Progress Report - Tests on Potential Ice Formation on Airfoils

              Daniel Guggenheim Airehip Institute
Akron, Ohio
1 STS ON P T • TI L lC I R TIOl .AIRFOILS
Progress Report, December , 1939
ethod of Computation of Potential loo Acoumulatlon on the Basie of
l.hirlins Arm Testa
Two valuee, 1dent1fJing the artificial rain. are recorded durin the teata
on the whirling arms
1. the total number of drops follin~ on a atill sheet held for e few
eeconds under the falling rain in a horizontal plane at the level in
which the test wing on the whirling arm is movingi
2. the ohordwiae distribution of' intercopted drops on the movin wing.
The t o sets of v luea, together with the knoml wing section and ei ze, win
velocity and angle of attack and t e rain drop size give all information
needed fol' a quantitative treatment o1 the potential ico f ormation.
The expectable thioknes£ 01 ioe on the nn is computed on the baeie of the
followin enalysie1 if D • the number of drops, fellin in t 1 t seconds on a
still sheet, coverin ! inches spanwiae, then the n mber of drops per second
and inch span iee le:
n
Do • •
•·tst
~hese drope. thouch concentrated in tho test eet-up for teeting convonienoe
in a small epaoe, are equivalent to un equ l number of atmoepheric rai11drops
falling on a etrip 1" wide and 21 r lon • ( be~ n the radi ue of the Ylhirlin15
arm to the center of the test i ng). Then ra indrops: counted on the still
sheet correspond to an atmospheric rain intensity
drops/equare inch, second.
Rain is customarily recorded by
rainfall per hour.
eteorolo iats using e.e basic unit inohee of'
Tho number of drope por Eecond per aq~are inch making up a rate
or h,tm inohee per hour (aseumln the rain is oomposed of drops
Gile) ii elven by the formula:
natm • hatm --~~~~~--
600 :x. ( x d3
drops/square inoh, second
'When d • di&meter of rain drops.
or rainfall
or oon1tant
If natm , tho number oi' drops per square inoh, eecond, makin up n re.in con­sidered
charaoter11tic for dnn eroua icln weather is k times the number of
drops Datm0 in the laboratory test, then wo know that the Dumber of drope in­teroepted
on tho win would build up only l/k times the ioe thickness that
could be expected on the same win under the eamo fli ght ·conditions in icin
we thor.
2
Daniel Guggenheim Airah1p Institute
Akron, Ohio
To make possible comparison oet een tho reoorda on the till shoete nd
those on the moving wing, th~ ~it area on the wing is taken to be
l" ohordwiae along tho surface x apanwi~e dietanoe or drop coverage; i.e.,
a
though the epanwiae coverage on the moving win > mllY be somewhat different
from that on the &till sheet due to the turbulenoe •et up by the dng motion,
the reduction to UDit area is made by dividing throu h the span iee diet&noe
of drop coverage, e, that had been found on the at111 sheet.
By means of this method of computation, any difference in apanwiae diatri­butlon
on the atill aheat or movin 1heet is aut~rr£tioally corrected for.
\ i th n0w ,
x
the total number of drops counted on the movin wing at the
diatonoe x from the nose , in a etrip of the width 111 ohordwiae
alone the surface and as lon epo.nwiee aa drope are interoepted,
for a time tr seconds of the teat run,
e find for the hei ht of potential ice formation at a point ~ on the win :
h • k • 600 • t • d3 ncwx inohe1/hour
Watmx a • tr
Acoording to definition, k is given byi
k •
•
lly ubstituting
k •
hatm
hteet
natm
previously found valuoa:
h&tm/600 " d3
n/a•tat•2Rn
lntroducin~ this value into the equ tion for h we obt~in:
u Wati.lx
inohea/hour
It TmE considered practical to give the potential ioe accumulation on the
win in inchee por minute, still uein in the 1ormula the rate of rain hatm
in inchee por hour, as furnished by meteorolo iete. .1th this change in
unite and subatitutin for R the radius of the whirlin orm in inoho1, we
come to the final form of the formula used for the evaluation:
hw t • 40.3 • hatm •
a mxm1n inohea/minute
Fir1ally, for the a•aumption that 0.20 inohea per hour represents a rate of
rain nth dunteroue ioing pote£tiel1tya
.~ , t • 8.06 • nowx • tat inohe11I minute
a mXmin n tr
•
I
Daniel Guu ouheim 1.1rehip lnetitut e
Akron, Ohio
3
Comparison of the ... easured Rain Interception w1 th Theoretical Complete Interception
For an nnalyeia and interpretation of the teet reaulta it will be helpful to
have a comparable theoretical standard value available.
