ARCHEF
. ..
Lab.
v.
Sch.eepoidê
The Institution of
MehanicJP°
FOUNDED IN 1847... FNCORPORATEDBY ROYAL CHA-RTER1N .1930
I
'S
Reprinted from PROcEEDINGS, 1946,
voL 155 (War Emergency Issue No. 19)
-The Thrust. of.a Marine Screw Propeller.
By..G. S. BAKER, O.B.E., D.SC., late R.C.N.C.
PUBLISHED BY THE INSTITUTION
The Thrust of
a
Marine Screw Propeller
By G S. Baker, '0B.E. D.Sc.,' late R..c.N.C.*
Part 1 of the paper puts forward the proposition that since the phenothenon of development of thrust is much the same in all screws, there shou'd be a common basis by which itcan be represented.
The characteristics of aerofoils are considered, first in flight singly, andthen the general effects
which arise from the interference of adjacent blades It is concluded from this work that for any blade there are two essentials to be fixed, the slip angle, and the slope of the lift curve as affected by aspect ratio and, or alternatively, cascade. This should afford a basis for plotting screw data.
Part 2 of the paper is an examinàtion of the results obtainedwith- over 100 model screws.
The data are given in the form of the thrust constant kT/sp to a base representing blade width. All the
results plot reasonably well iogether, and mean curves for screws with arious numbers of blades
are given. These curves enable the designer of-any screw of normal type to form an estimate of its thrust for any speed of advance -and revolutions per minute. Methods are given in the paper for
detecting eddymaking in the screw, and it is shown that a little roughness of blade surface, although having a material effect on efficiency, does not affect the thtust prediction.
PART 1. COMMON BASIS FOR REPRESENTATION OF THE DEVELOPMENT OF THRUST
When a screw propeller is advancing through the wateralong-its own axis, the thrust which it produces depends upon some six main variables: diameter, pitch, blade outline, number of blades, thickness and shape of blade Section, and boss shape or want of shape. By methodical experiments with models, a
great deal of data has been accumulated showing the effect upon the thrust and efficiency of the screw, Of varying one or more of
these factors. But what the relation of these separate sets of
data is to each other has always been more tir less guesswork, as also is their use for design purposes, when it is necessary to
vary one or.more of the factors assumed constant in the original
parent design of each set. -
-Yet it is clear from the generally accepted theory of the screw
propeller that the broad phenomena of- the --screw action are always alike, no matter what type of screw is used, so that all these charts of data must really represent the same phenomena, only biased by various internal details of the propeller. Clearly
any interconnexion of this kind, defining screw thrust, must rest upon one or other. of the general laws found in good theory. But
the difficulty of any purely theoretical apprOach. is that this
immediately involves certain assumptions which ignore or limit the effects of physical details in the screw. The same
objection arises t the purely experimental approach from alay given set of data, and it would appear that any common basis must be sought by examination of the comnton characteristics
of all screW data.
Much could be written about the characteristics of various propeller constants, but we are.concerned here only with those which relate to thrust. These must be governed by the same considerations as affect the lift Of a blade in straigiit flight, with, any additiOnal complications - arising from the fact that in the screw there, is some interference between the separate
blades.
In the theory of the lift of an isolated aerofoil, several well-known rules have been established. First there is a fixed
theo-retical relation for all thin aerofoils of infinite aspect ratio,
of whatever shape of section, between the angle of attack or The MS. df this paper was received at the Institution on 21st
September 1944.
* Late Superintendent, The William Froude Laboratory, National Physical Laboratory.
slip angle a and the lift force per unit area experienced by
the blade as represented by the lift constant CL defined as
Lift
4p(velocity)2 x (Mea)
This relation is given by CLt = 2a, where a is measured in
radiani-- from the angle at which lift is zero, i.e. the "no lift 'angle". 'Second, as the length of a blade relative to its chord
diminishes, i.e. as aspect ratio A diminishes, the lift coefficient CL also diminishes the loss 01 lift being given approximately
A
by the factor
These two rules, taken simply at their face value, mean that
in a propeller the lift derived from -the bla4es will depend
simply upon the effective slip angle a and the aspect ratio of the blades, i.e. upon the mean ratio of blade width to diameter. Of course the case is not so simple as that, but here are two
strong pointers: (a) blade section, having played its part in
fixing the zero lift angle from which a is to be measured can
then be ignored ;-$ and (b) the lift coefficient of the blades will
depend mainly on the mean ratio of blade width to diameter, and the slip angle. Small effects from cainbermay also show as
with a flat aerofoil. Again-the induced drag (for the sanie blade section) is lowest with an elliptic outline, and when this outline
is filled out the lift does not increase quite so fast as the blade area. Howev r, these small variations are better considered on
the propeller itself when some common basis has been achieved, and they do not affect the main- conclusions.
- When several aerofoils offinite aspect ratio are placed close
together in what is called a cascade, each affects the other. The
t Experiments with many -aerofoils have shown the correctness of the constant 277 for very thin aerofoils, but they also show that with
increasing thickness ratio this constant slowly falls. The following
table (see JACOBS, E. N., WxD, K. E., and PINKERTON, R. M. 133
National Advisory Committee for Aeronautics (U.S.A.), Technical
ReportNo..460, "The Characteristics of 78 Related Aerofoil Sections from Tests in the Variabledensity Wind Tunnel") gives the slope of
-CL, being given per one, degree_instead of radians:
--Maximum thickness
as per cent of --
-chord . . 0 4 8, 12 16 - 20 '24
Increase in Cr. per
1 deg. in a. . 0-1'l 0-105 0-104 0IO2 010 0-0965 0-091
- * Thrust distribution, singing, and cavitation are matters not
-202
THRUST OF A MARINE SCREW PROPELLER
012
0
.0 0!
