Helicopter Sizing by Statistics

AHS Forum 58, June 2002

Helicopter Sizing by Statistics

Omrii Rand Omr

Vladim Vla dimir ir Khr Khromo omov v

Faculty of Aerospace Engineering Technion Techni on – Israel Instit Institute ute of Technol Technology ogy Haifa 32000, Israel.

Presented at the American Helicopter Society 58 th Annual Forum, Montreal, Canada, June 11-13, 2002.

Faculty Facul ty of Aeros Aerospace pace Eng., Eng., Techni Technion on - I.I.T I.I.T..


Introduction •

Sizing is th the first and an important stage in helicopter preliminary design process.

•

Preli eliminary desig sign to tools ar are relatively simple and were developed for fast design cycles.

• “Des “Desig ign n tren trends ds”” anal analys ysis is is a wel welll know known n tech techni niqu quee in whi which ch fly flyin ing g conf config igur urat atio ions ns are are analyzed in order to conclude or identify a trend which is common to many configurations , and therefore, it may represent physical constrains which are not clear and evident at the the early stages. • “Des “Desig ign n tren trends ds”” anal analys ysis is is usef useful ul for for the the sizi sizing ng stag stagee in its broad sense : geometrical sizing and preliminary preliminary “sizing” “sizing” of performance, performance, power required, required, etc. • The The prese present nt stud study y is based based on a (part (partia ial) l) datab databas asee for more than 180 conventional single rotor helicopter configurations . The analysis has been carried out using advanced computerized correlation technique which is based on Multiple Regression Analysis.



The Analysis Methodology Analysis Methodology Multiple Regression Analysis (MRA):

Y = a X1α X 2β X 3γ ... . • A com compu pute teri rize zed d alg algor orit ithm hm has has bee been n cod coded ed to gene genera rate te and and sel selec ectt hundreds of combinations of independent variables, in order to identify the groups that provide high correlation measure. • The pu purpose wa was to to fi find de design tr trends th that co contain minimal number of independent unknowns (preferably one or two) that exhibit high correlation indicators. •

Error definition:

ε (%) ε (%) = 100

| EV - DBV | DBV

where EV where EV and and DBV DBV stand stand for the estimated value and the database value, respectively. For each case we AVER MAX shall present the averaged ε and maximum ε error obtained, defined by

ε

AVER

=

1 N εi N i∑ =1

where N where N is is the number of configurations involved,

and

ε i

ε MAX = max(ε i )

is the error calculated for the i-th i-th config configura uratio tion. n.



The Analysis Method ology (cont.) Multiple Regression Correlation Measure:

N

2

e ∑ e yi − yi j

=1 R2 = 1− i N

∑ e yi − y j

2

i =1

e where yi are the data base values, y is the averaged data base value, and yi are the estimated values.

Hence, R = 1 stands for a perfect correlation , while in most cases the minimal value of R was set to be above 0.9 in order to conclude that a correlation is of a value and represents a genuine trend.

The Database The database used is the one stored in RAPID/RaTE (R otorcraft Analysis for Preliminary Design / Rand Technologies & Engineering) - a desktop rotorcraft analysis package . RAPID/RaTE is designed to model general rotorcraft configurations, conventional helicopters and tilt-rotors. RAPID/RaTE performs trim response, mission analysis, vibration analysis, stability analysis, and both flight mechanics and aeroelastic simulations.

Faculty of Aerospace Eng., Technion - I.I.T.


The Analysis Method ology Scheme RAPID/RaTE Helicopter Configurations DATABASE

Generation of helicopter parameters combinations {X ,i i=1,2,…}

Filtering of Database configurations for selected parameters groups

Calculation of the MRA parameters a , α , β , γ , e t c .

and the multiple correlation measure R Evaluating error estimation cε AVER …...…. , ε MAX h

Identification of parameter combinations with high correlation measures

Helicopter Configuration Model

Helicopter “Design trends”



