Fuselage self-propulsion by static-pressure thrust - CAFE Foundation

AI AA-87-2935 

Fuselage Self-Propulsion by Static- 

Pressure Thrust: Wind-Tunnel 

Verification 

F.R. Goldschmied, Monroeville, PA 

AIAA/AHS/ASEE Aircraft Design, 

Systems and Operations Meeting 

September 14-1 6, 1987/St. Louis, Missouri 

For permission to copy or republish, contact the American lnstitute of Aeronautics and Astronautics 

1633 Broadway, New York, NY 10019

FUSELAGE SELF-PROPULSION BY STATIC-PRESSURE THRUST: 

WIND-TUNNEL VERIFICATION 

Fabio R. Goldschmied' 

Monroeville, PA 15146 

d' Abstract CAP = (QxAB25/qoUoV0~66) Fan air power 

.-.J 

- * 

The novel concept of body self -propulsion by 

static-pressure thrust has been introduced and 

verified in the wind-tunnel by direct integration of 

radial pressure distributions for self-propelled 

&symmetric bodies with slot suction BLC and stern 

jet discharge. 

This concept also means that power can be 

supplied only to BLC, since the jet discharge is 

achieved at jet total-head equal to free-stream's; 

the skin-friction drag is offset entirely by the 

pressure thrust. It is the most efficient form of 

body self-propulsion. It also has been shown that 

50% power reduction has been achieved as compared to 

the test body/wake-propeller NASA configuration, 

with only 1% of its mass flow. A total aircraft 

power reduction of 40% to 60% is feasible as 

compared to current General Aviation aircraft at 200 

!E" cruise speed. 

CDF = (F/qoYo'") 

c~~ = 'DW C~~ 

Cos = (QxAE20/~oUoV 0 

'Il' = 'DW + 'DS 

Nomenclature 

Airfoil chord 

Airfoil wake-drag 

coeff. 

Body wake drag coeff. 

Reference body wakedrag 

coeff . 

Body friction-drag 

coeff. 

Body pressure-drag 

coeff . 

66) Body equivalent 

suction drag coeff . 

Body total drag coeff. 

C - - CD = 

T- 

(T/%Vo.") Body thrust coeff. 

c = (P-Po/so) Static pressure coeff. 

P 

Cpt = (E-PO/%) Total pressure coeff. 

Cg = (AHz5/qo) Total-pressure rise 

coeff. 

CQ = (Q/UoV 0.66) BLC suction flow coeff 

Cm = (m/pouoV BLC suction mass flow 

coeff. 

Gms = 

AIAA 87-2935 

coef f . (01 

Fan shaft power coeff. [O] 

Jet diameter or 

propeller dia. [ftl 

Max. body diameter [ftl 

F Skin-friction drag [Ibl 

5 Body suction-slot width [it] 

E 

Fluid total-head [lb/ft2] 

bE 

Total-head rise [lh/ft2] 

Jet thrust of airfoil 

m = PQ 

jet-flap [Ibl 

Body length [ftl 

BLC suction mass 

flow [lb x secjft] 

Propeller speed [l/secl 

P 

2 

q = 1/2 pu 

Q 

Static pressure 

Dynamic head 

BLC suction flow 

[lb/f t2] 

[l b/ft2] 

[ft3/sec] 

R Body radius [ftl 

RL = (LU0/4 Length Reynolds Number [O] 

Rv = (U0V0'33/~ Volume Reynolds Number [O] 

T Thrust Pbl 

V Body volume [ft31 

U Fluid velocity [f t/sec] 

x Axial coordinate [ftl 

x Propeller shaft torque [ft-lb] 

w Wake-drag (measured by 

Subscripts 

0 Free-stream 

Consulting Engineer; Associate Fellow,AIAA j Jet 

Copyright 1987 by Fabio R.Goldschmied P.E. R Reference body 

wake traverse) [Ibl 

Boundary-layer 

displacement thickness [ft] 

Fan efficiency 101 

Boundary-layer momentum 

thickness 

[ftl 

2 

Kinematic viscosity [ft /set] 

2 4 

Mass density [lb-sec /ft ] 

Skin-friction [lb/f t2] 

Jet angle of jet-flap [deg] 

1 Edge of boundary-layer 

2 Suction-slot inlet (Sta. 2, Fig. 4, Ref. 22) 

5 Jet discharge (Sta. 5, Fig. 4, Ref. 22)

I. Introduction 

This paper attempts to focus the attention of 

aeronautical engineers on the great potential of 

aerodynamic static-pressure thrust AKA form thrust 

AKA negative pressure drag AKA negative form drag 

for fuselage self-propulsion. Over thirty years 

have elapsed since the initial aerodynamic research 

phase in the 1950's; younger engineers today seem to 

be totally unaware of this early work after HW 11. 

It is still relevant to quote J. B. Edwards 

1 

(1961) : "Our aeroplanes still follow the old 

concept of the powered glider, although thcy have 

become more refined as time has passed. It is truc, 

of course, that the acceptance of this concept 

results in a great simplification of the aircraft 

design procedure. One set of problems and 

considerations is divorced from the other and all is 

well, provided that consistent definitions of drag 

and thrust are accepted by the people working on 

these two separated sets of problems. The airirame 

group measures its achievement by the lift/drag 

ratio .... The engine group measures its cruising 

achievement in terms of specific fuel 

consumption ..." It would appear downright 

iconoclastic to even suggest that power can be 

usefully and efficiently applied to the airframe 

itself to increase lift and to eliminate drag, even 

to the point of creating "pressure thrust"; this is 

why some authors have employed the curious semantic 

appellative of "negative drag" for pressure thrust. 

Pressure thrust has been documented experimentally 

in several known cases. Perhaps the best-known case 

is that of the shrouded Dropeller: .I. E. Fanucci, et 

a1 (1974)' carried out an excellent experimental 

investigation at West Virginia University. Figure 1 

presents the test set-up and Figure 2 presents the 

measured thrust vs. power, with the three categories 

of propeller thrust, shroud thrust and total thrust. 

At max. power it can be seen that the shroud 

pressure thrust is 60% of the total, while the 

propeller reaction thrust is 40%. Another well- 

known case is that of the airfoil with jet-flap. 

I. M. Davidson (1961)3 discusses the jet-flap 

airfoil and states: "Naturally the jet reaction J 

itself has a thrust component of only J cos $ but 

the difference J(1-cos #) is recovered in the guise 

of an aerodynamic pressure thrust distributed over 

the surface of the airfoil'. 

-2- 

Fig. 1 ~ 

Wind-Tunnel 

Layout of Experimental 

Shrouded Propeller (From Ref. 2) 

c-----I 

0.25 0.5 0.75 1.0 

POWER HP 

Fig. 2 - Experimental Shrouded Propeller 

Performance: Thrust YS Power (From Ref. 21 

N A. Dimmock (1957) 4 presents experimental 

wind-tunnel results of a 12.5% thick airfoil with 

jet-flap at 0 = 58" from the chord line, as 

presented in Figure 3. The measured total thrust 

was 76.5% of the jet thrust, while the axial 

component of the jet thrust was only 52.5%. Thus 31% 

of the total measured thrust was pressure thrust and 

69% was reaction thrust. 

B. S . Stratford (1956)5 was very aware of the 

potential for reducing or reversing the pressure 

drag of an airfoil with jet flap. The following is 

quoted from his Ref. 5 (pp. 181 and 182): "The form 

drag (which is that part of the two-dimensional drag 

transmitted by the normal pressure forces and not by 

skin friction) may be associated with the boundary 

layer displacing the main flow from the true profile 

of the aerofoil and thereby preventing the full 

-

0.30 

AXIAL JET THRUST : 0.528 

AIRFOIL PRESSURE THRUST : 0.237 

1.0 

YET COEFFlClENr - Cs 

Fig. 3 - Experimental Jet-Flap Airfoil Performance: 

Measured Thrust/Jet Coeff . vs Jet Coeff. (From Ref .4) 

pressure recovery at the trailing edge. 

