1、II ,_ZIt tNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTE 2738 _/A PROBABILITY ANALYSIS OF THE METEOROLOGICALFACTORS CONDUCIVE TO AIRCRAFT ICINGIN THE UNITED STATES,By William Lewis and Norman R. BergrunAmes Aeronautical LaboratoryMoffett Field, Calif.WashingtonJuly 1952Provided by IHSNot f
2、or ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE 2738A PROBABILITY ANALYSIS OF THE METEOROLOGICALFACTORS CONDUCIVE
3、TO AIRCRAFT ICINGIN THE UNITED STATESBy William Lewis I and Norman R. Bergrun 2SUMMARYMeteorological icing data obtained in flight in the United Statesare analyzed statistically and methods are developed for the determina-tion of: (I) the various simultaneous combinations of the three basicicing par
4、ameters (liquid-water content, drop diameter, and temperature)which would have equal probability of being exceeded in flight in anyrandom icing encounter; and (2) the probability of exceeding any speci-fied group of values of liquid-water content associated simultaneouslywith temperature and drop-di
5、ameter values lying within specified ranges.The methods are particularly useful in the design of anti-icing equip-ment intended to bperate through the United States, to define simulta-neous combinations of the meteorological variables which could beencountered, and to ascertain the effectiveness of
6、the equipment inwithstanding the natural icing conditions to which it may be subjected.In addition_ a mathematical basis is provided for the future statisticalanalysis of meteorological icing data that might be obtained throughoutthe world.INTRODUCTIONThe program of research in aircraft ice preventi
7、on which has beenconducted by the NACA during the past several years has been directedprimarily toward the development of practical methods for the design ofthermal ice-prevention equipment for various airplane components. SinCea rational ice-prevention design requires a knowledge of the physicalcha
8、racteristics of icing conditions_ an important phase of the researchprogram has been an investigation of the meteorological conditions con-ducive to icing.The severity of an encounter with icing conditions is determinedprincipally by four factors; namely, the liquid-water content_ theiLewis Flight P
9、ropulsion Laboratory, NACA2Ames Aeronautical Laboratory, NACAProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACATN 2738diameter of the drops, the temperature, and the horizontal extent of theconditions. The meteorological investigation has, theref
10、ore, been con-cerned with obtaining measurements of these quantities in a wide varietyof natural icing conditions in order to establish the range and rela-tive frequency of occurrence of various values, and combinations ofvalues, of these quantities.During the period 1945 through 1948, a considerabl
11、e amount of datawas collected by the Amesand Lewis Laboratories. These results_ anddiscussions of various phases of the investigation, have been reportedin references i through 4. All of these results_ together with similardata from observations made by other organizations_ were used as a basisfor a
12、 listing of estimated maximumicing conditions recommendedfor con-sideration in the design of anti-icing equipment (reference 5)- Theprobable maximumvalues listed in reference 5 were estimated on thebasis of what was considered a reasonable extrapolation from a limitedamount of data, and the concept
13、of the probability of encounteringvarious simultaneous combinations of values entered only in a subjectiveand qualitative way.In this report, the available data obtained in icing flights in theUnited States are analyzed statistically and the results are presentedgraphically in two forms. In the firs
14、t form, the results are plotted toshow the various combinations of liquid-water content, drop diameter,and ambient-air temperature which have equal probability of beingexceeded. In the second form, plots are presented to determine theprobability of exceeding any specified value of liquid-water conte
15、ntunder the condition that the value is associated simultaneously withvalues of temperature and drop diameter lying within specified intervals.Both plots are based on preselected values of horizontal extent; however,methods for estimating values applicable to other horizontal extents arealso present
16、ed.Although the results of this report are directly applicable only tothe United States, an estimation of the conditions prevailing in otherlocalities of similar climatic conditions can be made based upon theresults presented herein. As meteorological icing data are accumulatedfor regions outside th
17、e United States, the methods of this report shouldprovide a framework for placing the data on a statistical basis that isnot limited in scope to the United States.SYMBOLSThe following symbols are used throughout this report:A,B,C designation applied to three events occurring simultaneouslybut not ne
