Abstract:Radar cross section near-field to far-field transformation (NFFFT) is a well-established methodology. Due to the testing range constraints, the measured data are mostly near-field. Existing methods employ electromagnetic theory to transform near-field data into the far-field radar cross section, which is time-consuming in data processing. This paper proposes a flexible framework, named Neural Networks Near-Field to Far-Filed Transformation (NN-NFFFT). Unlike the conventional fixed-parameter model, the near-field RCS to far-field RCS transformation process is viewed as a nonlinear regression problem that can be solved by our fast and flexible neural network. The framework includes three stages: Near-Field and Far-field dataset generation, regression estimator training, and far-field data prediction. In our framework, the Radar cross section prior information is incorporated in the Near-Field and Far-field dataset generated by a group of point-scattering targets. A lightweight neural network is then used as a regression estimator to predict the far-field RCS from the near-field RCS observation. For the target with a small RCS, the proposed method also has less data acquisition time. Numerical examples and extensive experiments demonstrate that the proposed method can take less processing time to achieve comparable accuracy. Besides, the proposed framework can employ prior information about the real scenario to improve performance further.Keywords: near-field to far-field transformation (NFFFT); neural network; nonlinear regression; radar cross section (RCS) measurement; regression analysis
The radar scattering characteristics of aerial animals are typically obtained from controlled laboratory measurements of a freshly harvested specimen. These measurements are tedious to perform, difficult to replicate, and typically yield only a small subset of the full azimuthal, elevational, and polarimetric radio scattering data. As an alternative, biological applications of radar often assume that the radar cross sections of flying animals are isotropic, since sophisticated computer models are required to estimate the 3D scattering properties of objects having complex shapes. Using the method of moments implemented in the WIPL-D software package, we show for the first time that such electromagnetic modeling techniques (typically applied to man-made objects) can accurately predict organismal radio scattering characteristics from an anatomical model: here the Brazilian free-tailed bat (Tadarida brasiliensis). The simulated scattering properties of the bat agree with controlled measurements and radar observations made during a field study of bats in flight. This numerical technique can produce the full angular set of quantitative polarimetric scattering characteristics, while eliminating many practical difficulties associated with physical measurements. Such a modeling framework can be applied for bird, bat, and insect species, and will help drive a shift in radar biology from a largely qualitative and phenomenological science toward quantitative estimation of animal densities and taxonomic identification.
Radar Cross Section Measurements Knott Pdf Download
The most common quantitative application of weather radar in biology has been for estimating animal densities, passage rates, or population sizes2,13. In these applications, the scattering contribution of individual animals is characterized by their radar cross-section (RCS), which is a measure of the power density of the scattered electric field relative to that which was incident on the object14. Values of RCS depend upon a number of parameters, including: shape, material, and size of the scatterer; wavelength of the incident radiation; incident and scattering angle of the radiation; and the polarization of the radiation with respect to the orientation of the scatterer. Radio measurements typically yield only a subset of this information, and consequently, radar biology has often employed the simplifying assumption that airborne organisms have uniform RCSs2,12,13,15,16,17. The paucity of available biological RCS data at diverse view angles and polarizations, especially for vertebrates, can primarily be attributed to the complexity of obtaining such measurements through laboratory and field observations. One imperative for expanding radar aeroecology beyond qualitative analysis and interpretation is development of standardized techniques for quantifying radio wave scattering at variable viewing angles in ways that can be extended across taxa, as well as for different radar wavelengths and polarizations.
The radar cross section (RCS) of a complex shape can be determined by direct radio measurement of the object or by electromagnetic modeling using one of several techniques. The tradeoffs between these approaches are based on the characteristics of the scattering objects as well as the probing wavelengths of interest. Generally speaking, RCS measurements are always possible; however, the practicality of conducting measurements on certain objects can be limited. This is typically the case for objects that are prohibitively large, such as aircraft, or especially small or unwieldy, as is the case for many flying organisms. Additional complications can arise when identical measurements must be made on scatterers of very different sizes and fragility (e.g., an aphid and a goose). In these cases, electromagnetic modeling provides a possible alternative, but not without its own limitations. With this in mind, it is often necessary to weigh the costs of accuracy, practicality, and convenience when choosing a method for RCS analysis. The following presents an overview of RCS modeling and measurement - both from theoretical and practical perspectives. It is our intention to address in detail the challenges associated with RCS analysis of flying organisms, and describe the approaches that we have applied to produce the results presented herein.
