MEDDELANDEN
FRANSTATENS SKEPPSPROVNiNGSANSTALT
(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)
Nr 33 ' GOTEBORG 1955
THE INFLUENCE OF PROPELLER
CLEARANCE AND RUDDER UPON THE
PROPULSIVE CHARACTERISTICS
BY THE STAFF OF SSPA
EDITED BY H. LINDGREN
GUMPERTS .FORLAG
GUTEBORG 1955
1. Synopsis
The present paper describes some special experiments which have
been carried out in recent years at the Swedish State
Ship-building Experimental Tank (SSPA).
Part I deals with experiments which were carried out for the
purpose of investigating the effects of propeller position and clearance
(or the shape of the aperture) on the propulsive characteristics.
Vibration and other practical considerations have not been taken into account in this connection. The experiments were carried out with a 15-knot cargo ship (V = 5725 m3, 6 = 0.65) in accordance with a
scheme devised by Mr. E. FREDMANIS, who also was responsible for
most of the analysis of the experimental results.
Part II is concerned with the effects of the presence of the rudder and its thickness on the propulsive characteristics. Sell-propulsion
and resistance tests were carried out with a model of a tanker (V = 22000 m3, 6 = 0.75) both without a rudder and with rudders of different thicknesses. Open water propeller tests' were also carried out,, both in the normal manner (without a rudder) and, in addition, in conjunction with rudders of different thicknesses. These experi-ments were carried out in accordance with the recommendations- of the
Sixth International Conference of Ship
Tank Superintendents (Washington, 1951).
Finally, a brief summary of the most important results from both series of tests is given in Section 10.
2. Symbols, Units and Methods of Calculation
The symbols have been chosen in accordance with tHe recommendations made by
the Sixth International Conference of Ship Tank
4
Ship Dimensions
L = length on waterline
Lpp = length between perpendiculars
= breadth on waterline
T = draught
Am = immersed midship section area
wetted surface area (including wetted shrface area of rudder and bossing)
17 volumetric displacement
distance of L. C. a forward of midships (Lpp/2) cce = half angle of entrance on 'Waterline
Rudder Dimensions
= max thickness of section = length of section Propeller Dimensions propeller diameter =- propeller pitch (propeller disc area
Ad developed blade area
1 --= blade width at 0.7 D/2
Kinematic and Dynamic Symbols and Ratios
speed in general
V5 --- speed of advance
V = ship's speed in Metric knots
R = resistance
T propeller thrust
Q =- propeller torque
n rate of revolution (revs, per unit time) Pe = effective power
Ps = shaft power (at tail end of shaft)
V Ve
- = wake fraction (TAYLOR)
T R
thrust deduction factor
= density of water {(102.0 kg sec.2/m4 for fresh water)(194.5 kg sec.2/na4 for sea water) = kinematic viscosity of water
11 Ive2 (0.7 Tt D n)2
REYNOLDS number for propellers
v
25 D2 4
Dimensionless Coefficients and Ratios 17
block coefficient
'
L.B;T
= - midship section coefficient
T V prismatic coefficient Ap, = length-breadth ratio = breadth-draught ratio = length-displacement ratio = L. C. B. forward og Lpp/2 as % of = pitch ratio
= disc area ratio
thrust coefficient ,C1 D4 n2 = = torque coefficient (2 P5 n2 ye = = advance coefficient D n KT .tiQ 27! P, = propulsive efficiency
= propeller efficiency in open water
Units and Conversion Factors
Metric units are used throughout.
For g (acceleration due to gravity) the value 9.81 ru/sec.2 has been used.
1 metre = 1281 ft. (recipr. 0.3048)
1 metric ton = 1000 kg = 0.984 British tons (recipri 1.016)
1 metric knot = 1852 m/hotir = 0.999 British knots (recipr. 1.001) 1 Metric HP = 75 m kg/sec. = 0.986 British HP (recipr. 1.014)
Methods of Calculation
The model-scale results from the resistance tests have been converted to the scale
of the full-sized ships in the conventional way in accordance with FROIIDE'S method.
The frictional resistance has been calculated using the formulae decided upon at the
Tank Superintendents' Conference') in Paris in 1935. No length
correction has ,been employed.