BASE FOR 2 BLADES
0I
BASE FOR.3 BLADES
0
0I
BASE FOR 4 BLADES
SCLsbp 0 0 006 00
4.
0IBASE FOR S BLADES
tK25
..--?'°
01 BASE FOR 6 BLADES
- . - 0 0!
- BASE FOR B BLADES
02
Fig; I. P1ottingof per Blade for Various Propellers. to Base of Blade Width-given by c/I)
Pitch ratio below 065.
o
,, between O65 and O8O.x ,, - ,, 080 and 10.
-+
,, lOand l2.-above. l2.
For explanation of double spots fo screws A, P55, an4 B13 pee Table 2, p. 206.
DIE
oIl'
308
2-main changes produced can be . summarized under three headings
:-A change of the zero lift angle always brings the effective
zero lift line nearer the face pitch line, or in sew terms
reduces the effective pitch of the screw.
A dilninution of slope of the CL value on a base of a. '(3) A diminution of the maximum value of CL which can be
developed by the blade.
A method of assessiné item (1) already given by the author leaves pointer (a) unaffected. There is considerakle evidence from the theory of cascades for flat' surfaces, that there' will be
some loss of thrust as the gap betweenthe blades diminishes.
-The experimental evidence with aerofoil blades is not very
definite, but suggests that at small angles of incidence (1-2 deg.
effective) it is less than theory suggests; but increases with slip angle, so that at 3-4 deg. the loss, is much as predicted ;* but
with gap/chord ratiost below about 08, the loss increases
steadily with slip angle and with diniinshing gap/chord ratio. Item (3) becomes important only within the- inner 30 per
cent of the screw radius, and more particularly on screws having
a low pitch ratio (about 06). The data on this phenomena are
very incomplete, but clearly indicate that whenblade sections
are placed close to Cach other with a gap/chord ratiof below
about 03, the CL value ceases' to increase at a quite' small
effective slip angle, varying upwards from about 3 deg. at a small
cascade pitch angle (12 deg.). -These effects of a cascade,
although of material importance in design, leave the two con-clusions or pointers, derived from consideration of an isolated blade, as quite authentic in a cascade, although the result is achieved in a more complicated way. The only qualifying
con-ditions to this will occur (i) when the root sections are very close together, and (ii) under the supposition which has been made so
far, that all blade shctions permit streamline flow froth leading
to trailing edge. The effect, of any breakdown of flow or loss of thrust near the bOss will be considered later.
The thrust of a screw is usually expressed in -one of two
"constant" forms, namely, either or Both of these
are of the same type as th'e CL for an aerofoil, but when plotted
on a 'base of speed/revolution constantY or -, theformer gives
a parabolic curve; and.the latter a straight or nearstraight line,
for all moderat& slips. In fact counting from the no-thrust point
given by an abscissa value Of Jo, the thrust constant increases steadily with slip or '(J0J), just as in the aerofoil the CL
con-stant increases with angle of attack. Accepting this experimental
fact, the changing of the blades of a screw in any respect
what-ever, can have only two effects so far as thrust isconcerned it
may change the point of no thrtst from which the straight-thrust
line starts, or the gradient with which it continues; and the
following sectiOn gives details of an investigation of this gradient. PART 2. EXAMIiATION OF RESULTS OBTAINED WITH
MODELS
A large amount of experimental model data has been analysed
on the above lines and the results tabulated. In many cases the
-curve of to a base of -f-- had slight curvature, both near
pn2D nD
the no-thruX point and at quite high slips. For simplicity it was'
necessary to -represent curve by a straight line, and such a
line was taken to,. agree with the - actual curve over the range
10-35 per cent slip. When produced to zero thrust, this line
gave a Jo value differing from the actual nothrust point ofthe
model, but the departure was always small, and there is some
reason fOr supposing that on a full-size propeller thedifference
- * This applies to all propellers over about 0'8 pitch ratio, provided
that the blade root sections have b'een properly designed. With very
low pitch ratios (0-5) there is always some losi at the inner part of the screw disk owing to the small gap/chord ratio, and item (3) is
then liable to becothe quite important near the blade roots, with loss of thrust and of efficiency as, a result.' ,
- t This is given by" SIfl at O'73D where 8 is the pitch angle, c the
- / v(0.7D)
blade width at this radius, anil = 'No.
of blades
THRUST OF A MARINE SCREW PROPELLER
' 203would be less than on the model. Many attempts have been
made in' the past to define the "effective pitch" of a screw
propeller; but this articular Jo value, from which the constant
T.
. ..'
-.
21)4 increases linearly-with (.7oJ), is a most definite and useful definition of this pitch. Methods of calculating Jo from
any screw design drawing have been given in previous papers*
by the author, and we turn to the consideration of the slope of
T
the straight line of -4to base 3.
