List_ a 1t'b titU tn abs, s Aarts 1. Figs. ta-g 3. FiUg. 3 Pfge 20. Fig. 4 Pagth 233r EQs.g, 5,thftsen I?a. Pa.ge,.,23.. Tables i & I4t Page 13.., Table 4. rPate. X a -or 1, di Cable VI. Ia e 1t Charts 1, 11, I11, IV, 4, VI,'111i

f 117/ / u'bK 6~~~~~~2~~aIl

REFERENCES. (1) Taylor, D. V., "Speed and Power of Ships" ( 2 ) Taylor, D. W., "Tests of Model Propellers of Various Blade Seotions", Transations of The Society of Naval Architects and Marine Engineers, 1930. (3) Troost, L., "Open-Water Test Series with Modern Propeller Forms, Part I: Four-Bladed," North East Coast Institution of hngineers and Shipbuilders, 1937-1938. Troost, L., "Open-Water Test Series with Modern Propeller Forms, Part 2: Three-Bladed," North East Coast Institution of Engineers and Shipbuilders, 1939-1940. (4) Principles of Naval Arohiteoture, Vol. 2, P. 160-167. (5) Aokerson, James Lee, "Test Results of a Series of Fifteen Models" Transa2tionRs of The Society of Naval wrohitects and Marine Engineers, 1930. (6) Bragg, E. M., "The Quasi-Wake Factor", Trnsactions of The Society of Naval Arohiteots and Marine Engineers, 1944, Pages 57, 58. (7) Tbid. Fig. 13. (8) Ibid. Fig. 19. (9) F. H. Todd, "The Effect of Stream-line Fin upon the Efficienoy of Ship Propulsion", Liverpool Engineering Society, Inc., 1934.

SYMBOLS a - pitoh-ratio of propeller, in wake. ab = pitch-ratio of propeller, in open. D = diame ter of propeller, in ft.. D = diameter of propeller, in ft., e = efficienoy of propeller in open test. 0 eb = basic efficienoy in open for oondition determined by vg and KT. n D RxVg IVTFP = towrope horsepower = 325.7 T In Open Test - X,. __= 9nD In Self-Propelled Test - KT = R in the determination of awI, R of K I t in the determination w. N = RPM = revolutions per minute. n = revolutions per second. qpe = quasi-propulsive ooeffioientc,'-Z- -. H = towrope resistane in lbs..

SYMBOLS (Cont.) f mas s-density of water. SH3 = shaft horsepower delivered to propeller. T = thrust in lbs. registered on thrust blook in self-propelled test. T * thrust in lbs. registered on thrust blook in open test. O t =I - R. va. v Y(Iuw) Vg - speed over ground in knots. v = speed over ground in feet per second, w = wake factor determined by use of R. (l-w) a pitch-ratio faotor. qwf wake faotor determined by use of R. (l-qwf) = pitoh-ratio factor. J a advance ratio "N. s a(-s) al Dt3 s = slip ratio

THE EFFEOCT QF 7i'AKr UPON PITCH-RATIO. The propeller data which is at the disposal of propeller designers was obtained from the tests of model propellers in the open oondition where the water was, nominally, at rest. These open tests were carried out systematically upon certain types of propellers; some with ogival shaped blade sections, some with airfoil shaped blade sections, Adm. Taylor has published the results of tests upon 3 bladed and 4 bladed propellers of the ogival type, and a oertain amount upon 4 bladed propellers of different airfoil types. Dr. Troost has published results of tests upon 3 bladed and 4 bladed propellers of certain airfoil types, and there are other data available, While these results were obtained under open conditions, the propellers that we design are to operate in the behind condition where the water has a follow-up velocity. It would be an unending task to test all the propellers for which we have open data behind all the different forms commonly used in praotise, eaoh propeller having a variety of transverse and vertioal locations in the wake. Each self-propelled test determines a few points in this vast area. The propeller designer is constantly endeavoring to work out a system that will correlate these

2. scattered points and deterrmine design factors that will enable him to predict from the open test data the action of the behind propeller at intermediate points not covered by self-propelled tests. The self-propelled test gives the designer all the information that he needs for the one particular oondition tested. It gives him the shaft horsepower that will be needed to propel the ship at the desired speed, and the R.P.'F. at whioh the propeller will deliver the needed thrust when working in the wake created by the model. The designer is not interested in the Q or the wake-factor unless he wishes to use the results of this self-propTLled test as a guide in some other design where the same type of propeller is to be used and no selfpropelled test is to be made. In order that the results obtained from the self-propelled test may be of use in this latter case, it is necessary to correlate the are obtained in the self-propelled test with some open efficiency given in Taylor's or Troost's charts, and to determine to what extent the wake developed behind the model supplants pitch-ratio in these same open charts. The wake-factor is a measure of the extent to which wake in the self-propelled test supplants pitch-ratio in the open test, where no wake is present.

