x 7 19 amps 250 watts 7,400 rpm 12 Nicads 12 x 8 24 amps 325 watts 6,900 rpm Table 9: Motor specifications and expected performance mapping Voltage Current Prop Watts RPM No Load No Load X7 (static flow) X7 (static flow) Table 9A: Performance Results obtained in Lab 28

29 Appendix B a) Flow velocity: 2.25 m/sec Date: 05/08/03 Obs. Parameter At beginning of At end of the No. the experiment experiment 1 Time 14:30 15:08 2 Temperature (ºC) Pressure (mbar) Relative Humidity 81% 81% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 10: Observations: Experiment paramters at V=2.25 m/s 29

30 Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 11: Observations: Measuring power consumption and propeller speed Voltage across DC motor Propeller Mechanical Back EMF Speed(RPM) Losses shaft power Efficiency of Motor Table 12: Calculation: Predicting shaft, Cp and J at V=2.25 m/s Cp J 30

31 b) Approach velocity: 3.19 m/sec. Date: 05/08/03 Obs. No. Parameter At beginning of the exp. At end of the experiment 1 Time 15:20 16:00 2 Temperature (ºC) Pressure (mbar) Relative Humidity 81% 77% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmerstat Voltage (V) Table 13: Observation: Measuring Experimental Parameters at V=3.19 m/s Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 14: Observation: Measuring Power Consumption at V=3.19 m/s 31

32 Voltage Across the Motor prop speed Mechanic al Losses Back EMF Shaft power Efficiency of Motor Table 15: Calculations: Shaft power, Cp and J at V=3.19 m/s c) Flow velocity: 3.9 m/sec. Date: 05/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 16:35 17:02 2 Temperature (ºC) Pressure (mbar) Relative Humidity 78% 78% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Table 16: Observations: Measuring experimental parameters Cp J 32

33 Voltage Across DC Motor Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 17: Observations: Measuring Power Consumption and prop RPM prop speed Mechanic al Losses Back EMF Shaft power Efficiency of Motor Table 18: Calculation: Shaft power, Cp and J at V=3.90 m/s Cp J 33

34 d) Approach velocity: 5.04 m/sec. Date: 06/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 11:20 11:49 2 Temperature (ºC) 28 ºC 28 ºC 3 Pressure (mbar) Relative Humidity 81% 81% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 19: Observation: Measuring Experimental Parameters Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 20: Observations: Measuring power consumption and RPM at V=5.04 m/s 34

35 Voltage across DC motor Prop speed Mechanic al Losses Back EMF Shaft power Efficiency of Motor Cp J Table 21: Calculations: Shaft power, Cp and J at V=5.04 m/s e) Flow Velocity = 6.36 m/s Date: 08/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 15:33 16:04 2 Temperature (ºC) Pressure (mbar) Relative Humidity 85% 85% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 22: Observations: Measuring Experimental parameters 35

36 Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 23: Observations: Measuring Power consumption and prop RPM Current through DC Motor Prop speed Mechanic al Losses Back EMF shaft power Efficiency of Motor Cp J Table 24: Calculations: Shaft power, Cp and J at V= 6.36 m/s 36

37 f) Flow Velocity = 7.34 m/s Date: 08/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 16:15 16:41 2 Temperature (ºC) Pressure (mbar) Relative Humidity 85% 85% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 25: Observations: Measuring Experimental Parameters Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 26: Observations: Measuring power consumption and prop RPM 37

38 Voltage across DC motor prop speed MechanicaBack EMF l Losses shaft power Efficiency of Motor Table 27: Calculations: Shaft Power, Cp and J at V = 7.34 m/s g) Flow Velocity = 8.11 Date: 08/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 16:48 17:22 2 Temperature (ºC) Pressure (mbar) Relative Humidity 85% 86% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 28: Observations: Measuring Experimental Parameters Cp J 38

39 Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 29: Observations: Measuring power consumption and RPM Voltage across DC motor prop speed ML Back EMF shaft powe r Efficiency of Motor Cp J Table 30: Calculations: Shaft Power, Cp and J at V= 8.11 m/s 39

40 h) Flow Velocity = 9.18 m/s Date: 08/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 17:32 17:55 2 Temperature (ºC) Pressure (mbar) Relative Humidity 87% 87% 5 Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 31: Observations: Measuring Experimental Parameters Obs. No. Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 32: Observations: Measuring Power Consumption and prop RPM 40

41 Voltage across DC motor Prop speed MechanicaBack EMF l Losses shaft power Efficiency of Motor Cp J Table 33: Calculations: Shaft power, Cp and J at V=9.18 m/s i) Flow Velocity = 9.63 m/s Date: 08/08/03 Obs. No. Parameter At beginning of the expt. At end of the experiment 1 Time 18:05 18:32 2 Temperature (ºC) Pressure (mbar) Relative Humidity Voltage across motor at no load (for measuring R a ) (V) Current through motor at no load (for measuring R a ) (A) Wattmeter 1 (W) Wattmeter 2 (W) Wattmeter 3 (W) P (mm of H 2 O) Observed Velocity (m/sec) Dimmer stat Voltage (V) Table 34: Observations: Measuring Experimental parameters 41

