The configuration of rotors significantly impacts the aerodynamic efficiency and noise emission of multicopters. To date, there are no general guidelines regarding how many blades a rotor should use for optimal aerodynamic performance and minimum noise emission. From the perspectives of aerodynamics and acoustics during the hovering condition, two key parameters, i.e., figure of merit (FM) and overall sound pressure level (OASPL), are evaluated to determine the optimal blade number (BN). The number of blades chosen in this study is BN = 2–6, which is largely observed in commercial multicopters. A genetic algorithm was developed to optimize blade design for each BN-rotor configuration. The individuals are evaluated by steady computational fluid dynamics (CFD) simulations and acoustic analogy for optimizations, and the detailed analyses of optimal ones are further explored by unsteady CFD simulations. The planform of the baseline blade is maintained, and the radial distribution of twist angles is the parameter for optimization. While generating the same thrust, the value of FM keeps increasing as the number of blades increases from 2 to 4, after which the FM value reaches a plateau. The value of OASPL keeps decreasing as the number of blades increases. The reason for the FM and OASPL value trends vs blade number is explained with the numerical simulation results, and a general design rule is suggested at the end.

1.
D.
Drikakis
and
T.
Dbouk
, “
Flow and acoustics of unmanned vehicles
,”
Phys. Fluids
34
,
100402
(
2022
).
2.
P.
Li
,
Y.
Yang
,
H.
Zhang
,
Y.
Liu
,
Q.
Li
, and
B.
Noack
, “
Aerodynamic and aeroacoustic impact of the axial distance upon contra-rotating rotors during hovering condition
,” AIAA Paper No. 2023-4071,
2023
, p.
4071
.
3.
Y.
Yang
,
Y.
Liu
,
Y.
Li
,
E.
Arcondoulis
, and
Y.
Wang
, “
Aerodynamic and aeroacoustic performance of an isolated multicopter rotor during forward flight
,”
AIAA J.
58
,
1171
1181
(
2020
).
4.
DJI
, see https://store.dji.com/hk-en/product/dji-mini-3-pro-propellers?vid=114351&set_region=HK&from=store-nav for “
DJI Mini 4 Pro/Mini 3 Pro Propellers
,
2023
;” acquired 6 November 2023.
5.
EHang
, see www.ehang.com/ehangaav/ for “
EHang AAV: The Era of Urban Air Mobility is Coming
,
2023
;” acquired 6 November 2023.
6.
R. G.
McSwain
,
L. J.
Glaab
,
C. R.
Theodore
,
R. D.
Rhew
, and
D. D.
North
, “
Greased lightning (gl-10) performance flight research: Flight data report
,”
Report No. NASA/TM-2017-219794
,
2017
.
7.
T.
Sullivan
, “
The Canadair CL-84 tilt wing design
,” AIAA Paper No. 1993-3939,
1993
, p.
3939
.
8.
J.
Aviation
, see https://www.jobyaviation.com/ for “
Joby Aviation—Joby
,
2023
;” acquired 6 November 2023.
9.
O.
Gur
,
J.
Silver
,
R.
Dítě
, and
R.
Sundhar
, “
Optimized performance and acoustic design for hover-propeller
,” AIAA Paper No. 2021-2222,
2021
, p.
2222
.
10.
N. M.
Nouri
and
S.
Mohammadi
, “
A multi-objective approach for determining the number of blades on a NACA marine propeller
,”
Brodogradnja: Teorija i praksa brodogradnje i pomorske tehnike
67
,
15
32
(
2016
).
11.
E. P.
Lesley
, “
Propeller tests to determine the effect of number of blades at two typical solidities
,”
Report No. NACA-TN-698
,
1939
.
12.
A. C.
Clark
and
D. R.
Leiper
, “
The free wake analysis, a method for the prediction of helicopter rotor hovering performance
,”
J. Am. Helicopter Soc.
15
(
1
),
3
11(9)
(
1970
).
13.
G. J.
Leishman
,
Principles of Helicopter Aerodynamics
, 2nd ed. (
Cambridge University Press
,
London
,
2006
).
14.
Y.
Jo
,
T.
Jardin
,
R.
Gojon
,
M. C.
Jacob
, and
J.-M.
Moschetta
, “
Prediction of noise from low Reynolds number rotors with different number of blades using a non-linear vortex lattice method
,” AIAA Paper No. 2019-2615,
2019
, p.
2615
.
15.
K.
Baskaran
,
N. S.
Jamaluddin
,
A.
Celik
,
D.
Rezgui
, and
M.
Azarpeyvand
, “
Aerodynamic and aeroacoustic characteristics of propellers with different blade numbers
,” AIAA Paper No. 2022-3108,
2022
, p.
3108
.
16.
K.
Baskaran
,
N. S.
Jamaluddin
,
A.
Celik
,
D.
Rezgui
, and
M.
Azarpeyvand
, “
Effects of number of blades on propeller noise
,”
J. Sound Vib.
572
,
118176
(
2024
).
17.
W.