The ability to advance biological radar applications, notably those dependent on polarimetry or quantification, requires complete descriptions of the radio-scattering parameters for the organisms of interest. Until now, only subsets of these data could be obtained through tedious measurements of harvested specimens, often limiting study species to those that are invasive or readily available10,30. The capability of radar for taxonomic classification of animals aloft has been widely anticipated33,34, but to date this potential has yet to be realized. The analogy in meteorological radar applications was achieved through polarimetric modeling studies of rain, snow, and hail35, and the resulting hydrometeor classification products have been successfully implemented in weather operations36. Electromagnetic modeling techniques such as those implemented in WIPL-D (www.wipl-d.com) represent the first step toward similar classification schemes for biological scatterers within the airspace.
This award was established to encourage students to pursue a career in the area of electromagnetic in electrical engineering or a related field at an accredited institution of higher learning. These grants are intended to support pre-doctoral students involved in research directed by a faculty member at their institution who is a member of the IEEE Antennas and Propagation Society. These grants are named in memory of IEEE Life Fellow, Eugene F. Knott, who was well known for his contributions to the theory, reduction, and measurement of radar cross section.
122 JOURNAL OF APPLIED METEOROLOGY Vot.um4Superpressure Balloons for Weather Research D. Rnx BOOr. ER ANn Lxers W. CoorzRThe Pennsyan Sa University, Universliy Park, Pa. nsctpt recdved 9 September 19)ABSTRACT A system of fabricating and flying several types of superpressure balloons has been developed. Thissystem includes balloons which are launched from the ground and from a light aircraft. These balloons havebeen used/or a study of airflow over mountains but are equally well suited for many other meteorologicalexperiments. A description of the essential techn/ques of udng these and other small superpressure balloonsis presented.1. Introduction The Department of Meteorology at The PennsylvaniaState University has been engaged since 1959 in a studyof the effect of the Allegheny Mountains upon convection. To a large extent this study has been concernedwith vertical air motions induced by the terrain. Theprincipal method of measuring these vertical motionshas been the tracking of balloons with a M33 radarsystem. During the years of making balloon measurementsseveral types of balloons, reflectors and special techniques have been developed and used. During the pasttwo years, as the number of tracking radars in weatherresearch has seen a sharp increase, the authors havereceived a large number of requests for informationabout ballooning techniques. This paper is written inthe hope that some of our expeiences will be of help tofellow investigators engaged in similar research.CSuperpressure balloons. A superpressure balloon ismade of a rigid (nonstretchable) material so that itsvolume is essentially constant with superpressure (excess internal pressure). The balloon will seek a densitylevel where the weight of air displaced by it is exactlyequal to the weight of the balloon, helium and allattachments. If the balloon is displaced above or belowthat density level, it becomes negatively or positivelybuoyant and seeks to return to its original level. Thus,it is in stable equilibrium on a particular density surface.The only way the balloon will be displaced from theequilibrium density level is by vertical air currents orby a change of mass or volume of the balloon itself.If the balloon is designed so that its mass can notchange and if it is free of leaks, it can be expected toremain at its equilibrium density level indefinitelyexcept for temporary displacements due to verticalair movements. Almost all superpressure balloons to date have beenconstructed of DuPont Mylar. This plastic materialhas a very high modulus of elasticity and an extremelylow permeability for helium. Thus, it would seem to bethe ideal material for superpressure balloons. However,it has a very low tear resistance and tests have shownthat it develops pinholes when it is creased sharply.Thus, it is necessary to exercise extreme care in themanufacture and handling of Mylar balloons.2. ConfiLmratlon Several configurations of Mylar balloons are availablefrom commercial balloon fabricators. A spherical shapeis desirable for many purposes but is difficult to manufacture since Mylar can only be extruded in sheets,requiring that Mylar spheres have several seams. Themost economical type to construct which approachesthe shape of a sphere is a tetroon (tetrahedron-shapedballoon) shown in Fig. 1. Current