Main Scheme of Helicopter Sizing Vertical tail average chord, ± 12%

Fenestron diameter, ± 7.7% Tail rotor diameter,

Tail Rotor RPM,

± 7.6%

Horizontal tail arm, ± 16% Horiz. tail area, ±29%

± 6.6%

Tail Rotor Solidity Hover Tip Speed 170-250

Fuel value (liters), ± 11.5%

m/sec Tail rotor Blade number

Main Rotor RPM,

Empty Weight, ± 9.3%

± 6.5%

Tail Rotor chord, ±10% Hover Rotor RPM,

Range with standard fuel, S/L

± 6%

Main rotor chord, ±10%

Useful load, ± 9.5%

Gross Weight Total power T-O, ± 14.3%

Overall length, rotor turning, ± 1.7%

T-O Transmission rating, ± 8%

Main rotor Blade number

Fuselage Length, ± 6.2% Tail Rotor Arm, ± 3.3%

Main Rotor Solidity Total power Max cont., ± 10.5%

Height to rotor head, ±7%

Disc load

Main Rotor Diameter, 6%

Max cont. Transm. rating, ± 9%

Vertical tail Arm, ± 4.2% Max speed, S/L

Width over landing gears, ± 10% Long range speed, ± 6.5%

Never exceed speed, ± 5.9%

Clearance Fuselage - Ground .3-.7 m


AHS Forum 58, June 2002 a MT = f ( D) aVT = f ( D)

F H = ( D)

Helicopter Geometry Sizing Parameters

F L = ( D) FW = ( D)

F L RT = f ( D)

c = (W0 , N B )

cTR = f (W0 , N BTR )

D LOAD & D = f (W0 ,V max )

σ = f ( N B , D, c)

cVT =

( DTR )

σ TR = f ( N BTR , DTR , cTR ) ΩTR = f ( DTR )

DTR = f (W 0 )

Ω = f ( D)

a HT = f (W 0 )

S HT = f (W 0 )



Main Rotor Diameter The " square − cube" scaling law: D ∝ W 0 1 3 40

) m ( r e t e m a i D r o t o R n i a M

40

) 30 % ( r 20 o r r E 10

30

D = f (W 0 ) 30 21 7

D = f (W0 ,V m )

6

0 Average error 20

Max error

D = 0.980 W 00.308, where D is in [m] and W 0 is in [kg ]

10

(ε AVER = 7%, ε MAX = 30%, R = .9606)

D = f (W (W0)) (W0, Vm ) ma D = ff (GW &V

Estimation 0 0

10

20

30

40

Main Rotor Diameter Estimation (m)

D = 9.133 W00.380 / V m0.515, V m is in [km / hr ] S / L (ε AVER = 6%, ε MAX = 21%, R = .9744).



Main Rotor Disc Loading 0

) m m / / g 80 k ( 70 ( g 60 g n n i i d d 50 a a o o 40 L L c c s 30 i s i D 20 D

10000

20000

30000

40000

50000

60000

100

) 2 2 90

10 0

Gross Weight (kg)

RAH-66 Comanche CH-53E

Mi-26 Mi-6 & Mi-22

) 2

m / g k ( g n i d a o L c s i D

80

Database configurations

70

RAH-66 Comanche Estimation

60 50 40 30 20


10

Estimation

ASI Ultrasport 254 0 0

2000

4000

6000

8000

10000

12000

14000

16000

Gross Weight (kg)



Wing & Disc Loading Comparison 60

Helicopter Database configurations Disc Loading (rotory-wing) Wing Loading Upper boundary (fixed-wing) Wing Loading Lower boundary (fixed-wing)

2 ) ft ) 50 2 / t b f / l( b l ( nig 40 g a d n i d oL 30 a o L cs k i 20 s i D D / g & n i g W in 10 W

2.94 (W

1/3

- 6)

Fixed-wing

[McCormick, 1995] 1.54 (W

1/3

[Current study]

- 6)

.334 (W

[McCormick, 1995]

1/3

- .74)

0 0

10

20

30

40

50

60

1/3

(Gross Weight, lb)



Wing & Disc Loading 1000

) 2 m / g k ( g 100 n i d a o L k s i D 10 & g n i W 1

Jet transport/bomber Some transport helicopters

586

Civil/utility low speed helicopters 73

73

Sailplane 30 20

7.5

Fixed-wing typical loading [Raymer, 1999]

Rotary-wing typical loading [Raymer, 1999]

Rotary-wing [Current study]



Main Rotor Blade Chord & Solidity 1

) m ( 0.8 d r o h C 0.6 e d a l B 0.4 r o t o R 0.2 n i a M 0

c = .0108 W 00.540 /

0.714 b

,

where c is in [m] and W 0 is in [kg ] (ε AVER = 10%, ε MAX = 41%, R = .9535).