The rate of growth in the boundary layer of 

2 

the momentum deficiency (p U 8) can be expressed 

by the momentum equation as 

d/dx (p UZ1 8) = T~ + 6*dp/dx (1) 

Now the drag of the aerofoil is equal to the 

momentum deficiency in the wake at infinity, thus 

2 

cD = (P uo em)wake/(1/2 P ‘2 ‘) 

Integration of equation (1) along both surfaces of 

the aerofoil therefore gives 

(2) 

~ 

-3- 

T.E. 

CD = (l/l/ZpU:C) J 70d~ + (l/l/ZpU)x 

0 

m (3) 

J 6*(dp/dx)dx (integrals along both surfaces) 

0 

The first term in equation (3) is the direct 

skin friction force (taking the surface force as 

being everywhere parallel to Uo), and so the second 

term must represent the form drag: 

‘D form 

00 

m 

= (l/l/ZpU) J 6* (dp/dx) dx 

(= J (6’/c) d (C )) (both surfaces) 

P 

0 

Equation (4) shows that the form drag is pro iced 

thick boundary layers in regions of rising pressure‘ 

for then 6* will be lar~e and dp/dx will be 

positive. This combination usually occurs towards 

the trailing edge of an aerofoil. However. any 

device which can manipulate the boundary layer so 

that the distribution of 6r makes the value of the 

integral zero or negative would be able to eliminate 

the form drag or even to provide a form thrust. 

Just as for the thrust augmentation considered in 

Ref. 6, this does not imply a creation of power, or 

even perpetual motion. 

An example in subsonic flow is that of an 

aerofoil with a constant pressure distribution, 

other than for a “pulse’ of suction very close to 

the trailing edge. It is arranged for transition to 

occur instantaneously at the peak of the pulse. The 

value of the displacement thickness 6* would 

decrease sharply at transition and, provided that 

the magnitude of the pulse were not too great, the 

displacement thickness would be smaller during the 

pressure rise than during the pressure fall; there 

would thus again be a negative form drag. The 

decrease in the total energy dissipation has been 

achieved by making the internal boundary-layer 

momentum transfer, or mixing, which now occurs 

largely at transition, take place at a high suction, 

so that the internal velocity differences are much 

smaller. This example is one which might possibly 

have practical application in its own right, but the 

present question is whether the form drag can be 

removed by high velocity injection. 

0 

(4)

~ 

To simplify the problem it is assumed that the wetted area and pressure drag is mentioned as an 

velocity of the propulsive jet is very high compared occurrence of small import 'without turbulent 

with that of the main stream. This implies a low separation". No information is given on prediction 

propulsive efficiency, but it justifies the neglect 

of both the small negative displacement thickness of 

methods for the allowable aftbody pressure recovery 

on convex/conical or concave aftbodies. In other u 

the jet and also the small change in the jet words, the aeronautical students are left in total 

velocity that could be caused by the pressure darkness about fuselage aerodynamics. However, this 

variations around the aerofoil. It also shows the does not truly represent the state of the art. 

source of the economy. With this simplification, Thirty years ago, P. A. Cerreta (1957)8 carried out 

suppose that the pressure distribution is such that an extensive subsonic wind-tunnel program of an 

the main stream velocity on the upper surface axisymmetric body with single-slot suction BLC and 

increases continuously to a peak value close to the transition tripped at 10% length (i.e., fully 

trailing edge and then, after a short length at this turbulent skin-friction) at the U.S. Navy David 

level, decreases almost discontinuously to the value Taylor Model Basin. The body configuration had been 

actually at the trailing edge; further suppose that proposed and designed by F. R. Goldschmied 

this is made possible by injecting sufficient of the (1954)gv'0 on the basis of the rational integration 

propulsive jet at the beginning of the short region of body pressure-distribution and suction BLC. The 

of peak velocity just to reduce the total momentum body was designed to yield a stepwise pressure 

deficiency to sero. After the mixing has occurred, recovery, i.e., the adverse-gradient region was 

the displacement thickness of the boundary layer reduced to zero length; the boundary-layer momentum 

plus jet will become approximately zero and will thickness was kept essentially constant across the 

remain so for the subsequent sharp pressure rise. suction slot and the concomitant pressure rise. 

Thus the integral in equation (21) will have a zero 

value for 6t when dp/dx is positive, so that the 

The measured wake-drag was very small, much 

below the computed turbulent skin-friction drag 

non-zero values elsewhere will then make the farm coefficient CDp = 0.0190; a listing of the test 

drag newtive, (i.e., pressure thrust)". 

results is given below in Table I, in order of 

ascending wake-drag, from 0.0003 to 0.0027. The 

11. Axisymmetric Streamlined Bodies 

suction drag is the "equivalent drag" Corresponding 

The popular definition of 'streamliningn for 

to the power required to bring the suction mass flow 

back to free-stream total-head. 

axisymmetric bodies is based on the absence of flow First of all, it can be noted that the first 

separation on the aftbody, even though the inviscid three runs were achieved with a wake-drag less than 

terminal pressure recovery C = 1.0 for convex or 

P 

conical aftbodies cannot be achieved in viscous 

2% of the streamlined airship drag for equal volume 

and speed; for practical purposes this may be termed 

flow. A wake must be generated, with its 'self-propulsion'. It is certainly relevant at this 

displacement effect; actual terminal pressure paint to quote Kuchemann and Weber (1953)ll: 

recoveries range from C = 0.10 to 0.20 and thus 

P 

even the best streamlined convex/conical bodies have 

"nother line of development may be the extreme 

application of boundary-layer suction, which uses 

pressure drags of the order of 15% of the total. It air from the boundary-layer on the aircraft surfaces 

can be noted that the axial pressure force in as working air for the engine and restores it to 

inviscid flow is zero: in the generally accepted full free-stream energy, instead of producing a 

view the pressure drag, at best, can only be reduced thrust farce to overcome the associated with 

to zero by suitable boundary-layer control. A the wake." 

typical treatment of fuselage aerodynamics for Kuchemann and Weber did not discuss the 

students is that given in the textbook by 

skin-friction drag that had not disappeared and 

7 

E. Schlichting and E. Truckenbrodt (1979) : while required a counteracting body thrust; they 

the inviscid flow is discussed at some length, considered only the momentum balance upstream and 

little is discussed about the actual viscous flow. downstream of the body. 

The skin-friction drag is stated to be essentially 

that corresponding to a flat-plate with the same 

L 

-4- 

'0

Table I - P. A. Cerreta (1957)' Data Summary 

The drag saving was an 

impressive 40%, based on the average of the five 

best .test runs. It is interesting at this point to 

Reynolds Slot Wake- Suction- Total- 12 

No. Width Drag Drag Drag note that 20 years later Brian Edwards (1977) 

a/L COW- - C 

c~s- -DT- discussed the concept of momentum restoration for a 

3 Nearly Self-Propulsion Runs (COWL M 1,1 A:- . ship Drad body with suction BLC and predicted theoretically 

4.6 ... 

4.36 

4.55 

0.008 

0.0c- M 

0.004 

0.0003 

n nnns 

0.0005 

0.0191 

n.ozn7 

0.0191 3 

0.0194 

0,0212 

0.0195 

the potential for 50% propulsion power reduction: 

aThe circumstance that makes this possible is the 

existence of the sucked mass flow. With boundarylayer 

flow control, most of the friction drag is 

10 Very Low Wake-Drag Runs (CDw < 5% Airship Drag). 

4.36 0.012 0.0007 0.0199 0.0206 

7.25 . 

