APPENDIX A
10 NACA TN 4314 APPENDIX A .
SYMBOLS — rate of climb, ft/min c distance traveled in icing, miles (nautical) D total distance traveled through cloud depth H, miles (nautical) $ Dt a collection efficiency of probe E H depth of complete cloud layer, ft I ice accretion (thickness) on ice-sensing probe, in.
Ie icing expectancy (number of encounters per year with total ice accretion exceeding specified value) total ice accretion through cloud layer H, in.
% N number of flights per year Ne expected number of flights necessary to exceed specified value of total ice accretion once P(H) probability of given cloud depth increment, 4H probability of given increment of Wa for given cloud depth H pH(wa) P(e) probability of icing being encountered during climb and descent phase of given flight P(It) probability of occurrence of specified value of total ice ac- cretion after icing is encountered during climb or descent probability of occurrence of specified value of total ice ac- P(%f) cretion for climb and descent phase of given flight P(WJ probability of occurrence of given increment of wa T temperature of icing cloud, ‘C v true airspeed, knots w liquid-water content, g/cu m NACA TN 4314 .
T?a w at l/2 H Xb saturation mixing ratio at cloud base, g water vapor/kg dry air x= saturation mixing ratio at altitude z in clouds, g water vapor/kg dry air z altitude, ft density of ice accretion on probe, g/cu m PI density of dry air at altitude z in clouds, kg/cu m Pz .
APPENDIX B
NACA TN 4314 APPENDIX B CALC!UIATION OF PROBABILITY OF AVE3AGE LIQUID-WATER CONTENT WHEN ICING IS ENCOUNTERED DURING CLIMB AND DESCENT The liquid-water content of clouds is determined by the physical process of cloud formation, in which water vapor iS condensed by ad~batic 1+ m cooling of saturated rising air. Thus, the adiabatic process increases a w the water concentration with increasing height above the condensation The water concentration at any level (or bottom) of the cloud layer.
point in the cloud may be greater than that obtained from condensation — because of precipitation falling from above. Generally> however) the water concentration is reduced by precipitation falling out of the clo-ud~ ““- ““ ‘-- Considering the and by the entrainment of dry air from outside the.cloud.
unmodified adiabatic process, the liquid-water content available for ice formations can be calculated based on below-freezing teuq?eratures and cloud depths that have been found to be characteristic of icing clouds.
The concentration of liquid water w at altZtude z above a cloud .
base b resulting from adiabatically lifted saturated air is given in terms of the saturation mixing ratios x by the following equation (ref. 6): w= (Bl)
PZ(xb - X2)
This results in a nearly linear increase of water content with height above the cloud base. Since the saturation ufixingratio increases with temperature, the water content at any point above the base increases with increasing temperature at the cloud base. Therefore, the water content available for icing becomes a function of the temperature at the cloud base and the height of the aircraft above the cloud base. During a vertical traverse through a cloud layer the average water content can be used in determining the general severity of the icing and the total amount of ice collected.
This average water content can be taken at one-half the cloud depth because of the nearly linear relation of the water content to the cloud depth.
The probability of encountering a particular average water content during climb or descent can be determined by combining the probabilities of cloud-base temperatures and cloud depth. Since these probabilities are functions of frequency distributions of these two variables, the distri- butions must be combined to give a probability distribution of water con- tent. The following procedure was used to obtain this distribution.
.
The variation of water content in the middle of a cloud layer was calculated from equation (Bl) as a function of the depth of the cloud .
NACA TN 4314 13 layer and the temperature at the midpoint in the cloud. The results are shown in figure 8 for below-freezing temperatures in 2° C intervals.
Temperatures at the cloud base were determined by assuming a pseudo- adiabatic lapse rate between the midpoint and the base of the cloud.
These teug?eratures are used in order to relate the calculated water con- tent to a frequency distribution of cloud temperatures measured in icing conditions. Such a frequency distribution obtained from airline data (ref. 5) is shown in figure 9.
These data are considered to have been measured while the aircraft were flying at random heights above the cloud base and therefore can apply to the middle of a cloud layer. This tem- perature distribution establishes a corresponding distribution of water content for a given cloud depth based on the water-content values from figure 8. The results are shown in figure 10 as probability distributions of average water content for 500-foot increments of cloud depth.
To cover a range of cloud depths, the probability distributions of figure 10 must be combined using a frequency distribution of cloud depths.
Such a distribution is showh in figure 11, which was also obtained from the airline data of reference 5.
