US3392934A - Technique to impede catastrophic yaw and magnus instability - Google Patents

Description

July 16, 1968 P Ls 3,392,934

TECHNIQUE TO IMPEDE CATAS'IROPHIC YAW AND MAGNUS INSTABILITY F'iled Jan. 26, 1967 2 Sheets-Sheet 1 INVENT OR ATTORNEY AGENT July 16, 19 68 P. DANIELS 3,392,934

TECHNIQUE TO IMPEDE CATASTROPHIC YAW AND MAGNUS INSTABILITY Filed Jan. 26, 1967 2 Sheets-Sheet f:

O I O" I a I 1 0 Q M 5 0O '-u\ E: l "3 a FIG. 5

United States Patent 3,392,934 TECHNIQUE T0 IMPEDE CATASTROPHIC YAW AND MAGNUS INSTABILITY Peter Daniels, Fredericksburg, Va., assignor t0 the United States of America as represented by the Secretary of the Navy Filed Jan. 26, 1967, Ser. No. 612,304 4 Claims. (Cl. 244-3.23)

ABSTRACT OF THE DISCLOSURE By the provision of narrow elongated slots along the leading edges and tip chords of cruciform fins, the roll characteristics of these fins may be significantly altered. This type fin, when applied to cruciform finned missiles and bombs, will appreciably impede Magnus instability and catastrophic yaw normally associated with such fin stabilized missiles and bombs.

Background of the invention The present invention relates generally to fin-stabilized aerodynamic bodies such as rockets, missiles, bombs and the like, and, more particularly, to a technique for substantially impeding catastrophic yaw and Magnus instability, two dynamic instabilities of cruciform finned ordnance devices.

Successful guided and unguided missile flights will depend to a large extent on the ability to predict and control the roll performance of the missile. In the development of many of the fin-stabilized missiles and ordnance devices, large initial release disturbances and other dynamic instabilities have long been noted as the major problem areas which substantially alter the course of these devices and prevent them from hitting their intended targets. These disturbances have been attributed to the so-called catastrophic yaw followed from the failure of the missile to reach its design rolling velocity. A phenomenon called lunar motion, i.e., a condition where the rolling motion frequency is the same as the pitching and yawing motion frequencies, has been found common to many of these failures. Accordingly, large de-stabilizing moments, i.e., asymmetries in bomb structure, may act on the missile and force the configuration into the condition of catastrophic yaw. A solution to the problem raised by bombs and missiles with lunar motion had been to cant the fins thereon so as to induce a sufiicient spin in order to de-equalize the yaw, roll and pitch frequencies over appreciable periods of time. It has been substantiated that a spinning of a system with canted fins starts at the angle of attack of zero, wheeras that of a system without canted fins starts at an angle of attack of about 36. With the canted fin, however, a tendency to develop large yaw persisted especially in the 250 pound bomb class, a condition which was felt to be due largely to a balance between the induced rolling moment resulting from the angle of attack and the built-in rolling moment resulting from the use of canted fins. Within a certain angle of attack range, the roll rate of the device will go to zero, producing a phenomenon called roll lock-in, and thus remaining in a fixed roll orientation relative to the pitch plane of the device. This phenomenon can be related to lunar motion in free flight where, for example, regardless of a finite rolling velocity, the same fin always presents the same side to the wind vector. Problems of catastrophic yaw have been found to arise from this locked-in lunar motion.

At high angles of attack, the rolling velocity of the device will increase to several times the magnitude of the zero-lift roll rate of the device to produce a phenomenon labeled roll speed-up which can be defined as Patented July 16, 1968 the abrupt or rapid increase in the steady-state rolling velocity with increasing angle of attack. A phenomenon known as roll slow-downa decrease in the steadystate rolilng velocity of the device with increasing angle of attack from zero degrees-will also take place. The roll speed-up phenomenon, which is probably due to the asymmetrical vortex pattern known to exist around spinning bodies at angles of attack, can trigger the wellknown Mangus instability."

Since these flight instabilities appear to be critically dependent upon the roll characteristics of the aerodynamic body, it becomes apparent that an alteration of the roll characteristics of cruciform canted fins will significantly affect the performance of the fin-stabilized missile or ordnance device.