Database configurations Estimation 0

0.2

0.4

0.6

0.8

1

Main Rotor Blade Chord Estimation (m)



Main & Tail Rotor Angular Velocity

5000

) 4500 M P 4000 R ( y 3500 t i c o 3000 l e V 2500 r 2000 a l u g 1500 n A 1000 r o 500 t o R 0

Main Rotor Database Main Rotor Estimation Tail Rotor Database Tail Rotor Estimation FENESTRON Database

0

5

10

15

20

25

30

Rotor Diameter (m)


35


Main & Tail Rotor Angular Velocity (cont.) Main Rotor: Ω = 2673. / D 0.829 where Ω is in [ RPM ] and D is in [m] (ε AVER = 6%, ε MAX = 35%, R = .9630).

Tail Rotor: 0.828 Ω [ RPM ] = 3475. / DTR (ε AVER = 7%, ε MAX = 16%, R = .9737) or 0.828 Ω [rad / sec] = 364. / DTR

where DTR is in [m].

) 800 M P R ( 600 y t i c o l e V 400 r a l u g n A 200 Database configurations r o Estimation t o R 0 n i 0 200 400 600 800 a M Main Rotor Angular Velocity Estimation (RPM)



Main & Tail Rotor Tip Speed 300 250 ) s / m200 ( d e e150 p S p100 i T

Main Rotor Database configurations Tail Rotor Database configurations Fenestron Database configurations

50

Main Rotor Estimation Tail Rotor Estimation

0 0

5

10

15

20

25

30

Rotor Diameter (m)

Main Rotor: V

TIP

= 140. D 0.171, where V TIP is in [m / sec]

V

TIP

0.172 where = 182. DTR , V TIP is in [m / sec]

Tail Rotor:


35


Tail Rotor Diameter 8

) 7 m ( r e 6 t e 5 m a i D 4 r o 3 t o R l i 2 a T

Database configurations Estimation

DTR = .0895 W00.391 where DTR is in [m] and W0 is in [kg ] (ε AVER = 8%, ε MAX = 25%, R = .9754)

FENESTRON Estimation

1

D F = .3081 W00.154 TR

FENESTRON configurations

0 0

10000

20000

30000

40000

50000

60000

Gross Weight (kg) 2 USAAMRDL Report 1974: D / DTR = [7.0 ÷ 7.3] − .27 DL {lb / ft }

RAPID/RaTE analysis:

D / DTR = 6.88 − .19 DL {lb / ft 2}



Tail Rotor Arm 25

20

) m ( 15 m r A r o 10 t o R l i a 5 T

RAPID / RaTE analysis: . a MT = .5107 D 1061 ,


where a MT and D is in [m] (ε AVER = 3%, ε MAX = 14%, R = .9907).

RAPID+ Estimation RAPID/RaTE Estimation USAAMRDL Report 1977 Ref. 13 Estimation

0 0

5

10

15

20

25

Tail Rotor Arm Estimation USAAMRDL Report 1977: a MT = (

+ DTR ) / 2 + .5 feet



Tail Rotor Blade Chord & Solidity 0.5

cTR = .0058 W 00.506 /

TR 0.720 b

,

) m ( where cTR is in [m] and W 0 is in [kg ] 0.4 d (ε = 10%, ε = 30%, R = .9437). r o h 0.3 C e d 0.2 a l B r 0.1 Database configurations o t (without FENESTRON) o R 0 l i 0.1 0.2 0.3 0.4 0.5 a 0 T Tail Rotor Blade Chord Estimation (m) AVER

MAX



Horizontal Tail Surface Area HT

. = .0021 W 00758 ,

where S HT is in [m2 ] and W 0 is in [kg ] (ε AVER = 29%, ε MAX = 214%, R = .9117).

9 8

) m 7 o ( l a i 6 e a r T A l 5 e a c t 4 a n f o r i 3 u z S r o H 2 f 2

Mi-26


1

Estimation

Mi-28

0 0

10000

20000

30000

40000

50000

Gross Weight (kg)


60000


Vertical Tail Surface Arm

20 18


16

) m 14 ( m r 12 A 10 l i a T 8 l 6 a c i t 4 r e V 2

Estimation

aVT = .5914 D 0.995, where aVT and D are in [m] (ε AVER = 4%, ε MAX = 20%, R = .9853).