According to the deductions made from aerofOil data in
part 1 of the present paper, this slope should be dependent on
one main factorthe aspect ratio of the blades; but for any
aspect. ratio the slope would vary with number of blades, as this is a prime factor in the gap/chord ratio affecting the lift coefficient. Moreover, the aspect ratio of a screw blade is very difficult to define. At low thrusts it may vary from infinitr at some parts to practically nil near the blade tips. In the method
already given for determining the effective pitch, the blade
section at 072D to 075D (for narrow- and wide-tipped blades respectively) was 'shown to represent effectively the whole,
blade, and the blade width ratio c/D at this section has been taken :as defining the aspect ratio for present purposes.
The straight line plotting of kT on a ,base of values of 3 can be represented by the formula
= k(J0J) =
k-)(-°)
- ksp
.' .(1)k being a constant defined by the slope of the curve, and s
being a slip given by
--°,
and p the effective pitch ratio J0.-All the available screw data have been analysed on this basis, and the values of k so found have been plotted' on a base of c/D, and these are given in Fig. 1. In the diagram are included results
from four sets, of Troost's data, from the Tank L.P. and B.W. sets of data, from a number of airscrewsItalian and Americans
some of Schaffran's screw data, and for a variety of model
screws Of varied type as tested in the tank for all classes of vessels,
a total of 110 propellers. Neither Froude's, Taylor's, nor Gawn's
data have been used, as these were all faired and 'cross-faired before publication, and the idiosyncracies of individual screws have been suppressed in the fairing. The range of pitch ratio in which a screw lies is denoted by the type of spot. It will be seen that the spots plot in a will-defined pattern in which all
screws having the same number of blades fall in separate groups. To guide the eye in looking at the results, mean lines have been
drawn for screws having the same number of blades, and these lines have then been plotted together in Fig. 2. The data are not
sufficient for good definition in all cases, but the lines give clarity
as to the general trend of the diagram. There is here, in fact,
a thrust diagram covering every screw of normal type, over the
usual working slip range. '
-But before accepting the generality of the diagram, something should be said as to the liability to error in the individual' spots,
and of any exceptional 'results not conforming to the pattern.
There are two sorts of error in interpreting model screw results,
and two departures from' the normal srew blade which lead to results not conforming to the general pattern of the diagram.
- Taking interpretation errors first, if two exactly similar screws
are made, one being only, say, 4 inches and the other 12inches
diameter, and if these are tested in water at corresponding speeds,
they will give widely' different results.. The smaller screw will
have a lower value of Jo, a still lower thrust curve, and an 'even
lower efficiency curvedepartures up to 20 per- cent in thrust have been found by such tests. This effect varies quite con-siderably from screw to screw. Ii many cases a screw may be tested at two widely spaced speeds and show practically no difference in the thrust - constant. It will be realized that the Reynolds number in any - such test varies very greatly from blade root to tip, but experience has shown that (1) it is never
BAKER, G. S. 1944 Proc. I.Mech.E. vol. 151, p. 313, Sixteenth
Thomas Lowe Gray LectOre, "Fundamentals of the Marine Screw
Propeller".
These have been obtained with blades on a long boss, without
ring or engine cowling, and at reasonably high,Reynolds numbers.
a
wise to test screws at a Reyoldsnumber*below 15 x 10, and
it is better to be nearer 4 x lO; and (2) it is never wise to use a screw less than 05 foot diameter. These limits apply to well-designed screws without eddymaking or breakdown in flow at
any part of the screw. With these precautions, some screw
propellers still show small variations when tested at fafrly widely
spaced speeds, or on different scales. It is believed. that this arises from one. of two causes: (a) a variation in the minimum drag coefficient due to increased turbulence or to accidental vibration or other disturbance; or (b) when the camber ratios of the blade sections are a little higher, there is a varying space on the suction face, between the transition point (laminar to turbulent flow) and the point at which a real separation of flow
takes place. Until this space is eJin,inated, small changes in lift, * This rwmber is taken on the blade section at 073D, using the
blade width at this section, and its resultant speed through the water
forlandvinthefomu1aRn=&
.03
CALEOFf
Fig. 2. . Average Curves ofkT/(JoJ) to Base c/D from Fig. 1
drag, and Jo will occur. Experience has shown that changes
arising from these errors do not alter the k value in equation (1),
but may cause small errors inJ0.
The second interpretation error arisesfrom any slight
curva-ture which the kr/J curve may have. In many cases (such
as destroyer and practically all moderately wide blade screws) the curve is quite straight. But in others, over' the first 5 or 10 per cent slip, the curve faust away froth any straight line drawn
t-Tis cutvature at very low slips is in the main due to the
varia-bility of the slip angle from boss to blade tip. For although one speaks of zero slip, this cOndition represents a balance between small positive
and negative slips o*r the blade. Thus screw B.W .9, at practically zero thrust, has the following slip angles. This means that a good
Fraction ofradius
02 03
04 05 06 0708 09
Slip angle,,deg. . ö i85 7 05
05 015 0O
dTHRUST OF A MARINE SC'EW PROPELLER
THRUST OF A MARINE
to give, the mean result at working slips. This falling-away is
much more ,marked when the tests have been made at a constant
speed of advance, tuther than at constant revOlutions per
second, the latter giving a steadier Reynolds number effect.