0.016 0.0007 0.0184 0.0191 

~ ~~~~ 

4.46 0.012 0.0008 0.0188 0.0206 

7.05 0.008 0.0008 0.0180 0.0188 

4.51 0.008 0.0009 0.0193 0.0202 

6.95 0.008 0.0009 0.0177 0.0186 

7.10 0.008 0.0009 0.0177 0.0186 

7.10 0.008 0.0010 0.0167 0.0177 

7.10 0.008 0.0013 0.0171 0.0184 

10.20 0.016 0.0013 0.0160 0.0173 

6.90 

7.20 

9.80 

10.10 

4.61 

6.95 

7.06 

7.10 

10.15 

..- ' 11.20 

17 Low Wake-Draa Runs (CDw- 

. . .~ 

11.30 

0.012 

0.008 

0.016 

0.016 

0.016 

0.012 

0.012 

0.016 

0.008 

0,012 

0.012 

0.0014 

0.0014 

0.0014 

0.0014 

0.0016 

0.0017 

~ ~~~ 

0.0018 

0.0018 

0.0019 

0.0010 

0.0019 

0.0164 

0.0166 

0.0161 

0.0161 

0.0198 

0.0165 

o.oi66 

0.0180 

0.0149 

0.0147 

0.0145 

0.0178 

0.0180 

0.0175 

0.0175 

0.0214 

0.0182 

o.ois4 

0.0198 

0.0168 

0.0166* 

0.0164* 

11.30 O.OQ8 0.0020 0.0142 0.0162.r 

10.00 0.008 0.0020 0.0147 0.0167 

4.41 0.012 0.0022 0.0178 0.0200 

6.95 0.008 0.0024 0.0157 0.0181 

11.30 0.012 0.0026 0.0131 0.0157t 

10.10 0.012 0.0027 0.0132 0.0159t 

Note: Asterisk indicates five best runs with 

minimum total power. 

It must be noted that these first three runs, 

while having minimal wake-drag, did. not achieve the 

lowest total drag, i.e., the sum of wake-drag and 

balanced by the flux of momentum change in the 

sucked mass flaw. It follows that the thrust that 

could be developed by restoring the sucked mass flow 

to its original momentum would very nearly 

counterbalance the whole of the friction drag. It 

can be shown that the vower required to do this is 

only half the power .that would be required to 

generate the same thrust in the most efficient 

conventional propulsive system, i.e., one-half of 

the power required by a system with Froude 

efficiency of 100%". It is not unreasonable to note 

that a prior 40% experimental drag reduction is an 

excellent basis for a theoretical prediction of 50% 

power reduction at a much later date. 

The Cerreta' test results were analyzed and 

discussed by Y. P. Earsche, F. A. Pake and E. R. 

Wasson (1957)13 and later by F. R. Goldschmied 

(1966)14; neither reference dealt with the thrust 

required to balance off the skin friction. Despite 

the excellent results, this work was deliberately 

ignored as iconoclastic since it is common knowledge 

that a 40% drag reduction on streamlined bodies can 

only be achieved with laminar skin-friction (even if 

it requires 114 BLC suction slots for a single test 

body, as demonstrated by W. Pfenninger (1977) ) and 

that it is quite unthinkable with transition tripped 

"equivalent suction drag". Far the lowest total 

drag, the average of the five best runs is given 

below: 

at 10% length. 

A second test program was carried out in 1969 

in the YcDonnell 8.5 x 12 Low Speed Wind-Tunnel with 

the same test model as modified with more extensive 

Length Reynolds Number 

BLC Suction Slot Width 

Wake-Drag 

Equivalent Suction Drag 

Total Drag 

7 instrumentation and several new suction-slot inlet 

$, = 1.104 x 10 

configurations. The test results were reported by 

g/L = 0.0112 

F. R. Goldschmied (1077)15 eight years after the 

G, = 0.0022 . . 

Y I, 

wsc. 

CDs = 0.0139 

Figure 4 shows a photo of the test model with 

COT = 0.0161 

China Clay coating to visualize laminar YS turbulent 

For comparison the streamlined airship body in 

'- 'the same wind-tunnel yielded CDw = 0.0267 at R - 

L - 

1.26 x lo7, with transition also tripped at 10% 

flow: free transition occurred at 73% length at I$ = 

6 

7 x 10 . The significant improvement over the 

length in the same manner. 

-5- 

Cerreta 1957 results is given by the addition of 

passive EL, i.e, the addition of a Ringloeb cusp at 

36

the slot's leading edge: the minimum required BLC 

suction mass flow is below that dictated by the 

G. I. Taylor criterion as presented by J. M. 

Preston, N. Gregory and A. G. Rawcliffe (1953)16 and 

much below the 1957 results. The comparison of the 

8 

196915 suction data against the 1957 data is given 

in Fig. 5. The Ringloeb cusp is also extremely 

helpful in the case of zero suction by preventing 

massive flow separation; however, the price is some 

increase of pressure loss. Even so, as shown in 

Fig. 5, the 1969 total drag is 20% less than the 

1957 drag. 

Pig. 4-Wind-Tunnel Test Body: China Clay Transition 

Study at RL = 7 x IO6 (From Ref. 15) 

In conclusion, the fundamental question raised 

by the Cerreta' and G~ldschmied~' experimental 

results is illustrated in Figure 6: what body thrust 

force occurs to offset most of the turbulent skin- 

friction drag, computed to be CDF = 0.0190, so as to 

bring the measured wake-drag down to the averaged 

CDW = 0.0022? This force cannot be anything else 

but a static-pressure thrust CT = 0.0190 - 0,0022 = 

0.0168, since there was no reaction thrust whatever. 

Indeed the suction mass flow was educted from the 

test body through a hollow strut and discharged 

outside the wind-tunnel. The power required to 

restore free-stream total-head to this flow was 

termed "equivalent suction drag", 

(QxAHZ& / ( B ~ ~ V ~ ' ~ ~ . 

'DS = 

-6- 

0 

I, 

0.014 0.02 0.03 

SUCTION COEFF. Cg 

Fig. 5 - Goldschmied Wind-Tunnel Tost Body: Drag 

Coeff. CD vs Suction Coeff. C for 1957 (Ref. 8) and 

1969 (Ref. 15) Test Proarams Q 

COT ~ 

0.0025 

b 0.0135 

Fig, 6 - Axial-Force Layout for Test Model with 

Turbulent Skin-friction and BLC Aftbody Suction 

(Data from Ref. 8) 

"* 

I 

._",

..,. .*.- 

111. Self-Propelled Streamlined Bodies Table I1 - Summary of Confinuration Designations 

A wind-tunnel test of a self-propelled model was conf. 00 - open Noizle, Free-Transition-Figs. 7 and 8 

ieeded to complete the experimental verification Of cod. 50 - open Nozzle, Transition Trip at 58% Length 

... the Goldschmied integrated aerodynamic concept, since Conf. 10 - open jqozzle, Transition Trip at 10% Length 

both the 1Q578 and the 196915 tests had the BLc Conf. 01 - Short Tailboom, Free Transition - Fig. Q 

suction mass flow educted through a hollow strut, as 

Conf. 51 - Short Tailboom, ~ ~ ~ ~ Trip ~ iat t58% i ~ n 

mentioned above. In 1981 a third wind-tunnel test 

program was carried out, again at the David w. Taylor 

Length 

~ ~ at i 10% p 

Naval Ship R&D Center (DTNSRDC), under DARPA Length 

sponsorship: the old test model was resurrected and Conf. 02 ~ ~ i l b ~ ~ ~ ~ ~ ~ ~ / - ~ ~ ~ ~ ~ ~ 

modified with a machined cusped leading-edge for the 

Fig. 10 

suction-slot, an internal sUction/ProPuleion ll,oco Con?. 52 - ~~ilboom/Emp~nnag~, Transition Trip at 58% 

RPM 6n dia. axial fan and also a tailboomlempennage 

Conf. 11 - Short Tailboom, ~ ~ ~ ~ ~ i t i ~ 

Length 

assembly designsd to achieve neutral static stability. 

Con?. 12 - ~ ~ i l b ~ ~ ~~i~ ~ / 0 10% ~ ~ ~ ~ 

Three configurations were tested: with open nozzle, 

with short tailboam and with tailboom/empennage; each 

configuration was tested with free-transition, and 

with transition trips at 58% and 10% length. 

For convenient reader's the 

configuration designations are given below. 

Fig. 7 - Starboard Photo View of Test Model with 

Open-Jet Aftbody (Conf. 00 From Ref. 18) 

Length 

- 

~ ~ ~ ~ ~ i t i ~ 

A very extensive wind-tunnel test: program Was 

carried out with these nine self-propelled 

configurations; the test results have been reported by 

F. R. Goldschmied (1986)17, (1982)18 (1983)" and by 

H. J. BOWS and E. J. Neumann (1982)2d. An application 

of the test data to an optimized LTA system was 

presented by F. R. Goldschmied (1983)"; another 

application to Mini-RPV and small General Aviation 

aircraft design was presented in 1984 

22 . In view of 

the success obtained with the %-year old forebody, 

corroded and pitted as it was, in maintaining laminar 

flow up to 73% length with free transition, despite 

the flat pressure distribution, considerable further 

optimization work was carried out at DTNSRDC by B. J. 