Summary of the invention The invention involves a novel technique in an attempt to solve two of the principal problems of current bomb, rocket and missile designcatastrophic yaw and Magnus instability. This technique contemplates the removal of material in narrow elongated slots along the leading edges and tip chords of fins in the canted, finstabilized missiles and ordnance devices. The passage of air permitted by these slots will significantly alter the roll characteristics of cruciform fins.

Brief description of the drawings FIG. 1 is a schematic side view of an aerodynamic body incorporating the slotted fins of the present invention;

FIG. 2 is an end view of FIG. 1 showing the cruciform configuration;

FIGS. 3 and 4 are alternate planforms for the fin showing the slots of the present design; and

FIG. 5 is a graphical comparison of slotted fins versus solid fins in angle of attack and spin rate.

Description of the preferred embodiments Referring now to the drawings, wherein like reference characters designate like or corresponding parts throughout the several views, there is shown in FIG. 1 a device 10 which may be either a rocket, missile, bomb or some other ordnance device, having a body 11 and a plurality of fins 12 at or near the aft end of body 11. The fins are aranged in cruciform fashion as in FIG. 2, and are canted with an average fin cant angle of approximately 3.0 degrees. At the leading edges of fins 12 and at their tip chords, narrow elongated slots 13 and 14, respectively, are provided in any conventional manner. These slots permit a prescribed amount of air to pass through fins 12 in order that their roll characteristics be significantly altered. It has been found that such a modification will serve to effectively impede the two dynamic instabilities of catastrophic yaw and Magnus instabilityphenomena hereinabove -definedclassically inherent behavoirs of fin stabilized missiles, etc., which are exhibited when initially released. Workable slot dimensions and locations were arrived at through experimentation with fins 12 in a wind tunnel. The width of slots 13 and 14 were gauged at W, W being the fin 12 base width, and were located at /sW from the leading edge and tip chord sides, respectively.

In FIG. 3, an alternate fin 15 is shown, of trapezoidal planform, having slots 16 and 17 located and dimensioned in a like manner as slots 13, 14 for fin 12.

Another fin configuration which may effectively serve in impeding catastrophic yaw and Magnus instability of the device 10 is shown in FIG. 4. Here a fin 18 of triangular planform is provided with a slot 19 of a similar dimension and location to that of slot 14.

FIG. 5 reveals a study of the roll performance of the solid fin without slots as compared to the slotted fin according to the instant invention. The performance is plotted in the parameters of angle of attack (degrees) and spin rate (r.p.m.) of a cruciform rectangular fin arrangement. As is evident from the graph, both solid and slotted fins commence spinning at approximately the same r.p.m. in a free stream velocity. The solid fin, however, after going through a relatively abrupt roll slow-down phase, becomes locked-in at a minimum angle of attack of 19 and subsequently moves into its roll speed-up phase at an increasingly rapid rate until it begins leveling ofit at approximately a 50 angle of attack. The \roll lock-in region is a condition at angle of attack wherein the device will not spin but is preceded and followed by a finite rolling velocity. It is during this spin halt phenomenon that the device has been found to exhibit the undesirable catastrophic yaw characteristics in free flight. Roll lock-in can be accounted for by the probable combination of (a) the rolling moment due to rolling velocity which retards the moment causing the missile to roll, (b) the rolling moment due to fin cant produced by the differential lift due to the canted fins, and (c) the induced roll moment resulting from the asymmetrical forces acting on a cruciform fin missile at both an angle of attack and a nonsyrnmetrical fin roll orientation relative to the plane of missile pitch. If average values of (a) and (c) are assumed, a value of angle of attack will be reached where (a) (b)=(b). At this point the missile will stop rolling.

The roll speed-up phenomenon, felt to be due to the asymmetrical vortex pattern known to exist around spinning bodies at angles of attack, can trigger the well-known Magnus instability.