The attributes of the water in which the open tests were made usually differ from the attributes of the water in which the behind propeller is to operate in three main particulars, temperature, degree of salinity, and motion. The open tests are usually conduoted in fresh water which is at rest and whose temperature is around 70 degrees, F. The behind propeller, more often, is to operate in salt water whose temperature is around 50 degrees, F., and this water has a follow-up velocity. If we make use of the non-dimensional quantities - Lr T gn -U and %? ='FL for propeller design, differenoes of temperature and degree of salinity can be taken care of by means of the factor P; difference in the motion attribute is taken oare of by means of the wake-factor, The use of this factor to determine the extent to which wake supplants piteh-ratio can be illustrated by means of Fig. I. The curves of effioiency and pitoh-ratio in this figure are takelln from Cha,t I for Taylor's ogival, 4 bladed propellers. The points a, a', b, b', and c, represent the results of Ackerson's tests upon propeller 928 behind Model 2933. Assuming the full-sized ship

to be 400 ft. long, the propeller was 16.75 ft. in diameter and 13.50 ft. in pitch. It was 4 bladed and without rake, the sections were ogival, the mean-width-ratio was 0.25; and the blade-thickness-ratio was 0.05. The tip waE 4.35 ft. below the surface. At 14 knots the?AP.*1" were 99.2, H.i.P. = 2135, and S.IT.P. 2930. The test showed a thrust-deduction faotor of 0.190 and a g value of 0.730. tience, J = 0.855, MR 0.12 (point a) R --— t 0.148 (point a') In a previous paper I have advocated the use of R in determining FT. Present practise is to determine it by the use of R. The use of R is inconsistent with our praotise in determining the I - t values of gq3g and tU. In both of these oases we use the EHP based upon R. qp = EP, N P - Slip g2: -qwf Why should we change to R in determining the wake factor? I - t In rig. I the Jg value of 0.855 and the KT value of 0.12 determine the point a, and the KT value of 0.12 and the pitch-ratio value of.806 determine the point b. At b the J value is 0.6E3. The ratio g 0.683 = 0.799 or wf = 0.201.

4a If one prefers to use R and determine w, instead of using R to determine qwf, the same Figure oan be used. The J value of 0.855 and the KT value of 0.148 determine the point a' and the K value of 0.148 and the pitch-ratio value of 0.806 determine T bt. ht b' the J value is 0.62....I(I-w) 0 = 0.725, or 0 8 027.55 or w = 0.275.

I consider the qwf value of 0.201 to be the more consistent value to use in determining the extent to which wake supplants Ditch-ratio since it is determined from R, as are also the values of qn. and BU. Fig. I can be used to illustrate another method of determining to wihat extent wake supplants pitch-ratio in the self-propelled test. Ivhen the propeller of.806 pitch-ratio was tested in the open, the KT value developed at J = 0.855 was 0.045, as shown at point c, and it took a pitch-ratio of.955 to develop a KT value of 0.12 (point a), and a pitch-ratio of 1.015 (point Da_) to develop a KT value of 0.148. If we work on the assumption that K = R the follow-up velocity of the water behind the model during the self-propelled test increased the KT value from 0.045 to 0.12. If we are working on the assumption R that i 3 I - t, the follow-up velocity plus the augmented thrust due? n.-D - to the existence of a region of low pressure between the model and the propeller, increased the KT value from 0.045 to 0.148. The factor for this third method, using constant Jg instead of constant KT as in the two methods above, might be called the quasithrust factor, (qtf), and the augmented quasi-thrust faotor, (aqtf). The atS in this case would be determined from the ratio 0_Q = (I-qtf) 0.12 = 0.375, or tf 0.625. The t would be determined from

6. Q,J ~=~ (I-aqtf) = 0.304 or aatf = 0.696. 0.1 48 I am not advocating the use of this third method but merely call attention to it to emphasize the fact that the end served by any such faotor is to determine to what extent the motion of the water in the self-rropelled test supplants pitch-ratio in the open test. When the propeller operates in the open, a KT value of, 0.12 can be obtained with a pitch-ratio value of.955 when J3 - 0.S55. This gives a slip angle value of 2~-33' since f tan -- tant when the propeller has a pitoh-ratio of.806, the slip angle ~ (o~-52 at a J; value of 0.355. When this propeller operates in the wake of 4odel 2933 the follow-up velocity of the water increases the slip angle from 0~-521 to 2 -33' and the KT value from 0.045 to 0.12. It is more logioal to use a KT value derived from R than to use, as at present, the value of fT derived from i.* In the open test of the model propeller, increase of KT at oonstant Jg value is obtained by increasing the slip angle through the agency of inoreased pitoh-ratioo The flow of the propellr t the propllr is not impeded by the presence of a hull and there is not the oolumn of water at reduced pressure ahead of the open propeller that there is in the self-propelled test.

