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! I

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

REPORT No. 194

INVESTIGATION OF SLIPSTREAM VELOCITY

By J. W. CROWLEY, Jr.

WASHINGTON

GOVERNMENT PRINTING OFFICE

1924

https://ntrs.nasa.gov/search.jsp?R=19930091260 2020-05-08T18:08:08+00:00Z

•

AERONAUTICAL SYMBOLS.

1. 11UNDAMENTAL AND DERIVED UNITS.

Metric. English.

Symbol. 1-------------------.-------1----------------.-----------1

Unit. Symbol. Unit. Symbol.

Length .. . I t F

meter.... . ................. m. foot (or mile) ........... ft. (or mi.). Time ... . . second .... ,., ... , ... " ... ,. sec. second (or hour) ..... ,. sec. (or hr.). Force ... . weight of one kilogram. . .... kg. weight of one pound . . .. lb.

Speed .... .... .' ..... m/sec ............ . ......... m.p.s. mi/hr.. ................. M. P. H. Power... P kg.m/sec .................... . ......... 1 horsepower .............. IF

2. GENERAL SYMBOLS, ETC.

Weight, W=mg. Standard acceleration of gravity,

g= 9.806m/sec.2 = 32.l72ft/sec.2

W Mass m=--, g Density (mass per umt volume), p

Standard density of dty air, 0.1247 (kg.-m.­sec.) at 15.6°C. and 760 mm. = 0.00237 (1b.­ft.-sec.)

Specific weight of "standard J} air, 1.223 kg/m! = 0.07635 1b/ft.s

Moment of inertia, m7c2 (indicate axis of the radius of gyration, le, by proper subscript).

Area, S; wjng area, Sw, etc. Gap,G Span, b; chord length, c. Aspect ratio = b/c Distance from c. g. to elevator hinge,f. Coefficient of viscosity, JI..

3. AERODYNAMICAL SYMBOLS.

True airspeed, V

D . . 1 V ynaIDlc (or Impact) pressure"q=2 p %

Lift, L; absolute coefficient OL=q~ , D

Drag, D; absolute coefficient OD =-S q . Cross-wind force, 0; absolute coefficient

0. =!L C qS

Resultant force, R (Note that these coefficient.s are twice as

large as the old coefficients Lo, De. ) Angle of setting of wings (relative to thrust

line), i" Angle of stabilizer setting with reference to

thrust line i,

Dihedral angle, 'Y

Reynolds Number = p Vl, where l is a. linea.r di· JI.

mension. e. g., for a model airfoil 3 in. chord, 100 mi/hr.,

normal pressure, O°C: 255,000 and at 15.6°0, 230,000; .

or for a model of 10 cm. chord, 40 m/sec., corresponding numbers are 299,000 and 270,000.

Center of pressure coefficient (ratio of distance of C. P. from leading edge to chord length), Gp •

Angle of stabilizer setting with reference to lower wing. (i~-i,.) = fJ

Angle of attack, a Angle of downwash, E

•

--- -- --

REPORT No. 194

INVESTIGATION OF SLIPSTREAM VELOCITY

By .J. W. CROWLEY, Jr.

Langley Memorial Aeronautical Laboratory

1

ADDITIONAL COPIES

OF Till PUBLICATION MAYBE PROCURED FROM

TilE SUPERINTENDENT OF DOCUMENTS

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AT

5 CENTS PER COPY

REPORT No. 194.

INVESTIGATION OF SLIPSTREAM VELOCITY.

By J. W. CROWLEY, JR.

SUMMARY.

These experiments were DliLde by the ational Advisory Committee for Aeronautics at the request of the Bureau of Aeronautic, fLVy Department, to inve tigate the nlocity of the air in the ~lipstream in horizontal and climbing flight to deLcrmine the form of eApre ion giying the slipstream yelocity in term of the airspeed of the airplane. The method used consi. I, d in flying the airpInne both on a level cour e and in climb fLt full throttle fLnd mea. uring the slip­stream velocity at eyen points in the slip tream for the " 'hole peed range of the airplane in buth condition. In generi'L1 the ro ult ho,,' thfLt for both conditions i. e, horizontal and climbing flights- the relation between the slip tream \'elocity T'. and airspeed T' cao be rapre-ented by straight lines and onsequently the equation are of the form:

Vs=m V +b.

"There m and b are constants. METHOD.