(19s3)23, (1Q86)24, by J, Bowe (lg85125, by 

R. L. Walker (1985)26 and by J. F. Slomski and D. C. 

McMillen (1986)27. The general objective of this 

considerable work was to maximize natural laminar flow 

on the forebody at the higher Reynolds Numbers by 

prescribing the forebody pressure distribution and 

achieving the required shape. It was also realized 

that aftbody slot suction has a significant beneficial 

feedback on transition, as compared to the 

conventional aftbody scattering substantial pressure 

oscillations from the separated or quasi-separated 

thick boundary-layer. A new realistic system approach 

to transition prediction will be presented in 1988, 

including feedback effects. 

For the purposes of the present study, Ref. 19, 

"Jet-Propulsion of Subsonic Bodies with Jet Total-head 

Equal to Free-Stream's' is the most cogently relevant. 

. .... 

Fig' Stern Photo View Test with Open Free-transition tests of Confs, 00 and 01 show that 

-7-

Fig. 9 - Photo of Wind-Tunnel Installation of Test 

Model with Short Tailboom Jet Aftbody (Conf. 01, 

From Ref. 18) 

Fig. 10 - Photo of Wind-Tunnel Installation of Test 

Model with Tailboom/Empennage (Conf. 02, From Ref. 

18) Wake-Rake is also Shown at Right. 

1V. Press-re Thrust Dcrcrmin:lt.ian by D?dial 

Pressure Inteuation 

As discussed above, some forn of body thrust wns 

icdicated by the large discrepancy between measured 

wake-drae and computed skiwfriction drag 2s observed 

in wind-tunnel tests of tha Coldschmied body with 

slot-suction IlLC8,''; houever, this thrust was not 

idcntifiod as a static-pressure thrust in Rcfs. 8, 13, 

14, 15, 17, 18, and 20, nor '*as it moasured by 

integration of the radial pressure distribution. The 

first item is to establish the inviscid pressure plot 

for the nldealn body with a semi-infinite 

tailboom to the effect of the stern jet. The 

body profile and the axial inviscid pressure 

distribution are presented in Fig. 11 from Ref. 15; 

the tabulation below is reproduced also from Ref. 15. 

It must be noted that the machining of the cusp edge 

in 1981 changed slightly the "ideal" shape and thus 

the inviscid pressure. 

The radial inviscid pressure distribution is 

plotted in all the five Figures 12, 14, 15, 16, 17 and 

18 which present the wind-tunnel experimental data 

from the 1981-82 DTNSRDC development program (Refs. 17 

thru 20). It is to be understood that the integration 

of the inviscid pressure distribution yields zero 

axial force. The experimental data are plotted as 

shown; there are insufficient test points in the 

radial area of the stepwise pressure rise: the radial 

gap of the suction slot is quite obvious in the stern 

photo of Figure 8. A wind-tunnel check run should be 

done to remedy this deficiency by simply installing 

three or four pressure taps. Thus the inviscid line 

equilibrium flight was achieved in the DTNSRDC wind- is followed for the along the stepwise 

tunnel with jet total-head equal to free-stream's and pressure rise, a suggestion was made by Bruce J. 

jet velocities below 70% of free stream's. The @olmes ( 1 ~ 8 7 that ) ~ ~ the vortex generated by the 

average of the best five runs yielded s suction flow Ringloeb cusp at the suction-slot's leading edge must 

COeff. c - 0.0118, a jet velocity ratio = have a significant local effect but it has been not 

Q - 

u5/uo 

0.679 2nd a total-head ratio B5/qo = 0.982. The fan possible as yet to quantitiee this effect properly, 

air power average was CHP = 0.0129; this power was in inviscid flow, which would decrease the 

expended exclusively for BLC, with no possible inteerated Dressure thrust. 

contribution to reaction thrust. It can he noted at 

this paint that, at the same volume Reynolds Number, 

free-transition tests of streamlined bodies A and M 

presented by I. E. Abbott (1932)28 yields a drag 

coefficient CDw = 0,0242, i.e., twice the above fan 

air power coefficient CEP = 0.0129. The thrust force 

counteracting the computed free-transition skin- 

friction CDF = 0,010 was not identified in Ref. 19. 

This identification is the next task. 

I 

Figure 12 presents the radial pressure distribution 

far Conf. 00 (Open Jet and Free-Transition), as shown 

in the photos of Figs. 7 and 8; it can be seen that 

the forebody pressure is very well in line with the 

inviscid, while both the midbody and aftbody pressures 

are more positive than the corresponding inviscid. 

The radial integration shows a thrust coefficient CT = 

0.0244 while the calculated skin-friction is GDF = 

.'

Table I11 - Inviscid Pressure Listinas for Ideal Body 

x/o 

u 0.00100 

0.0187 

0.0437 

0.0687 

0.0937 

0.1375 

0.1875 

0.262 

0.337 

0.387 

0.412 

0.487 

0.575 

0.675 

0.775 

0.875 

1.025 

1.125 

1.225 

1.325 

1.475 

1.575r 

1.675 

1.875 

1.975 

2.075 

2.137 

-' 2.187 

2.237 

2.287 

2.337 

2.387 

2.418 

2.427t 

2.432 

2.436 

2.438 

2.441 

2.443 

2.445 

2.448 

2.451 

2.453 

2.458 

2.463 

2.468 

2.473 

2.487 

2.497 

2.537 

2.562 

2.587 

2.612 

2.662 

2.687 

L ' 2.737 

2.737 

2.837 

120" Body Diameter1 

R/D 

0.00276 

0.0386 

0.0727 

0.0990 

0.1203 

0.1514 

0.1830 

0.224 

0.259 

0.280 

0.291 

0.319 

0.347 

0.377 

0.402 

0.424 

0.452 

0.466 

0.478 

0.488 

0.496 

0.497 

0.495 

0.480 

0.467 

0.450 

0.438 

0.425 

0.411 

0.393 

0.372 

0.344 

0.322 

0.313 

0.306 

0.300 

0.295 

0.290 

0.286 

0.282 

0.278 

0.274 

0.270 

0.263 

0.257 

0.250 

0.244 

0.228 

0.218 

0.181 

0.163 

0.148 

0.133 

0.110 

0.100 

0.0844 

0.0844 

0.0671 

2 . 2 

R in 

0.00304 

0.595 

2.125 

3.920 

5.788 

9.168 

13.395 

20.070 

26.832 

31.360 

33.872 

40.704 

48.163 

56.851 

64.641 

71.910 

81.721 

86.862 

91.393 

95.257 

98.406 

98.803 

98.0100 

92.160 

87.235 

81.000 

76.737 

72.250 

67.568 

61.779 

55.353 

47.334 

41.473 

30.187 

37.454 

36.000 

33.810 

33.640 

32.718 

31.809 

30.913 

30.030 

29.160 

27.667 

26.419 

25.000 

23.814 

20.793 

19.009 

13.104 

10.627 

8.761 

7.075 

4.840 

4.000 

2.849 

2.849 

1.800 

C 

-P- 

0.986 

0.812 

0.620 

0.479 

0.384 

0.310 

0.219 

0.121 

0.0600 

0.0170 

-0.0058 

-0.058 

-0.081 

-0.127 

-0.165 

-0.194 

-0.227 

-0.247 

-0.272 

-0.301 

-0.327 

-0.335 

-0.335 

-0.331 

-0.333 

-0.363 

-0.369 

-0.383 

-0.380 

-0.348 

-0.345 

-0.370 

-0.337 

-0.117 

0.521 

0.217 

0.335 

0.401 

0.431 

0.444 

0.454 

0.468 

0.502 

0.532 

0.556 

0.675 

0.604 

0.620 

0.629 

0.629 

0.627 

0.622 

0.607 

0.596 

0.566 

0.566 

0.480 

-9- 

-0 2 

.e27 c ? 