- - - - - |Ng-S l - i=:; I I I

7. Designers vwho use R to detertmine ST virtually claim that tncrease T-t of KT by means of such a column of water at reduced pressure has the same effect upon efficiency as increase of KT through inoreased slip angle. They have no valid basis for such an assumption. No doubt, the net propelling force in thekself-propelled test is somewhat larger than'R, the tow-rope resistance of the model, but it certainly is not as large as R. If designers believe that the net propelling thrust is really R, then they should have the courage of their conviotions T - t and use q v4ues obtained from the expression c = ).is The non-dimensional quantities J and XT = orient us in the Darticular chart that we elect to use and establish the basic efficiency that should accompany the operation of the propeller under those conditions, (see efficiency at a or a', Fig. I). This efficiency holds whether the propeller operates in soft water or hard water, in fresh water or salt water, at one depth or another depth, in water at rest or in moving water. tuoh di.fferences make it necessary to change the pitch-ratio iwhich obtained in the open in order that the desired values of Jg and KT may be attained in wake. The aonditions that exist in the wake of a ship form are not as ideal as in the open test and the efficiency in wake will be less than the basic efficiency in

the open. It is the purpose of the wake factor to determine to what extent the basic pitch-ratio at I or a' must be changed to allow for the motion of the water behind the model. The efficiency will be determined by ie t e rr.!'e n.i' J and % - R but the pitoh-ratio will be by Jg (I-qwf) and g rr A n g'IT=. * If R i a used instead of R, then the efficiency is I D) determined by Jg and FT = J...) and the pitch-ratio by JT uQ i4n4 nD K m (t I, (see tig. 1). The necessity for determining the efficiency and the pitah-ratio at different points is illustrated by Fi.g. 2 which gives the results of tests upon two airfoil propellers, one for a single screw Lake Freighter and one for the twin screw "iaerica". The curves marked e and KT (open) are plotted from data obtained from the open tests cf the propellers. The curves of KT (behind) and n are plotted from the self-propelled tests. In both cases two sets of curves are given, one based upon the use of R and one upon the use of R. Theseif-propelled results oover J.t speeds Jfrom t to 1b.. knots in the case of the single serew Freighter, and from 12 to 24 knots in the case of the "America". The value of t I-qwf) is the ratio of the values of Jg at b and a, while the value of (I-w) is the ratio at b' and a'. The gp values should

9. be compared with efficiencies related to a or a' and not with the efficienoies e and e' which are given by b and b' The open efficiencies corresponding to corditions at a and A'are obtained under open conditions that parallel as closely as possible the self-propelled conditions for which we wish to knowr the qQ~ values. The JT; values are the same, the thrust values are the same; the only differenc e is that in the ooen tests, where there is no wake, the slip angle is obtained by using a larger pitch-ratio than in the self-propelled tests where the same slip angle is obtained by means of a smaller o-itoh-ratio combined with wake. It is true that the KT value is the sa,me at a as it is at!, and is the same at a' that it is at b'. HIowever, since,T R the K, value may be constant with wide variations in the values ofr and R. In the case of the single screw vessel whose tests are shown in Fig. 2, let us assume that V = 12k., RPM = 88, the needed thrust, R,= 59700 lbs., D, 16.5', and a = 0.939. Then vr - 20.27' and n = 1. 167... J= 07 T 38, 59 700 =1 *Jg79- x 16'. 5...T i. 67 3(.6;-5 )T =0J93'

10. KT value of 0.193 intersects the K'T(open) curve at a J value of 0.61. Since vg and D have not changed, this means that A has increased from 1.467 at a to 2.015 at b, and T-,, or R, has increased from 59,700 lbs. to 112,700 lbs.. If we are using R, then T0T=,.239, I-t since t = 0.194. i K value of 0.239 intersects the K (open) curve at a J value of 0.493, which means that n has increased from 1.467 g at I' to 2.492 at b'. This would cause To, or R, to inrease from 59,700 lbs. at a' to 172,500 lbs. at bt'. The design condition which we have established and for hfich we wish to know the efficiency calls for the following quantities: To R - 59,700 lbs., RPM = 88, J= = 0.838, KT = 0.193?itch-ratio=0.939 twith wake present, These conditions are met in the open test of B-4-55, Chart III, in every particular except one. The slip angle necessary to produoe a v vwlue of 0.193 irl produced by a pitch-ratio of 1.14 alone without the help of any wake, instead of by a pitch-ratio of 0.939 and whatever w~a1.ke the model produced. These conditions are not met to the same extent at line b e since: To = R = 112,700 lbs., RP1T = 120.1 Jg = 0.61, KT = 0.193, Pitch-ratio 0.939 with no wake present.

11. The conditions at bt et' are still further afield:To = R = 172,500 lbs., RP 1419.5, J = 0.493, KT = 0.193, lPitch-ratio = 0.939 with no wake present. It is obviously absurd to take the efficiency which prevails at e (Fig. 2), where JY = 0.61 and the thrust is 112,700 lbs., or at e' g where J 0.493 and the thrust is 172,500 lbs., as arplyint in any way to the condition where Jg T 0.838 and the thrust is 59,700 lbs.. It might seem as if the efficiency which prevails at d (Fig. 2) might be used, but that would be enuivalent to using the efficiency at (Fig*. 1). The efficiency at cdwas obtained when the KT value was 0.096 in Fig. 2 and does not apply to the condition where the'1T value is 0.193 or 0.239. The open test of the propeller that is to be used in the selfpropelled test does not supply information that can be used to determine the efficiency in wake. Tests of the propeller at larger pitchratios are needed since the behind propeller working in the wake of the model generates thrust at a slip angle that can be duplicated in the open only by a largier pitch-ratio. If the propeller belongs to a f~mily for which we do not have a chart similar to those that accompany this paper, we may make use of the chart for the family that seLf$s