The inYestigation was made on a standard Vought ( VE- 7) training airplane with Navy propeller No. 047542. The velocity in the lipstream wa mepsured b:r "en specinl Pitot L<ltic head (Fig. 1) mounted on a streamline wooden spar which ran radiall), from the exhaust mnnifold to the leading edge of the top wing. The heads were distributed along this spar as shown in Figure :2 , the in ide one being '* 'inches from the exhaust manifold and the oth(lr at 6-inch pttces , so that the region im-estigated extended well heyond the lip trearn . The spar wa mounted 0.32 diameter back of the propeller ftnd n free as po ible from any inter­ference of bnl,eing wir(ls or other obstructions. IIowever, it is felt that the read ing of the in­nermost head may be som what erratic due to its proximity to the cxhau t manifold. The e FlO. I.- Pi .tot s ta ti c hr ad.

head nnd a universally moun ted Pitot stati head fur mea 'uring the airplane's e1.il'speed (Fig. 3) were connected to the J atiollHI . \. clvi ol'Y Committee for Aeronautics multiple }'(lcol'ding mano­meter 1 which recorded the (light readings simultaneou '1r. The deLta were Qbtained as follow :

1. In horizontal Bight the throttle was opened wi]e at m'lximul1l speed, gnlClually closed until the peecl of mi.nimum power wa reached, and then opened wide at minimulU speed. A level flight pcl,th was maintained by mean , of a stato cope and the reading' recorded at airspeed increments of 10 1\1. P. II.

2. In climbing flight the throttle was opened \lride for the wh01 run, begi11l1ing \\'ith high speed horizontal flight and pulling the nirplane up through it entire range of climbing angle and ending with minimum speed in horizontcll night. ...\.. before, the reading "'ere taken at air­speed increments of 10 111. P. II.

1 Nationll .\dyisory Committee for .\e .. onnulics Heport No. 11 , or engineerillg di\'isioll, McCook]. ield , ~ eri.llg:;o .

86060-24 3

- ----- .,..--- - - ---- - - - -

4 REPORT N ATlON AL ADVISORY COMMITTEE FOR AERONAUTICS .

Four runs were made [or each condition with the r adial spar mounted on the right side. Then the installation of heads was changed to the corresponding position on the left side of the airplane and two additional runs made for both conditions.

All the flight:::; were made at an altitude corresponding to a density of 88 per cent (± 2 per cent) standard den ity and the speeds giyen are the indicated speeds for that den ity.

Before the flight te ts the he'1ds were tested in the Committee's wind tunnel for effects of misalignment with the relative wind. Also everal flights were made with a yaw meter head mounted in place of the Pitot static head to determine the amount of yaw of the lipstream.

PRECISION. The capsules used on the multiple recording manometer were calibrated against a water

column before and after th e test, and hould be precise to ± 2 M. P . H. The yaw meter recorded a maximum yaw of 3.75° corresponding to an error of 0.6 per cent of the slipstream velocity, the velocity reitding heing too great.

1' IG . 2.-)]ouutillg of Pitot ~ t'l lic h eads. FI G. 3.-Cni" ersall y mounted Pitot s lalic airspeed bead.

RESULTS.

The results are plotte L in Figures 4, 5, and 6. The slipstream velocities obtaine in the two run made with the in tallation of heads on the opposite side of the airplane agree very closely with the others and are plotted 'with them in Figure 4. To obtain the mean slipstream velocity Vs, as plotted in Figures 5 and 5, the velocity at each airspeed head wa con idered a acting oyer I1n annular area. As this area is directly proportional to the square of the distance of th e point illY sLigated from the cenLer line of the crank haft , the data were plotted with tbe individual value of slip tream velociLy as ordinates and the square of the distance from Lhe center line of- the crl1nksha[t a ab ciss£8. The mean ordinate of this curve or tbe mean slipstream velociLy was obLatned beL ween the fuselage and the place of zero slip . In every ('a c tbe position of zero slip was found to be almost directly behind the propeller tip , o the distance to the propeller t ip was u'ed t),S tbe outside limit of the slip tream. For con en­

ience, the daLa obLained at the same approximate air peed ( ± 2 M. P. H.) were plotted together as in Figure 4. It should be nOLed, therefore, that each experimen tal poin t in Figures 5 and 6 reprcsenL d~),La obLaine 1 from at least three l'Wl. T\\TO point computed on the basis of the momentum theo ry are abo plotted in Figures 5 and 6 for comparison. 2

, Assuming the sUr slream area to Le 0.8 the Fopeller di sc area, and that the velocity 01 the air is unilorm over the slipstream, Irom the momentum theory 01 propulsion we have the lollowing rela tion:

Equating (1) and (2) a nd reducing Wbere 1',= velocity ol slipstleam ( It ./sec.) .