0 i.0 1.5 2.0 2.5 3.0 

x,3 S,#(:NS1Sh'LISS R X : I LEhCIii 

Fig. 11 - Axial Plot of Profile and Inviscid 

Pressu,re Distribution for Ideal Goldschmied Body 

with Circular-Arc Aftbody and Infinite Tailboam 

(From Ref. 15) 

c1 " 

Y w 

1 

0 

0 

0 

,oo 

w 

5 

", 

", 

w 

E 0. 

" . .t c 

1 

-0. 

-0. 

SELF-PROPELLED CONF. 00 

Free Transition 

Suction-Flow Coeff. CQ = 0.0114 

Computed Skin-Friction CDF= 0.010 

Integrated Pressure Thrust CT=0.024 

0 20 40 60 BO ino 

RADIAL AREA PARAHETER R* sg.in. 

Pig. 12 - Radial Pressure Distribution for Self- 

Propelled Conf. 00 (20" Dia.): Inviscid 

and Experimental

0,010 (transition at 65% length, see Fig. 4 ). The I.' 

wind-tunnel model has ~ ero thrust, as shown in Fig. 

13: C = 0.0144 corresponds to equilibrium flight and 

Q. 

it indicates therefore the minimum required suction 'I. 

flow. The excess thrust AC - 0.0144 T- would certainly 

suggest that more detailed radial pressure data are 

needed along the stepwise pressure rise, along the 0.1 

lines suggested by B. J. Holmes (1987)". Figure 14 

presents the radial pressure distribution for Conf. 

50: it can be seen that the experimental forebody 

pressure is very well in line with the inviscid, while 

the midbody and aftbody pressures are somewhat mare u' 

positive than the corresponding inviscid. The 

" o., 

integration yields a thrust coefficient CT = 0.0176 2 

while the calculated skin-friction is CDF = 0.0125 

a_ 

(transition at 58% length). Thus an excess thrust AG 4 

= 0.0176-0.0125 = 0.0051 is apparently indicated; this 

means again that more detailed test data are needed 

along the stepwise pressure rise since the apparent 

pressure thrust is 40% greater than the computed skin- 

friction drag 

3 

1. m 

0.90 

0. Bo 

0 0.70 

a 0.60 

0 

3i 

i? 0.50 

3 

e 

0. 0.40 

0.9 

0. a 

0.1c 

[ 

-0. I! 

I I I 

Inviscid Flw Step 

Conf. M,-d 

Zero Drag I 

Flw I 

. 

L I 

.I 

I 

*! ;.. 

I 

I 

--*--- -- 

Suction Flw Caefficlent - CQ5 

Full AftbadL 

Attachement 

__- 

Fig. 13 - Correlation of Pressure Step Across 

Suction-Slot with Suction-Flow Coeff. C 

Q 

(Conf. 00 from Ref. 19) 

, "I 

~ 

u 

3 

u 

-10- 

O., 

-o,, 

-0. 

SELF-PROPELLED CONF. 50 

Transition Trlp @ Sm Length 

Suction-Flow Coeff. cQ = 0.0217 

Computed Skin-Friction CDF = 0.0125 

q\ 

,-- -. 

Integr'ated Pressure Thrust Ci : 0.0176 

I \ 

orag Area 

0 20 do 60 80 

RADIAL AREA PARAMETER R' rq.in. 

Fig. 14 - Radial Pressure Distribution for Self- 

Propelled Conf. 50 (20" Dia.): 

Inviscid and Experimental - 

Figure 15 presents the radial pressure distribution 

for Conf. 10 (Open jet and transition trip at 10% 

length, Figs. 7 and 8); it can be seen that the 

experimental forebody pressure is very well in line 

with the inviscid, while the midbody experimental 

pressure is more positive than the inviscid pressure 

and the aftbody experimental pressure is less positive 

than the inviscid pressure. The integration yields a 

thrust coefficient CT = 0.0166 while the computed 

turbulent skin-friction is C DF = 0.0190; there is a 

thrust deficiency of ACT = 0.0166 - 0.0190 = -0.0024, 

i.e., the indicated pressure thrust does not balance 

off the turbulent skin-friction by itself. In Fig. 6 

there is shown from the Gemeta* data, with transition 

trip at 10% length, that a body thrust CT = 0.0168 had 

to occur, since the computed turbulent skin-friction 

was CDF = 0.0190 and the measured wake-drag was C 

DW = 

0.0022. Thus the integrated pressure thrust C - 

100 

b' 

u' 

T - L 

0.0166 is in excellent agreement with the predicted 

0.0168.

0 

d 

20 

40 

RADIAL AREA PARAMETER R' 

60 

54.i". 

80 100 

I 

0 

20 

RADIAL 

40 60 

AREA PARAMETER R' sq.in. 

80 100 

Fig. 15 ~ 

Pressure Distribution for Self- 

Fig. 16 - Radial Pressure Distribution for 

Propelled Conf. 10 (20" Dia): 

Inviscid and Experimental 

Unpropelled Conf. 00 (20" Dia.) : 

Inviscid and Experimental at C - 0 A; - 

Radial 

Finally, it is of great interest to the aircraft 

Fig. 16. The aero-suction drags are not catastrophic, 

due to the passive BLC effect of the cusp; for free- 

designer to know the pressure drag of the body in the transition the total drag would be cDw = o,olo + 

case of zero BLC suction (because of engine failure). 

0.0050 = 0.015 and for tripped-transition the total 

Figure 16 shows the radial pressure distribution plot 

drag would be CD1 = 0.0190 + 0.0120 = 0.031. This 

for Conf. 00 (open jet and free-transition) for the 

latter value can be compared to 0.0267 for the 

case of aero BLC suction: the pressure drag is C 

UP = streamlined airship body with tripped transition at 

0.0050 since an excellent pressure recovery of C - 8 

P 

0.45 was achieved with only the passive BLC of the 

cusp. A good pressure recovery for a conventional 

streamlined body is C = 0.20, as shown below in Fig. 

P 

18. 

Figure 17 shows the radial pressure distribution 

plot for Conf. 10 (Open jet and transition rip at 10% 

length) for the case of zero BLC suction: the pressure 

drag is CDp = 0.0120 since the cusp is less effective 

sith the much thicker turbulent boundary-layer. The 

L 'pressure recovery is only C = 0.10, down from 0.45 of 

P 

-11- 

the same volume Reynolds Number, as given by Cerreta . 

I,, order to properly assess the above results, it 

is necessary to present the evidence for conventional 

self-propelled streamlined bodies, which all show 

pressure drag to some substantial degree. 

It seems to be extremely rare to find plots of 

experimental radial pressure distributions for 

streamlined bodies in the aerodynamic literature, as 

if it was a matter beneath notice; only a few axial 

pressure plots are given, to emphasize the agreement

" 

a. 

L 

Y 

w 

0 

2 

1 .0 

0.8 

0.6 

0.4 

" 0.2 

", 

2 

m 

w a. 

u 

$ 0 

h 

", Y 

-0.2 

-0.4 

9. 0.6 

u c 

-0.4 

2 0.8 

1.0 

UNPROPELLEO CONF. 10 

Transition Trip @ 10% LeWtn 

Suction-Flaw Caeff. Cg = 0.E 

Computed Skin-Friction CoF = 0.0190 

Integrated Prea~we Drag Cop = 0.0117 

distribution, both inviscid and experimental for the 

Inviscid Pressure 

- Ideal Body - 4:2:1 naval airship model tested by Cerreta 8 ; the 

.. 

0 20 40 60 80 

RADIAL AREA PARAMETER Rz rq.in. 

- - 

between the experimental points and the computed 

inviscid plot "over 95% of the body length". The 

pressure drag is given by the disagreement over the 

last 5% body length. Such an axial pressure plot is 

presented in Fig. 18 for the naval airship model '4' 

8 

tested by P. A. Cerreta : the inviscid terminal 

pressure recovery with the convex aftbody is C = 1.0, 

P 

while the experimental terminal pressure is C = 0.22. 

P 

Pressure drag is inescapable. On the other hand with 

cusped aftbodies, the inviscid pressure recovery can 

be tailored by body shaping to meet realistic 

expectations at the given Reynolds Number, as 

predicted by the Goldschmied (1965)30 turbulent 

separation criterion. Figure 19, as taken from Ref. 