12. to come nearest to the propeller in question. In Fig. 2 are shown portions of the KT curves taken from the different charts for a pitch-ratio of 0.939 for the single screw, and for a pitch-ratio of 1.00 for the twin screw. The propeller B-4-55 seems to come nearest for the single sorew, so portions of the efficiency curves for that pronoeller for constant A, values of 0.193 and 0.239 are shown. The basic effiieeney values, eb, should be determined by the intersection of these curves with the line a a' In the case of the twin screw, Taylor's "D'T" propeller seems to come nearest to the propeller of the "America" and portions of the efficiency curves of the "D" propeller at constant K,, values of 0.125 and 0.139 are shown. The disturbed and turbulent condition of the wake accounts for the fact that the ce values of twin screws are lower than the eb values by V4: or so. The same would be true for single screws if we had any open tests of propellers with rudders and vanes back of them. These devices increase the efficiency of propulsion by 830% or so. le find, therefore, that the qpc values of single screws, after making allowance for about 4% wake loss, are about 4% greater than the eb values of open propellers tested without rudders and fins. While iost of our propeller design is concerned with single screws,

--- a —- - pl;jm lCLq tva ME A- - 9 - - "Ir - - - l6 I r - @5EN~~~~~~~~~~~~~~~~~~~~1

- -m~7;1Ugf, Hz I ENl~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ l~~~~~IrL lE 31~1~

13. all of our open data applies, strictly, to tiwin screws and we have to design single screws on a Tshoe string" of data, as far as open data is concerned. The characteristics of the chart Dropellers are shown in Table I and fall, in general, into three groups. CGroup I differs from most modern ogival section propellers in having no rake and no variation of pitch-ratio. Group II differs from most modern airfoil propellers in having no rake, no skew, no pitch-ratio variation, and a rather large hub. Group III differs from most modern propellers in the large amount of pitoh-ratio variation near the hub, and the "twash back" of the blade section at the following edge. Table II shows the pitch-ratio necessary to deliver a given ST value at a certain value of J. Ogival section propellers are the best thrust producers, i.e., will produce a given thrust with a lower pitch-ratio, but at the expense of efficiency. The type of section used in Group III is inferior in thrust and efficiency' to the type used in Group Ii, but would probably be more efficient when backing. The effiiency given for Troost's propellers is the blade efficiency, i.e., the drag of the hub has been subtracted. The efficiencies given on the charts shold be reduced by about 0.01 in comparing them with effiiencies given on Taylor's oharts.

14* It should be kept clearly in -mind that in adoptingr a p articular chart for reference purpcses we are not a-dopting that narticular type of propeller..Te are merely using the numerals on that particular pitch-ratio grid to give us the pitch-ratio numeral for our type of propeller. The results of the self-propelled test locate the point a in Fig. T, and noint b is determined by the numeral that we have uised to designate the pitch-ratio of the propeller tested. The effective pitch-ratio of any propeller is an tunknowmn cuantity and does not need to be Irnown. +1! that pitch-ratio d(oes is to identify a partic ular rropeller fc,r vhich wte have test dat a, and enables a reproduction to be made. There may be five pnroelleer s used in the tests that give tis the data from.which such charts as I to rII are constructed. The resu4lts of such tests may be plotted under the head ofor I -— 2 — 3 —-4 —-5, or face pitch-ratio, 0.6 —0.8 —I.00 —1.2 —1.4, or exrerlmental pitch-ratio, 0.685 —0O.88 —1.095 —1.316 —1*532 Since the object of the identifictation is to enable one to have a full scele propeller made that will have certain non-dimensional characteristics exhibited by the 8" model, a system of identific,tion that

15, is related to the process of mrinufacture seems desirable. Since the face pitch-ratio gives definite information to this end, it would seem to be the logical choice. In Fig. I, the relation between efficiency, K', and Jg, remains fixed for variations in specific gravity and motion of the fluid. The compensating element is pitch-ratio, and the pitch-ratio grid slides to the right or to the left to compensate for these variations. In the oase of the single-screw Lake Freighter model in Fig. 2, the wake, or motion condition, of the water, was such that the pitch-ratio grid moved to the right a considerable distance until point b coincided with point a. In the case of the twin-screw "Amerioa", the lesser wake called for a smaller displacement of the pitch-ratio grid. In the case of a propeller working up stream against a current strong enough to nroduce negative wake, the Tgrid movement would have been to the left and e larger pitch-ratio than that at a would have to be used. The parameter (I-qwf), or (I-w), makes allowance for a number of differences between the open and the self-propelled conditiors. In the open test the water is solid, with practically uniform velocity of approach in all parts of the supply stream, and the direction of flow is parallel to the centerline of the shaft. The water, which was