\' ~airspeed ( It .!sec.) . D = diameter 01 propeller (ft .). A,=slipstream area

Tbrust~ ill ( 1'.- n ~~ A . 1'.( V, - V)

~ . OO15 D' V ( 11, - V )

'I' h t 5['0 P ~ rus =-T'-

( JI J/) Jf =3~OOO P....'! .- II VD 'l

oil ~ mass 01 air Ilassing through pl'opeller in ] second . p ~ horsepower. ~ ~ propeller efficiency .

(1)

(2)

:t: 0.:. 160

~ 140 12

1120

IJ)IOO ~ Ii) 80 ~ 'v 60 ~

INVESTI ATIO T OF 'LIPSTREAM VELOCITY,

Curves of slipstream velocity

• Run e " Cil a> o

I 2 3 4 Oppasite

side

Note: Plane of readings 0.32 diameter back

of propeller

f-- I-Meon alr!s~e~d- f--f--1-- f-- = 83.5 M.P.,;J= 1-1---f-- Climbing fligh1 f--f--

. 1:2- 1-1-

I ' '-f--

I 8- f--f--Il I-f--

0 " 10.: ). I~ 'I~ I I ,

:t: 0.:. 160

~/40 8 t 20

1/)100 ~ I/) 80 ~ 'u 60 .Q

f-r-1--f--

11 0

~ 40 2

~ 0.:. 160

~ r{l40

2/20 .k \1)100 ~ I/) 80 ~ 'u 60 ..Q

f--f---f---

I ~

M~ah bi)s~e~d f-I-I- = 58.0 M.P.Ht I-f--I- Climbing fngh1 f-'-

"g 1--

I· 1--

18- f--,l l-

e 0

0 I I I l'~ ~ I

345 Distance from t crankshaft, ft.

~Mean alrs~e~d-1-1-'- = 117.5 M.P.H. I-f--f--- Climbing flight

I I f-I-f--

~I )ok , 1:2-

-'-

-I' 18- -let ,

-I--f---I-

0

k

-1~a'!' b)s~e~d - f--I-- = 66.8 M.P.~~t I-f-- CH"mbing fngh~ f--f--

,:2- 1-1-

I · 1-1-

,8- -i-

,~ -:--'-

I , . N. ,

I 345

Distance from tt. crankshal'f, ft,

-:-I- M~a;" ~1)s~e~J-f-r-1-+= 51.5 M.P.H. +:--- 1--

-- Horizontal fn9?t f--

1:2-1--

/ . f---,g. 1--

I l f---

/ . I 1:' '''- 0 !"W- /

13-. 1 0 fl1--~ ~ 40

2 3 4 5 ~ 40

2 3 ' 4 Distance from <l. crankshoft, ft.

5 3 4 Distance from tt. crankshaft, ft.

5 Distance from <t. crankshaft, ft.

-f-- - Mean ai)s~e~d -I- :t: 0.:. 160

~ f{I40

I-f-I-Meoh b,)s,6e~d-1--r-+ = 82.0 M.P.H.,+:-

f-- f-- M~ah b,)s,6e~d- '-I--f-- -:to = 66.5 M.P.H. +--f-- f--I- f--- 1-1-~= 113.0 M.P.H. - -I-f--I- Horizontal fli91't - ,.-1-

,:2- -f--, .--I-

1-1- Horizontal (/191't f---I-f-'-

':2-1-1-

H- I . f--I-

1-1- Horizontal fli9?t '-I-

I;:. f.- 'f" t-. 1/ KL 'L 18-

Id:

-I--f--

1120

1/)/00 ,g. f--f--

Id: ~f--

111" -

. I 0,.... " .... - r;: . "'" J I

~ I.Q. I ..... . ,..- . 0 ..... , Ii""

I/) 80 ~ q~.

0 -.l.. 0 , I

3 4 Distance from <t. cran kshaft, ft.

~

5

'v 60 ..Q

~ 40 2

, I I

3 4 Distance from <t. crankshaft, ft.

5

Id: I 'I

3 4 Distance from <t. crankshaft, ft.

FIG. 4.-Slipslrcam velocity curves for VE-7.

/.30

120

hlO

• Climbing flighf o HOrizontal flight -r.---+--i '" By momentum theory

fIlM Horizont al flight

-+

I ~O 60 80 100 120 Mean airspeed MPH. (Indicoted)

FlU. 5.-blipstream velocity, VE-7.

