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Aug. 21, 1962 B. w. MCCORMICK ET AL 3,050,024 TORPEDO PROPULSION AND CONTROL Filed June 26, 1957 3 Sheets-Sheet 1 1FIG. BARNES W. M‘CORMICK JOSEPH J. EISENHUTH GEORGE F. WISL/CENUS IN VEN TOR.5 Aug. 21, 1962 B. w. MCCORMICK ET AL 3,050,024 TORPEDO PROPULSION AND CONTROL Filed June 26, 1957 3 Sheets-Sheet 2 BARNES W. M‘CORM/CK JOSEPH J. E/SENHUTH GEORGE F. W/SL/CENUS‘ IN VEN TORS FIG. 3 BY I Z6” 7/4 _' AT ORNEYS Aug. 21, 1962 B. w. MCCORMICK ET AL 3,050,024 TORPEDO PROPULSION AND CONTROL Filed June 26, 1957 3 Sheets-Sheet 3 O Propeller .::.§ ‘"25 FIG. 8 BARNES W. M‘CORM/CK JOSEPH J. E/SENHUTH GEORGE F. WISLICENUS IN VEN TORS BY | ' 'ArroR/vEys United States Patent @?fice 3,050,024 Patented Aug. 21, 1962 2 1 in cross-section each station indicated in FIGURE 2 and showing the disposition and con?guration of the cross 3,050,024 TORPEDO PROPULSION AND CONTROL Barnes W. McCormick, Spring?eld, and Joseph J. Eisen huth and George F. Wislicenus, State College, Pa., as signors, by mesne assignments, to the United States of America as represented by the Secretary of the Navy Filed June 26, 1957, Ser. No. 668,267 6 Claims. (Cl. 114-20) section of each station with relation to the cross section of each other station, a hypothetical stack-up line which passes through each cross-section, the angle at which each cross-section is disposed with reference to the longitu dinal axis of the torpedo and the camber of each cross sec tion. FIGURE 4 is a front elevation of one ?n showing in This invention relates generally to torpedoes and more 10 particular the twist or skew in the leading edge of the ?n. particularly to propellers and stabilizer surfaces for a FIGURE 5 is a rear elevation of the ?n shown in FIG torpedo. As used herein, “stabilizer surfaces” have ref URE 4 and shows in particular the twist or skew in the erence to the ?xed means utilized to render a torpedo trailing edge of the ?n. stable during travel which generally also contains mova FIGURE 6 is a fragmentary side elevation partially in ble “control surfaces” for controlling or changing the di 15 section of a propeller and ?n combination in accordance rection of travel of the torpedo, with the invention and showing the intersection of the The concept of propelling torpedoes and maintaining streamline with the propeller and ?n at mid-chord radii them stable in travel has remained unchanged almost of respectively rp and rf. from the date of the ?rst practical torpedo. This con FIGURE 7 shows the relation of the cross section of cept generally includes a long cylindrical body having a the propeller at the radius rp to the cross section of the tapered rearward portion provided with a propeller at the ?n at the radius r, shown in FIGURE 6 and also shows most rearward point and usually four ?xed stabilizer sur velocity diagrams for the streamline of FIGURE 6 at faces extending outwardly at right angles just forward of these respective radii, the velocity diagram at the radius the propeller. The prior art is replete with innovations of the basic concept, but for both practical and technical 25 rp being shown adjacent the propeller cross section and the velocity diagram at the radius rf being shown adja reasons few, if any, have as yet ever met with substantial success or come into Widespread use. Further, the above mentioned innovations have almost without exception been concerned with providing increased power, increased efficiency, increased stabilization, increased maneuver ability and the like. It was not until recently that designers of torpedoes be came interested in the noise generated by the torpedo dur cent the ?n cross section. FIGURE 8 is a velocity diagram at the quarter chord line of a ?n constructed and formed in accordance with the invention. FIGURE 1 shows the rear portion 15 of a torpedo of conventional design having a substantially smooth outer surface 16 over its entire length and provided with a propeller 17 attached to its rearmost portion and adapted ing travel and this has led to a considerable interest in the phenomenon of cavitation. However, so far as is known, 35 to propel the torpedo in a forwardly direction by con— ventional means such as for example, an electric propul heretofore all such efforts to reduce noise with regard to sion motor, propeller shaft and associated components (not shown.) Disposed rearwardly of the propeller 17 into practical use, especially with regard to the develop ment of a hydrodynamically stable torpedo that is fast, 4.0 and af?xed to the rear portion 15 of the torpedo in non rotatable relationship therewith are a plurality of sta that produces a minimum of noise and that can be bilizers or ?ns 18 (in this case, eight) integrally mounted launched in accordance with conventional methods. on a hub 19 the exposed outer surface of which forms It is, therefore, a principal object of this invention to a continuation of the rear portion 15 of the torpedo and provide a propeller and stabilizer surfaces for a torpedo cavitation have not met with substantial success or come the propeller hub 21. As best shown in FIGURE 2' 45 and by way of example, the hub for the stabilizers may Another object of this invention is to provide a propel be removably attached to the torpedo by means of a rigid ler and stabilizer surfaces for a torpedo having improved shaft 22 non-rotatably disposed within a hollow