16. originally at rest, is given a sternward velocity. In the behin. condition, the water has a follow-tDu velocity which is reduced or entirely eliminated by the action of the propeller. The water in the supply stream is under reduced pressure and permeated with eddies and vapor nockets., The direction of flow has inZward and upward components and the velocitv of flow varies in different parts of the supply stream. The parameter (I-cwf) cannot be interpreted in terns of velocity alone, and the product of V and (I-qwf) is not the velocity of the propeller relative to the surrounding water. Tn the expression the two quantities in the denominator have Just ags distinct and corporate identities as the two quuntities in the numerator arnd can no more be merged than can N and Il The above expression can be put into the form - open) (-a25 (behind) 1) ~ ~ "'':Bu( o~o'.n )-~'": (2) In the self-propelled test, where wake is present, a given FEIP will be developed at a certain speed, Vg, by a propeller of a given pitch-ratio

; nwr; zrl -IIETItR )] - - ~~~~~~~'"~~'A 4 rr~~~~~~~~~~~~~~' ~~~~~~~~~~~~~~~~~~~u L ~ ~~~~~~~~~~. h Ib I 9 br arlI 4

1't at a smaller number of revolutions than that same propeller can develop that FHP in the open condition where no wake is present. The parameter (I-qwf) expresses the effeot of all the differenoes mentioned above upon the quantities that go to make up the Bu expressions derived from open and self-propelled tests. In the same way, the expression - IT D I ND (I -qwf DJopen (qwf) - behind, (3) Cr behiad (I-qwf) (,{) * open The wake factor oannot be interpreted in terms of velocity alone; it makes allowance for numerous differences not directly connected with velocity. Therefore, the propriety of using Va= Vg(I-w) in the expression for useful horsepower, U, is questionable. The only logioal form for Bu is the one given above, - Bu G 2 2 g Pitch Ratio Factor It is unfortunate that the faotor derived from the relation between Bu(behind) and Bu(open) in Eq. 2, or betweenS(behind) and (open) in Eq. 4, has taken the form (I-qwf) or (I-w). The quantities ~, or w, are never used by themselves but always in the form (I-qwf) or (I-w). The emphasis placed upon R or E makes it seem that in goilng from a

18. value of 0.20 to a value of 0.21 there is a variation of 5%, whereas, in reality, this variation in the value of the wake factor makes a variation of only 1.25% in the values of (I-qwf) or (l-mw). Since this is the factor which determines the extent to which the open pitch-ratio must be reduced to aocomodate the propeller to the wake conditior s and give the desired values of J and K%, the factor (I-qwf) or (I-w) will be referred to as the pitch-ratio factor. Since this faotor covers a variety of differenoes not direotly connected with the velocity of the wake created by the model when towed, it is unwise to try to t tie it up with that wake value. Attention should be called to the lines on the Charts that show the effects of changes in revolutions and diameter. In most cases it desirable to use as large a diameter of propeller as possible, but if, with the number of revolutions fixed, the resulting value of KT is less than 0.125 for airfoil propellers, or less than 0.15 for ogival sections, the efficiency will be improved by using a smallexidiamster of propeller. C;hile a low number of revolutions usually gives a higher efficiency than a high number, there are cases in the higher range of KT values where it is better to use the higher number. The effect upon effiieoncy

19, of increasing the number of revolutions is shovm on the Charts by the lines marked "Effect of Increasing n'". The tendency of these curves to run parallel with the efficiency ctLrves at certain combinations of Jg and K, shows that there are certain areas in which there may be wide variations in revolutions, and less wide variation in diameter, without an appreciable change in the efficiency. This, in turn, indicates that in those areas the wake-factor, or quasi-wake-factor, does not have to be selected with meticulous oare where it is a question of efficiency only. If one is dealing with "revolution consoious" machinery and it is considered necessary to hit a certain number of revolutitons "on the nose", a more painstaking selection of wake values has to be made. If a mistake is made in estimating the wake effect and a quasiwake factor of 0.11 or 0.09 is used instead of 0.10 for twin sorews, the propeller efficiency will be only slightly affected, in the regions mentioned above. In the case of single screws, it will make little difference whether a quasi-wake factor value of 0.19 or 0.21 is used instead of 0.20 * Let us take the case of the single-screw propeller for the LakeFreighter shown in Fig. 2. That propeller had a pitch-ratio of 0.939, and the results of the self-propelled test at 12 knots showed a J value

20. of 0.838 and a K T value of 0.193. If we use a portion of Chart III, as shown in Fig. 3, for Troost propeller Bl-455, these co-ordinates locate a point M; the EK value and the pitch-ratio value of 0.939 locate point h at a J value of 0.61. The (I-qwf) value, when this Chart is used, will be 0.728, since (I-qwf), 0661. 0.728. 0.838 Let us suppose that we did not have the benefit of the self-propelled test at our disposal and that we overestimated the wake effect, taking it as 0.282 instead of 0.272. Then (I-qwf) 0.718, and 0.838 x 0.718 = 0.602. This value of Js gives point b' in r'ig. 3, and the g pitch-ratio of 0.93 wiould be indicated instead of 0.939 which went with the qwf value of 0.272. This lower pitch-ratio would cause the rpm to increase from 88 to about 88.8. This increase in rpm would cause Jg to have a value of 0.83 instead of 0.838, and %T to have a value of 0.1896 instead of 0.193. These co-ordinates locate point I' in Fig. 3. If we had underestimated the wake effect and used a f value of 0.262, then (I-qwf) = 0.738, and the J value that locates point b" would be 0.838 x 0.738 = 0.618. This would cause us to choose a pitoht0io of O.948, and the rpm would be about 87.2. Wiith these revolutions the value of Jg would be O.R46 and the value of KT would be 0.1967, locating point a". The basic efficiency of all of these three points