150

140

50

I--

V \

' - ~ 1--

• Climbing flight I 1-- 0 Horizontal flight

'/ ~ BY ,moTenturn theory

V Climbin~ flight /. ~

~ '/ V y o

/0 "., v< Ho"rizonfol flight

V ,,/

4Cko 60 80 100 120 Meon airspeed MPH. (Indicated)

FIG. 6.-Slipstream velocity, V E- 7.

-r--:-f--1--

5

5

6 REPORT NATIO CT AL ADYISORY CO IMITTEE FOR AERO.l,TA TICS.

Referring to Figure 6 it will be een that for borizonLal flight the curve of r. against V, except for the very low speeds, is ~), sLraight line and iLs eq uation may be wriLten:

V.= mV+ b. m = 1.0 b = lO.OM. P.H. Vs = V + 10.0 M. P. I-I.

Also from the same figure it will be seen that the curve for climbing flight is a traight line and its equation may be written:

Vs= mV+ b m =.75 b = 40.5 M. P. H. Vs = .75 T + 40.5

The di tribution of the ,elocity along the radial line in the Ep tI'eam i plotted in Figure 4 and 7. Eiflel's 3 curves for a model propeller are inserted for compari on .. The agreement

Dis/once from (, crankshaft. ft. is particularly good and 1.70 a I 2 3 4 5 2.40 it is in tere ting to note

hi V£ 7: I Dffel model Ero~ to ~ V/NO ==.138) Ii Vou

b- 4f-.435 ~ c - --:+- .480 d- --:+- -.530 e- .. - .592

ff- ~,-.558

1.60

1.50

1.40

1.30 , .I ::..

~/.20 I , 1.10 I

,I , 1.00

,I I 0..90 ,

g- r-:t-r ·584

II

1),-

I /'

/ /"

.",

I: G~/m 'ing flight

I " Horizontal flighf 0.80

; a

~ b ~

C ; -;..

:!..~ e ; 'i-r-':"

9

;

;

:

,\ \

i-"I \ \N

.\ ~'.I

f..'\

\\ ,~

~ :

t::. . ~ <

i

2.20

200

1.80

1.60

::.. ~/.40

I.2D

1.00

0.80

0.60

I ~-,-, / .3 ;

I 1/ l -' I , I ; : I . 4 I / i ). ; , / : I / .5 ; I ,'\., ~ , / ~ L / , Z~ L I .8 :; ,

; . .9 ~I ~

I 'F,' l : :

--------------- ... --2:,

lhat with reference to the airplane, the air just out ide the slip stream ha a velocity whi h i less than the velocity of the undisturbed a i r. Similar results 11 a v e b en found at the . P. L. with model propel-101'S . I

The Llu'u tforboth horizontal and climbing flight as computed on

20 30 40 50 50 0.400 10 20 30 40 50 50 the basi of the momen-,I I I Ii I I iI II J : ~~-----------------~

I; -' ... 10

Distance from (, crankshaft in % propeller diameter tum theory is plotted FIG . i.- ' Ii (lstroa lll \ elocity t urves , in Figure .

The ordinate intersected between the Lwo thrust curves repre 'ents the thru t available for climb. Knowing this value, the air pced along the path and the weight of the airplane, the rate of climb may be calculated from Lhe fol­lowing expl'e sion:

Rate of climb = V ~ Where

V = the ai.rspeed in fL. /min. W = weight of the airplane. Ta = thrust available for climb.

This computation has been made H,nel the curve of rate of climb against airspeed has been plotLed in Figure 8, To check the computed rate of cljmb a flight was made and the actual raLe of climb be­tween 0 and 3,000 feet wa obtain <l at ajrspeed of 70, 80, 90 , and 100 M. P. H. Thi curve has al 0

been plotted in Figure The computed curve represents the rate of climb at per ent tundard density and the observed curve repre enL the rate of

• Nouvelles Reoherches SUI La R esistan ce de PAir et AYiat ion.

1000

.~ 800

.t "" .....

~-600

~ .... Cl QJ400

~ 200

o

-I--k;hrust in J climbing flight

SOD

~ ~ ~

f / ~ "" c--

~. ~ L. f Thrust n Rate of

h~I-_~CltmbL-f\ f r om

f light - .1 ~ L\ obser=-

Rote of c limb ..- vation from thrust, bY" momentum theory

400

300 ~

100

\ \

50 7D .90 110 130 a Mean airspeed, M.P H

FIG. - Perform a uoe of \ ' E -7 from slipstream datu .

• Reports and Mem ora nda No. 371.