propeller cavitational characteristics. shaft 23 and a bolt 24 adapted for threaded engagement A further object of this invention is to provide new and novel stabilizer surfaces for a torpedo that cooperates 50 with the rigid shaft 22 or the like and provided with a‘ conical rear portion 25. with the propeller in a new and novel fashion. For the number of fins shown in FIGURE 1 the hub 19 A still further object of this invention is the provision for the stabilizers is preferably formed separately and the of a propeller and stabilizer surface arrangement that will root section 26 of each completed ?n 18 permanently at et?ciently propel a torpedo by means of a single propel ler while maintaining a zero net torque and that will be 55 tached thereto as \by welding or the like. In the preferred that result in improved torpedo performance. less susceptible to cavitation and will be more effective in embodiment as shown in FIGURE 1 each ?n 18 extends controlling the torpedo. radially to about the diameter of the torpedo and the leading edges 27 of each stabilizer surface or ?n 18 is disposed about within one ?n chord length of the rearmost Another object of the invention is the provision and location of new and novel stabilizer surfaces for a torpedo that are less susceptible to cavitation and that allow the use of propellers having improved cavitation character istics. These and other objects and features of the invention, together with their incident advantages, will be more readily understood and appreciated from the following detailed description and the drawings which illustrate an embodiment of the invention in which: trailing edge 28 of the propeller 17. As shown in FIGURE 2 and FIGURE 3 each ?n 18 has a plurality of stations designated respectively A, B, C, D, E, F and G wherein the radial cross section of each stabilizer surface or ?n 18 at each different station is disposed at a speci?c and individual angle to the longi tudinal axis of the torpedo (represented by lines 33 in FIGURE 3) and has a speci?c camber the determination of which is described hereinafter. By reference to and FIGURE 1 is a perspective view of the rear portion inspection of FIGURE 2 and FIGURE 3 it can readily of a torpedo incorporating the present invention. FIGURE 2 is a fragmentary side elevation partially 70 be seen that each stabilizer surface or ?n 18 has an indi vidual stack-up line 31 passing through different points in section of one ?n mounted on a hub and showing the in the cross sections of each different ?n at each station location of various stations on the ?n. and that each l?n is respectively twisted or skewed the FIGURE 3 is a diagrammatic representation showing ‘3,050,024 3 4 same amount and in the same manner about its stack-up being designed to replace conventional stabilizer surfaces disposed and mounted forwardly of the propeller substan line 31 such that the leading edge 27 of each ?n forms tially the same degree of stability will be maintained if the following is held true: an arcuate surface both in a longitudinal and radial direc tion as shown in FIGURE 4 and such that the trailing edge 32 of each ?n forms an entirely different arcuate edge as shown in FIGURE 5 as and for the purposes described (1) hereinbelow. The remaining restrictions on the chord distribution are In order to fully describe the construction and opera those imposed by ?n cavitation performance as will be tion of the ?ns 18 reference is now made to FIGURES 6 through 8 of the drawings as an aid in the description of 10 more thoroughly discussed hereinbelow. The design of the ?n for torque cancellation requires the manner employed in formulating the ?ns and to fully the determination of the radial distribution of bound cir describe their vunique con?guration. culation I‘f that will be needed for torque cancellation. The preferred ermbodiment of the present invention con With reference now to the propeller-?n combination templates the operation of a normally ?xed set of stabilizer 34-35 as shown in FIGURE 6 and which is merely rep surfaces or ?ns immediately behind a given single pro resentative, it will be noted that the streamline 36 which peller, that the stabilizer surfaces or ?ns satisfy the sta passes through the propeller 34 at midchord at a radius of bility requirements of the torpedo, that they produce a net torque equal and opposite to that produced by the rp, intersects the ?n 35 at midchord at a radius of rf. A propeller and that they have a cavitation performance at representative velocity diagram for the streamline 36 rela least as good as that of the propeller. tive to the propeller section at radius rD and the ?n section at radius rf is shown in FIGURE 7. Because of the mag nitude of the angles involved the assumption may be made that the induced velocity wt of the ?n section lies in a transverse plane as shown in FIGURE 7 and therefore has no axial component. The rf having the same inflow as that at rp may be calculated from continuity considera Since the con ?guration of each '?n is substantially identical with every other ?n, reference is made hereinbelow in substance to the design of a single ?n. In the following discussion let: ri=radius at which streamline passes through the ?ns at midchord rpzradius at which streamline passes through the pro peller at midchord rph=hub radius of propeller tions as rr=\/rp2—rph2+r?? 3O rm=hub radius of ?n Rp=propeller