The figure that seeme to be moat helpful in this respect is the total intercep­tion
of all the wator oonterJt iD the 1paoe • ept by y.·ing. Thie figure will be
called ''available interception" in this report.
The available interception on a 8urfaoe elemont or on tho total wing ie equal
to: water content in unit air volume x reeultant velocity of wing motion and
rainfall x projooti on o1' n ne eurfaoe element (total wing) on plane porpendi­cul
r to direction of resultant velocity.
Thi flgur ie dependent on rate of rainfall, drop 11 ze--and com1eoted with
the drop eize, velocity or fall of the drope--wlnc speed, wing aection, wing
size, angle of nttaok of win against flight path, inolincition of flight path
• Bainet horizontal plone.
The water content in the volume unit le equal to rate of' rainfall divided by
fallinb volocity of drops. tor e iven rate of rainfall, the .ater content
per volume unit inoreeeee nth decreaein drop eize.
The av ilable thicknes~, in inches per minute, is now given by:
• water content/unit apace • 60 • Vresultnnt • coa o-'x
Tho water content por unit spaoe i~ equ 1 to
3600 • 'Ydrop
The resultant velocity ie
Tre1ultant :s f 00
C ·• ?'A , ae indicated in Fig. 2a, is computed to:
CC I J",_ • COS
• -sin
• in
A ain, e find for '?fr'
-I
8 I"
"'drop • ooa 1f
v + "'drop. ein 7/,
-' ~~~~~l ~~~~
• + 1ln v .. tan 1'
vdrop• 01.11 ¥-
lntroduoinc:; theao vol11ea in our formula for hwth l.n
hwth • hatm f .. co•"'lf ( vdrop + v· Ii V->j ~ minx 60·vdrop
we obtain:
\
'
--··-....... - Akron, Ohio
4
Aesuminc th t co_ ~ s not much different from 1, th t t n lY L<.. v , and
.,drop
th t, f'or sm 11
reduoed to:
h ti.
h,;thmin • 60
wher i hw ..
thmin x
h tm.
v • ., . d, ot,.
o(
the sine is equal to tho ngl , this formula i•
•
,
+ ain lf) J · •i~ (z:,. -ol
v 11 ble ice thicJnees formation at point x of wing
aurf.aoe in inohe per minute
r te of rainfall in inoh er hour
irpl no velocity in feet por 1eoond
fallln velocity of ra i ndrop• in feet per second
n le of fll ht path ag in1t hori&on
n le of attack of wing-- n le between flight path and
refer noe axie of wing
ngle bet~een rof r nae xi of win nd 1urr c tan ent
at point x.
The drop f lling volooitie are
Fig. 2.
iven in Fi • 1, th ratios Vdrop in
v
ffect of hort Span of ing on Teet R ult1
The te1t1 on the Whirlin rm are made with in e of •quaro wing area , i . e. ,
of ep n eg 1 to the chord. Thia win~ outlino wae ohoaen bocnus , on the
one h nd , it e dea1rable to uee tie l re t poi ible win chord and highest
speed possible with the 1rlinB arm of the lnetitute, which condition re­quired
a em 11 r a or the wing, i.e., 11 e n when tho chord a to be
1 r ge. On the other band, a hord-•p o ratio of 1:1 on the baei of ex11t­in
literature, so ~ ed to be t he large t poe ibla one that would etill give
flo condition n r the Bfan center simil r to th t of lon p n n •
"i'v o t
of the
t aerie• w r de to oheok th influ nee of the ehort aspect ratio
in odel upon the deeired inform tion on drop intero ption:
) the erodynamic 1ressuro distribution lon the center chord or the
23012 win with nd ithout lots e me surod for a n ber of nncles;
b) the drop interception on
rn sured.