31, shows an inviscid axial pressure distribution for 

an axisymmetric body with concave aftbody with a 

terminal pressure C = 0.41; two experimental pressure 

P 

distributions are also shown: at lower wind-tunnel 

speed the flow is well attached with a terminal 

pressure C = 0.375 while at higher speed the flow is 

P 

fully separated with a terminal pressure C = 0.24 (in 

P 

good agreement with Cn = 0.22 of Fig. 18). The 

r 

accuracy of the Galdschmied turbulent separation 

criterion is illustrated in Fig. 20, taken from Ref. 

31, showing the experimental pressure drag increment 

loo far the test body in the wind-tunnel against the 

computed pressure recovery parameter. A very sharp 

drag rise occurs, once the computed "limitniis 

Fig. 17 - Radial Pressure Distribution for exceeded. 

Unpropelled Conf. 10 (20" Dia.) : 

It 

32 

can be noted here that J. S. Murphy (1954) 

Inviscid and Experimental at C, = 0 

carried out an extensive experimental investigation of 

% 

convex and concave aftbodies in a wind-tunnel, 

' focusing on axisymmetric turbulent separation. It is 

corresponding axial pressure distribution is given in 

Fig. 18. The total wake-drag coefficient was CDw = 

0.0262 and the pressure drag has been determined to be 

~ 

u

distribution, as expected, yields zero Pressure drag, drags of 30% are not uncommon for self-propelled 

while the experimental distribution yields a Pressure streamlined bodies; this is not generally accepted by 

drag coefficient CDp = 0.0029 or 14.5% of the total aeronautical engineers afflicted by the flat-plate 

wake-drag CDw = 0.020. syndrome, 

The above pertains to bare unpropelled streamlined 8. c. M~Lemore~~ has presented a thorough wind- 

4 bodies. Considering self-propulsion for streamlined tunnel investigation of a streamlined airship body 

d 

bodies, the nost efficient mode is the pusher wake- 

propeller; the pressure drag will be increased from 

50% to 75% by the propeller flow field. Thus pressure 

0 0.2 0.4 0.6 0.8 

x/L AXIIIL DI3TThl:CE PAMl4ETER 

with wake-propellers: the propeller efficiency of 120% 

(propeller thrust) yielded a propulsive efficiency of 

only 103% because of enhanced body pressure drag. 

This pressure drag increment amounted to 16% of the 

bare body's drag or 75% of the bare body's pressure 

drag. 

Fig. 19 - Axial Pressure Distribution of Body I .fl 

with Concave Aftbody: Inviscid, Experimental 

with Attached Aftbody Flow and with 

Separated Flow (From Ref. 31) 

Fig, 20 - Experimental Pressure Drag Increment 

vs Computed Turbulent Pressure Recovery Parameter 

(Goldschmied Criterion, Ref. 31) 

(Parameter G is defined in Ref. 30 and 31) 

It can be readily seen that switching pressure drag 

into pressure thrust can yield very large power 

savings for self-propelled bodies, since the initial 

step is the elimination of a drag as high as 30% and 

in the second step some or all the skin-friction is 

balanced off. 

UNPROPELLEO NAVAL AIRSHIP MODEL 

Tranntion Tnp @ 10% Length (Ref.81 

~iiailcr Area 

Exp. Wake-Drag Cow = 0.0262 

Cxp. OraQ OmWlld 0rai integrated Pressure Drag Cgp=03058 

240 

-13- 

I 

0 20 40 60 80 100 

~AOIAL AREA PARAMETER R' sq. in. 

Fig. 21 - Radial Pressure Distribution for 

Unpropelled Naval Airship Model (20" Dia.) : 

Inviscid and Experimental Data from Ref. 8

Y 

r 

rn 

1 .o 

0.0 

0.4 

UliPROPiLLiD AlRSHlP "AKRON" 1403EL 

(b) Free-transition, with empennage drag increment 

ACD = 0.004 - To be compared against the integrated 

Coni. 02: CDR = 0.0280, 

Free lran~ltlon (NACA Rpt.4301 (c) Transition tripped at 10% length. Data from 

Exp. Ilake-Drag Cow = 0.020 Ref. 8 with empennage drag increment AC - 0.004 - To 

Integrated Pressure orag cop = 0.0029 

-1 

0 20 40 60 DO 100 

2 

RiiDlAL AREA PARAMETER R Sq. 1". 

Fig.22 - Radial Pressure Distribution for 

Unpropelled Airship "Akron" 20" Dia.Mode1 

be compared against the integrated Conf. 12: CDR = 

0.0310. 

A propulsive system efficiency index will be 

defined as the ratio of the reference drag coefficient 

and of the propulsion power coefficient: 

Propulsive Efficiency Index 

D - 

= (CDR/CHPs) xhere CHPs may be the 

IPS 

experimental wind-tunnel value of the integrated 

system, including a fan efficiency lF. 

Fan Air Power Coeff. 

CnPs = (CgCa/qOUoVO~Gs~F) or the experimental 

34 

shaft power value from the McLemore (1962) 

body/wake-propeller tests. 

Propeller Shaft Power 

CHPs = (2nnX/qoUoV o.66 or the computed power 

coefficient for the jet-thruster from simple one- 

dimensional theory, including a two-stage fan 

2 

efficiency qn . 

Inviscid and Experimental Data from Ref.33 Other significant parameters are as follows: 

Y. Propulsion Evaluation 

(d/V0'33) - Jet or propeller diameter ratio 

C_ = (m/pu,,~o.66)- Propulsive mass flow coefficient 

Y " 

C = (E.-P )/ ) - Total-pressure coefficient 

In order to complete this preliminary study, it Pt 1 0 9 0 

would seem advisable to carry out a comparative 1 0 

U./U - Jet or propeller outlet velocity ratio 

propulsion performance evaluation between the 

integrated aerodynamic system approach of Goldschmied 

Cpj = (P.-p )/qo - Jet or propeller static-pressure 

1 0 

coefficient 

and conventional bodyfpropulsion systems such as 

bodyfwake propeller and body/jet-thruster. The usual 

Integrated System 

drag comparison cannot be made, since the body and the 

propulsion cannot be considered separately for the 

integrated system and for the body/wake-propeller: 

power will be considered, for a given body volume and 

speed. 

The best conventional streamlined body will be 

taken as the reference; a set of drag coefficients CDR 

will be used, to yield the body drag at the same 

volume Reynolds number, Rv = 2 x lo6 as the integrated 

system's wind-tunnel tests, for the following three 

conditions: 

The propulsion parameters of the aerodynamic 

integrated system are presented in Table IY for 

configurations with and without empennage and with and 

without tailboom. The data are taken from Ref. 17 and 

20. 

A typical plot of fan air power coefficient cnp 

versus axial force coefficient (as measured in the 

wind-tunnel both by strut force and by the wake rake) 

is given in Fig. 23 for Conf. 51. The wake data ape 

to be preferred because of the inadequate strut 

calibration procedure. 

.u/ 

W 

(a) Free-transition. Data from Ref. 28 - to be 

compared against the integrated Conf. 00 and 01: 

CD = 0.0240, L 

-14

-1 

Table IV - Integrated System Propulsion Summary 

parameter 00 01 - 02 12 

Empennage 

Tailboom 

Transition Location 

Volume Reynolds No. RV x 108 

Fan Flow Coefficient, C 

Fan Pressure Rise Coefficient, Cu 

Fan Air Power Coefficient, CHP 

Fan Efficiency, 7 F 

Fan Power Coefficient, CBPs = (CW/qF) 

Jet Velocity Ratio, U./U 

1 0 

Jet Static-Pressure Coefficient, C 

pj 

Total-Pressure Coefficient, C 

Pt 

Jet Diameter Ratio, d/V0'33 

Q 

NO 

No 

Free 

1.94 

0.0118 

1.10 

0.0130 

93.5% 

0.0139 

0.674 

0.52 

0.970 

0.147 

NO 

Yes 

Free 

1.94 

3.0115 

1.04 

0.0120 

93.5% 

0.0128 

0.669 

0.52 

0.965 

0.147 

Yes 

Yes 

Free 

1.97 

0.0124 

1.064 

0.0132 

93.5% 

0.0141 

0.715 

0.54 

1.05 

0.147 

Yes 

Yes 

10% length 

1.63 

0.0150 

1.133 

0.0170 

93.5% 

0.0182 

0,690 

0.57 

0.044 

0.163 

body. Two wake propellers were tested: Propeller 1 

had four blades and diameter ratios d/D = 24.0 inj50.8 

in = 0.472 over body diameter and d/V 0'33 = 24.0 

inJ68.2 in = 0.351 oyer body volume equivalent. 