21* is practically the same. my machinery suitable for ship propulsion should be able to accommodate itself to revolutions of the order of 88.8 or 87;2 instead of 88.0 without appreciable loss of engine efficiency, or without introducing operational difficulties. The Charts show that high values of Jg are, in general, desirable g and that the KT value of 0.125 is a minimum for air-fpil propellers and that 0.15 is a minimum for ogival section propellers, As a matter of fact, the bombined efficiency of ship form, machinery, and propeller, will nrobably be a maximum when KT is somewhat larger. Wihatever change is made in n to increase or decrease the value of J will also increase or decrease the value of KT, resulting in a diagonal path across the Chart, as shown by Line at A in Fig. 3. The Charts show in what areas changes in revolutions and diameter can be made to advantage, and in what areas the basic efficiency is unaffected by such ohanges. It has been stated above that the wake factor was a measure of the extent to which wake in the self-propelled test supplanted pitch-ratio in the open test. We are not ooncerned with the actual value of the pitch-ratio which obtained in the open test. ihat we are concerned with is the relation between the Jg value at which the desired wT was

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22. attained in the self-propelled test, i.e., 0.855 at a in?ig. I, and the Jg value on any Shart at which the SIeO11 t(K was attained and the Ditch-ratio label attached to the propeller is identical with that attached to the propeller tested behind the model, i.e., 0.68 at b in Fig. I. In Fig. I the results of tests upon an ogival type propeller were plotted upon a portion of Chart I. If the same results had been plotted upon the other Charts, the values of the pitoh-ratio faetor would be as given in Table III and would have varied from 0.799 to 0.737, dependent upon tho chart used. The values of eb and eso would also vary, but the ratio of qpe to eb, as given in Column 7, varies through a smaller range than does the ratio of qpo to eo, as given in Column 9. The value of the pitch-ratio factor for any given propeller is atfeoted by the oharacteristios of the model in front of it, the speedlength ratio, the wake condition, the position of the propeller in the wake, the thrust per sq. in. of effective blade area, and the appendages in front of, and behind the propeller. The pitch-ratio faotor can be determined by plotting the results of self-propelled tests in the manner shown in Figs. 5 - 11. Self Propelled Tests If the curve of R.P.M. were a stmlght line and the curve of E.H.P.

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23. varied as the cube of the speed, as shown in full lines in Fir. 4, the results of the entire test would plot in one point, A, as shown in the upper part of that figure. Any deviation from that "ideal" condition, such as is shown by the dotted lines, eauses the results to plot in the form of a loop. Different combinations of deviations from the "ideal" condition result in the different loops shown in the Figures. If the R.P.M. curve were straight and the X.1HP. curve deviated from the "ideal", the loop would become a vertical line. If the F.H.P. curve varied as (speed)3 and the R.P.MiT curve deviated from the "ideal", the loop would become a horizontal line. It is considered by some designers that the upper economio limit of speed for any given commercial form is the speed at which the power varies as (speed)3. This would be the speed at which the loop beoomes tangent to the horizontal. Single Scarews Each self-propelled test, then, gives data for only one significoant point. These points have been taken from Figures 5 to 11 and plotted in Fig. 12. The lower part of Figure 12 gives the pitch-ratio factor determined by referring the self-propelled data to the propeller's own KT(pn) curve, which is usually given as a part of the data obtained in the open test of the propeller. The middle portion of the figure gives the KT

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24. values at whioh the propeller operated and shows the relation of that value to the 1value for maximum propeller effioiency. Sinoe at the outset of any design we do not have the P(open) curve for that propeller, it is oonvenient to have the pitoh-ratio factor referred to one of the standard Charts in whioh the oomplete family history of a propeller is given. bhis has been done in the upper part of Fig. 12 and showrs the pitoh-rstio fat;or in terus of Type D propeller, Chart V. In Aakerson's tests the rudder used was of the simpliftid fair-foro type and the tests upon Propellers 64 and 65 show that the pithob-ratio factor deoreases as we go from the fair-form type to the Oontraorudder with its oontra fin. If a modern rudder had been used in the Aekeraon tests the factors would have been lower in value. Propellers 99 and 102, in addition, a oontra-propeller post ahead of the propeller and this would cause the pitch-ratio faotor to have a lower value. Presumably, propellers 64 and 65 had suffiielnt surfaoe for the normal oondition but were overloaded when the resistance was inoreased 45%. The result of overloading a propeller, or of providing insuffioient effetaire surface, is to increase the value of the pitoh-ratio factor. In th Aerson tests the propellerr and ols1 hado th hoaroateoristios shown in Table IV. The propellers of 1.00 pitho ratio were of