All the self-propulsion experiments were carried out according to the so called
Continental method (GEBERs)2) with the skin-friction correction applied as a towing
force. The results have been converted to full scale in the conventional manner. In converting the measured values to ship scale, no corrections for scale effects, air resistance, hull condition etc. have been applied.
3. Ship and Propeller Data
As mentioned in the Synopsis, a model of a 15-knot cargo ship (No. 401) was used for the experiments described in Part I and a model of a large tanker (No. 501) for those dealt with in Part II. The main particulars of the ships concerned are given in Table I.
Table I
Modified here. See Some Systematic Tests with Models of Fast Cargo Vessels by
H. F. NORDSTROM, Publication No. 10 of the Swedish State Shipbuilding Experi-mental Tank, Goteborg, 1948, p. 7.
See Congres International des hirecteurs des Ba88i71S, Paris, 1935, p. 86. Units Model No.
401 Model No. 501 Cargo Tanker Model Scale 1: 15 1: 22.5 Number of propellers 1 1 L ... ... . .... . ... . .... . m 103.40 156.00 .. ... .. .... .. . . ... .. m 100.58 152.40 B m 14.48 20.80 T m 5.93 9.04 V in2 5725 22000 S mE 1966 4894 LIB 7.14 7.50 BIT... ... .... ... .. . ... . 2.44 2.30 L/17113 5.78 5.57 6 0.645 0.750 fl 0.982 ' 0.993 (P 0.656 0.755 1/2 oce ... ... ... . degrees 10.5 29 tILpp %
1.5
1.0Propeller No. P40/ Dimensionsin mm Fig. 1 Dimen:ions in n,n7 Fig. 2 876
1) Numbers in brackets refer to the list of references on p. 25.
Model No. 501, which had been used previously in a systematic series of tests (see [1]1)), was fitted with a 1 mm tripwire at Station No. 19. No tripwire was Used with Model No. 401. Both models were made of paraffin wax.
Particulars of the propellers (Nos. P401 and P457) are given in ship scale in Figs. 1 and 2 and in Table II. It should be stated here
that Propeller No. p 467 was based on TROOST'S B.4.40 Series [2].
Propeller No. P 467 _4876 027111. 480 314 V79 637: '
Table II
') Pitch at the outer sections.
I. The Influence of Propeller Clearance and Aperture Form
On the Propulsive Characteristics
4. Scheme of Tests
As stated in Section 3, the tests were carried out with Model No. 401 and Propeller No P401. Beginning with the propeller in the normal position in a normally shaped aperture (No. 401-A in Fig. 3) the propeller was moved forward (No. 401-B) and aft (No, 401-C).
Fig. 3 Units Propeller No P401 Propeller No P467 Model Scale 1 : 15 1:22.5 Number of blades 4 4 D m 3.800 5.670 m 3.050 4.876 Pip
... ... .. .. .
0.80 0.86 44 40 Rake degrees 13.3 1.5.0In addition, the propeller aperture was altered by fitting a plate
1 mm in thickness in the plane of the centreline (No. 401-A with plate and No. 401-C with plate). The shape of each plate is indicated by 'dotted lines in Fig. 3. Each of these alternatives was investigated
by means of self-propulsion tests.
Resistance tests were carried out only with the model with a normal aperture withOut the plate. The effect of the plate on the resistance
was regarded as being so small that it could be neglected when
calculating the propulsive efficiency, 77, and the thrust deduction factor, t.
Open water tests were carried out in the normal manner with
Propeller No. P401.
5. Test Results
The tests results are shown graphically in Figs. 4-8.
The results of the open water tests with Propeller No. P401 are
given in Fig. 4. These results have been used in calculating the. values. of the wake fraction.
Propeller No. P4o/
0,1 02 0.3 04 0.5 06 0.7 08
.7= n
Fig. 4
9.
/2o
Mode/ No. 401- A
Mode/ No. 4o/- B Mode/ No. 4o/-C
Propeller No. P40/
..15oo
J000.
2Soo
500
In Figs. 5 and 6, the effective power, Pe, the shaft power, P., and the revolutions, n, are shown plotted to a base of ship speed, V.