The probability of a given water con- tent increment P(wa~ was then computed using figures 10 and 11 in the following relation: (B2) The combined probability P(wa) is the product of the two probabilities if the frequency distributions of temperature and cloud depth are con- sidered unrelated. The resulting average water-content probability in the form of a cumulative distribution curve is given in figure 5.
14 NACA TN 4314 AFTENDIX c CALCULATION OF TOTAL ICE ACCRETION PROBABILITIES WHEN ICING IS ENCOUNTERED DURING CLIMB AND DESCIINl The amount of ice accretion I is calculated to correspond to an ice thickness that would accumulate on the icing-rate meter probe over a distance D by the relation wDE I = 0.0634— (cl) pI Since the probe is only 0.1 inch in diameter, a high collection efficiency E can be assumed. The ratio E/pI can, therefore, be taken as a~roxi- mately 1.0 (with proper units factor), which approaches the maximum ice .
accretion conditions for any aircraft component.
.
— .
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NACA TN 4314 15 The total amount of ice accretion resulting from a climb or descent through a cloud layer is the product of an average water content wa in the cloud and the distance traveled through the cloud layer. This dis- tance Dt (as shown in sketch) canbe expressed in terms of the cloud depth H and the ratio of the true airspeed V to the rate of climb C by the relation Dt=H& (C2) Substituting equation (C2) in equation (Cl) gives the total ice accretion It on the probe through a cloud layer as It = 1.056x10-3 (waH)(E/pI)(V/C!)
(C3) where E/pI= 1.0 The probability of encountering a particular total ice accretio~ in an icing cloud P(It) at a given value of V/C depends on the probabili- ties of given values of the product waH.
Frequency distributions of total ice accretions for constant V/C ratios were calculated using the distributions of wa (fig. 10) and H (fig. 11) in a procedure similar to equation (B2).
The resulting total ice accretion probability distribution for a range of V/C ratios is shown in the form of cumulative distribu- tion curves in figure 6.
APPENDIX D
NACA TN 4314 a .
APPENDIX D CALCULATION OF ICING EXPECTANCIES FOR CLIMB AND DESCENT PHASES OF HIGH-ALTITUDE FLIGHT The probabilities of relatively small :iceaccretions occurring during .- the climb and descent phase of any given flight p(Itf) can be determined OY u) by couibining the probability of icing being encountered during the climb w or descent phase of the flight P(e) with the probability of exceeding a specified value of total ice accretion after icing is encountered p(It); this can be expressed as (Dl) P(Itf) =P(e)P(It) a The expected number of flights necessary to-exceed a specified value of total ice accretion once can be expressed as (D2)
‘e”&T”*
Suuallprobabilities can result in a significant number of actual occurrences when the over-all operation of a fleet of high-altitude — aircraft is considered in which a large number of flights per year N are conducted. From this viewpoint the icing expectancy G in terms of the number of icing encounters per year with total ice accretions ex- ceeding a specified amount can be considered for over-all aircraft opera- tions. This can be calculated from the relation (D3) Ie =N/Ne =NP(e)P(It) This over-all operational probability of total ice accretions is shown in figure 7 for a range of climb and descent conditions considering air- — craft operations involving 1,200 and 100,000 flights per year with an icing encounter _probability P(e) of 0.05. The particular operation in- volving 1200 flights per year represents the operation of the instrumented fighter-interceptor aircraft, whereas 100,w fli@ts per ye= ~Y reP- resent couibinedlarge-scale airline operations of a fleet of jet — transports.
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NACA TN 4314 REFERENCES 1. Lewis, William, and l?ergrun,Norman R.: A Probability Analysis of the Meteorological Factors Conducive to Aircraft Icing in the United States. NACATN 2738, 1952.
2. Perkins, Porter J., Lewis, William, and Mulholland, Donald R.: Sta- tistical Study of Aircraft Icing Probabilities at the 700- and 500- Milibar Levels over Ocean Areas in the Northern Hemisphere. NACA TN 3984, 1957.
3. Jones, AlunR., and Lewis, William: Recommended Values of l&teoro- logical Factors to be Considered in the Design of Aircraft Ice- Prevention Equipment. NACA TN 1855, 1949.
4. Perkins, Porter J., McCuUough, Stuartj and Lewis, Ralph D.: A Simplified Instrument for Recording and Indicating Erequency and Intensity of Icing Conditions Encountered in Flight. NACA RM E51X16, 1951.
5. Perkins, Porter J.: Statistical Survey of Icing Data Measured on Scheduled Aibline Flights over the United States and Canada from Noveniber1951 to June 1952. NACARME55F28a, 1955.
6. Lewis, William: Meteorological Aspects of Aircraft Icing. Compendium of Meteorology, Am. Meteorological Sot., 1951, pp. 1197-1203.