:ing wi t h nd without end plates..,,..
,
Test result or aeries n) are shown here in f iGuree ~. 3b nd 4 and
um:n rily in figure 5. The mea urem ate indio ta th t the air 1low about
the c ntor of the hort span wine on the hirlinc rm 15 equivalent to
that bout long-1pon airplane v.-ing at ernaller auglee of attack.
Daniel Guggenheim Ai r ship Instit ute
Akron, Ohio
6
erod~nomioally , nn en le of 10° of the win on the whirling arm oorreeponda
to about 4° of an Teraue modern airplane wing.
Teet reaulte 01 eeriea bJ are iven in Figs. oa, 6b, 60.
oeasure::icnt of this eeriee is, clearly, 'that ther e 1e no
in the interception, when end platea are attached to the
1noreaae or the off otive span 1 brouoht about.
The resul t of the
perceptible change
wine and thereby an
The end ple. tes 'dli oh were a ttaohed to the win'-' would change the ir foroea
on the win eo that they would occur about at the eame on le or ttack ae for
a normal airplane wJn~. Fig. 6 indicatee the reault nt normal force coeffi-oiente
On_ •
11 -w q•S or lift coefficients 0~11 • nL• S r or Tari OUI ~d ng OU t -
l1nea. ,
• • nor1:18.l force, actin perpendicular to win reforence axie; value
obtained by integration of pr esure distribution
L • lift foroe, perpendicular to flight Telocity
q • Telocity heod of flight v loclty
S • wing area
L • :N • coa
• an~le of attaok • angle between wing axie snd flight velocity.
rig. 5 indicate• that the ttaohoent of end plate1 hown in Fig. 1 and Fig. 8
bring about mor than a doubling of the foroe coefficients. If, nevertheless,
~i •· 6a, 6b nd 60 ahow no ch nge in the droplet interception, the indication
ie cle rly that, t least for the•e ~articular drop izee, the lift-connected
part of the air flow is without important influence on the drop interception,
but that the droplet inter ception pattern depo11ds mainly on· the geometric
angle of tho in ond of the veloci tiee ot' wing or.id 1'allin dropa.
Specific Teet losul ta
A fe typical pot ntiel ioe £ccwnuletion curves have been iven in previous
reports.
ri • 9 indioete the proeent scope of the in~eatigation.
In vie of the foot that the tests comp letely evoluated to date do not
per it dra ing of final canclusione , thore nre included here only o few
fi urea (Figs . lOa and lOb) indicatinl the effect of speed on the total
interoeption. The trend ie gener lly a deore ~c of the ratio of intercepted
to a.ve 1 lable rain with increase in speed.
Thle reeult is o~poaite to the theoreticBl prediction by Rita. Ho ever,
there is no error in the teet rrangement apparent that would bring about a
false reeult in tlis direction and there are etronf theoret1oal reaeona to
oxpect that for tho drop 2izes used in th i~ investigation the theoretical
results by Ritz--not further explained in his ref.ort--are not v lid.
1HT
5-15-40
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Figure 7. Photograph showing 40" chord and 4011 span wing with
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T STS 01~ POT5N •.. !Cc. FOR;JAt.IIOl O:N AIRFOILS
Pro6rese Report. Deoember, 1939
ethod of Computation ·or Potential Ioe .ooumulation on the Bnsie of
•hirlint rm 'Ieate
Two valuee, identifying the artificial rain, are reoorded durinG the test1
on the whirling arm:
l. tho total nU?Db.er or drops falling on a still eheet held for a few
aecondo under the falling rain in a hor1iontal plane at the level in which
the teat wing on the whirling arm is moving)
2. tho ohordwiee distribution of interoopted drupe on the moving wing.