- - -- - - -.--~-.-~---------~~--~~-.~~.----------

INVESTIGATION OF SLIPSTREAM VELOCITY. 7

climb at 91 per cent standard density. The condition are sufficiently close for comparati,e purpose. The maximum rate of climb i the same by both methods and although the actual performance cune indicate the maximum ,alue of rate of climb at a higher airspeed than does the computed curve, the discrepancy is slight and probably within the accuracy of the measurements. .

Value of R. P. 1\1. was observed in all the e te ts and a curve of R. P . M. against air peed ha been inserted for reference (Fig. 9).

1800

..-D.

1700 ~"

. ~

1600

• 1500

~

r.-"" • I I

I I

~ Q;

1400 I

I I I I \ \

1300 I I \

1200

1\ \

1/00 ~

100~0 50

V /. / ..

Climbing flight ;,rV< ,/"

"/ " 0>

~ ~ / • ill.---- " l{ / '"

.,, / /

Horizonfol fll~hf V 1/

/ f'RUn 2 0 Horizontal 0 " 3 -

/ I flighf Q" 4 • " #

/ " Jim.!"" I r~ ~ -?' .e /

flight <D" 3 ® " 4 -* " # I I

#.1 OPPIosif7 s i de

60 70 80 90 lOa /10 Indicated airspeed M.P.H.

FIG. 9.-Reyolulion5 per minute \"5. airspeerl, YE-7.

o CLUSIO S.

-

r--

r---

r---

120

Besides the fact that the expre sion for the value of the slip tream velocity may be repre­'ented by a straight line, the most noteworthy fact brought out by this report is the good compari on between wind Lunnel and free flight re ults and the results obtained by the com­putation based upon th momentum theory. A erie of te t on a single airplane of one type may not produce any conclusi,e evidence but it doe point strongly to the conclu ion that for the usual uses to which a knowledge of the slipstream velocity is applied, namely, slipstream corrections in preliminary performance calculations and design, the momentum theory is sufficiently accurate.

REFERENCES.

Slipstream Correction in Performance Calculations. N. A. C. A. Report No. 71. Preliminary Experiments to Determine Scale and Slip-Stream Effects on a 1/24 ize Model of a JN4H Biplane

N. A. . A. Report No. 122. ouvelles Recherche Sur la Resistance de l'Ai r et Aviation (Eiffel), p. 333.

An Investigation into the Nature of the F low in the Neighborhood of an Air crew. R. and M . 371. Experimental Determination of the Slipstream Behind the Air crew of a Pu her. R. and M. 3 2. Exploration of the Air peed in the Air crew 'lipstream of a Tractor Machine. R. and M . 438. Exploration of the Slipstream Velocity i1.1 a Pusher Machine. R . and M. 444. On a Method of E t imating, from Observation on the Slipstream of an Air crew, the Performance of the Ele­

ments of t he Blade and the Total Thrust of the Air Screw. R. and M . 460.

o

Positive directions of axes and angles (forces and moments) are shown by arrows.

Axis.

Force (parallel

Sym- to axis) Designa.tion. symbol. bol.

Longitudinal .... X X Lateral ... ...... y y Normal ......... Z Z

Absolute coefficients of moment

Diameter, D Pitch (a) Aerodynamic pitch, po.

(b) Effective pitch, pe (c) Mean geometric pitch, Pc (d) Virtual pitch, pv (e) Standard pitch, p.

Pitch ratio, p/D Inflow velocity, V' Slipstream velocity, V.

Moment about axis. Angle. Velocities.

Designa-tion.

r~lIin~ ..... Pltc~g ... yawmg .....

Linear Sym- Positive Designa- Sym- (com1o-direc- Angular. boI. tion. tion. bolo nenta ong

L M N

axis).

Y~Z roll ..... <P 'U P Z~X pitch .... e f} q X~Y yaw ..... 'II w r

Angle of set of control surface (relative to neutral position), O. (Indicate surface by proper subscript.)

4. PROPELLER SYMBOLS.

Thrust, T Torque, Q Power, P

(If "coefficients " are introduced all units used must be consistent.)

Efficiency 71 = T VjP Revolutions per sec., nj per min., N

Effective heli..-x: angle <I> = tan-l (2;"n) 5. NUMERICAL RELATIONS.

1 IP = 76.04 kg. m/sec. = 550 lb. ft/sec. 1 kg. m/sec. =0.01315 IP

1 lb. = 0.45359 kg. 1 kg. = 2.20462 lb.

1 mi/hr.=0.44704 m/sec. 1 m/sec. = 2.23693 mi/hr.

1 mi.=l609.35 m.=5280 ft. 1 m. = 3.28083 ft.