Froude found the same difficulty with his 1904 data, -and based
his effective pitch on the thrust curve between 10-35 per cent slip. The same process has been adopted in this analysis, and
this falling-off' has been ignored. But even so, it is always
possible to vary a mean line so drawn, and to steady this, the Jo value was worked out by the method already given for every screw; and where it was possible, the mean line in such cases
was drawn through this calculated Jo value. As will be shown in
the next paragraph, this calculated value of J0 is a valuable test of the "freedom from trouble" in the screw.
Next, as to -the departures from streamline type of- blade
section, the most common departure is tile circular back section.
The angle of the tangent to the suction face at the trailing edge
of flat-faced circular back sections is given in Table 1.
-TABLE 1. Cndui.it- BACK FLATFACED SECTIONS
We know that even at low speeds eddymaking will occur when this angle exceeds 20 deg., and at high speeds (near 30 to 40 knots) when it reaches 10 deg. On a propeller the thickness ratios of the blade sections will vary from about 020 to 003 from blade root to tip, and it follows that with circular back sections eddymaking will be present near the boss under all conditions, and will spread nearer to the tips as the speed is
increased.
This eddyinaking has a twofold effect. In Fig. 3 the' section ABC leaves an eddying tail ADE, and the effective section fOr
stream flow is CADB, and the lift is limited on the suctiOn side
abaft E. The effective no-lift angle -of such a section relative
B
TRAIIrING EDGE
Fig 3
to AC is much smaller than that calculated for ABC on the
assumption of no breakdown. It follows, therefore, that
when-ever a screw is suffering from eddyniaking, it should in the first place have an effective pitch lower than that calculated for'good
flqw over the blades; but 'the thrust will be above that properly belonging to this lower pitch, although lower than that for the
non-eddying pitch. -
-Three screws already 'made, and tested were chosen. to test
this effect. All had rather narrow blades of circular back
sections. All of them gave too low a value of-J0 and showed
serious departures in thrust from the aropriate mean curve
in Fig. 2. Particulars of these three screws, and their test data, are given in Table 2, and in Fig. 1. These were modified by
increasing the chord at the blade roots as much as the boss
deal of the 'blade is working with positive pressure on the back and -negative on the -front face. Tests of inverted aerofoils '(see LOCK,
C. N. H., and Towm, H. C. H. l,924-5 Technical Report,
Aero-nautical Research Committee, Reports and Memoranda No. '958,
vol. 1, p. 160, "Lift- and Drag of Two Aerofoils. Measured over
360 dog; Range of Incidence"-) of thickness ratios 0168 and 0-086'
(flat faces) 'show that under these conditions the slope of the CL curve
drops, and in a screw this means that the experimental mean pitch will vary in this region according to which sections are working at
positive or negative angles. This 'is confined to small slips and plays
nO part at all over the working slip range with which we- are con-cerned--one reason for neglecingit iii this analysis.
LEADING EDGE
SCREW PROPELLER
205would allOw, using the increased blade width to ease the angle of the suction face at the trailing edge. The type of change is shOwn in Fig. 4, the alteration being confined strictly to the curvature near the trailing edge on the inner two-thirds of the
diameter. This alteration was not sufficient in any case to
- entirely remove all the eddies, but was sufficient to show the
cause Of the discrepancies between the actual results and those
to be expected from a reasonable screw, namely, the loss of
Fig. 4. Screw Bi3 with Circular Back Sections
- Original sections A
-Modified sections B j
see Table 2.pitch (hence an increase in revolutions for'any thrust), a high
torque, and a varying k slopegenerally above that given by
Fig. 2.'
-The drOp in when eddymaking is rOduced in these three
sJ0
screws is shown in Fig. 1, p. 202. As there *as a residue of
eddymaking still present with the modified screws, the mean curves have been drawn below their lowered values.
Consider-able eddymaking was also present on screw L.P.3 (eight blades), and for the same reason - the mean curve for eight
blades has been drawn below the L.P.3 spot. -.
Tie author ventures to generalize here, and to state that 'when these two "faults" occur in the thrust curve of a screw, i.e. a too
low J0 and too high k value, the screi is suffering from
eddy-making and its efficiency can be materially improved.
The'change in efficiency brought about by these root changes,
as shown in Table 2,is surprisingly large, much too large to be attributed to the mere change in drag, and there is a suggestion
here (which perhaps future experiments may check) that it
arises far more from the increased fore-and-aft flow through
the centre of the screw produced by the odifled root sections,
and a resultant reduction of rotaiy velocity set up in the screw. 'With circular back or any such section, the rate of expansion.
of the water gap at the trailing edge between consecutive blades
at the rbot section can rise very high,* resulting in a disturbed
and retarded general flow at the centre of the race.
The main' diagram, Fig. 1, represents two effects both tend-ing the same way, both dependtend-ing on the abscissa cfD. The first is the tip or aspect, ratio effect. The loss of' lift or thrust
coefficient per unit blade area, from thi c,atse, increases as c/D
*BAYR, G.. S. 1934 Trans. Inst. N. Architects, vol. 7ó, p. 337, "The Design-of Screw Propellers,-with Special Reference to the
Single-screw Ship". . -'LONGITUDINAL ELEVATION 'THICKNESS -AND LINE --
L
, ..'.-'
9 : DEVELOPED' SECTIONS\
Thickness ratio of blade
section . . .
