Патент USA US2409604код для вставки
Oct‘ 15, 1946. R. w. WOOD 2,409,603 » METHOD AND APPARATUS FOR GENERATING CURVES Filed Nov. 22, 1945 ' BY 2 Sheets-Sheet l ‘7 _. m 32.”; ZWW w 22%,‘, MTORNEYJ Oct. 15, 1946. R, w, wool) 2,409,603 METHOD AND APPARATUS FOR GENERATING CURVES Filed Nov. 22, 1945 2 Sheets-Sheet 2 ‘ E -' INVENTOR. 746w‘ WOrQer‘ #1600’ BY M 52»; . 9%, ATTORNEY)‘ 2,409,603 Patented Oct. 15,1946 UNITED STATES PATENT OFFICE 2,409,603 METHOD AND APPARATUS FOR GENERAT ING CURVES RobertWarner ‘Wood, Princeton, N. J., assignor, by mesne assignments, to Kaiser Fleetwmgs, Inc., a corporation of California Application November 22, 1943, Serial No. 511,291v 7 Claims. (01. 88-24) " 2 1 ellipse. This invention relates to the‘ generation of The minor axis of the ellipse will vary . ratus which are capable of producing second de-‘ with the angular positionof the opaque element C and'the contour will be changed correspond gree curves of the desired contour without the necessity for arduous mathematical calculation. ingly. Instead of a circle, it is possible to use other conic sections such as the ellipse, parabola In industry, curves of varying contour are use~ in] for many purposes, and particularly in the ' or hyperbola, and the ‘shadows projected will have designing of high speed aircraft second degree the shape of the element projected and its angu curves and particularly to a method and appa the correspondingly varied form, depending upon lar position. In addition, the element projected curves are employed in effecting the desired streamlining of the exposed surfaces. The meth 10 may be adjusted angularly about two aXes per od heretofore used to generate such curves in volves complex and laborious mathematical cal~ culations. In plants where a multiplicity of dif ferent curves is required as the basis for template shapes, modi?cation of design frequently involves 15 additional calculations. These require consider able time of expert mathematicians. Errors sometimes occur in such calculations, involving repetition of the work. The method is therefore 20 a serious item of cost and delay. t is the object of the invention to provide a simple and effective method of and apparatus for generating second ' degree curves which are pendicular to the axis w-a and its position with respect to the source of light P and. the screen S may be adjusted. It is not essential that the screen S be perpendicular to a line passing through the center of the element C, since it also may be arranged to be tilted about horizontal and vertical axes, although this is not normally necessary for the practice of the invention. In every case, and regardless of the relative adjust ment of the element C and the screen S, the projected shadow will be a conic. It is well known that the edges of shadows are not sharp and well de?ned but are somewhat “fuzzy” owing to diffraction. If shadows are produced by a light issuing from a point source, mathematically accurate and available without DO ,vi loss of time for reproduction and use. the phenomenon of di?'raction may easily be Another object of the invention is the pro observed. Di?‘raction from the edge of an opaque object takes the form of bands of light and shadow. It is di?icult to indicate these bands» precisely, but I have endeavored to do so in Fig. 2. gree curves having any desired. form. in which 5 indicates the shadow, 5 a light band Other objects and advantages of the invention and 1 a dark band beyond which there are a will be apparent as it is better understood by ref series of light and dark bands merging into the erence to the following speci?cation and the space 8. These bands are more distinct when accompanying drawings, in which Fig. 1 is a diagrammatic illustration in per 35 the source of light is very small, while the spac vision of a method and apparatus vwhich may be used by a relatively unskilled operator without mathematical training to generate second de ing of the bands depends upon the distances from spective of the principle involved: Fig. 2 is an elevation illustrating ‘the diffraction hands at the edge of a shadow; Fig. 3 is a diagram representing the procedure whereby the shape of the desired curve is de 40 termined; and P to C and from C to S. This spacing can be computed accurately. The apparatus can be ar ranged to make the bands quite narrow, and one of the bands can be selected to'be ?tted to the design requirements of the desired second degree , Fig. 4 is a view in perspective illustrating a practical apparatus for the application of the invention. My invention is based upon the principle that projections of comics are still conics, although the projections may have characteristics di?er ent from the original. As a simple illustration, curve. ' Although the element C is shown, for purpose of illustration, as an opaque body, the conic section to be projected can, of course, be an opening in an opaque body or it may be delineated as a transparent line or slot in an opaque body, or it in the form of a conic, in this instance a circle, may beformed from a thin curved member such as a wire. The only important consideration is that the element C be capable of casting the shadow of a conic section when disposed in a beam of light and rotatable about one or more is disposed in the beam and rotated partially axes, preferably three, in order to facilitate modi if a beam of light from a point source P is pro jected onto a screen S and an opaque element 0 ?cation of the curvature of the shadow to ?t the about an‘ axis a—a, a shadow X will be projected upon the screen and will have the form of an 55 desired conditions. 