Froude
, “
On the elementary relation between pitch, slip, and propulsive efficiency
,”
Report No. NASA-TM-X-61726
,
1920
.
18.
F.
Weick
,
Aircraft Propeller Design
(
McGraw-Hill Book Company, Incorporated
,
1930
).
19.
G. A.
Williamson
,
B. D.
McGranahan
,
B. A.
Broughton
,
R. W.
Deters
,
J. B.
Brandt
, and
M. S.
Selig
,
Summary of Low-Speed Airfoil Data
(
University of Illinois Low Speed Airfoil Tests
,
2012
), Vol.
5
, p.
116
.
20.
R. W.
Deters
,
G. K.
Ananda Krishnan
, and
M. S.
Selig
, “
Reynolds number effects on the performance of small-scale propellers
,” AIAA Paper No. 2014-2151,
2014
, p.
2151
.
21.
F.
Yunus
,
E.
Grande
,
D.
Casalino
,
F.
Avallone
, and
D.
Ragni
, “
Efficient low-fidelity aeroacoustic permanence calculation of propellers
,”
Aerosp. Sci. Technol.
123
,
107438
(
2022
).
22.
H.
Qi
,
P.
Wang
,
L.
Jiang
, and
Y.
Zhang
, “
Investigation on aerodynamic noise characteristics of coaxial rotor in hover
,”
Appl. Sci.
12
,
2813
(
2022
).
23.
F.
Farassat
,
P. A.
Nystrom
, and
T. J.
Brown
, “Bounds on thickness and loading noise of rotating blades and the favorable effect of blade sweep on noise reductions,” in International Specialist Symposium, Helicopter Acoustics (Langley Research Center, 1978).
24.
D.
Kurtz
and
J.
Marte
, “
A review of aerodynamic noise from propellers, rotors, and lift fans
,”
Report No. NASA-CR-107568
,
1970
.
25.
K. S.
Brentner
and
F.
Farassat
, “
Modeling aerodynamically generated sound of helicopter rotors
,”
Prog. Aerosp. Sci.
39
,
83
120
(
2003
).
26.
H. H.
Hubbard
, “
Aeroacoustics of flight vehicles: Theory and practice. Volume 1. Noise sources
,”
Report No. NASA Reference Publication-1258-VOL-1
,
1991
.
27.
D. B.
Hanson
and
M. R.
Fink
, “
The importance of quadrupole sources in prediction of transonic tip speed propeller noise
,”
J. Sound Vib.
62
,
19
38
(
1979
).
28.
E.
Grande
,
D.
Ragni
,
F.
Avallone
, and
D.
Casalino
, “
Laminar separation bubble noise on a propeller operating at low Reynolds numbers
,”
AIAA J.
60
,
5324
5335
(
2022
).
29.
F.
Farassat
, “
Derivation of formulations 1 and 1A of Farassat
,”
Report No. NASA/TM-2007-214853
,
2007
.
30.
M.
De Gennaro
,
D.
Caridi
, and
M.
Pourkashanian
, “
Ffowcs William-Hawkings acoustic analogy for simulation of NASA SR2 propeller noise in transonic cruise condition
,” in
Proceedings of the V ECCOMAS CFD
,
2010
.
31.
T.
Murata
and
H.
Ishibuchi
, “
MOGA: Multi-objective genetic algorithms
,” in
IEEE International Conference on Evolutionary Computation
(
IEEE
,
Piscataway, NJ
,
1995
), Vol.
1
, pp.
289
294
.
32.
Y.
Liang
,
Y.
Yang
,
X.
Shan
, and
Z.
Wang
, “
Effect of airfoil dimple on low-Reynolds-number differing laminar separation behavior via multi-objective optimization
,”
J. Aircr.
59
,
1243
1256
(
2022
).
33.
H.
Wang
,
L.
Gao
,
G.
Yang
, and
B.
Wu
, “
A data-driven robust design optimization method and its application in compressor blade
,”
Phys. Fluids
35
,
066114
(
2023
).
34.
A. C.
Patrao
,
D.
Lindblad
, and
T.
Grönstedt
, “
Aerodynamic and aeroacoustic comparison of optimized high-speed propeller blades
,” AIAA Paper No. 2018-4658,
2018
.
35.
M. A.
Clarke
and
E.
Botero
, “
Aeroacoustic optimization of VTOL rotor blades
,” AIAA Paper No. 2023-0209,
2023
, p.
0209
.
36.
S.
Chae
,
K.
Yee
,
C.
Yang
,
T.
Aoyama
,
S.
Jeong
, and
S.
Obayashi
, “
Helicopter rotor shape optimization for the improvement of aeroacoustic performance in hover
,”
J. Aircr.
47
,
1770
1783
(
2010
).
37.
P. L.
Volsi
,
D.
Gomez-Ariza
,
R.
Gojon
,
T.
Jardin
, and
J.-M.
Moschetta
, “
Aeroacoustic optimization of MAV rotors
,”
Int. J. Micro Air Veh.