Returning to FIG. 5 of the drawings, it is apparent that by the mere provision of slots, the fins can be pitched some 13 higher than the solid fin configuration before roll lock-in occurs. The advantage of this is obvious from the graph. Minimum lock-in is delayed until the missile reaches an angle of attack of approximately 32. Insofar as roll speed-up is concerned, it can be observed that the slotted fin configuration has only a slightly greater spin rate in this region than it had to zero angle of attack. The result is that the possibility of Magnus instability has been reduced since the normally large variation in spin has been significantly impeded.

Based on the results of the wind tunnel test, which data is shown in FIG. 5, an explanation for the effect of fin slots on non-linear rolling motion is suggested. The roll moment due to fin cant and the induced rolling moment are known to be steady air-loads. However, the lift distribution which produces the roll moment due to fin cant is a symmetrical lift and is located nearer the fin leading edge span and tip chord. The induced rolling moment, on the other hand, is produced by shielding and is consequently located primarily nearer the interior of the fin. Also, the phenomenon of roll speed-up is assumed to be due to vortices shed along the leading edge span and tip chord of the fins. The strength of these vortices, therefore, determines whether the fins remain locked-in or develop an instability in spin. Accordingly, simple slots located near the leading edge span and tip chord of cruciform fins should spoil primarily the induced rolling moment at lower angles of attack, allowing conventional spinning to take place in the region where lock-in formerly occur-red. At higher angles of attack, where the vortices are primarily shed, slots should reduce the strength of these vortices and lock-in or considerably reduced spin will occur in the region where speed-up normally occurs. In addition, it is possible to suggest that if suffi cient static margins and good damping characteristics can be obtained for missibles stabilized with slotted fins, then instabilities due to roll speed-up and roll lock-in could be significantly reduced.

From the foregoing, it becomes readily apparent that the two principal problems of current bomb and rocket design-catastrophic yaw and Magnus instability have been effectively treated by the instant novel technique which involves no moving parts, adds no additional weight, and can be incorporated into existing and newly designed devices in any uncomplicated conventional manner. High speed aircraft have also encountered the abovementioned dynamic instabilities along with long slender bombs, highly sophisticated test rockets, upper atmosphere probes, etc., all of which may be stabilized by the instant novel technique.

The aforedescribed invention has been made in an illustrative manner, it being understood that the terminology which has been used is intended to be in the nature of words of description rather than of limitation. Accordingly, the invention is not exclusive of optimum values relating to fin planform, fin cross-section, aspect ratio, Reynolds number, Mach number, etc.

Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described.

What is claimed is:

l. In an aerodynamic body such as a rocket, missile, bomb, and the like having a plurality of canted, cruciform fins which induce a decrease to zero of the steady-state rolling velocity of the body as the angle of attack is increased from zero degrees and which subsequently induce an abrupt increase in the steady-state rolling velocity with a further increase in the angle of attack, whereby the body may experience catastrophic yaw at zero rolling velocity and Magnus instability during and after the abrupt increase in rolling velocity, the improvement wherein said fins are formed with a leading edge and a tip portion having an edge substantially parallel to the longitudinal axis of the body; and two slots in each of the fins, one slot extending along a major portion of the leading edge substantially parallel thereto and the other slot extending adjacent a major portion of the tip edge in a direction substantially parallel to the longitudinal axis of the body;

whereby the angle of attack at which the zero rolling velocity occurs is substantially raised and the rolling velocity in the region where the abrupt increase in rolling velocity occurred is substantially reduced, so that catastrophic yaw and Magnus instability are impeded.

2. In the aerodynamic body of claim 1, each of the fins being of rectangular planform.

3. In the aerodynamic body of claim 1, each of the fins being of trapezoidal planform.

4. The aerodynamic body of claim 1 in which the slots have a width of approximately A of the fin base width and are located approximately of the fin base width from the leading and tip edges, respectively.

References Cited UNITED STATES PATENTS 2,145,508 1/1939 Denoix 2443.23

2,409,945 10/1946 Lowes 10249.2 X

3,113,517 12/1963 Kelley et al. 2443.24 X

3,333,790 8/1967 Durand 244-3.23

FOREIGN PATENTS 1,064,569 12/1953 France.

BENJAMIN A. BORCHELT, Primary Examiner. VERLIN R. PENDEGRASS, Examiner.

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