0 0

5

10

15

20

25

30

35

Main Rotor Diameter (m)



Vertical Tail Average Chord ) m 3.0 ( l i a T l 2.5 a c i 2.0 t r e V 1.5 f o d r o 1.0 h C 0.5 e g a r 0.0 e v 0 A

Database configurations (Diameter < 3.5 m) Database configurations (Diameter > 3.5 m) Database configurations (FENESTRON) Estimation (Diameter < 3.5 m) Estimation (Diameter > 3.5 m) Estimation (FENESTRON)

cVT = .909 DTR0.927

Fenestron

. cVT = .161 DTR1745

DTR < 35 . m

(ε AVER = 12%, ε MAX = 43%, R = .9709) 1

2

3

4

Tail Rotor Diameter (m) For Fenestron configurations

5

106 . cVT =6 .297 DTR 7

D .9 m 8 TR > 35

where cVT and DTR are in [m]

cVT ≈ DTR Faculty of Aerospace Eng., Technion - I.I.T.


Configuration Length 40

h t g n e L e g a l e s u F

35 30 25 20

L

15

. = 0.824 D 1056

(ε AVER = 6%, ε MAX = 17%, R = .9807)

10

where

5


0

Estimation 0

5

10

15

20

25

L

30

and D are in [m]. 35

40


F L RT = 1.09 D 1.03 (ε AVER = 2%, ε MAX = 9%, R = .9982)

where

RT and

L

are in [m]. 0

5

10

15

20

25


30

35

) m ( 50 g n 45 i n 40 r u 35 T r o 30 t o 25 R , 20 h t 15 g n 10 e L l 5 l a r 0 e v 40 O



Fuselage Height and Width 9

) m 8 ( d 7 a e 6 H r o 5 t o R 4 o 3 t t h 2 g i e 1 H

H

(ε

AVER

= 7%, ε

=

0.642 D 0.677 Mi-26

= 25%, R = .9371) and D are in [m]. H

where

MAX


8

0 0

5

10

15

20

25

30

Mi-6 & Mi-22

35

7

Main Rotor Diameter (m) W

(ε

AVER

=

= 10%, ε

where

W

0.436 D 0.697

MAX

6 5

EH 101

4

= 40%, R = .8818)

3

and D are in [m].

2 1 0

0

5

10

15

20

25

30

35

40



) m ( s d i k S / s r a e G g n i d n a L r e v O h t d i W


Fuselage-Ground Clearance

) m 0.8 ( d 0.7 n u o r 0.6 G 0.5 e g 0.4 a 0.3 l e s u 0.2 F e c 0.1 n 0 a r 0 a e l C

Database configurations 10000

20000

30000

40000

50000

60000

Gross Weight (kg)



Empty Weight & Useful Load 0

10000

20000

30000

40000

50000

60000

Gross Weight (kg)

35000 30000 ) g k ( 25000 t h g 20000 i e W 15000 y t p 10000 m E

Helicopter Database configurations

W E

Rotor-wing Estimation Fixed-wing Estimation [McCormick, 1995]

=

0.4854 W 01.015,

(ε AVER = 9%, ε MAX = 30%, R = .9932), where

W E and W 0 are in [kg] 7000

5000

6000

0

5000

W U

=

0.4709 W 00.99,

4000 3000


2000

WU and W 0 are in [kg]

1000 0 0

2000

4000

6000

8000

10000

12000

14000

Gross Weight (kg)


) g k ( d a o L l u f e s U


Empty Weight & Useful Load (continued) 14000

) g 12000 k ( n o 10000 i t a 8000 m i t s E 6000 t h g 4000 i e W 2000

W0 = W PL + WF + WC + WE   

W U

. .4709 W00.99 +.4854 W01015 ≅ W 0

Useful Load Est. + Empty Weight Est. Empty Weight Estimation Useful Load Estimation

0 0

2000

4000

6000

8000

10000 12000 14000

Gross Weight (kg)



Empty Weight & Useful Load (continued) 100

% , 90 t h g 80 i e W 70 s s 60 o r G 50 / t 40 h g i e 30 W 20 y t p 10 m E 0

Fixed-wing [McCormick, 1995]

Fixed-wing [Raymer, 1999]

Rotary-wing [Raymer, 1999]

*

Rotary-wing [current study]

80 74 70 60

Upper bound

50 45 42 30

Lower bound

* Group Weight Statement of the US military .