14
,
175682932110708
(
2022
).
38.
H.
Aytug
,
M.
Khouja
, and
F.
Vergara
, “
Use of genetic algorithms to solve production and operations management problems: A review
,”
Int. J. Prod. Res.
41
,
3955
4009
(
2003
).
39.
M. A.
Silvestre
,
J. P.
Morgado
, and
J.
Pascoa
, “
JBLADE: A propeller design and analysis code
,” in
International Powered Lift Conference
(AIAA,
2013
), p.
4220
.
40.
Y.
Yang
,
Y.
Liu
,
H.
Hu
,
X.
Liu
,
Y.
Wang
,
E. J.
Arcondoulis
, and
Z.
Li
, “
Experimental study on noise reduction of a wavy multi-copter rotor
,”
Appl. Acoust.
165
,
107311
(
2020
).
41.
D. C.
Akiwate
,
A. B.
Parry
,
P.
Joseph
, and
C. C.
Paruchuri
, “
On the balance between the tonal and broadband noise of uninstalled propellers
,” AIAA Paper No. 2021-2308,
2021
, p.
2308
.
42.
Siemens Digital Industries Software
,
Simcenter STAR-CCM+, Version 2021.3
,
Siemens
,
2021
.
43.
Y.
Yang
,
L.
Veldhuis
, and
G.
Eitelberg
, “
Aerodynamic impact of a streamwise vortex on a propeller
,”
Aerosp. Sci. Technol.
70
,
108
120
(
2017
).
44.
T.
Wang
,
Y.
Yang
,
X.
Chen
,
P.
Li
,
A.
Iollo
,
G. Y.
Cornejo Maceda
, and
B. R.
Noack
, “
Topologically assisted optimization for rotor design
,”
Phys. Fluids
35
,
055105
(
2023
).
45.
N. A. R. N.
Mohd
and
G. N.
Barakos
, “
Computational aerodynamics of hovering helicopter rotors
,”
J. Mek.
34
,
16
46
(
2012
).
46.
D. K. Reddy
G
,
M.
Verma
, and
A.
De
, “
Performance analysis of vertical-axis wind turbine clusters: Effect of inter-turbine spacing and turbine rotation
,”
Phys. Fluids
35
,
105122
(
2023
).
47.
N. S.
Zawodny
and
D. D.
Boyd
, “
Investigation of rotor-airframe interaction noise associated with small-scale rotary-wing unmanned aircraft systems
,”
J. Am. Helicopter Soc.
65
,
1
17
(
2020
).
48.
D.
Balch
and
J.
Lombardi
, “
Experimental study of main rotor tip geometry and tail rotor interactions in hover. Volume 1. Text and figures
,”
Report No. NASA-CR-177336-VOL-1
,
1985
.
49.
G.
Barakos
and
A. J.
Garcia
, “
CFD analysis of hover performance of rotors at full-and model-scale conditions
,”
Aeronaut. J.
120
,
1386
1424
(
2016
).
50.
R.
Jain
, “
Hover predictions on the S-76 rotor with tip shape variation using helios
,”
J. Aircr.
55
,
66
77
(
2018
).
51.
N. S.
Zawodny
,
D. D.
Boyd
, Jr.
, and
C. L.
Burley
, “
Acoustic characterization and prediction of representative, small-scale rotary-wing unmanned aircraft system components
,” in
American Helicopter Society (AHS) Annual Forum
,
2016
.
52.
K.
Deb
,
A.
Pratap
,
S.
Agarwal
, and
T.
Meyarivan
, “
A fast and elitist multiobjective genetic algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
6
,
182
197
(
2002
).
53.
G.
Subashini
and
M.
Bhuvaneswari
, “
Comparison of multi-objective evolutionary approaches for task scheduling in distributed computing systems
,”
Sadhana
37
,
675
694
(
2012
).
54.
H.
Jiang
,
H.
Wu
,
W.
Chen
,
P.
Zhou
,
S.
Zhong
,
X.
Zhang
,
G.
Zhou
, and
B.
Chen
, “
Toward high-efficiency low-noise propellers: A numerical and experimental study
,”
Phys. Fluids
34
,
076116
(
2022
).
55.
A.
Gessow
, “
Effect of rotor-blade twist and plan-form taper on helicopter hovering performance
,”
Report No. NACA-TN-1542
,
1948
.
56.
Y. H.
Yu
,
C.
Tung
,
J.
Gallman
,
K. J.
Schultz
,
B.
van der Wall
,
P.
Spiegel
, and
B.
Michea
, “
Aerodynamics and acoustics of rotor blade-vortex interactions
,”
J. Aircr.
32
,
970
977
(
1995
).
57.
Y. H.
Yu
, “
Rotor blade-vortex interaction noise
,”
Prog. Aerosp. Sci.
36
,
97
115
(
2000
).
58.
J. C.
De Winter
,
S. D.
Gosling
, and
J.
Potter
, “
Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data
,”
Psychol. Methods
21
,
273
(
2016
).
You do not currently have access to this content.