The results shown in Fig. 5 are those obtained from the version with a normal aperture (without plate) and with the propeller in different positions. As may be seen from this diagram, over the greater part of the speed range, the lowest values of P. were obtained with the prdpeller in its normal position No. 401-A. The version with the propeller further forward than normal (No. 401-B) required
f2 /4
Shijo Speed, V, 4, knot's
Fig. 5
1.90
160
o
/60,
/40
/2o
Model No. 4o/-A, Without Plate - Mode/ No. 4o/-A, With Plate
Model No 4ol-C, Wilh Plate
Propeller N. P40/
Ship Jpeed, V. 1/9 knots
Fig-. 6
about 1-2 % greater shaft power, while the version with the pro-peller moved aft (No. 401-C) required about 2.5 % greater shaft power than No. 401-A at the lower speeds and slightly less shaft power at the higher speeds.
In Fig. 6, the two versions with a plate in the propeller aperture
are compared with the normal version. No definite tendency is
noticeable here, except for the fact that the plates apparently had a favourable influence on the results. Model No. 401-C (with plate)
/S
9Soo
30ffle
19 8o 70 6o /0 /0
Mode/ Na. 4O1- A
- - - Mode/ No. 40/-B
Mode/ No. 4oi-C.
Propeller No. P40/
/3 /4,
Ship Speed, V, in knots
Fig. 8 0 /2 Bo 70 6o So 40 /3
Ship Speed, v. in knots
Fig. 7
Model No.4o/-A ,thou/ P/ole
Mode/ No. 4o1-A, With ./-6/ole
Mode/ No. 4o/-C, WithP/a/e
/3/4,oe//er No.P4o/
Jo
'2o
3O
13
required about 1-2 % less shaft power than the normal version
(No. 401-A, without plate) over the greater part of the speed range. Values of propulsive efficiency, i, wake fraction, w, and thrust deduction factor, t, for the various alternatives are given in Figs. and 8. The relatively small differences which,are apparent may be partly due to inaccuracies in measurement and the diagrams do not therefore give any definite indications. It should, however, be noted that in both series of tests, the highest wake fractions were obtained with the propeller in the furthest aft position.
II. The Influence of the Rudder and its Thickness on the
Propulsive Characteristics
6. Scheme of Tests
Open Water Tests
A normal open water test (without rudder) was carried out with Propeller No. P467. Then, in order_ to determine the effect of the rudder on the wake fraction, further open water tests were carried
out as suggested by VAN MANEN [3] and HARVALD [4], among others,
both with rudders of different thicknesses and with a 2 mm plate abaft the propeller (at the same distance from the propeller as in the corresponding self-propulsion test). The rudder dimensions and position are shown in Fig. 9.
Two different experimental arrangements were employed in the open water tests with rudders. In the fkrst arrangement, the rudder was attached to the shaft bossing, i. e. the resistance of the rudder had no direct influence on the measurements. In the second arrange-ment, on the other hand, the rudder was connected to a .bearing on the propeller shaft itself, so that it moved axially with the latter; the rudder was prevented from rotating with the shaft by means
of a guide connected to the shaft bossing. The propeller thrust
measured in the second case was therefore the difference between
the total generated thrust and the resistance of the rudder in the
propeller race.
The second arrangement is illustrated in Fig. 10. The, rudder itself consisted of a 2 mm plate to which were fastened wooden side pieces gMng, the required form and thickness. The forward part of the plate was attached to the outer ring of a ball bearing, mounted
14
guide p/o4
fixed rinq
Di"ens/en., for Ni.00'e/ b7mm777 Fig. 9
prope//er 1)041 propel/el. cone
-'''''61110171Sr
ra& 11.11FM
'shall bossing boll bearing propeller she15
on the propeller shaft. The after part was attached to a ring which served as a sliding bearing for axial movement of the rudder relative to the shaft bossing. In order to prevent the rudder from rotating, a strip of plate, which was fixed to the shaft bossing by a further. ring, fitted freely into a slot in the trailing edge of the rudder, thus
providing a guide. The friction in these additional bearings and
guides was allowed for automatically, since its effects would be included in the calibration measurements taken after each series of tests.
Resistance and Self-Propulsion Tests
Resistance tests were carried out with Model No 501 (see Table I) both without a rudder and also with the two thickest rudders.
The self-propulsion tests on this model using Propeller No. P467 were carried out firstly without a rudder and then with rudders of three different thicknesses.