25. the right size and we-re operating at KT values which caused them to have T a qpc value about 0.02 larger than the propellers in the other group, ghich were too large. If the tests had been nrade with contra-fins and rudders in place of the simplified fair-form rudders, the qpc values Kvould have been higher and the pitch-ratio factors somewhat lower. The model ahead of these propellers had a longitudinal coefficient of 0.671 in all the tests and the resistance was increased about 65% by increasing the displacement from 6400 tons to 12800 tons and changing the ~ ratio. It seems likely that the pitch-ratio factor in the lower Dart of Fig. 12 would have been about 0.79 for the nropellers of 1.00 pitchratio with modern anpendages. In the case of the other tests shown in the lower part of Fig. 12, the models had the Lake Freighter characteristics, the longitudinal rdsnatic coefficient being about 0.87. The speed-length ratio appropriate for this fullness is from 0.45 to 0.50. When the propeller surface was adequate, the pitch-ratio factor averaged about 0.74. When the load upon the propeller was augmented 45% artificially, and the blade surface became inadequate, the pitch-ratio factor had a value of about 0.81.?resumably for prismatic coefficients between 0.67 and 0.87 the pitch-rati0 factor, for nornnal loading, would vary between 0.79 and 0.74. As pointed

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26. out above, when operating with KT values suitable for best over-all eoonomy, the pitch-ratio factor can be varied by 0.01 or 0.02 without producing any appreciable effeot upon the efficiency, and the revolutions will be affected to the extent of 1% or 2%. If the maohinery is suitable for marine propulsion and has been conservatively rated as to power, this variation in revolutions will not be of any consequence, If the pitch-ratio factor is obtained by the use of Chart V, for Type D propeller, the pitch-ratio factor will vary from about 0.75 for prismatic coeffiebnts of 0.67, to 0.80 for prismatic coefficients of 0.87. TWrIN SCREWS. The three examples of twin screws given in Figs. 11, 13, & 14, are rather heterogeneous in character, as shown by Table V but serve to bring out certain points that may be of interest. In the case of the "tHoover", the KT (open) curve was not available, so the KT curve for Taylor's 3 bladed propeller with a hub ratio of 0.20 was used for comparison. If results were available for such propellers with a hub ratio of 0.27 instead of 0.20, the KT curve would probably be lower and the value of the pitch-ratio factor would be nearer 0.93 than 0.96. In the case of the "North Carolina" the KT (open) curve was

27* available and the pitoh-ratio faotor was 0.938. Here again, if the Taylor propeller had been tested with a hub ratio of 0.25 D, the Taylor K curve would have been lower and the KT ourve of the "North Carolina" when self-propelled would have coincided more nearly with the Taylor IT ourve, which in Fig. 14 lies almost entirely above it. Using the Taylor curte for comparison in both oases we would have a pitch-ratio factor of O.93 for bossing and a factor Qf about 1.00 for brackets. This differenoe in factors with and without bossing is due to the difference in direction of flow of water to the prsopellers with and withP out bossing. Propellers will have a higher efficiency and lower pitohratio factor if the flow of water in the supply stream is direoted againsi the direction of motion of the propeller blade. With outward turning propellers, the blade is rising when working in the water nearest the hull. The preseneo of bossing directs the water horizontally in its approach to the blade. If the end of the bossing is shaped to form a oontra-fin, the efficiency will be improved and the pitoh-ratio factor decreased. If the bossing is removed, the flow of the water is upward, parallel to the direction of the buttock lines, and the propeller blade has to overtake the water. The resultant direction of motion imposed upon the water leaving the blades has a large upward oomponent which is

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28. useless for propulsion. S;ihen the direction of motion of the water supplied to the propeller is opposed to the direction of motion of the propeller blade, as would be the case if the propeller were inturning, the resuiltant direction imposed upon the water is more nearly horizontal. 4;fhere brackets are used, the brackets adjacent to the propeller should have a contra-vane shape, direoting the water against the motion of the blade. The h*er qpc values that appear in the figure for the "North Carolina" aire due largely to the fact that the propellers are operating at a J, value of 1.02, while the "H'oover" propellers are acting, at a value of 0.87. The apparent poor performane oa f the TiToover" propellers is due partly to the fact that the qpc values are compared with the performance of 2U- blades with a hub ratio of 0.20, while the "H'ioover" had 02=6 blades with a hub ratio of 0.27. CLkoSSTFICATION OF PROP;JLLERS. The actual performance of a propeller in the self-propelled test, compared with the performance of propellers in Charts I to VII is the best mneans of classification. Factors such as rake and skew, which bulk large on the drawing board, may be of minor importance in actual performance. A study of Fig.s. 5-11 will show that the propellers fall into the three classes mentioned above and have thrust capacities that compare