,
0043 0065 0088 0lll 0134
0182-Angle of tangent at
increases, and occurs mainly at the blade tips. 'The second
arises from a form of cascade effect, which, however, differs from that for flat blades in chat in a screw propeller it is-
com-plicated by the varying intake velocities from leading to trailing
edge of 1,lade, and by, the change in these due to the cascade effect. This has its maximum.effect at the blade roots and loses its importance at blade tips. Clearly the pure aspect ratio effect does not depend on number of blades but only on c/D, but the
blade interferencej' effect will take a sudden jump as additionaF
blades are added to a screW, and will increase with c/D in all cases
With very narrow' blades, both these effects will be small
-hence all 'the mean 'curves tend to approach a common value independent of the number f blades near the origin. The data at this end of the diagram are all for air propellers; But apart
from the question of cãvitatidn, the diagram' should apply
indifferently to air and water, and these air data serve to define the initial slope of the thrust line into which.all the mean lines. must run. .The only apparentindication ofsystematic effect of pitch upon the ordinate value is when the effective pitch ratio
is below 0'65 and the blades are a little wide. 'The effect is fairly
well defined for four-bladed screws, and the dotted line here
shows the average value when the effective pitch is (556. Screw
C having two blades also shows this effect, its effective pitch ratiO being 0'41. Such other variations with pitch which the diagram shows do not4 follow any system, and are probably
due to difficulties 'in interpreting experimental data or to
experimental errors in the data themselves.
One other .change in normal design leads to a result differing' from that predicted from 'these mean curves. If the blade.tips
are thickened up above the usual straight line from boss to
blade tip, the effective pitch will be slightly higher thah pre-dicted by the method previously given, and the slope of the kT curve will be a small percentage greater than that shown by the curves. It is for this reason that the plotted results for screw
K28 are above the average for the flve-bladed screws. This
- statement is based on the results of four screws (including K28).
-. The data are not extensive enough for any 'precision, but with
practical changes the variation is not great. It requires a fair amount of experimental work to define properly some of the mean lines andsmall variations of this kind. But allowm.g that.
adjustment and extenshin .are still required, these curves enable t A rather unusual example of loss by pure blade interference is
given by Dowson (Proc. I.Mech.E.- 1938,. ol. 138, p. 267). He
experimented with turbine blades spaced various distances apart in a steam turbine, correcting his results by 'special tests to zero blade-tip clearance. His-results therefore roughly correspond to infinite aspect ratio. The torsional force per unit area of blade is given as
Screw A is with the original C sections, screw B with modified root sections.
-* At'20 rp.s. this falls to 0143,Jo rising to 0'92.
the designer of any screw of normal type to form an estimate
of its thrust for a given condition represented by a fixed advance
speed and speed of revolution. This will hold good over all the usefui slip range, i.e. to about 35-40 per cent slip. Above this slip all kT curves are flattèning, so that in the 'slip region of 100 per cent to 90 per cent the kT value is reasonably constant,
provided the' screw does not break surface. The higher the
camber ratio of the blade sections, and the lower the value of the
gap/chord ratio, the sooner this falling-off begins. In this may
lie the explanation of the low ratio of
-t
for- the Tk L.P.
series with wide blades. These screws always work at a high slip,
and the spots average the- curve up to 40 per cent slip at least, and are affecte4 a little by this curvature of the kT curve at the' higher slips.
In the previous analysis it has been accepted that the blade surface was smooth, or. at least that its effect on thrust was the same in all cases. To test this, one of the B.W. set screws has been deliberately roughened, irs four stages. The roughness in' the first two cases was made by rolling a milling tool over the blade surface; first on the back and then on back and face. In
the 'second two cases, the coarsest sandpaper was wiped heavily
and diagonally (in two directions) across the back and then the face (on top of the other roughtiess). The results of the tests are given in Table 3. Some simibir tests made in- the Washington Tank, but with a still rougher surface are shown in Table '4. There are several conclusions which can be drawn from the
data, but two only need be mentioned here.
First, a good aerofoil blade screw can take slight roughness without change of pitch or of slope of the thrust curve, the ls of efficiency being sirnply due to increased drag on the torque. In other words, ilittie roughness of the blades wiji not alter the
speed of revolution for the ship, although the power required will
be raised by the extra drag, which has caused the drop in
efficiency.
Second, when the roughness is sufficient to promote eddy-making there is an immediate drop in the effective pitch. With the aerofoil type of blade of low camber there is little loss of slope of the thrust curve, but this loss is greatly increased on thick circular back sections. The loss of efficiency is a serious matter, but this will be considered in a later paper dealing with drag generally; the immediate purpose in quoting these 'tests is to show that small variations in roughness of surface of blades do not affect the slope of the thrust curve in a good screw. For
those who wish for further support to this conclusions reference may be made to test$ on Soughene'd aerofoils in the compressed
Screw Diameter,
feet
c No. of
blades pitch ratioFace
Calculated effective pitch ratio
Thickness ratio of
blades Experiment jesuits
At At Effective . k Maximum
073D root . 'pitch ratio' efficiency
- -. perblade 55A . . 038 128' 0149 0-64 F. ' 05 - 019 3 1-29 150 0107 55B . . .- " 023 148 0125 070 "1'3A . -. ' - . - ' . 040 115 0-126 - 0'613 B. . 1'0 0'14 3 10 1205 0'112 13B . . ' ' 0-26 1'215 0'116 . 0675 - . 035 0'86 ' 015 0645 0'81 . 0"19 2 0'77 , 092 0'085 B . . ' . . 024 088 0145* 0-685
0164 0-28 051 ' 0'74 1-0 - i"6 Joans,R., and WILLIAMS, D. H. 1936 Technical Report, Aero-nauticl Research Committee, Reports and Memoranda No. 1708,
-- =
-Chord
-Force
= .
