Scaling Analysis of Propeller-Driven Aircraft for Mars Exploration

Transcription

1 Scaling Analysis of ropeller-driven Aircraft for ars xploration Tianshu Liu ISAS, JAXA, Sagamihara, Japan & Department of echanical & Aeronautical ngineering Western ichigan University, ichigan, USA

2 Objective To give a criterion for feasible cruising flight of propeller-driven aircraft on ars and provide a guideline for the design of such a artian aircraft

3 artian Atmosphere Density ressure H 0.04 p 4.H 774.

4 artian Atmosphere Temperature Speed of Sound T 6.H 86.8.H 68. a

5 artian Atmosphere Dynamical Viscosity

6 Adaption of IW-VIW Relation in Flight Testing: ffects of Density and Gravity for ars Flight IW D0 ref S ( VIW ) KW S ( VIW ) where the standard velocity and the generalized power: ref VIW V ( / ) / / ref ( / ref ) IW / / ( W / Wref ) ( W / Wref )

7 ower-velocity Relation on arth Related to artian arameters where the velocity and the power are related to those on ars D SV KW SV 0 / / ) / ( ) / ( W W V V / / ) / ( ) / ( W W

8 Scaling Relations: ower and Velocity where / min, / S W a V / min, / S W bs 4 / 0 4 / 4 D K a a K a b D 0,min / / / / /,min V g g S W g g a V S / g g S W g g b S /,min / / / / /,min

9 Scaling Relations: ower and Velocity V.5V,maxR,min.46,maxR,min Scaling Relations: Lift oefficient L, g g V V L, In cruising flight on arth and ars, the lift coefficient remains the same, i.e., L, L,

10 Scaling Relations: ropulsive ower prop prop 4 J r AS S V c S V where the power coefficient is defined as c prop /( SV ) prop r AS ( 4 / J ) ropulsive ower Scaling: prop, prop, c c,,

11 ower riterion for ruising Flight on ars ropulsive ower Available: prop, c c,, W 7 / 6 ropulsive ower Required:,maxR.46 b / S g g / / W 7 / 6 where the following scaling relations are used prop, W 7 / 6 S W / S

12 ower riterion for ruising Flight on ars ower Ratio riterion: / R,max, prop g g c c b 0.87 / /,, / S,maxR prop, c c b 0 4.6,, / S

13 Further Formulation of ower riterion for ruising Flight on ars W W Weight onstraint:,wing W,prop W,motor W,others W / S x x x where W, prop / A,motor / prop, W (W,wing W, others )/ S

14 Further Formulation of ower riterion for ruising Flight on ars ower Ratio riterion: x 4 / x x x where A/ S x x prop, / S x W / S Disk-to-Wing Area Ratio ropulsive ower er Unit Wing Area Wing Loading b( A / S ) prop prop J J

15 Further Formulation of ower riterion ower Ratio riterion: / 4 AR e / prop, r f ( x,x ) 5 / 4 motor prop, D0 prop, where ( / A / S ) J J f ( x,x ) / ( / )x x / x x

16 Further Formulation of ower riterion ower Ratio riterion: / L, 6 motor prop, D0 prop, / prop, r f ( x,x ) where f ( x ,x ) / ( / )x x / 5 / ( A / S ) x x J J Requirements for ruising Flight on ars: / L, / D0 rmotor prop,

17 ower riterion for ruising Flight on arth: A Reduced ase ower Ratio riterion at Altitude H: H 0.87 / S b c c,h,sl ( H ) SL / ondition for the ax Altitude of Typical Aircraft: H ( H max ) / SL.095b / / S / 0.6 H max.9km

18 Upper Bound of Total Weight Upper bound by setting UB(W ) / 4 A / / prop, S / UB(W ) B W,w pm g( y,y ) where the weight function is g( y / / /, y ) y y ( y y ) y W,motor / W,w pm y W,wing / W,w pm B / / 4 ( g rmotor prop, ) / A,prop / S,wing