practice is to placethe load straps so that the balloon flies with one cornerpointed downward. This attitude yields a different dragcoefficient for upward and downward air motion whichis a definite disadvantage for vertical air motion measurement. Better results may be obtained by attachingthe load straps halfway between the corners so thatdrag is more nearly the same in all directions. A numberof 2 rail tetroons with a nominal volume of 0.32 cubicmeters were purchased and flown by the authors. Angelland Pack (1960, 1962) have reported good results withballoons of this same design. The authors have developed another type of Mylarsuperpressure balloon which is very suitable for theirstudy. This balloon has a simple pillow shape which isrelatively easy to fabricate and can have either a highor low drag coefficient depending on the attitude inwhich it is flown. Further, the drag coefficient is easilymeasured and is the same for downward as well asupward air currents past the balloon. The pillow balloonshown in Fig. 2, made of 1 roll clear Mylar, is designedF:mUtR-1965 D. RAY BOOKER AND LYNN W. COOPER 123Fro. 1. A tetroon (tetrahedron-shaped balloon) made of 2 mil clear Mylar.]"m. 3. A "torpedo" balloon marie of - mil metalized Mylar. $Fro. 2. A pillow shaped balloon made of 1 roll clear Mylar.to carry a corner reflector and is usually launched froma location 20 to 30 miles upstream from the radar. It istowed to its equilibrium altitude in a vertical attitudeto reduce drag and is then separated and flown in ahorizontal attitude for a large vertical drag. Theseattitudes are easily governed by properly attaching thetow balloon and corner reflector.3. Launching balloons from aircraft In many research experiments it is desirable to havea radar-tracked balloon located at a particular pointin space at a particular time, such as at the edge of orwithin a cumulus cloud at a certain stage of development. Such precise placement of balloons is practicallyimpossible with ordinary ground-launch techniques.To solve this problem the authors developed a systemfor launching superpressure balloons from a light aircraft. This system allows up to three balloons to bedelivered to the desired altitude and location andreleased at appropriate times.' These "torpedo"*balloons which were designed andbuilt by the authors can fly at any altitude up to 7000Fro. 4. A "torpedo" balloon being loaded into its launching tube.it in a standard atmosphere and withstand superpressures up to 110 mb without exceeding the modulusof elasticity of the material. They weigh less than 32grams. A "torpedo" balloon is shown in Fig. 3. The materialis 0.5 rail aluminized Mylar which serves as its ownreflector when flown in a vertical attitude. When flownhorizontally, the target shows extremely variablecross section because of the small cross section presentedby the end of the balloon when it is parallel to theradar beam. Therefore, when flown horizontally, theballoon must carry an aluminized mesh reflector. Theattitude of flight is determined by the placement ofthe valve, the heaviest part of the balloon. Obviously,a horizontal attitude is best if vertical air motions areof primary interest. Otherwise, a vertical attitude isused. The balloon is loaded into a "torpedo tube" as shownin Fig. 4. For reasons explained in a later section, theballoon is only partially inflated on the surface but asthe airplane climbs to the proper altitude the ballooninflates to its full volume and builds up the desiredamount of superpressure. The "torpedo" is corn124 JOURNAL OF APPLIED METEOROLOGY VO.JME4pletely enclosed in the tube by caps on the front and !60back ends. A cable operated release mechanism opensa valve on the front cap and ejects the disposable rearcap. The ensuing rush of air through the tube instantly 140forces the balloon out the rear.We believe this technique has considerable promise,not only for our present study of terrain effects upon 120convection but in other studies of the dynamics ofcumulus. A good example would be a direct measurement of convergence and/or vorticity near the base ofa cumulus cloud. Our aircraft can release in quick L]00succession a triangle of balloons in the proper patternaround a cumulus at the altitude of desired measure- coment. The balloons would all be adjusted to fly at the 80same altitude. The enclosed area and the trajectories crof the balloons can be measured by using a trackingradar or by ?PI scope measurement. Convergence andvorticity would be determined by measuring the changeof size and rotation of the enclosed area.4. Characteristics of superpressure balloons The principle of superpressure balloons implies aconstant volume with superpressure. In reality, nomaterial is commercially available which will notstretch a measurable amount with moderate superpressure. However, a certain amount of elastic