7. Test Results
Open Water Tests
Figs. 11 and 12 show the results obtained from the open water
tests. Fig. 11 refers to the arrangement in which the rudder was attached to the shaft bossing, while Fig. 12 contains the results of the tests in which the rudder was fixed axially relative to the pro-peller shaft. For comparison, the curves of results obtained from the normal open water tests (without rudder) have been included in these figures.
In Fig. 13, the curves of Kr and KQ obtained from the normal open water tests are compared with those 'obtained from the tests
with the thickest rudder attached by both methods behind the propeller. As was to be expected, the method of connecting the
rudder had no effect on the KQ-curve. On the other hand, the vertical difference, KI,T, between the two KT-curves obtained with the two rudder arrangements, provides a measurement of the axial component
of the resistance of the rudder, lir, in the propeller race. This difference has been calculated at various J--Values for the two thickest
rudders and also for the basic plate. The values afe shown in the form of curves in Fig. 14.
1 6
/0 Kr /00/(0 4
2
Rudder Connected to Propeller sfhaft-Bas.ring Propeller No. P467
Without Rudder
Plote Rudder 12.emm
Rudder /3.Sthm 0 0.093 Rn 2.5- 2.8 -/os -Rudder I. 27.ornm 00./2,6 ' Rudder 4o. 5,,,,n 0.279 02 Fig. 11 08 Jo
Table III shows the resistance of these rudders at 15 knots,
calculated by three different methods as follows:
By using KT -valueslifted from the curves in Fig. 14.
By calculating the frictional resistance, using the SCHOENHERR
line, and applying ScuoLz' [5] Correction for form effect, thus,
Cfr Cf (1 2.4
ti)
where Ch.= resistance coefficient for the rudderC, = resistance coefficient for a smooth plate in turbulent flow (ScH0EN4ERR)
tll = thickness -- length ratio of the rudder section.
EOM
IIMPOM
...:.,'..---.,,...--,,...
\ \ \
\ .4.-:'.--:.:',,
. `,,N:IN
,R
\ \ 11. \ 1111112& .1--:' ... \N. \* , \ '.I i 1WA"
ss ......k,....
\..,... , \..,....\. `.\\...\,.. Ail!
;VI, \ ss,. AI\Pal
A .Al
mit
...
: 0.4 0.6 ve 0 n 7o 60 So 30, 2o . /oRudder Connected to Propeller Shaft Propeller No. P467
Without
Rididdel-Plate Rudder 1. 2.12 tot
Rudder t 27o rnrn 0-0./86 Rudder f4o.S,nn4 0.0.279, /0 17 _..._ 3
iiii,mmourommi
-IMIlli
',,,...s,MIIIII,
N.FAI
sw:1,.
011
Iir
.111
J Ve Fig. 12In this case, the rudder has been regarded as a free plate, moving at a speed equal to the speed of advance at 15 knots.
3) By taking the difference in the model frictional resistance with
and without the rudder. It has been assumed in this case that
the surface of the rudder is an integral part of the wetted surface of the model and that its resistance is part of the total resistance of the model and the rudder together.
It will be seen that, in the case of the normal rudder (t// --= 0.186), its resistance in the propeller race (calculation method 1) is about six times greater than that part of the calculated total model
resis-tance which can be attributed to the rudder (method 3). This
considerable difference must primarily be due to the very high speed
of flow past the rudder, when the latter is in the propeller race.
2 4 2 70 60 So 40 30 2o /0 0
18
- Without Rudder
Rudder t-4o....4infri, 0-0. 279 connected to propeller -chaff
Rudder 4o. $171 In,O. O. 279 Carthected to ,rhaft-hos.siig
/oo 2o Fig. 14 /0 1.0 nce)
MI
If R,-Re.r/Zrtc T,. .j3 ( Rr . Rqddei 04 n.?win
MEM
'Vial. WIR.ltr,En=
;Ng\.
..,:,.\:.
.0.2 04 06 08 ve Fig. 13Plate Rudder 12.ormo,
Rudder I 2'7.ornfr,
= Rudder. 40.5emn 1,4
0.2 0.4 06 0.8
Table III
Resistance of Rudder as Percentage of Total Resistance at 15 knots
19
The conventional definition of wake fraction, based on thrust
identity, can be written:
WT
(
where J'
is obtained from the self-propulsion test andDn,
the corresponding J
lln
ve is read from the K7;-curve resulting fromthe normal open water test (without rudder).