19 Upper Bound of Total Weight: Weight Function

20 Table. Scaling Laws and Derived Results for ropeller Aircraft on arth Quantity Upper Limit or ax TO Weight Scaling Law W TO.8 W Wingspan / b 0.46W Wing Area / S 0.06 W ean hord / c W Aspect Ratio 8.5 Body Length l / 0.4W ax Body Diameter / d W Wet and Wing Area Ratio 4.5 Body Fineness Ratio 8.5 Wing Loading / WL 5 W Reynolds Number Rec 4 / 6. 0 W ruise Speed Vmax R / 6 5.5W ruise ower 7 / 6.67 W wing wing body max R,aircraft ower Available. 5.5W ngine Weight W 0.7 W prop engine ax L/D.9 Oswald fficiency e arasite Drag Induced Drag ropulsive fficiency Dara, Swing DIn, S wing / e prop D,Swing Scaling Laws for Typical ropeller Aircraft on arth Note: () Units: Newtons for weight, m for length, m for area, m/s for velocity, Watts for power, kg/m for density, and Newtons/m for loading. () The mean relative errors associated with the scaling laws are indicated in Liu (006).

21 Disk-to-Wing Area Ratio for Typical ropeller Aircraft on arth

22 Service eiling for Typical ropeller Aircraft on arth

23 arametric Domains for ruising Flight of - and -ropeller Aircraft on arth

24 arametric Domain for ruising Flight of The Helios rototype on ars Table. arameters of Several ropeller-driven Aircraft arameters S A / S b ruise H max Typical Aircraft km 0.09 Helios km 0. Sample artial Aircraft km.07

25 Design arameters of the JAXA artian Aircraft Wing arameters b.4 m Wing span w c 0.48 m ean wing chord w AR 5. Wing aspect ratio S.5 m Wing area 0.4 kg/m Wing surface density S,wing

26 Design arameters of the JAXA artian Aircraft ropulsion arameters D 0.66 m ropeller diameter prop h prop 5 mm ean blade thickness S prop / A 0. ropeller solidity prop 797 kg/m ropeller material density (carbon fiber) prop, 0.8 ropeller efficiency on arth prop, 0.8 ropeller efficiency on ars n Number of propellers ( A/ S ) 0.8 Reference disk-to-wing area ratio r motor 70 W/kg otor power-to-mass ratio 40 kj/kg nergy density of batteries batteries Initial Input Aerodynamic arameters 0.0 Zero-lift drag coefficient D0 e 0.8 Oswald efficiency

27 Upper Bound of Total Weight of the JAXA artian Aircraft

28 arametric Domain for ruising Flight of the JAXA artian Aircraft

29 Relation between otor ower and ass: Specific ower of otor

30 JAXA Noth et al. (009)

31 Output arameters of the JAXA artian Aircraft Table 4. ass Distribution of Sample ropeller-driven artian Aircraft m 4.4 kg Total mass m 0.94 kg Wing mass,wing m,prop 0.75 kg ropeller mass m,motor.6 kg otor mass m.5 kg Other mass,others Table 5. erformance arameters of Sample ropeller-driven artian Aircraft.07 ower ratio on ars V 65 m/s ruising velocity on ars,maxr R 60 km ruising range on ars. h ruising endurance on ars 84 W ruising power required on ars,maxr 90 W ropulsive power available on ars prop, L, 0.46 Lift coefficient on ars W / S 4.5 N/m Wing loading on ars

32 onclusions The power ratio criterion is given for cruising flight of propeller-driven aircraft on ars The power ratio criterion is validated by examining typical propeller-driven aircraft and the Helios on arth in several interesting cases The power ratio criterion indicates that the preliminary design of the JAXA artian aircraft could be feasible for cruising flight on ars

33 onclusions Specific Requirements for JAXA artian Aircraft: The lift-to-zero-lift-drag ratio: / = 6 L, D0 The power-to-weight ratio of a D motor: = 000 W/kg The propeller efficiency: = 0.8 inimizing the weights of wing and propellers

34 Further Topics Aerodynamics optimization: Wing/airfoil design and testing ropeller optimization/design and testing Optimization under suitable constraints on solar power source, batteries, structures etc.