stretchis desirable for air motion measurements. The effectof elastic stretch and shrinkage as the balloon fliesthrough waves, is to reduce the restoring force. Thisallows the balloon to follow the air motions moreaccurately since it reduces the tendencv to return to itsequilibrium level. An ideal superpressure balloon forair motion measurements would be one which has zerorestoring force, large drag and small mass so that itwould exactly follow air movements. However, this isvery difficult to achieve. The next best idea is to obtaina balloon which has as small a restoring force as possibleand whose response to air motion is known so that theballoon trajectory can be rectified to give the airtrajectory. The stretch characteristics of some balloons we haveused were investigated at room temperature. The resuits which appear in Fig. 5 show per cent change involume versus superpressure. The 0.32 cubic metertetroon, made of 2 rail clear Mylar, shows less than 2.5%elastic stretch up to the point M where the modulus ofelasticity was considered to have been exceeded. The0.17 cubic meter pillows, manufactured by our personnel of 1 mil clear Mylar, have about 3.5% elastic stretchup to the modulus of elasticity. The difference of stretchcharacteristics between the two types is primarilyattributable to the difference in shape. The tetroonwithstands more superpressure because it is made ofheavier Mylar. The torpedoes, because of their slendershape withstand more superpressure but have lesselastic stretch up to the modulus of elasticity.4O2O00 2 4 6 8 I0% CHANGE of VOLUMEFro. 5. Superpressure vs. per cent change of volume curves for several balloons.5. Response of pillows to air motion The accuracy of superpressure balloons in representing air trajectories is an important consideration. Sincethe balloon seeks to fly at a constant density surface, itresists vertical motions to an extent governed by therestoring and the drag forces on the balloon, It isdesirable to have a large vertical drag coefficient and asmall restoring force. This combination allows theballoon to follow the vertical air currents as closely aspossible. The pillow balloons are flown in a horizontalattitude to maximize the vertical drag. We have triedto determine the accuracy of the balloons by a numerical 'means. The drag coefficient was measured by allowing aninflated balloon and a reflector with a known free liftto rise through calm air. The rise rate was measured bythe tracking radar. This method yielded a drag coefficient of 1.23, a value which is in agreement with thetheoretical value for a cylinder at the Reynolds numberencountered by the rising balloon. A computer program was written to simulate asuperpressure balloon in a given sinusoidal wave,considering the drag and restoring forces which wouldFEBRUARY 1965 D. R A Y B O O K E R A N D L Y N N W. C O O P E R 125act on the balloon. The program considers the effect ofelastic stretch of the balloon with varying superpressure.For the sake of brevity the details of the program willnot be given here. Twenty five different combinations of wind speed andamplitude covering all of the usual lee wave dimensionswere computed. The balloon and air parcel were assumed to start at the same point and move downstreamat the same rate. A typical air parcel trajectory and theresulting traiectory of the balloon are shown in Fig. 6.The results show that the balloon will underestimatethe amplitude and indicate the position of maximaand minima too far upstream. The amplitude of thefirst wave is more seriously affected than the amplitudeof later waves. The average measured amplitude difference over the first two wavelengths is 75 ft or 15%low, The measured wavelength is slightly shorter forthe first wave but is accurate for later waves. A complete set of curves showing the corrections tobe made for observed waves to obtain true wave dimensions based on the machine calculations have beenmade for the pillow balloons. These curves would notnecessarily be accurate for balloons with different dragcharacteristics but similar curves can be easily constructed by using the existing program.6. Radar reflectors The most common use of balloons and reflectors isfor upper wind measurement. For many purposes, it isonly necessary to obtain winds to about 20,000 ftaltitude. This normally does not require tracking theballoon to excessive ranges. Therefore, the simplest andleast expensive reflector is best for this purpose. Ourcandidate for the best reflector in this case is a simplecylinder of aluminum foil about inches in diameterand about 4 ft long, as shown in Fig. 7 on the right.A better reflector is obtained by wrinkling the aluminumfoil as shown in the figure. Corner reflectors are commercially available invarious sizes and are necessary if long tracking rangeis desirable. However, they are generally fairly