0'008 0-012 0'018The last two figures are conjectural.
0-022 0'.025 0-028 "The Effect of-Surface Roughness on the Characteristics of the
Aero-foils NA.C.A. 0012 and R.AF. 34".
206
THRUST OF A MARINE SCREW PROPELLER
THRUST OF A MARINE SCREW PROPELLER
TABLE3. EFFECT OF ROUGHNESS ON.SCREWB.W..6
Diameter = io foot; 4 b1ades c/D O4;.fine pitch ratio 09; Reynolds number approximately 55 x l0.
TABLE 4. EFFECT OF GREATER RouGm.ESs.:- Aiws's SCREw (Soc. N: ARCHITECTS AND M. ENG., 1929)
DiamCter = 08 foot; 4. blades; c/D Ol9; face pitch ratio = 077; Reynolds nuniber above 155 x 10g.
air tunnel. The results show that. on a normal aerofoil section
(RA.F 34)thickness ratio 0127with an :8-inch chord,
the addition of carborundum particles, 00O 1 inch size, with a high density, lo*ered the slope of the- CL curve on a base of angle by only 5 per cent at a Reynolds number 5..106; but this
roughening on the suction faqe only had an effect less than
1 per cent. -
-Acknowledgements. The work described above has been
carried out is part of the research programine of the National Physical Laboratory, and this paper is published by permission
of the Director of the Laboratory The author desires to
acknowledge the assistance received from Mr T. L. G. Clarke of the staff of the Ship Division of the Laboratory, who has
- been responsible for a great deal o the experimental data and
the greater part of the analysis.
APPENDIX
NOMENCLATURE
T Thrust of screw in pounds.
n Revolutions per second, n0 value when T = 0.
v Speed of advance along axis in feet per second.
kT-Jo
S
p
p Density of fluid = 1-938 for fresh water; 199 for salt
water.
D Diameter in feet.
A - Aspect ratio. For a blade in open flight this isthe ratio
Area of one side (chord)2
-- 9 Pitch-angle (effective).
a Effective slip angle of screw blade, or angle - of attack in
straight flight. : -.
t Maximuni thickness of an3i blade sectiOn.
e Width or chord of blade section at O72D - 075D.
Circumferential distance between consecutive bldes at
IT(0.73D) - .
-mean radius - .
No of blades
CL Lift coefficient of a blade
-.4p (resultant velocity)2 (area)
L
T
-- pn2D4
= speed-/revolutions constant.
Value of at which a straight kT line cuts base.
Slip measurd from J0.
Effective, pitch ratio = Jo.
Surface
- - .
-. -
-Rughness,
inch -.--- Thickness ratio ofblades at
. Effective pitch -ratio - kT .' Maximum efficiency . Effective - thp for maximum efficiency 073D
-. 02D
(1) Smooth-
003 019 0946 0126 0653 023(2) Short sharp cuts with radial ridges
on suction face alone
-Max 000l5; mean 0-0(1 003
-0i9
. -O946 0126 - 0-64 -025(3) As above (2), but on both face of
blades -- -Max. 000l5;' mean - 0-001 -003 -. 0-19 0938 -. 0i24 . --0635 - -025
(4) Additional long sharp diagonal outs
on suction face . - . . 000l3 003 -019 -0904 . 0l23 06O 025
(5) As above (4) but on both faces . '000l3 003 019 1914 0l20 0-575 027
- Surface -Roughness, inch -Thidaiesi ratio of
blaTdes.at Effective
pitl
ratio -Maximuña efficiency -Effective slip for maximum - - - -. 073D . 0-2D -- . -
.-
efficiencyGround but not machined
-
0 065 0 225 0 93 0 111 0 635 029Stippled paint on both surfaces . . 0-008 -. - - .
-
. 0-87 0-100 0-48 0-33/
208
Professor A. M. ROBB, D.Sc. (University of Glasgow), wrote that the fundamental assumption underlying all the author's
work in thispaper was that a curve of kT on a bale of "effective"
slip was a straight line; "effective"slip was calculated from the
"effective" pitch. This assumption was not,justifiable. Evidence
0.6
0-3
SI Fig.5
on the matter was provided by Fig. 5,'which showed curves
of
kr on a base of effective slip for three of. the propellers of Taylor's ,seres. No. 1 was for the narrowest and thickest
propeller of the series, with face-pitch ratio 0-6, and No. 30c for the widest and, thi±uest, with face-pitch ratio 20. No. 1,2
CommunicatiOns
lay between the others, but nearer in proportions and in
face-pitch ratio to No. 1 than to No. 30c. From these curves it
would appear that the relation between kT and effective slip
was not linear. For these three propellers he values of the effec-tive pitch were determined from the face-pitch slips at which the
thrusts were zero. In spite of the author's scepticism indicated on p. 203 there was ground for the' belief that the values of the effective pitch were substantially reliable. Sin'ce, 'however, the / scepticism regarding Taylor's results was' accompanied by an indication of satisfaction with Troost's results a selection from them was given in Fig. 6. The curves were prepared from the diagrams published by Troost* in 1939-40.,..They confirmed that the author's fundamental assumption was not justifiable.