If instead, J is read from the KT.-curve resulting from the open water test with the rudder attached to the shaft bossing (say JO, the corresponding wake fraction is given by
` Ji
The difference, if any, between these two wake fractions can be regarded as the effect of the rudder on the wake fraction given by the usual method. This may be expressed by
J1 J
awT, - T
ji
and similarly, on the basis of torque identity,
wQr = w(2,.=
where a and b are as indicated in Fig. 13.
Method of calculation Rudder t = 40.5 mm t// = 0.279 Rudder t = 27.0 ram 0/ = 0.186 Plate. t = 2.0 mm _
1. Open water tests (Fig. 14) ... 7.7 3.6. 1.7
2. SCHOENHERR line with form
correc-tion - 0.8 0.8 0.6
3. Difference in model frictional
resist-ance with and without rudder.
.
90
/Zo
//o
IS
Ship Jpsycl, V, in knenti
I Fig. 15 /6 ./0000 9000 000 7000 2000 0 AI ode/ No. -10/;7004.4 Sol Pro,oalier Rudder 1.4.24.ms, I.220"..., I. 4a..fortm No. P 467
--- -
-41.0bir .- -- --:-.0dedeler =-- --.- Ruder, Ø.a09.3 0 .0/46 0.0. 279 -.Ai ...n.,...'...f ....:....-. ,.,pr./
l''.",
111
Al.. .?./r..A.::
-.40
um
.... ... ...The method of basing the wake fraction calculations on the results of the open water tests with the rudder attached to the shaft bossing,
gives values which, as is evident from Section 8 below, are not influenced by the rudder. On the Other hand, if the KT.-curves
obtained from the open water tests with the rudder connected to the propeller shaft are used for calculating the wake fractions, the
values-so derived are not independent of the rudder. The latter method
involves identifying the total thrust generated by the propeller under sell-propulsion conditions (the thrust necessary to overcome the total resistance of the model and the rudder together) with the thrust measured in the open water test which constitutes the difference between the total generated hrust and the rudder resistance. This
method of calculating wake fraction has not been included in
-Section 8.
Resistance and Self-Propulsion Tests
The results of the resistance and sell-propulsion tests are given in Fig. 15.
As expected, the rudder. had only a small effect on the resistance results. The rudder and its shape appear to have more influence on the propulsive characteristics. Both the revolutions, n, and shaft power, P., decreased in the presence of the rudder in these tests
(see Fig. 15) over more or less the whole of the speed range.
The normal rudder (t// = 0.186) was apparently the most suitable over the greater part of the speed range.
8: Wake
The wake fractions have been calculated by several different
methods and the values are plotted in Fig. 16.
The values of w7,* given in the upper diagram have been obtained on the basis of identical values of the thrust ocefficient K. under self-propulsion and open water conditions- Similarly, the values of wQ have been obtained on the basis of equal values of the torque
coefficient, KQ.
The lower, part of Fig. 16 shows the wake fraction values obtained in accordance with the method usually adopted at the Tank, ;whereby
WT WQ
9 9
4.0
o Jo
2o
Model No. So/ Pope//e r No. P 46 7
14
/4
IS
/S
Ship Speed. V, L7 knol.s
Fig. 16
The thick curves, as is evident from the figure, indicate the wake fraction values calculated by means of the results from the normal open water test (without, rudder). The rudder and its thickness clearly have a marked influence on the wake fractions obtained by the normal method.
The values indicated by the thinner curves were calculated with the aid of the results of the open water tests with the rudder placed
behind the propeller (fixed relative to the shaft bossing). The wake fractions (both w, wQ and w) calculated in this way from the results of the tests with different rudders agree well with the values based
/6
/6
-
-
-- - -
-Open Water Test Without Rudder
Open Wo/er Tests With Rudder
Connected &Prop Shaft earsmg Sell-Propu/sion rrsts
Wahout Rudder
Rudder t./3.Srnm 0.0093
Rudder t.2ZoMO70.0./86
Rudder 1.4o 5 n2rn //%=0.279
-
--- -_ -_ _._ _..-_.._._ _
._ 14. /5 0 Jo 2e +8o 7o 60 so 30 /0
Ship Jpeed, V, in knot's
, Fig. 17
/6-93
on the tests carried out without any rudder. As explained in Section 7, the influence of the rudder has been eliminated from the wake and transferred to the propeller characteristics.