Propeller 2 had three blades and diameter ratios d/D = 

0.33 

16.4 inJ50.8 in = 0.322 over body diameter and d/V 

= 16.4 inJ68.2 in = 0.240 over body volume equivalent. 

At the point of equilibrium flight, thk best Propeller 

1 configuration had a blade angle ,O = ZO', an advance 

L 

2 

c 

ratio U Jnd = 0.90 and a propeller power coefficient 

3 5 

(from measured shaft torque and speed) (2anXjpn d ) = 

0.060; this translates into a body power coefficient 

CBP = 0.0204, with a propulsive system efficiency 

index qps = CD/CRPs = 0.0210/0.0204 = 103%. 

An axial velocity traverse was taken aft of the 

wake propeller, yielding an average velocity ratio 

Fig, 23 - Fan Air Power Coeff. CBP vs Axial 

Force Coeff . (Conf . 51, From Ref. 18) 

BodyJWake-Propeller System 

U./U = 0.961; the static-pressure coefficient on the 

1 0 

body at the propeller location was G = 0.175 and the 

pj 

ayerage total-pressure coefficient was C = 1.10. 

Pt 

Finally, it is of interest to compute the propulsive 

mass flow issuing from the propeller; the mass flow 

M~Lernore~~ has presented a thorough experimental coefficient was C = m/pUoV0'66 = 0.0868. For the 

m 

investigation of subsonic body/wake-propeller systems, smaller Propeller 2, at the point of equilibrium 

which was carried out in the NASA Langley Full-Scale flight, the best configuration had a blade angle p = 

Wind-Tunnel at Reynolds numbers of 17.5 x lo6 (length) 20", an advance ratio U Jnd = 0.65 and a propeller 

or 4.84 x lo6 (volume). The body length/diameter power coefficient ZrnX/pn'd5 = 0.056; this translates 

ratio was LID = 242 inJ50.8 in = 4.76 and the body into a body power coefficient CBPs = 0.0236, with a 

volume was V 

3 

= 184 ft . The basic drag coefficient, propulsive system efficiency index 7 = CD/CEPs = 

PS 

without propeller, was CD = 0.0210 for free 0.0210/0.0236 = 88%. 

transition, in good agreement with the 0.024 value The traverse was taken aft of the wake propeller, 

6 

taken at % = 2 x 10 from Ref. 11 for the reference yielding an average axial velocity ratio U./U = 

1 0 

-15-

0.987; the static-pressure Coefficient on the body at A two-stage axial fan is assumed for the jet- 

2 

the propeller's location was C = 0.1Ql and the propulsor, with a fan efficiency; qF = 0.935 = 0.874. 

Pj 

average total-pressure coefficient was c = 1.179, The body/jet-propulsor power coefficient will be: 

Pt 

Finally, the propulsion mass flow coefficient was C = 

m 

0.0415. McLemorea4 also quotes results for a fin- cws = Cm/0.874 [(U./U )2 - 11 

I O 

mounted propeller, with a propulsive system efficiency 

index of 75.5% and for a mid-body strut-mounted A. Free-transition Body/(Equal Mass Flow 

propeller with 70.8% propulsive system efficiency For this casel the reference body drag coefficient 

index. por the propulsion evaluation, the is CDR = 0.024; the mass flow coefficient Cm equals C 

Q 

experimental propulsive system efficiencies of of Conf. 01: Cm = C - 0.0115. 

0 - 

Propeller 1 (103%) and Propeller 2 (88%) will be 

applied to the reference body with free-transition and Uj/u,, =2.043 

with empennage (CDR = 0,028). Thus in Table Y, 

nPPropulsion Evaluation Summary", for the body/wake- Cpt = (E. - Po/%,) = 4.17 

I 

propeller 1 the power coefficient is CAPs = 0.0271, 

and for bady/wake-propeller 2 the power coefficient is 

d/Y0'33 = 0.0846 

CHPs = 0.0318. 

CBps = 0.0417 

Body/Jet-Thruster Systems 

Equal Jet Mass Flow 

The body/jet-thruster system symbolises the 

aircraft fuselage with jet-engines mounted on 

The propulsive system efficiency index is 

vps = CDR/CHPs = 0.024/0.0417 = 57.5%. 

W 

horizontal struts in the rear. The first body/jet- 

E. 

thruster system is based on the assumption that the 

Free-transition Body with Empennage (Equal Mass 

Flow) 

propulsion mass flow is equal to that of the 

corresponding integrated system. The inlet velocity to Far this Case, the reference body drag coefficient 

the propulsor will be taken to be uo and the static- is 

\J 

CDR = 0.028; the mass flow coefficient Cm equals c Q 

pressure coefficient C will be taken to be zero in 

of Conf. 02: Cm C - 0.0124. 

Pj 

Q - 

all the eases below. 

"0.66 U./U = 2.129 

T = m (U. -U) = F = C D ~ 1 0 

1 0 

(U./U ) = 1 + 0.50 (CD/Cm) 

1 0 

and the jet diameter will be: 

= (E. - P / ) = 4.53 

Cpt 1 0 % 

d/V0'33 =0.0861 

CBps = 0.0500 


= CDR/CBPs = O.O28/O.OSOO = 55.9%. 

d/V0'33 = [(Cm/0.785) - (Uo/Uj)]o~5 VPS 

The air porer requirement of the jet propulsor is C. Tripped-transition Body with Empennaae (Equal Mass 

given by: - Flow 

For this case, the reference body drag coefficient 

Q(qj - g) = 1/2PCmu~vo.66 [(uj/u,) - 111 

is CDR = 0.031; the mass flow coefficient Cm equals C 

Q 

of Conf. 12: Cm = C 0.0150. 

Q 

The air power coefficient is: 

CHP = (Q(q.- )/ UoVo'66) = cm [(uj/uo) 2 - 11 

1% B 

Ui/Uo = 2.033 

L 

-16 

C = (E. - P / ) = 4.13 

Pt 3 0%

d/V0'33 = 0.0969 

CHPs = 0.0404 

CUP = 0.0537 The propulsive system efficiency index is 

S 

-The propulsive system efficiency index is: 

7PS 

= CDR/CBps = 0.031/0.0537 = 57.7%. 

VPS = CDR/CHPs = 0.028/0.0404 = 69.3%. 

F. Tripped-transition Body with EmpennaRe (Equal Jet 

Diameter1 

Equal Jet Diameter 

The second body/jet-thruster system is based on the 


is CDR = 0.031 and the jet diameter ratios of Conf. 12 

assumption that the jet diameter is equal to that of is d/V0'33 = 0.163. 

the Corresponding integrated system, while the mass 

flow is allowed to vary. The inlet velocity will be 

uj/"o (uj/Uo - 1) = 0.743, 

taken to be Uo and the static-pressure coefficient C 

'j 

will be taken to be Zero in all the cases below. c = (Ej - p,/g) 

Pt 

= 2.241 

2 

m = %/4 d pU. 

3 

Cm = 0.0312 

C m = 0.785 (d/V0'33)2 U./U 1 0 

U./U I O = (U./U I O 

0.33) 2) 

- 1) = (0.50 CDR/0.785 (d/V 

D. Free-transition Body (Equal Jet Diameter1 


is CDR = 0.024 and the jet diameter ratio of Conf. 01 

is d/V0833 = 0.147. 