2,409,603 3 4 Just as a straight line is determined uniquely by two points or by one point and a tangent line at that point, a second degree curve is deter 24. It is not necessary, of course, to use the en tire outline of a conic section. Any selected por tion thereof may be projected in the manner de mined uniquely by ?ve points, by four points and scribed until a curve is found which conforms to a tangent line at one of them, or by three points 5 the ?ve conditions which are initially marked and tangent lines at two of them. The latter condition is indicated in Fig. 3, in which 9, I0 and II are predetermined points, and I2 and I 3 tangents at the points 9 and II. The curve M ‘upon the surface 24. It remains only to ?x the curve of the pro jected shadow. The simplest procedure when all adustments have been made is to shut off the is a conic conforming to these conditions. In 10 source of light, substitute a photosensitized sur designing curved surfaces such, for example, as face for the surface 24!, and then expose the sur those used in streamlining airplanes, it is pos face to light from the source for a sufficient inter sible to ?x the ?ve conditions which determine val to secure a photographic image. This opera the desired curve. Heretofore, as already indi tion must be conducted obviously without inter cated, it has been the practice, when the ?ve ference from extraneous light or otherwise in a conditions have been determined, to proceed by dark room. Instead of photographing the image, elaborate mathematical calculations, to ?x it may be ?xed by marking points on the surface enough remaining points on the curve so that 24, which may be subsequently connected to de it could be accurately drawn. My invention lineate the desired curve. Any other procedure avoids this di?iculty by the practical application may be utilized to obtain a ?xed representation of the principles hereinbefore discussed in the of the curve which may be utilized subsequently simple apparatus hereinafter described. in the form of templates or other mechanical Referring to Fig. 4, I5 indicates a housing for means for reproducing the curve. The curve as a light source such as an are between carbons ?xed may be enlarged to any desired scale before l6 and H which are supplied with electric cur rent through conductors I8 and I9 from any suitable source. A condenser lens 20 directs a it is translated to a template or other device. The apparatus as illustrated affords the nec essary elements in simple form adapted to secure beam of light from the source through a small universality of adjustment to reproduce substan aperture 2|. tially every available second degree curve. Some . The housing I5 is connected by a track 22 to 30 of the adjustments can, of course, be eliminated an easel 23 carrying a surface 24 which is prefer where the range of desired second degree curves ably white. The easel 23 may be fixed or movable is limited or where great accuracy is not essen on the track 22. It is preferably movable to tial. The elements illustrated need not be in the permit relative adjustments as may be required. Between the housing I5 and the easel 23, a particular form in which they are shown. For ‘ example, any source of light and means for pro block 25 is supported for longitudinal movement jecting a beam thereof through a small aperture along the track 22. It is provided with a groove may be utilized. Many forms of such devices are 26 in which a block 21 is adjustable transversely well known. Likewise, the means for adjusting of the track 22. A standard 28 on the block 21 the element 36 about its three axes and otherwise 40 supports a spindle 29 which is capable of vertical may be modi?ed, the form illustrated being and rotational adjustment and is held in the merely a simple and satisfactory arrangement. desired position by a set screw 30. Mounted on The easel 23 may be supported ?xedly or may the spindle 29 is a frame 3| to which a second be made adjustable by any of the ordinary de frame 32 is pivotally connected at 33. The frame vices available for that purpose. 