heavy,expensive and offer a considerable drag force. Largecorner reflectors are not generally needed for the M33radar. Inexpensive and efficient corner reflectors suchas the one shown in the middle of Fig. 7 can be madefrom three 18 inch squares of household aluminum foil.For fast-rising balloons, the horizontal members arestiffened by - inch dowels. These corner reflectors canbe tracked to about 30 n mi with the M33. Slightly moreefficient corner reflectors can be made by using 18 inchcircles of aluminum foil in constructing the reflector.Longer tracking ranges are easily obtained by doublingthe size of the reflector elements. The measured radarcross sections of various reflectors that we use arepresented for comparison in Table 1. It is often desirable to obtain the greatest radar crosssection for tracking to long ranges with the least amountof weight. Radar reflective mesh is available for thispurpose. This extremely light material is metalizednylon which is woven into a net with the spacing of the -6 -4 r Tmiecor Fro. 6. Air parcel and resulting balloon trajectories for a waveof 6 n m[ wavelength, 1000 ft amplitude and 30 kt horizontalwind speed.Fro. 7. Two corner reflectors and an aluminum foil cylinder used as targets for the M33 radar.TABLE 1. Measured radar cross sections of various reflectors. (3 cm) radar cross section Reflector (cm)6 in. aluminum sphere 1.8X 102Rectangular 12.7 in. aluminum foil corner reflector* 1.2 X 104Circular 9 in. aluminum foil corner reflector* 2.0X 104Two rectangular 12.7 aluminum foil corner re- 6.0X104flectors*Rectangulr 12.7 in. radar reflective mesh corner 9X104 reflector*Rectangular 25 in. aluminum foil corner reflector 2.6Xi048 in. long by 10 in. diameter aluminized pillow 4X 10TMflown in a horizontal attitude48 in. long by 10 in. diameter aluminized pillow 6.0X10a flown in a vertical attitude36 in. long by 4- in. diameter aluminum foil cylinder 6X 10 * Dimensions are from center to extremity.** This value fluctuates badly during the flight.126 JOURNAL OF APPLIED METEOROLOGY VOLOE4threads such as to make it an efficient reflector for agiven wavelength. The material is available for X, C,and S band radiation from the Suchy Division, Inc.,New York City. It is easily formed into cylinders orskirts similar to the aluminum foil cylinder or madeinto corner reflectors.7. Separation of balloons at altitude When any balloon is designed for level flight at afairly high altitude, it is usually necessary either to towthe balloon to its altitude or to release it far upstreamin order to attain flight level in the area where measurement is desired. For many reasons it is more desirableto tow the balloon. However, this requires a reliablemethod of separating the balloon from its tow balloononce it has reached its altitude. Our solution to this problem was simple and reliablewhen done correctly. The severing mechanism is asimple fuse shown in Fig. 8. The principal ingredient is ashort length of small cotton rope which has beenthoroughly soaked in a saturated solution of saltpetreand water and then'allowed to dry. Cotton rope, treatedin this way, has a constant burning rate for any givenventilation rate. The string which is to be severed is alength of soft cotton wrapping string which is insertedthrough the midpoint of the fuse and then tied intoseveral knots as shown. Experience has proven that it ispractically impossible to cause cotton string to burn pasta knot in any wind speed. Therefore, several knots tiedabove and below the separation point provide plenty ofassurance that no burning material will reach theground. A properly constructed system will burn outwithin one minute after separation. The fuse is ignited on both ends so that it will remain balanced and provide maximum assurance of asuccessful separation. The length of the fuse is governedby the altitude desired, the rise rate of the balloon system and the burning rate which is also a function of therise rate. The burning rate versus rise rate is easilydetermined with radar-tracked pibals of varying riserates which carry known lengths of fuse which arerigged to drop the reflector at some altitude. The timefrom lighting until separation of the reflector and therise rate are measured and the burning rate computed.The'length of fuse L for separation at altitude/-/of asystem with rise rate R and burning rate B is (H, ft) (L, in.)