18、cessarily independentlyProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2738 3CDDcrADeFMtn0PPAPABCP (A)Pc(A,B)PePGchord length, feetmean-effective drop diameter, micronsthe smallest drop diameter for which drops will impinge upona thermal elem
19、entinterval of drop diameter, micronsNaperian base of logarithmscollection efficiency of an airfoil section_ percentfactor by which liquid-water-content values are multipliedto make them applicable to other distances of cloud hori-zontal extent, dimensionlessweight rate of water intercepted, pounds
20、per hour per footof airfoil spanan integeran icing condition considered to be defined by specificationsof the three variables, liquid-water content, temperaturedepression below freezing, and drop diameterprobability of overloading any given element of a thermalanti-icing systemprobability of the occ
21、urrence of event Aprobability of the simultaneous occurrence of threeevents, A, B, and Cprobability of the occurrence of event B, under the condi-tion that event A will occurprobability of the occurrence of event C under the condi-tion that both events A and B will occurprobability that any random i
22、cing encounter will be char-acterized by a combination of values of the variables(liquid-water content, temperature depression below freez-ing, and drop diameter), in which each variable must, res-pectively, equal or exceed a specified value of thatvariableprobability defined by the Gumbel probabili
23、ty distributionand expressed by equation (A1)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACATN 2738LkPi probability thatj for a random icing encounter, the followingthree conditions will simultaneously be fulfilled:(1) liquid-water content exc
24、eeding a specified value;(2) temperature within a specified interval; and (3) dropdiameter within a specified intervalprobability that drop diameter will have a value lying withina specified range (AD)probability that temperature will have a value lying withina specified range (AT)Pwi(AT)Qprobabilit
25、y that liquid-water content will be equal to orgreater than Wi under the condition that the temperaturelies within a specified range (AT)probability defined by the probability function Q(T) fora fixed value of TQ(T) probability function, determined by the variation with tem-perature depression below
26、 freezing for the most severeicing conditions, of the percent of icing encounters inwhich the temperature depression belOw freezing is lessthan certain specified valuesR probability that the maximum liquid-water content in an icingencounter is equal to or greater than W, under the condi-tion that th
27、e temperature depression below freezing isequal to or greater than Tprobability function expressing R in terms of W and T_Y probability that the liquid-water content associated withthe maximum value of drop diameter in an icing encounter isequal to or greater than W, under the conditions that thetem
28、perature depression below freezing is equal to orgreater than T and the maximum value of drop diameteris equal to or greater than DR (W,D,T) probability function expressing R in terms of W3 D, and TS probability that the drop diameter is equal to or greaterthan D, under the conditions that the tempe
29、rature depres-sion below freezing is equal to or greater than T andthe liquid-water content is equal to or greater than WS(D,W,T) probability function expressing S in terms of D3 W, and TS ! probability that the maximum value of drop diameter in anicing encounter is equal to or greater than D, under
30、 thecondition that the temperature depression below freezingis equal to or greater than TProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 2738 5S (D,T)s(D)tTTTcrATATUVWWO .o5Wo .6_BAWx(Zprobability function expressing S in terms of D and Tcompo
31、site distribution function consisting of parts of eachof the functions S(D,0,O) and S(D,O)airfoil thickness, percent of chord lengthtemperature existing in an icing condition# oFtemperature depression below freezing, equal to 32-T, Ftemperature depression below freezing at which the heat out-put of
32、the thermal element can bring the surface tempera-ture of the element just to freezing temperature, Finterval of temperature, OFinterval of temperature depression below freezing, Fa constant which denotes the mode in the Gumbel probabilityequationairspeed# miles per hourliquid-water content, grams p
33、er cubic metervalue of liquid-water content corresponding to a probabilityvalue of 0.09 defined by the Gumbel probability equationvalue of liquid-water content corresponding to a probabilityvalue of 0.63 defined by the Gumbel probability equationinterval of liquid-water content, grams per cubic mete