radius w=rotational speed in radians per second wt=tangen=tial velocity induced by propeller wa=axial velocity induced by propeller k=spacing factor giving change of wa with axial distance For best operation and especially for good cavitation performance the stabilizer surface or ?ns must be designed to operate with a speci?c propeller or type of propeller, hence from the design of such a propeller induced veloc ities of the propeller will be known and the following ex pression, for torque of the propeller not including pro?le losses, can be written: wf=induced velocity of the ?n section wf,25=velocity induced by the ?ns at the quarter chord-line F :Prandtl’s tip loss factor Bpznumber of propeller blades (2) R QD=BDP T Jami/wear. D 40 (3) ‘The torque of the ?ns corresponding to the velocity diagram shown in FIGURE 7 can also be written, again neglecting pro?le losses, as: Bfznumber of ?ns Fir-abound circulation of ?ns I‘p=bound circulation of propeller blade p=?uid mass density Initially, it may be convenient to cancel torques locally. Qp=torque produced by the propeller Therefore, again from continuity considerations, where Qf=torque produced by the stabilizer surfaces l3=propeller blade section angle rfdrf=rpdrm Equations 3 and 4 lead to the expression: ?1=angle from transverse plane to zero lift line of a ?n section ?m5=angle from transverse plane to a tangent of the mean camber line at the quarter chord point lf=distance of ?n from the torpedo center of gravity for new design l'r=distance of ?n from the torpedo center of gravity for existing torpedo V'=in?ow velocity at stabilizer surface of existing Since as already mentioned, ‘the ?ns are preferably de signed to extend to substantially the maximum radius of the torpedo, it is important from the point of view of cavitation to extend loading of the ?ns over the ‘full radius of each ?n. For this reason it is preferable to ?rst calcu late I‘f from Equation 6 and then to modify this I} to extend out to the full radius of the ?ns, maintaining the Cf=?n section chord of new design 60 same total torque but leaving unchanged the 1‘; near the C',=?n section chord of existing design hub for the purpose of minimizing the possibility of a R’f=?n radius of existing design cavitating hub vortex. r’fh=hub radius of ?n for existing design Once the radial distribution of I} for torque cancella tion has been established the physical con?guration of the In the design of ?ns as contemplated by the present invention stability requirements involve the choice of a ?n 65 sections, i.e., the ?n section angles, the ?n section cambers, and the like may be determined in the following manner. planform with suf?cient area to stabilize the torpedo. In The ideal approach for the design of each ?n would be to the preferred embodiment the total ?n height is restricted use an exact lifting surface theory for a ?n in a rotational to the diameter of the torpedo, hence the area is therefore in?ow. Such a formulation is, however, an imposing one. dependent on the choice of the radial chord distribution torpedo and should be such as will meet the stability needs of the 70 Also, no readily usable factors are available such as Prandtl’s “tip loss factor” or Goldstein’s “K” factor used torpedo. It has been found through experience that Equation 1 as given hereinbelow may be used for ?nding the necessary chord distribution for replacing conventional stabilizer surfaces and consequently allowing a determi nation of chord distribution. in propeller design whereby the circulation may be related to the induced velocity at each section as a function of the relative radius, angle of in?ow and the number of ?ns If the new ?n or ?ns are 75 involved. An acceptable approach, the validity of which — 3,050,024 5 has been proven by experience, is to use Weissinger’s lift camber, the geometry and orientation of each section is ing surface approximation ‘for wings described in “The Lift Distribution of Swept-Back Wings,” 1'. Weissinger, satis?ed by ?nding the camber which will satisfy Equations N-ACA TM. No. 1120, March 1947, which accounts for tion if desired may be based on mechanical considerations rather than on hydrodynamic considerations. the rotational in?ow only as a non-uniformity in the in?ow 7 and 8, simultaneously. The choice of thickness distribu Certain aspects of improving the cavitation performance velocity. Weissinger’s so-called L-rnethod states in sub of the ?ns have already been mentioned hereinabove. For stance that for a given lifting surface, if the bound cir instance, it was noted that the chord distribution must culation is assumed to be located at the quarter-chord line, meet the requirements necessary for good cavitation per then the distribution of the bound circulation must be such that the resulting ?ow is tangent to the surface at 10 formance. One of the ways in which cavitation perform ance may be improved is to increase the ?n or force the three-quarter chord line. This is equivalent to the producing area so that the cambers required and con statement that the angle of the resultant velocity at the sequently the magnitude of the minimum pressures are three-quarter chord point must be the same as the angle reduced for the individual hydrofoil sections. One of the of the zero lift line. This angle, and hence the angle for each section, may be established by determining wf at each 15 controls available for ?n area is the distribution of chord along each ?n, hence increasing the chord lengths will station or alternately, from the geometry of FIGURE 7 improve the cavitation performance. Further, the total and by use of the formula: ?n area may also be increased by increasing the number of ?ns to allow a reduction of the loading on each ?n and thereby improve cavitation performance. The determination of the values of W: is most conven iently accomplished by the use of an electromagnetic analogy. The analogy that may be utilized is that of substituting the magnetic ?eld about a conducting wire Still further, as mentioned hereinbefore, the choice for the 1} distribution is another control that may be used to improve cavitation performance. By redistributing I} to be substantially constant over the majority of the length for the induced velocity ?eld about a vortex. In the 25 of the ?n no particular section will be overloaded and con-sequently will have no accompanying poor cavitation analogy referred ‘to hereinabove a common wire repre senting the bound vortex is located at the quarter-chord performance. Further, the maintaining of 1} equal to the propeller I‘ near the hub reduces the possibility of hub line and to it are attached other closely spaced wires rep resenting the trailing vortex system. A source of alter vortex cavitation. Still further, the gradual decreasing of If near the tips of the ?ns reduces the possibility of tip nating potential is connected to these wires and is dis tributed in such a manner that the span-wise distribution of current in the bound vortex wire is proportional to the vortex cavitation. span-wise distribution of P1. By measuring the induced voltages at the three-quarter chord point these voltages tained by camber alone thereby allowing a substantially As noted hereinabove all the lift of the sections is ob constant chord-wise distribution of pressure to be main may be translated into induced velocities. The effect of 35 tained at the sections and it is the presence of such a dis tribution that prevents the existence of low pressure cavita numbers of blades may be obtained by again taking meas tion producing regions. NACA Series 16 sections which urements at the relative positions of other ?ns at the have the ?at pressure distribution just mentioned for zero three-quarter chord points. By adding the results the or very low angles of attack have been used in practice effect of the entire system of ?ns may be obtained. The analogy and use thereof referred to hereinabove 40 with satisfactory results and may be used if desired. The provision of stabilizer surfaces designed to operate is thoroughly discussed and described in “Development of in combination with a propeller (as shown and described Electromagnetic Analogy for Computation of Induced herein), thereby allowing the propeller ‘to be designed Propeller Velocities,” a thesis by Barnes W. McCormick, for operation on a clean torpedo body of speci?c design, Jr., published 1949, the Pennsylvania State University, to which reference is made. The determination of wt, such 45 has shown that the index of cavitation for both the propeller and stabilizer surfaces on such a torpedo may be as for example in the manner described immediately here reduced over that presently existing with regard to prior inabove allows the determination of the direction of the practices by as much as a factor of four or ?ve and at the zero lift line of each station along the ?n. The determina~ very least a cavitation index may be secured that is gener tion of the angle of zero lift for each station allows the determination of the proper cambers and section angles 50 ally not obtainable with prior art practices under even the most ideal conditions. on the basis that, for good cavitation performance all of It will be readily appreciated that in the arrangement the lift of the sections must be obtained from camber and development illustrated in the drawings and described rather than by any angle of attack. The proper determina by way of example hereinabove may be varied and modi tion of camber requires that the camber of the sections be determined on the basis of the stipulation that the 55 ?ed according to requirements. As may be apparent latitude is available in the design of the ?ns with regard resultant velocity at the quarter-chord line be tangent to to ?n area, ?n length, number of ?ns and section camber the mean camber line at that point ‘for the reason that and section angles and the like since they are generally determination of the zero lift line and the slope of the lift interdependent, the modi?cation of one being compensated curve of a section is not su?