9. Propulsive Efficiency and Thrust Deduction Factor
Fig. 17 shows the values of 77 and t, obtained without a rudder and with the two thickest rudders, plotted to a base of speed, V.The presence of a rudder causes an increase in the thrust deduction
factor. Likewise, an increase in the thickness of the rudder has a
similar effect.
-The propulsive efficiency, n, has an apparent optimum depending on the rudder; the values of n obtained without a rudder and with the thickest rudder are lower than those obtained with the rudder of normal thickness.
Mode/ No. So' Pro,oe//er No, P467 Rudder
Rudder 27o rnrn 0./86
°A
=--- Rudder 1. 9o..finm r,4 .0.279
'7
24
10. Summary
The Influence of Propeller Clearance and Aperture Form on the
Propulsive Characteristics
In one of his papers [6], AYRE gave some information on the influence of propeller clearance on the propulsive characteristics and he came to the conclusion that, from the propulsive point of view, the clearance between the propeller and the rudder should be as small as possible and that a large clearance forward of the propeller is desirable.
This question is, of course, connected with the form and fullness ,of the ship and also with the type of propeller, but in the case of
the example under consideration here, no definite tendency in agreement with AYRE'S conclusions could be discerned. For example,
it was found (see Section 5) that with the propeller placed furthest aft in the normal aperture, worse results were obtained at the lower speeds than with the propeller in its normal position (Fig. 5, 401-C). On the other hand, when the forward part of the aperture was filled
in with a plate, the best results were obtained with the propeller
furthest aft (Fig. 6, 401-C with plate). In general, it wasfound that, in spite of the considerable differences in clearance and aperture form, the maximum variation between all the experimental results
was ± 2 %.
The fact that the position of the propeller had relatively little
influence on the results in this case indicates that the most suitable clearances should be determined on the basis of practical considea-tions.
The Influence of the Rudder and its Thickness on the Propulsive Characteristics
The importance of the rudder in relation to
the propulsivecharacteristics of single screw ships is well known. It is evident
from Fig. 15 that a rudder of normal thickness has the effect of
decreasing the required shaft power by up to 5 % in the case of this particular ship (in comparison with the alternative without a rudder). The results shown in this diagram also indicate that the most suitable rudder from the propulsive point of view is that with a thickness-length ratio tll of about 0.2.
A
25
In order to obtain similar flow conditions in the self-propulsion and open water tests, it has been suggested that open water tests should be carried out with a rudder behind the propeller HARVALD [4] says that *it is the mode of action of the propeller which is altered by the presence of the rudder, rather than the physical wake.*
Fig. 16 shows
the wake fractions calculated with the aid
of results from both normal and with rudder open water tests.
It will be observed that the wake fraction, whether based on thrust or torque identity, becomes practically independent of the rudder when the results of the with rudder open water test are used in the calculation. On the other hand, when the wake fraction is calculated in the usual way (using the results of the open water test without
a rudder) the influence of the rudder on the wake is apparently
considerable and the results become dependent on the form of the
rudder.
Acknowledgement
Thanks are due to Mr. DACRE FRASER-SMITH, B. Sc., for trans-lating the paper from the Swedish.
List of References
EDSTRAND, HANS, FREIMAN'S, E. and LINDGREN, Hs: »Experiments with Tanker Models D, Publication No. 23 of the Swedish State Shipbuilding Experimental Tank, Goteborg, 1953.
TROOST, L.: »Open Water Test Series with Modern Propeller Forms, Trans,
N.E. C. I., Vol. 67, 1951.
yam 4.A1EN, J. D.: uinvloed van de ongelijkmatigheid van het snelheidsveld op het ontwerp van scheepsschroeven», Ned. Scheepsbouwkundig Proef-station, Publicatie No. 100, 1951.
HARVALD, SVEND AAGE: Wake of Merchant Ships* (The Danish Technical Press, Copenhagen, 1950).
SbIOLB, NORBERT:' i>rber eine rationelle Berechnung des Stromungswiderstafides
sehlanker K6rper mit beliebig rauher Oberflache»,-Jahrbuch S T G, 1951. AYRE, Sir Amos Some Observations Concerning Resistance and Propulsion*,