32 carries a support 34 having a pivot 35 for the p. U Various changes may be made, therefore, in the element 36 corresponding to the element C of procedure as described and particularly in the Fig. 1, that is, an element having the outline of apparatus employed without departing from the a conic section. As will be readily apparent, the invention or sacri?cing the advantages thereof. element 36 is adjustable about the three axes X, I claim: ' Y and Z of the adjacent diagram by rotating the 0 1. An apparatus for generating curves com element on the pivot 35, rotating the frame 32 prising a plane surface on which a plurality of on the pivots 33 and rotating the spindle 29 on points not in'a straight line and through which the standard 28. In other words, the element the curve is to pass may be indicated, a support having the outline of the conic section is uni for said surface, a point-light source mounted to versally adjustable about the three axes. It also 55 project a beam of light toward said surface, a may be moved longitudinally and transversely of curved outline, a support on which said curved the track 22 to vary its relative position with outline is mounted in the beam of light, and respect to the source of light and the easel 23. means for adjusting the angle of the plane of In carrying out the invention, the points 9, I0 said outline relative to the axis of the beam of light. and II, and the tangents I2 and I3, which are to determine the desired curve, are marked upon 2. An apparatus for generating curves compris the surface 24. The element 35 is then adjusted ing a plane surface on which a plurality of points about its three axes, and its relative position with not in a straight line and through which the curve respect to the source of light and the easel 23 is ‘is to pass may be indicated, a support for said modi?ed until the selected diffraction band of surface, a point-light source mounted to project the shadow coincides with the points 9, Ill and I I a beam of light toward said surface, a curved and is tangent to the lines I2 and I3. The re outline, a support on which said curved outline sulting outline of the diffraction band is the pre is mounted in the beam of light, means for ad cise curve desired. If the desired curve cannot justing the angle of the plane of said outline rela be obtained by the described adjustments of the 70 tive to the axis of the beam of light, and means element 36, another element of conic outline may for adjusting the support for said outline bodily be substituted therefor. Thus, outlines of a cir relatively to the point-light source. cle, ellipse, hyperbola or parabola may be used 3. An apparatus for generating curves com to secure shadows which are modi?cations of prising a plane surface on which a plurality of these conic sections projected upon the surface 75 points not in a straight line and through which 5 2,409,603 the curve is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support on which said curved 6 angle of the plane of said surface relative to the axis of the beam of light. 6. An apparatus for generating curves com prising a track, a plane surface on which a plu outline is mounted in the beam of light, and rality of points not in a straight line and through which the curve is to pass may be indicated, means for adjustably supporting said surface lar axes relative to the axis of the beam of light. from said track, a point-light source mounted to 4. An apparatus for generating curves compris project a beam of light toward said surface, a ing a plane surface on which a plurality of points 10 curved outline, a support adjustably mounted on not in a straight line and through which the said track on which said curved outline is mount curve is to pass may be indicated, a support for ed in the beam of light, and means for adjusting said surface, a point-light source mounted to pro the angle of the plane of said outline relative to ject a beam of light toward said surface, said the axis of the beam of light. surface being mounted substantially normal to '7. .An apparatus for generating curves com means for adjusting the angle of the plane of said outline about three respectively perpendicu the axis of the beam of light, a curved outline, a support on which said curved outline is mounted in the beam of light, and means for adjusting prising a track, a plane surface on which a plu rality of points not in a straight line and through which the curve is to pass may be indicated, a the angle of the plane of the outline relative to support for said surface, a point-light source the axis of the beam of light. 20 mounted to project a beam of light toward said 5. An apparatus for generating curves compris surface, a curved outline, a support on which ing a plane surface on which a plurality of points said curved outline is mounted in the beam of not in a straight line and throuh which the curve light, said last-named support being mounted on is to pass may be indicated, a support for said sur the track and adjustable there along between the face, a point-light source mounted to project a 25 point-light source and said plane surface, and beam of light toward said surface, a curved out means for adjusting the angle of the plane of the line, a support on which said curved line is mount outline relative to the axis of the beam of light. ed in the beam of light, and means for adjusting the angle of the plane of said outline, and the ROBERT WARNER WOOD.