‘icient for the calculation of a lift coef?cient, ‘and hence, the camber of the section since 60 by or allowing modi?cation of another to a greater or lesser extent. Moreover, the present invention is not the velocity that must be used as a reference for the angle necessarily limited to a single propeller application, al of attack is not clearly de?ned. As noted immediately though such is believed preferable, and may be adapted hereinabove the determination of the resultant velocity is for steering a torpedo. dependent on ?nding the induced velocity Wf_25 at the quarter-chord point as shown in FIGURE 8 which induced 65 It is, therefore, to be understood that while the present invention has been described in its preferred embodiment, velocity may be found by integrating Biot-Savart equations it is realized that modi?cations may be made, and it is or by use of the electromagnetic analogy, reference to desired that it be understood that no limitations upon the which has been made hereinabove. The angle of the invention are intended other than what may be imposed resultant velocity may be determined from the formula: 70 by the scope of the appended claims. let-25 =taIF1 V-l-kFun ) (8) 2Fw¢ — wf.25 Since vfor a given family of airfoils, the angle of zero lift What is claimed as new and desired to secure by Letters Patent of the United States is: 1. Stabilizing means for a torpedo having propulsion means including a propeller at its rearward end com and the slope of the mean camber line at the quarter-chord point may both be known as a function of the maximum 75 prising: a non-rotatable hub element disposed rearwardly 3,050,024 g) 7 0 of the propeller and on the longitudinal axis of the tor pedo; means connecting said hub element to the torpedo; and a plurality of ?ns radially carried by said hub and having a plurality of diiferent stations, said ?ns having a predetermined angle and camber for each said diiferent station determined by the propeller water exit conditions at each said different station, said angles and said camber creating a net torque equal and opposite to that created ?n middle portion having ‘a substantially ?at load char acteristic less than the maximum load characteristic of the propeller, said ?n outer portion having a load charac teristic that decreases in an outwardly radial direction, each of said ?ns having a plurality of radially disposed di?erent stations, said ?ns having a predetermined angle by the propeller in operation and reducing the magnitude and camber for each said di?erent station determined by the propeller water exit conditions at each said different station cooperating to produce a net torque equal and of low pressure areas on the ?ns. opposite to that created by the propeller in operation and reduce the magnitude of low pressure areas on the ?ns. 2. Stabilizing means for a torpedo having propulsion 5. The combination as described in claim 4 wherein means including a propeller at its rearward end compris there is provided a minimum number of said ?ns such ing: a non-rotatable hub element disposed rearwardly of that the projected area of said ?ns in ‘any one plane is the propeller in close proximity thereto and on the longi tudinal axis of the torpedo; means connecting said hub 15 sut?cient to maintain stability. 6. In a torpedo having ‘a substantially smooth outer element to the torpedo; and a plurality of ?ns radially surface and propulsion means including a propeller at its carried by said hub and having a plurality of different rearward end the combination comprising: a propeller, stations, each said station having an airfoil cross section said propeller being designed for operation with said disposed at a predetermined angle to the flow of water smooth torpedo body; a non-rotatable hub element dis from the propeller at each said station, each said di?er posed rearwardly of the propeller in close proximity ent station additionally having a predetermined camber thereto and on the longitudinal axis of the torpedo; for producing a torque opposite to that created by the means connecting said hub element to the torpedo; and propeller in operation, the net torque produced by the a plurality of ?ns radially carried by said hub and hav ?ns being substantially equal and opposite to that cre ing a plurality of different stations, each said station hav ated by the propeller, the said angle of each said station ing an airfoil cross section disposed at a predetermined substantially reducing the formation of low pressure angle to the flow of water from the propeller at each said areas over substantially the entire surface of each said station, each said different station additionally having a ?n. predetermined camber for producing a torque opposite 3. The combination as described in claim 2 wherein the camber of each diiferent station is selected such that 30 to that created by the propeller in operation, the net torque produced by the ?ns being substantially equal and the resultant water velocity at the one-quarter chord line opposite to that created by the propeller, the said angle is tangent to the mean camber line at that point. of each said station substantially reducing the formation 4. Stabilizing means for a torpedo‘ having propulsion means including a propeller at its rearward end having an inner portion and a predetermined load characteristic comprising: a non-rotatable hub element disposed rear wardly of the propeller and on the longitudinal axis of the torpedo; means connecting said hub element to the torpedo; and a plurality of ?ns radially carried by said hub, each said ?n having an inner portion, a middle por 40 tion and an outer portion, said ?n inner portion having a load characteristic substantially the same as the load characteristic of the inner portion of the propeller, said of low pressure areas over the entire surface of each said ?n. References Cited in the ?le of this patent UNITED STATES PATENTS 2,355,413 2,746,672 2,795,394 2,798,661 Bloomberg ___________ __ Aug. 8, Doll et a1. ___________ __ May 22, Slivka et al ___________ __ June 11, Willenbrock et \al. ______ __ July 9, 1944 1956 1957 1957 at’a.wA"3.