U./U (U./U - 1) = 0.707, U./U = 1.479 

1 0 J O J O 

C = (E. - p /q ) = 2.18 

Pt I 0 0 

Cm = 0.0250 

CBPs = 0.0337 


CBps = 0.0443 

Uj/Uo = 1.497 


"p" 

= CDR/CBps = 0.031/0.0443 = 69.9% 

Evaluation 

The complete results are presented below in Table 

V, 'Propulsion Evaluation Summary". In terms of 

propulsive system efficiency, the integrated Conf. 02 

(free-transition, with empennage) is best with 198.5%, 

while the corresponding body/wake-propeller systems E 

and B have 103% and 88% and the bodyljet-propulsor 

systems B and E have 69.3% and 55.QX. In terms of 

propulsive mass flow, the integrated Conf. 01 and the 

corresponding body/jet-propulsor system A have the 

lowest C = 0.0115, 

m 

while the body/wake-propeller 

system 1 has the highest Cm = 0.0889; the mass flow 

= CDR/CBps = 0.024/0.0337 = 71%. 

ratio is 7.55. 

7PS 

In terms of jet total-head coefficient, the 

E. Free-transition Body with Empennage (Equal Jet integrated Conf. 01 has the lowest C = 0.965, while 

Pt 

Diameter 

the body/jet-propulsor system B has the highest total- 

For this case, the reference body drag coefficient head coefficient value of 4.53; the bodyrwakeis 

CDR = 0.028 and the jet diameter ratio of Conf. 02 propeller system 1 has a value of 1.10, which is 14% 

is d/V0'33 = 0.147. higher than that of Conf. 01. 

In terms of jet velocity ratio, Conf. 01 has the 

Ui/uo (Uj/Uo - 1) = 0.825, Ui/Uo = 1.536 

lowest value of 0.669, while the body/jet-propulsor 

system B has the highest value of 2.128. 

= (Ej - po/g) = 2.358 

In terms of jet static-pressure, all the integrated 

CPt 

'd Cm = 0.0260 

-17- 

configurations have jet static-pressure coefficients 

well over 0.50, while the body/wake-propeller systems

Configuration 

Integrated Conf. 00 


Integrated Conf . 02 


Body/Wake-Propeller 1 

Bady/Wake-Propeller 2 

Body/Jet-Propulsion A 

Body/Jet-Propulsion B 

Body/Jet-Propulsion C 

Body/Jet-Propulsion D 

Body/Jet-Propulsion E 

Body/Jet-Propulsion F 

Table V - Propulsion Evaluation Summary 

=2rlO) 

6 

0.33 

d/Y Lm- 

0.147 0.0118 

0.147 0.0115 

0.147 0 0124 

0.163 0.0150 

0.351 0.0869 

0.240 0.0415 

0.0846 0.0115 

0.0861 0.0124 

0.0969 0.0150 

0.147 0.0250 

0.147 0.0260 

0.163 0.0312 

among aeronautical engineers, that the best that can 

be done with axial pressure forces is to achieve near 

zero pressure drag with unseparated concave aftbodies. 

In this study, the integration of the radial pressure 

17,20 

distribution of the self-propelled Conf. 10 

(transition tripped at 10% length) yielded a thrust of 

0.0166; the agreement with the above 0.0168 is indeed 

remarkable, as it demonstrates the nature of this 

thrust force. 

- C pt VjD0 

0.970 0.674 

0.965 0.669 

1.05 0.715 

1.044 0.690 

1.10 0.961 

1.18 0.987 

4.17 2.043 

4.53 2.129 

4.13 2.033 

2.18 1.479 

2.36 1.536 

2.24 1.497 

-Pj G - CHPS_ 

0.52 0.0139 

0.52 0.0128 

0.54 0.0141 

0.57 0.0182 

0.175 0.0271 

0.191 0.0318 

-0.10 0.0417 

-0.10 0.0500 

"0.10 0.0537 

"0.10 0.0337 

-0.10 0.0404 

"0.10 0.0443 

Ips- 

172.6% 

187.5% 

198.5% 

170.3% 

103.0% 

88.0% 

57.5% 

55.9% 

57.7% 

71.0% 

69.3% 

69.9% 

are below 0.2 and the body/jet-propulsor systems are In 1983 Goldschmied" presented the experimental 

practically at the free-stream level, with values wind-tunnel evidence that the self-propelled freebelow 

0.1. 

transition models (Confs. 00 and 01) were in 

It is quite evident that the integrated system equilibrium flight with jet total-head equal to free 

presents propulsion characteristics which are far stream's and jet velocities less than 70% free 

superior to, and radically different from, those of stream's. In this study integration of the radial 

conventional systems. 

pressure distributions seem to yield thrust much 

greater than the computed skin-friction O.?lO; there 

VI. Summarl: 

can be no doubt that body self-propulsion has been 

achieved by static-pressure thrust, with all the power 

Thirty years ago the experimental wind-tunnel data applied to BLC and none to reaction thrust. This is 

of Cerreta' demonstrated conclusively a 40% reduction indeed a significant milestone in applied aerodynamics 

in "equivalent drag" (including BLC power) as against for General Aviation aircraft. 

a streamlined body of equal volume, with transition A propulsive efficiency evaluation was also carried 

tripped at 10% length on both bodies; this voided the out, on the basis of the conventional badylwakestill 

popular "flat-plate syndrome" that substantial propeller and body/jet-thruster configurations; the 

body drag reductions can only be achieved through efficiency index ranged from 88% to 103% and from 55% 

laminar skin-friction. 

to 70%, respectively. On the other hand, for the 

The same Cerreta data also showed experimental self-propelled Goldschmied system the efficiency index 

wake-drags as low as 0.0022, while the computed ranged from 172% to 198%; also it is well worth noting 

turbulent skin-friction drag was 0.0190; clearly a that the mass flow required was only 15% of that for 

body thrust force of 0.0168 had to occur to make this the best wake-propeller and 50% of that for the jethappen. 

This voided another belief, still current thruster with equal jet diameter. 

-18- 

YII. Conclusions 

In conclusion, since the fuselage represents at 

least 50% of the total aircraft drag, fuselage self- 

propulsion by static-pressure thrust should yield at 

'W 

least 25% total power reduction. 

A preliminary design study by F. R. Goldschmied 

(1984)" for 200 MPE cruise speed indicates a u

potential 60% power saving for 2-seat aircraft and 40% 9. F. R. Goldschmied, "Proposal for the study of 

power for 4-seat aircraft, as to Application of Boundary-Layer Control to Lighter- 

than-air CFsft", Goodyear Aircraft Corp. Rpt. 

specific current designs. A similar study was GER-5796, 1954. 

presented by the same author (1986)35 for general 

aviation aircraft based on the McLemore (1962) 

body/wake-propeller configuration. 

Pressure thrust is the most efficient form of 

fuselage self-propulsion; it is based on the best 

34 10. F. R. Goldschmied, 'A Theoretical Aerodynamic 

Analysis of a Boundary Layer Controlled Airship 

Bull", Goodyear Aircraft Corp. Rpt. GER-6251, 

1954. 

11. D. Kuchemann and J. Weber, wAerodynamics of 

Propulsion", McGraw Bill Book Co., 1953. 

possible implementation of the BLC system. It cannot 

be overemphesized that the most careful 

be 12. B. Edwards, "Laminar Flow Control-Concepts, 

Experiences, Speculations", AGARD Rpt. 654, 

given to thc optimization of this system for any given "Special Course on Concepts for Drag Reduction", 

aircraft design application. 

April 1977. 

Acknowledgements 

The contributions of Justin McCarthy and of Dennis 

Bushnell are gratefully acknowledged by the author. 

At the David W. Taylor Naval Ship R&D Center, 

McCarthy convinced the author that a new look was 

needed by pointing out, again and again, that the 

skin-friction drag was always there, acting on the 

body's wetted area, no matter what was done to the 

boundary-layer at the tail, At the NASA Langley 

Research Center, Bushnell was the first to suggest the 

pressure thrust concept for bodies and to hold many 

useful discussions with the author 

References 

1. J. B. Edwards, 'Fundamental Aspects of Propulsion 

for Laminar Flow Aircraft". Boundary Laver and 

Flow Control, G. V. Lachmann, Ed.', Vdl. 11, 

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2. J. B. Fanucci, et al, "Navy V/STOL Aerodynamics: 

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Lachmann, Ed., Vol. I, Pergamon Press, 1961. 

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---' 

-19. 

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~ 

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optimization of Mini-RPV and Small GA Aircraft", 

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36 

37 

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L; 

W

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