Since there 'was here a matter of principle it was necessary to
investigate the conditions under which a curve of kT on a base of effective 'slip should be a, straight line. For this purpose the
basic consideration was that given by the author on p. 201,
namely the linear relation between lift and angle of incidence. Accepting that relation it was possible to determine the desired relation for an element of a. propeller blade. Fig.. 7 showed an
element of a blade working under thi condition ,of constant
axial speed and varying rotary speed. The rotary speed at which
there was no lift was denoted'by N0. Corresponding to the
speed N0 the' transverse path of the element was represented
by A0B or by 2r(xR)N0, where (xR) was the radius of the
element. Corresponding to a rotary speed 'N greater than N0 the transverse path of the element was represented by AB, or 2v(xR)N. The constant axial path was represented by BD, or
Va. At the higher rotary speed the element was travelling
relatively to thewater .at an angle of incidence and developed
the lift L which, varied as , and as the square of the speed..
The path of the element in space was represented by AD and
'the speed V = 2r(xR)N/cos .. Leaving out of account any
drag force. -'
Thrust = L cos = a1 V2ç6 cos = a2N27/ cos .
But cos cc= 2ir(xR)N/AD -. 'and
tanCD/AB =
P0(NN0)/AD, .wheré Po was the pitch correspondinj to..
the no-lift line. Then:
a2N2P0(NNo)AD .'
ThruSt
-
AD,. 2v(xR)N -' - .a3N(NN0)a2bN.
This was the' basic equation developed by R. E..Froude. It was
consistent with momentum theory, which-gave
-Thrust = 2pAVa2(1+a)a. '
Since 1+a
1/(1sj)anda
&1/(1s1)theequationbecameSI
. 2
Fig. 6' ' Thrust = 2pAVa2. S1 2 1 V6\N2PC
(1_si)2 -
2p4Va . lp)
-i
=
pAN2(Po2_ V$) = aN2hN for P0 and Vg constant.* TROOST, L. 1939-40 -Trans. N.E. Coast Inst. Engrs. and Ship-builders, vol. 61, p. 91.
-COMMUNICATIONS ON .THE THRUS
If when N = -N0 the thrust was zero
Thrust = aN2(1
-) = aN2s1, where s1
was the. slipmeasured in relation to the no-lift line. The equation was for unit diameter. For diameter D it became thrust = aD4N2s1, a given by Froudé, whence kr = const. x s1 'for any propeller.
Since the drag had been omitted in the above consideration the
linear relation between kr and s1 was dependent on the omission
of the direct effect of that quantity; an indirect effect was included inasmuch as the lift was normal to the direction of
avance.
-The foregoing consideration was based on the angle of
in-cidence being measured from the no-lift line. It was not affected
by the angle being from the no-thrust line. The change from one line to the other was equivalent merely to a minor change of the axes of the lift curve and to a corresponding shift in the position of zero value of kr; if kr was plotted on "no-lift" slip
kr was zero at zero slip, whereas if it was plotted on
"no-thrust" slip, commonly referred to as effective slip, there should
be a positive value of k at zero slip if the effect of the drag be
left out of the consideration. .
-Thus it would appear that departure from the linear relation between kr and s1 was associated with the operation of drag, and the extent of the departure might be largely, if not wholly,
a measure of the drag. There was, however, an alternative
method of determining the effect of drag, which being more
closely concerned with the author's paper to the North East
Coast Institution was being outlined in the discussion on that
paper.
Meantime it was necessary to. remark that the thin line as-.sociated with the curve of k for No. 12 propeller in Fig 5 was
deriied from the use of Froude's equation T = BD.2 Va2y Pi± 21
the correcting factor having been omitted. Since the value of Pi used in the equation was that appropriate to No. 12 propeller the thick and thin lines should, apart from the departure from
the linear relation due to drag, agree if the slope of the kT
curve was determined only by the effective pitch. Elucidation of this matter, and an indication of the reason for the disagreement of the thin and thick lines near the origin, might be gleaned from
the discussioti of the author's other paper.
It was suggested that the value of the author's extensive
analysis would have been enhanced if the same general approach
had been adopted, but without basing it on the unjustifiable
assumption which had been discussed above. It was suggested also that consideration of -the cascade effect should be left .iri_
abeyance until test records were available from
multiple-bladed propellers with exactly similar blades; there was. too wide a difference between the parallel cascade investigated in'
aeroplane theory and the tapered cascade formed by thefl blades
of a ship propeller.
Dr. E. V. TELFER (Ewell) wrote that the statement (in Part 1)
that the blade lift depended mainly on blade mean width ratio and slip angle was not sufficiently correct since this ignored the effect of blade number, which clearly reduced the thrust per blade although not an aspect ratio effect. The latter effect was essentially due to the tip' vortex action, and in most cases was probably independent of blade number.