29. favorably with the "C"art rronellers, except in a few cases. Propeller f80 was understlrfaced for its rarticular 4ob and showed a low qpe value at normtal- load. Proeeller.# 65, though apparently of ample salrface, had characteristics that affected its thrust caaoaity at lower values of J As stated above, "washing back" the after edge of the blade caurises a reduction in effective surface, as does excessive redtuction of nltch-ratio near the hub. IMBXZ34OTN I F V'` OIThL'LEMS. The single screvw works in the way of a watve crest where the direction of rotation of the'water adds to the ware~ effect,. JOhen the irnmersion is less than 0.75D, the pitch-ratio factor wrill be affected and will dacrease in value (see kerson test points 2, 3 and test points when trim is 16 ft. and 18 ft., Fig. 12). The propellers in Aokerson test 43 and #4, were overcoming the same resistance as were the propellers in test!1 and #2, but the latter propellers had an immersion factor of 0.661 and 0.61, respectively. Twin screws are working in the way of a -wave hollow and the effect of the rotation of the water particle is to counteraot the wake produced by the form. A.s the propeller comes nearer the surfae, the pitch-ratio factor increases, as is shown by Fig. 15 whioh gives results for the

30. tA.merica?l at four( drafts, on an even keel. The propellers of the "'rmerica'" viwere rore like C in sectional shape but were more like D in thrust capacity. The effect of decreased imriersion cormmenced to boe felt W4sen the minnersion ratio was 0.97. Trhe difference in the effect of propeller izmersion upon single screws and twin screws is shown in'ig. II. Thile the pitch-ratio faotor for twin screws reverses its trend when the immersion factor is less thran 0.97, in the c-a-se of the ~':.tmerica', it can gc.s low as 0.54 in the case of:~in ie screws before reversQ'l t'Y:e. ploleoe.?la-:oi. contra-fins antl rudders bolck: of the propellers slows them dowrn,arnd causes the pitclth-ratio f.-ctor to be srialler. This is shown by the tests made upon propellers 1i764 F nd #65,'igs. 5 & 6. 7liminating shaft bossinpgs in the case of twin screws, rmakes it necessary to icarease the nitch if the sanme revolutions are to be imaintained. In other words, the pitch-ratio factor is increased. The pitch-ratio factor s,hould be decreased if use is to be made of any of the contra devices in front of, or behind the propeller. SIZE 0P 2'ROPEJLLER. small propeller works in the worst part of the wake, where the

31* water is rnost turbuilent, and wlere it La3 to rtruigvle hard to get its supply of Crater. Consequently, the thrust deduction factor inoreases and the propeller is nearer the onvitating point than a larger propeller would be. It is conceivable that a propeller night be so s.mall and its suip>ly strea,m so nermeated with water vor va voids that it woul.d produce no more thrunt vrith Wtake than the open propeller, with a solid supply stream, would produce without wake. In this case the pitch-ratio factor'wootuld increase to 1.00. In the tests of propellers #6t., 6, 6 99, #102, where the resistance ams Ix.Orealsed 455 by artiYiciil macrs, the nitohratio acLtor increased as shown in able Vt. The nozle%. ilp the case of 102 rrotects the suppl.y stream fromr the demcralizini effects experienced by the others, and the pitch-ratio factor was practically unaffected. Increase in mean-width ratio is one of the ways of counteracting the harmful effects of a turbulent wake, permeated with water vapor voids. Eowever, there is a virtual reduction of area when the edges of the blade are "washed back", as in the Troost wheels; when the pitch-ratio is unduly reduced at the hub; and when a large hub is used. There is stream line flow around the hub which neutralizes a certain protion of the wake effect, and this effect increases with increase in the size of hub. If

32. the pitch-ratio is unduly reduced in the neighborhood of the large hub, this portion of the surface becomes ineffective and the thrust is concentrated unon the outer portions of the blades..LP1,TTFr P AO OF VAL I Ct F ITCE- RAT' TITCA FCTOR The Pitch-ratio factor cannot be tied up too closely with the form.wkn-e rroduced by the model. The very qualitites in a model which produce a large wake and vwould naturally call for a small value of pitchratio factor, give rise to turbulence, cross flow, and cavitation, and make access of water to the Dropeller diffioult.;ll these, in their turn, would call for an increase in the value of the nitch-ratio factor in order that the desired thrust may be produaed. ils a consequence of these conflicting oonditions, we find that the pitch-ratio f'actor has the rather narrow limits of variation shown in Fig. 12, The ratio of qpc to eb is, in general, higher as the KT value at which the propeller operates is nearer to the KT value for maximum efficiency. In Fig. 12, Propeller #64 operates at a K, value of about 0.20, while the KT value for rraximum effioiency of Group 2 propellers is 0.125. Propeller #65 operates at a KT value of 0.17, while the value for maximum efficienoy of Group 3 propellers, at a Jg value of 0.77, is about 0.13. Propeller ~99 is operating at the KT value whioh gives maximumtn propeller

33 efficiency., study of Figures 5, 6, ai 8 will show that the ratio of qpC to eb is highest in the case of Propeller #99 and lowest in the case of 164. Ilowever, the fact that the propeller is achieving a high efficiency does not imply that the design of which it is a nart woulld not have a hither economnic efficiency if the K value were higher than that called for from the point of view of propeller efficiency alone.