.- IJ w TWLB 1. - SOH31ASY OF IC.7M DATA EOS CLIMB MO I$3SC6WY! 03 JET-FIf3E’53RD?2ESCEFTCR AIRCRAFT Seattle (Nov. 183s - Sept. 1956) Uonttu DJ.uth (@. 1855 - m 1956) Data rows F9quenoy Bequenoy of - Freqc9ncy of - roquanoy Total *r of 32 loing of icing in O1OW5J clrm6B Io- In cloud Iolng clOuaB clouds Ioln&t llght metrate( enetratw ?.Omnta.l .m@a’8te nommtem IBi-letrate metrate( noountmv — — June July o o 0 0.09 390 I 89 I 11 o .1s 0.03 0.16 5 55 A142.
(May tioluded) S@.
! I I 1 I WY 0.10 0.05 0.50 (Ins.rfl.lmt number or fl@hte) 2 12a 16 .8 oat .
0.07 0.32 0.21 50 0.32 146 .31 16 0.28 0.09 10 3 176
T
Iiov .
I Eeo .
0.15 10 0.07 22 4 0.23 144 21 0.48 0 .CM 0.18 4 8s
I
I?eb .
— 0.18 0.05 0.26 31 0.33.
93 28 0.19 0.06 Total
x?_L_E-
0.1s 0.05 0.2s 214 59 Totulu both 174 areaB - \ d , ,,. , , 6697 ‘ ‘ , I )17, ,.1” 1,, IId. i ,, ,.
CV-q back, # , TASIZ II. - lINCOUWl%RS WITH M6MUR2D ICS ACCFZTIMS Rate of Fllot rem.ark~ nab Location Preueure Cloud type MnulatLve TmP&IrO , True altitude Ollmb or ion c3i2Bpe& Month ray ‘mm mph of IO*, aeOoent, iometion, rt rt/min in.
(a) ------------------- 3 21 1850 -9.3 402 6,100 0.028 --- — -------------- 9,400 4 23 134B -15.4 314 ------------------- 24 ---- Wuth 20,400 4 -10.8 474 ------------------- 429 lo,2m 16 0940 -11.9 6,800 -15.8 332 ------------------- 4 Qo ---- 11 29 2135 Columbu6 , N . Hex< -23.9 504 Cirroatratw ------------------- ------------------- 11 30 1515 Portland, Oreg .
-7.9 355 4,800 ) ------------------- -- -- ---- -1.2 1s0 .------.----------- -- -- ---- -1.I..2 271 2 1 0930 545 Jz slight Ioing -16.3 Llgbt ioimg 2 12 0100 .~.9 404 7,500 ----- --- ------ ------..--------.-- -- -- ---- -----_------- ------------------- -- -. ---- Seattle -12. s 394 -- ---- -21.6 440 20,000 ------------------- -- 28 1906 -7.2 417 6,900 ------------------- 5 27 1s55 -15.5 470 13,50il ------------------- s -------- — --------- 4 ?! 1340 -4.4 346 11,700 4,s00 L@i-lt Ioing 1 6 MO) -2.7 285 16 ---- Duluth 0.059 -11, s 364 9,900 to 9,000 31CQ a Stratocumlue ------------------- 4 ----- 5,000 ---- d Ioed windnhleld 19 1010 : 12 0100 350 6,100 to 4,300 12CXJ d Light iozng -9.1 to -6.6 ‘-- tratu~ Seattlo -.-----..------------ 2 12 1115 .11.1 to -s.1 550 6,100 to 3,100 1300 d 290 ---- d Piakad Up frtmt 11 1 loos 1 -11.9 13,330 cumliLuB H k ---------.---- --- -------- 4 9 0s00 0.090 17>OOQ CIJMuJ.lm Very li2ht ice PuY.uth 16 0s40 -12.6 to -11.6 329 11, CQO to 9,200 3S00 (d) Stratootmilul! ------------------- 4 0.152 11,300 to 9,100 1200 (d) 1/2 in. rime ice on 5 5 14s1 Duluth -1s.4 to -10.9 324 cumulus mlngn; engine loe noted ---------------------- -15.1 to -9.1 316 9,000 to s,4ml 1100 (d) 2 12 1455 Seattle Stratu9 1 m 0945 Seattle 0.4W -10.7 to -16.2 41s 11,330 to 14,s00 1000 (0) stratmn Moderate Flmn 100 aCMmb, CJ demcent, d.
hl
_-r: 1.
Figure 1. - Lacatlon or ice-aeruing probe on fighter-lnteroeptm alroraft.
, . .