Fuel Value W0 = W PL + WF + WC + WE

W = 0.0038 W0 0.976 Rg 0.650, F

  

W

Rg =

U

3000

) s r e t i l ( e u l a V l e u F

Range with standard fuel at sea level

(ε AVER = 11%, ε MAX = 33%, R = .9942), where W F is fuel value in [liters],

2500

W 0 is in [ kg],

and Rg is range with standard fuel, S / L in [ km].

2000 1500 1000

Database configurations 500

Estimation

0 0

500

1000 1500 2000 2500 3000

Fuel Values Estimation (liters)



Speed 1.0565, V NE = .8215 V M

1.0899 , V LR = .5475 V M (ε AVER = 6%, ε MAX = 31%, R = .9408),

(ε AVER = 6%, ε MAX = 20%, R = .9399),

where V NE is never exceed speed (S / L) in [ km / hr], V LR is long range speed (S / L) in [ km / hr],

V is in [km / hr ], ) r h / m k ( L / S ; d e e p S

Long Range Speed Database configurations Long Range Speed Estimation Never Exceed Speed Database configurations Never Exceed Speed Estimation

400 350 300 250 200

V

150 100 50 0 0

50

100

150

200

250

300

350

Max Speed; S/L (km/hr)



Take-Off Total Power & Transmission Rating 0

10000

20000

30000

40000

50000 Gross Weight60000 (kg)

25000

) W20000 k ( O T 15000 r e w o P 10000 l a t o T 5000

P TO = .0764 W 0 1.1455, (ε AVER = 14%, ε MAX = 37%, R = .9891), where


is the take - off total power in [ kW ] and W 0 is in [kg ] TO

12000 10000

0 8000

T TO = .0366 W 0 1.2107 , (ε AVER = 8%, ε MAX = 22%, R = .9943), where

6000 4000 2000

T TO is the take- off transmission rating in [ kW ] and W 0 is in [kg ]

0 0

5000

10000

15000

20000

25000

30000

35000

Gross Weight (kg)


) W k ( g n i t a R n o i s s i m s n a r T O T


Max Continuous Total Power & Transmission Rating Max Continuous Total Power Estimation 0 12000

l a t o 9000 T s ) W u o k u ( 6000 n r e i t w n o o C P 3000 x a M

3000

6000

9000

0.9876 V 0.9760, P MC = .0013 W0 M

12000

(ε AVER = 10%, ε MAX = 37%, R = .9889), where P MC is the Max Cont. total power in [kW ],

Database Estimation

W0 is in [kg], V is Max speed in [km / hr ] CH - 53E

12000

EH 101 9000

6000

EH 101

0

1.3393, T MC = .000141 W0 0.9771 V M

3000


T MC is the Max Cont. transmission rating in [kW ], W0 is in [kg], V is in [km / hr ]

0 0

3000

6000

9000

) W k s ( g u n o i u t n a i t r n n o o i C s s x i a m M s n a r T

12000

Max cont. transmission rating estimation (kW)



Power & Transmission Loading Power loading = the ratio of the take off gross weight over the maximum engine power. Transmission loading = the ratio of the take off gross weight over the take-off transmission rating.

g n i d a o L n o ) i s s W i k / m g s k n ( a r T / r e w o P

10 9

MINI-500 BRAVO

8

Transmission Loading Database configurations Transmission Loading Estimation

7

Power Loading Database configurations

6

Power Loading Estimation

5 Mi - 26

4 3 2 1 0 0

10000

20000

30000

40000

50000

60000

Gross Weight (kg)



Power & Transmission Loading 10

n o ) i s s W8 i k m s / g n k ( 6 a r g T i n / d 4 r e a o L w o P 2

s t f a r c r i a d e r e w o p r e l l e p o r P

9

6.4

6.3

6 4.9

3.5 2.6 1.8

0

Fixed-wing typical power loading [Raymer, 1999]

Rotary-wing typical power loading [Raymer, 1999]

Rotary-wing power loading [Current study]

Rotary-wing transmission loading [Current study]



RAPID/RaTE Helicopter Sizing Software


Helicopter Sizing by Statistics

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