= (R, ft/min)(B, rain/in.) Although vertical air motions can cause appreciablevariations in the rise rate of the balloons, these errorstend to cancel if the separation altitude is a few thousandfeet above the release point. Careful consideration ofthe factors given'.'above should result in a separationwell within 400 ft of the equilibrium altitude.Fm. 8. A cotton-saltpetre fuse used for separation of balloons at altitude.8. Preparation of superpressure balloons If the virtual temperature and pressure are known inthe inflation shelter as well as at flight altitude, thenecessary amount of lifting gas and ballast for a givenballoon can be accurately calculated. The procedure forthis is given by Angell and Pack (1960). Although these calculations are not excessively complicated, our experience has been that it is difficult toperform the calculations for each balloon under fieldconditions. Mistakes and consequent balloon failuresresult. A general graphical solution for the equationsinvolves only one nomogram to simplify the launchingprocedure. The following is a description of the nomogram shownin Fig. 9. An enlarged version of this nomogram isused by the authors for the solution of all balloonlaunch problems. Let us consider the following equation: L,,= V(pa--m,)--W=Lg--W,where L=net lift of the balloon Lg= gross lift of the balloon V= volume of the balloon W= weight of the balloon and all attachments p= density of air surrounding the balloon p= density of the filling gas. Obviously, net lift, L,, must be zero in order for aballoon to float at a particular level. The problem ofcausing a balloon to fly at any given level is that ofadjusting W so that it is equal to the gross lift, L of theballoon at that level. The nomogram in Fig. 9 givesLo for many volumes in terms of pressure level orstandard altitude for an ambient virtual temperatureof 0C. Since the flight level virtual temperature isseldom 0C, a temperature correction scale is providedat the bottom. Note that the constant volume lines areFEBRUARY1965 D. RAY BOOKER AND LYNN W. COOPER 127O O ' / / / l,\\k\V IfitlJ /, ////II,\\\\-1NI //, ////11\\1\-W,11, I Y/l, ///%11 l/V//. ///I Y/Y//. ///A%I /Y/Y// /// V/Y/Y//. /// /y/y//. / //y/y// / ///Y/Y/E// /// X//Y/Y/// /// ///Y/E/Y// /// / ://Y/E/y// /// /// //X/X/Y// // / //// '//X/X/y// '// 'J/l/. '//X/X/V// '// / ///, '//X/K/M// // / ////. //X/X/y/ // - """'" "''': L /J//J //// 'X/A/ X/M /j ///J //// '//A/X/M/ J //// '//// //A/X/M/ // ///' ////' //// ///V/ / // / /////, //// //X/V/j /// , ///// '//// 1/// //X/M/j /// V///// ////j /// //J/M/ // ///// ///// ////. /// M / . /// //// //////. '/A//. // /J: J//// '////./// '//VA/V/ // /J// ///// ///.'/// '///V/. / /////. ///// ////J/// '//VA/M/. // V/l/// /////, //// //// /IVY/M/. //. //// //// ///// ////////V/. / / /J: ////' '///// //////////M//. / / /// ////// //// '/// '//// /IMP/V/. // ///// /// //// ////'/// //X//. '// ////// ///// ///j //// ///. /// / '//. ///// '///// ///// /// ///. //X/. '//. //// /// /// '//// /// /X// '/ /// ///// //// ////. //// // ,'//. - ///// ///// ///// ///// /// '/// :/. ///// /I// /// /// '///. '/// .//V/ / :,, :, ,-. ,,. : ., ?.,. ?. ,, .,:,: .. ?. - - - // /. / ' _._-: - ? o o0 0 0 0 0 0 0 o ') (;3 3 0 U3LO '3 q 'SRSSHd "SOl 'QIS - , 3128 JOURNAL OF APPLIED METEOROLOGYbranched in two directions, depending on whether thetemperature is positive or negative. An easy way to understand the nomogram is to consider that 'for any given volume at some non-zero ambient temperature there is an "equivalent volume"which would give the same gross lift if it were at 0Cambient temperature. The equivalent volume is foundby projecting up a constant gross lift line from theappropriate volume-temperature intersection to the 0Csea level line. The equivalent volume is read at that point.Conversely, the real volume for any equivalent volumecan be found by projecting down a constant gross liftline to the ambient temperature and reading the truevolume at that point. The use of the nomogram can best be demonstratedby an example. Assume that the following data applyto a balloon launch:a. balloon weight, Wb 300 gmb. pressure inside shelter, P, 900 mbc. virtual temperature inside shelter, T, +20Cd. net lift of inflated balloon in 150 gmshelter, Le. pressure at flight level, -Ps 750 mbf. ambient virtual temperature at flight -- 15Clevel, Tsg. desired superpressure at flight level 40 mbAPth. stretch at AP=40 mb 2% Let us also assume that the volmne of the balloonis not known. The weight of the empty balloon, Wb, iscarefully determined (300 gm in this case). The balloonis then fully inflated but not superpressured and the netlift of the inflated balloon is measured (150 gm). Thegross lift of the balloon volume in the shelter is Lo,= L,+Wb = 3007 150 = 450 gm. The point described by the450 gm, 950 mb intersection on the nomogram designates the equivalent volume at 0C. The ',real volume isfound by following this volume line to'sea level, projecting down a constant gross lift lm%:to the sheltertemperature of +20C where the true volume of 0.458ms is read. If the volume of the balloon is known theabove steps can be eliminated. The next step is to determine the gross lift of theballoon at flight level in order that the proper amountof ballast may be attached. This requires finding anequivalent volume corresponding