6697 ‘ ‘ PROJECT ICR NATIONAL MWISORY COMM171?IEE FOR AERONAUTIC LEWIS FLIQEPll PROPUEXION J&30RAT~Y 21000 mmmm RD CLEVELAND 35, OHIO P w ICING DATA SHM3T P * ev@.ment meaeumments of dxs@erlc ocddtime being film r=ordd Pkaee Note: !keae &ate neter Eat.matlcmy stark Vpwl emountzaillg icing bylwAiOing mt.eTintJmelmraf% (Ret.rdlng light-green), and tips 10 minute. - end of icing reta cycle (Iaing rate M@--) . h O= to ~ tJM lY3COr&3d iIL?O_tiLW thiB fQL70 mt b= PP3P=’4 filled out for Eaab flight ragmlL9Es of tiether ioing condltione were encmmtered.
Organization Pilot Aircraft No.
21 Mar.
Date of Flight Flight Plan Take off Time (100al ) 1850 4OX1O3 Duration or Flight 1 hlw 30 min
No q
Wa6 iolng encountered YeB~ 3500 to 5000 ft Altitude of Iolng Cloud Type Stratut3 30 sec Duration of Recorder operation Rema??ka: Green light was on about 30 see, Amber for only 10 to 12 aeo.
0 1 2 3 Duration of Flight-hour6 N F lUgure 2. - Sample of special log sheet Bupplied to wpplement reoorded data, NACA TN 4314 .
.
3OX1O3 .
I 8 12 9.
o 4 — (a) Seattlearea.
3OX1O3 .
I
I
4 8 12
o
Number of flights encountering icing (b) Duluth area.
.- — .- Figure 3. - Histogram of <itu.dedistribution — of icing encountered duTing climb and descent. h .
1, — — — — — — — — — — — — — . — — ) \ — — — — — — .2 — — .
\ .1 — — .
— — — .08 — — — — — — — — .06 — — — .04 — —
I
— .02T .01.
— — — — j
1 2 I Mmiber of encounters with ice accretions equalling or Figure 4. - Cumulative ice accretions measured on sensing probe during climb and descent arranged according to mmiber of encounters in which particular ice accretion values were equalled or exceeded.
.
.
.
\ .8 \ I .6 \ .4 \ .2 .1
-L
.08 .
.06 w“ .04 .02
T
,01 I .008 \ .006 I .004 — .002 .
.001 0 .2 .4 .6 1.0 1.2 “1 4 - ““”~ Average liquid-water content, g/cu m ,.
Figure 5. -- Probability distribution of average liquid-water content based on adiabatic lifting in icing clouds encountered during climb or descent.
.
.
s ~ h \ < — — \ — — — — — — — — — — — — — — — — — — — Tot Ice accrettm, It, in.
Figure 6. - Probability distribution of total ice accretion on ice-sensing probe for range of climb end descent ccadltlons.
.
.— .6 I I I I m I@ectd number of ioiw enowtern per rep in which a total ice accratim wculd be exoawhd, I- I “6697 , * v a t ;: 1[1 ,: ,1, ;1 ,,1,1 ,, .
I ,,1, , .,, i!,,’ ,,,
J-rrttl
-3 “ .8 .6 x \ .4 \.
< .2 .1 P \ .08 w \ .06 \ ~ .04 .02 .01 / )008 \ .006 \
o
,034 - .002 -2a- j5 5 -25 -30 — 0 -5 -lo Icing cloud temperature, T, ~ Figure 9. - Cumulative frequency distribution of temperatures of icingc1oW.
.
w ? , — — > — —
z
7 F3- iii ,- — i ~ — 7 ...
— — — I-1
— — —
— — — —
/
/
/
— — —
—
/
/
/
— —
—
~ — —
— — —
— — — —
—
—
— —
— — — —
— — — —
— — —
— — —
— — — —
—
— — —
—
Liqui{ t at m{ 3alf d9Dth of oloud layer, Ha, K,/OU n Fkwm 10. - R+xbiliby dimtritutlOnS or li’auid+atmr 0911t.nt in middle of oloufl baamd MI timpei-abure di.tributicm or ~ra 9 roi- sev~el aloud deptba.
,, ,1 .
1- I .8 \ .6 ( i .4 \ \ .2
T
.1 b .08 \ Y ,–: .06 \ , .04” \ .02 .01
L
.008 I .006 .004 .002 .001
IL
0 1000 20 00 3000 4C o 7C Cloud depth, H, ft Figure 11. - Cumulative frequency dlstrlbutlon of depth of an icing _ ,, .— cloud layer –v NACA-Lm@eyFld& Va.