The influence of blade number, moreover, could not be
merely a cascade effect, as the author. suggested,, but resulted from the increased velocity induced through the propeller disk by an additional blade reducing the effective incidence angle on all blades. This followed immediately from the fundamental
relation equating blade thrtist and disk momentum; and the
a author's pointer (a) was, because of this, certainly not true.'
Knowledge of cascade effect at the moment was very confused
since the cascade analogy was only very approximate and ignored altogether the influence ,of the pressure reduction
induced by the combined boss vortex.
In Part 2, the atithor got over Some of the basic error in the pointers when he adopted thrust rate per blade as his ordinate
- values in Figs. 1 and 2: The fact, however, that different curves
were found for each blade number confirmed the misconception
T OF A MARINE SCREW PROPELLER
209of the pointers. The mergence of all curves at very small /D values was merely latitude in fairing, since all curves should at
least pass through the origin. The thrust rate function was
known to be fairly independent of effective pitch ratio at high
pitch ratios, but there was an influence present at low pitch
ratios which must be respected to steady such data. Incidentally,
since the majority of the National Physical Laboratory data were determined at constant advance instead of. at constant speed of revolution, a considerable scattering of the data was inevitable. Generally the effect would be to oversthte the thrust
function due to the reducedJ0J value asociated with a given
thrust. The .use of a calculated jo in preference to the experi-mental, was thus more understandable than commendable.
The use Of a calculated'Jofor reviewing the freedom from
trouble of a screw was quite another matter, and was a practice which could ,be thoroughly recommended. Most of. the early
National Physical Laboratory data thus reviewed always
showed perplexingly low efficiencies. .
-.The author discussed, the effect of roughness both in his
present paper and his contemporary paper to the North East Coast Institution. The effect of small roughness was capable of quite another explanation. If the blade sections were originally suffering from laminar flow, the small roughness induced
tur-bulent flow, which increased blade resistance but also improved
the back suctions, particularly towards the leading edge. Thus the gain in suction thrust balaticed the increase in friction drag;
the torque, however, received both the friction and suction.
increments. It was wrOng, therefore, in his submission, to endow "a good aerofoil screw" with the fictitious ability of withstanding
small roughnesses, since the peculiarity was obviously due to the greater laminar proneness of the aerofoil model and would have no counterpart on the ship. Adding sufficient or greater
roughness to an lready turbulent model would have quite
another effect. Here the roughness reduced the back suctions and their thrust contribution; the friction was, increased, but now the two components were additive in reducing thrust but opposed in their torque influence. This was the normal full-scale effect and clearly was the explanation of the "Clainton" and other similar tests. He suggested that the author's diagnosis was not correct and should be revised.
The five-bladed scres 1(28 to-which the author referred was not thickened at the tips as he stated, but had normal root and tip thickness, with a "hollow" back resulting from a constant-stress design of blade. It also had a pronounced skew-back in association with a forward rake. As K28 was a commercially tested screw it was probable. that the author did not wish to
disclose this further relevant infOrmation.
To facilitate the use by other investigators of the author's
basic data it would be valuable if a diagram showing the relation of c/D to disk area ratio per blade could be given.
Dr. G. S. BWR wrote that Dr. Robb had missed the most
important point in -his pper, viz., that it was based on experi-mental and not theoretical data. The elaborate production of a
very elementary equation for thrust of a non-frictional propeller
was quite beside the point: the essential experimental fact was that, Over the working slip range, thousands of experiments
showed that the kT/J curve was a straight line. At low slips
there was a small departure from this line, for reasons he had
given, and at high slips there was another departure owing to the
change in flow over the bladebut they were not concerned
with these. He had called the point where this straight line cuts the thrust base .70 or the, effective pitch. It was not necessarily the so-called "experimental mean pitch", or rio thrust point;
but could be 'calculated by the methods given, and with its
help a close approximation to the actual thrust could b found by the linear law given. Taylor's results were closely examined when the data was being plotted, but there appeared too much uncertainty about the low slip values for ,accurate assessment of zero effective pitch. No principle entered into this, and none had been tised except to.plot-the results in the form chosen.
As regards Dr. Telfer's criticism, he had approached cascade effect in a propeller as cautiously as he could. Its effect upon the no-lift angle in straight flight seemed fairly clear, and he
left the resti.e. the effect upon v.elocityto come out in the
210
COMMUNICATIONS ON. THE THRUST 0F A MARINE SCREW PROPELLER
of the. combined boss vortex, or rather the va±iation in.this due
to multiple blades. Even if a theoretcal exrëssion could be
obtained for this, it would only apply to an assumed stream line flow, and he very much doubted whether this would repre-sent the conditions behind the boss of a screw. What had been
implicitly assumed was that this- effect would vary with number
of blades. Dr. Telfer argued that a small degree of roughness on a blade section, sufficient to change laminar to turbulent flOw, would add to the suction on the back of the blade, and -hence to the thrust. Why? The thickness of the frictional layer
would still be exceedingly small, and have no effect on the flow,
unless it caused it to depart from the. blade sirfacein that event the thrust would diminish and not- increase, as in his
second case.
He had not: stressed the convergence of all the curves in
Figs. 1 and 2 to a common slope for small blade widths ;.but-since
hispaper was written, a paper by V. D..Naylor,* dealing with a
family of narrow-bladed airscrews, supported this convergence. * Aircraft Engineering, 1944, voL 16, p. 310, 'A Master
Thrust-- Curve for Airscrews". - .