42 Obs. No. Voltage across DC motor Voltage across DC motor (V) Current through DC Motor (A) 2 Propeller Speed (RPM) Table 35: Observations: Measuring Shaft power and prop RPM Prop speed Mechanic al Losses Back EMF shaft power Efficiency of Motor Table 36: Calculations: Shaft power, Cp and J at V = 9.36 m/s Cp J 42

43 Appendix C 1) Matlab Code to determine relationship of back emf and Mechanical Losses with RPM under no load conditions. speed1 =[ ]; speed2 =[ ]; speed = [speed1 speed2]; backemf1= [ ]; backemf2= [ ]; backemf= [backemf1 backemf2]; ML1= [ ]; ML2= [ ]; ML = [ML1 ML2]; P = polyfit(speed,backemf,1); Q = polyfit(speed,ml,3); R= polyval(q,531) 2) Matlab Code to cross-plot Power vs RPM curve to Power vs Velocity curve X2 = [ ]; Y2 = [ ]; Q2 = polyfit(x2,y2,3); V = [ ]; P1(1) = polyval(q2,1000); P2(1) = polyval(q2,2000); P3(1) = polyval(q2,3000); P4(1) = polyval(q2,4000); p5(1)=polyval(q2,5000); p6(1)=polyval(q2,6000); p7(1)=polyval(q2,7000); X3 = [ ]; Y3 = [ ]; Q3 = polyfit(x3,y3,3); P1(2) = polyval(q3,1000); P2(2) = polyval(q3,2000); P3(2) = polyval(q3,3000); P4(2) = polyval(q3,4000); p5(2) = polyval(q3,5000); p6(2)=polyval(q3,6000); p7(2)=polyval(q3,7000); X4 = [ ]; Y4 = [ ]; Q4 = polyfit(x4,y4,3); 43

44 P1(3) = polyval(q4,1000); P2(3) = polyval(q4,2000); P3(3) = polyval(q4,3000); P4(3) = polyval(q4,4000); p5(3) = polyval(q4,5000); p6(3)= polyval(q4,6000); p7(3)=polyval(q4,7000); X5 = [ ]; Y5 = [ ]; Q5 = polyfit(x5,y5,3); P1(4) = polyval(q5,1000); P2(4) = polyval(q5,2000); P3(4) = polyval(q5,3000); P4(4) = polyval(q5,4000); p5(4) = polyval(q5,5000); p6(4)= polyval(q5,6000); p7(4)=polyval(q5,7000); X6 = [ ]; Y6 = [ ]; Q6 = polyfit(x6,y6,3); P1(5) = polyval(q6,1000); P2(5) = polyval(q6,2000); P3(5) = polyval(q6,3000); P4(5) = polyval(q6,4000); p5(5)=polyval(q6,5000); p6(5)=polyval(q6,6000); p7(5)=polyval(q6,7000); X7 = [ ]; Y7 = [ ]; Q7 = polyfit(x7,y7,3); P1(6) = polyval(q7,1000); P2(6) = polyval(q7,2000); P3(6) = polyval(q7,3000); P4(6) = polyval(q7,4000); p5(6)=polyval(q7,5000); p6(6)=polyval(q7,6000); p7(6)=polyval(q7,7000); X8 = [ ]; Y8 = [ ]; Q8 = polyfit(x8,y8,3); P1(7) = polyval(q8,1000); P2(7) = polyval(q8,2000); P3(7) = polyval(q8,3000); P4(7) = polyval(q8,4000); p5(7) = polyval(q8,5000); p6(7) = polyval(q8,6000); p7(7) = polyval(q8,7000); X9 = [ ]; 44

45 Y9 = [ ]; Q9 = polyfit(x9,y9,3); P1(8) = polyval(q9,1000); P2(8) = polyval(q9,2000); P3(8) = polyval(q9,3000); P4(8) = polyval(q9,4000); p5(8) = polyval(q9,5000); p6(8) = polyval(q9,6000); p7(8)= polyval(q9,7000); X10 = [ ]; Y10 = [ ]; Q10 = polyfit(x10,y10,3); P1(9) = polyval(q10,1000); P2(9) = polyval(q10,2000); P3(9) = polyval(q10,3000); P4(9) = polyval(q10,4000); p5(9) = polyval(q10,5000); p6(9) = polyval(q10,6000); p7(9)=polyval(q10,7000); X11 = [ ]; Y11 = [ ]; Q11 = polyfit(x11,y11,3); P1(10) = polyval(q11,1000); P2(10) = polyval(q11,2000); P3(10) = polyval(q11,3000); P4(10) = polyval(q11,4000); p5(10) = polyval(q11,5000); p6(10) = polyval(q11,6000); p7(10)=polyval(q11,7000); RPM1 = [V;P1]'; RPM2 = [V;P2]'; RPM3 = [V;P3]'; RPM4 = [V;P4]'; RPM5 = [V;p5]'; RPM6 = [V;p6]'; RPM7 = [V;p7]'; 45