34、rindependent variable in the Gumbel probability equationa parameter which depicts the concentration of a frequencydistribution about the mode in the Gumbel distributionequationSubscripts1iany selected icing conditiona representative value of a variableProvided by IHSNot for ResaleNo reproduction or
35、networking permitted without license from IHS-,-,-6 NACATN 2738ANALYSISThe data used in this analysis consist of 1038 sets of values ofliquid-water content, drop diameter, and temperature obtained during252 encounters with icing conditions. Values of liquid-water contentand drop diameter were measur
36、ed by means of the rotating multicylindermethod. All data available at the time of preparation of this reportwere used in the analysis, including (1) data obtained by the AmesandLewis Laboratories and published in references l, 2, 3, 4, and 6;(2) data contained in the monthly reports of the Air Mate
37、riel CommandAeronautical Ice Research Laboratory, the major portion of which is pre-sented in reference 7; and (3) data obtained by United Air Lines (refer-ence 8) and American Airlines (reference 9) during icing flights withDouglas DC-6 type airplanes.For the purposes of this analysis, the basic un
38、it of data is theicing encounter which consists of all measurements made during flightthrough a single area of continuous or intermittent icing conditions.This area was separated from other icing conditions s by relativelylarge areas in which no icing was observed. The problem consideredherein is to
39、 determine the probability that an icing encounter chosenat random will include conditions of a given severity averaged over acertain distance. Since most of the rotating-cylinder observationsrepresent averages over distances of about 3 miles in cumulus cloudsand l0 miles in layer clouds, these dist
40、ances are regarded for purposesof data reduction as standard values of horizontal extent, applicableto data from the two principal cloud types. The probabilities obtainedon this basis may be applied to other distances by using the data con-cerning the relation between horizontal extent and average l
41、iquid-watercontent obtained from continuous records of the rotating-disk icing-ratemeter. (See reference 3-) It has been assumedthat the greatest valuesof liquid-water content and drop diameter measured by the rotating cyl-inders during an icing encounter represent maximumvalues averaged overthe sta
42、ndard distances of 3 or lO miles. This assumption is probablyapproximately true, since a particular effort was madeto obtainrotating-cylinder data during the periods of most rapid ice formation.Since the variations of temperature during a single icing encounterare usually not very great, the most se
43、vereicing conditions measuredduring a particular icing encounter then will be either the greatestvalue of liquid-water content and the corresponding value of drop diameter_or possibly, the greatest value of drop diameter and the correspondingvalue of liquid-water content. Both of these possibilities
44、 for a severe8The term “icing condition“ as used herein denotes a state of the atmos-phere defined by a set of values of temperature, liquid-water content,drop diameter, and pressure altitude in which the temperature is belowfreezing and the liquid-water content is greater than zero.Provided by IHSN
45、ot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2738 7icing condition are considered in the probability analysis which, forthe sake of convenience, is developed in three phases.The first phase of the analysis is the classification of the avail-able data acco
46、rding to cloud type and geographical location; the secondphase is the determination of the particular combinations of liquid-water content, drop diameter, and ambient-air temperature, for a givenhorizontal cloud extent, that have the same probability of being simul-taneously equaled or exceeded in a
47、 random icing encounter; and the thirdphase is the determination of the probability of exceeding any specifiedgroup of values of liquid-water content associated simultaneously withtemperature and drop-diameter values lying within specified ranges.Classification of Data According to Cloud Typeand Geo
48、graphical LocationFor classification purposes in this report, clouds will be dividedinto two classes, cumulus clouds and layer clouds; and the area of theUnited States will be divided into three regions, the Pacific coastregion, the plateau region, and eastern United States with boundariesas indicat
49、ed in figure 1. This system of classification divides theobservations into six cases as indicated in table I, which includesinformation relating to the number of icing encounters and the numberof individual measurements of liquid-water content and drop diameter foreach group. The two cases for which the greatest amount of data area