to the real volume atthe virtual temperature at flight level. This is done byfollowing the 0.458 ms volume line downward on thetemperature correction scale to the flight level virtualtemperature of --15C. It is found that our balloon at--15C is equivalent to a 0.487 ms balloon at 0C. Theflight level gross lift is read from the 0.487 ms line atflight level 750 mb as 420 grams. Thus, the balloon andall attachments must apparently weigh 420 gm. However, there is one correction yet to be made. As explained above, the balloon will have a finite amount ofstretch with superpressure and will lift, therefore,slightly more than indicated. Correction for this issimply accomplished by adding to the weight in proportion to the amount of stretch, 20-/0 in this case. Thus, W= 420+0.02X420= 428.4 gm.Since the balloon weighs 300 gm, there remains 128.4gm for the reflector, string and all other attachments. The amount of filling gas in order to have the balloonarrive at flight level with 40 mb of superpressure remains to be determined. This amount of gas must besuch that the balloon becomes fully inflated somewherebelow flight level and builds up 40 mb of superpressureas it continues to rise to flight level. The difference between flight level pressure and the pressure where theballoon fills out varies with lapse rate. For an isothermallapse rate this difference is simply equal to the desiredsuperpressure. A good approximation can be obtainedfor other lapse rates by adding 10% to AP for eachdegree of lapse rate greater than isothermal (expressedin deg C per 50 mb). Thus, if the lapse rate were 3Cper 50 mb below flight level a superpressure of 40 mbwould give a pressure level of 750+40+0.3X40=802mb where the balloon would fill out. A gross lift of445 gm is read on the 0.487 ms line at 802 mb. Sincethe balloon will be only partially inflated from thesurface to this point the assumption of a constant freelift is justified. The balloon will attain full inflation atthe proper altitude if it is given a free lift in the shelterof 25 grams with all attachments included. This canbe done by adding known weights equal to the desiredfree lift, deflating the balloon until zero lift is achievedthen removing the known weights. For low level flights with cold ambient temperaturesthe balloon must often be superpressured in the shelterin order to achieve the desired superpressure at flightlevel. The solution to the inflation problem is the sameas above except that the amount of superpressure mustbe measured and adjusted to a proper value based onthe following equation: or AP P. P+AP T TThe regulation of supcrprcssure is simply accomplishcdby using a manometer calibrated in millibars. In thisspecial case, the net lift must be determined by takingthe difference between the gross lift at flight level andthe gross lift in the shelter with allowance for stretchduc to superpressure. These figures are read directlyfrom the nomogram. If the ambient temperature iscold and the shelter is heated the nct lift in the sheltermay be negative and the superpressure higher than atflight level. This is of no consequence, however, becausethe balloon will become positively buoyant and superpressure will decrease as soon as it is taken into thecolder air.FEBRUARY 1965 D. R A Y B O O K E R A N D L Y N N W. C O O P E R 129 If a[[ the parameters are accurately known, it isreasonable to expect equilibrium within 200 ft of theintended flight level.9. Summary Ballooning operations using the above techniqueshave proved to be reliable and are considered to giveaccurate information about the movement of air ifproper consideration is given to the balloon response toair motion. The discussion has been restricted to considerations which apply to measurement of motions ofthe order of 10 miles in the horizontal and 1000 ft inthe vertical direction. Superpressure balloons are usefulfor measurement of air motions on larger and smallerscales but other factors not considered here must betaken into account. More detailed information on any portion of thispaper will be gladly furnished to interested persons.Results of investigations using these ballooning techniques will be given in forthcoming papers. Acknowledgments. The radar cross section measurements were accomplished with Mr. Larry Davis. Muchof the computer programming was done by Mr. JohnHirsch. Thanks are also due other members of theDepartment of Meteorology at The Pennsylvania StateUniversity for many days of testing and flying superpressure balloons. REFERENCESAngell, J. K., and D. H. Pack, 1960: Analysis of some preliminary low-level constant level balloon (tetroon) flights. Mon. Wea. Rev., 88, 235-248.-- and , 1962: Analysis of low-level constant volume bal loon (tetroon) flights from Wallops Island. J. Atmos. Sci., 19, 87-98. 2ff7e9595c
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