The two sets of vuluee, together with the known wing eeotion and size, wing
"felooity and c.nglo of' attack and the rain drop eize give all information
needed for a quantitative treatment of tho potential ice for:tstion.
The expectable th1okneae of ioe on the wing is computed on the basia of the
£ollowing an lyeies if n • the number of drope, falling in t 8t 1econd1 on a
still sheet, oovering e inohee epanwiae, then the number of drops por eeoond
and inch 1panwise ies
no • n •
a· "st
Theee drops, though oonoentrated in the teat aet-up for te~tin g convenienoe
in a emall ~paoe, are equivalent to an oqual number of atmospheric raindrops
fallin on a strip l" wide ana 2R" long. (R bein the radius of the whirling
arm to the center of' the test wing). Then raindrops oounted on the still
sheet correspond to &n atmospheric rain iDten~ity
n t • n drops/square inch, 1eoond.
a Illo s. tat. 2R1r
Bain is customarily recorded by eteorologists using ae basio unit inches of
rainfall per hour.
Tho number of drops per eecond per square inch mnkin up a rate of rainfall
of hatm inches per hour (asauminc the rain ie oom10 ed of drops of constant
size) is civen by the formulai
hatm
Datm d --~--~----
600 :X Af X d3
when d • diameter of rain drops.
If llo.tm , the number of dropo per eg re inch, seoond. making up a r in oon­sidered
oharacteristio for de£goroue ioine weather ie k timea the number of
drops Datmo in the laboratory test, then \!Je kno., that the number of drops 1n­teroepted
on the wing would build up onl~ l/k times tha ioe thickness that
oould bo expected on the same ·ng under the some flight ccnditione in ioin
Vleather.
2
To make possible a oompari1on between the records on the etill sheets and
thos on the movin wing, the unit area on the win i1 tnken to be
l" ohordwi10 x •panY11e diatanoe of drop coverage J i.e., though the 1panwi1e
a
oov r •on the moving wing may be eo o.hat different from that on the etill
1heet due to tho turbulence eot up by the win motion, the reduotion to unit
area ia de by dividinb tbrvu h the apanwia dietanoe of drop cover E•, 1,
that had been found on the still sheet.
By meane of thi s method of computution, any difference. in apanwise dietrlbu­tion
on the still 1heet or moving eheet 1a automatically corrected for.
With n0w
x
, the total number of drope counted on the moving wing at the
diatanoo x from the noee, in a •trip of the width l" chordwl1e,
and a1 long apan,7iae ae drops are intercepted. for a time tr
1econda of the test run,
e find for the height of potential ioe formation at a point x on the wings
hw • k • 600 • n • d3
atmx
Accord in to definition, k is giv n bys
k. hatm
hteat
• natm
Dat1no
Dy eub1titutin previously found values:
k • hatin/ 600 • 1T • d3
n/,.tat•2Rn
Introduoin this value into the equation
h a t mx • 2Ril • ha tm
nowx
•
' . tr
for h atmx we
• tit
tr
•
obte.lni
It E coneid rod praotioal to give the potential ice ocumulation on the
wing in inohca per minute, till ueing in the fo~mula the rate of rain hatm
in inchee per hour, as furnish d by meteoroiog1sts. With thia ohango in
unit• and aubetituting for R the radiue of tho mirling arm in inches, we
come to tho fin 1 form of the formula uaed for the evaluations
hwat"'- • 144,000 • hatm • no•x • tat
·7Amin n tr
Finally, for tho asaum.ption that 0.20 inohe1 per hour repreeente
r in with dan eroue icin~ potenti ality:
n . tm -s 28 ,800 • nowx • tat
--Wa Xmi:n n tr
rate of
3
Comparison of the eaaured Rain Interoeption with Theoretioal Complete
Interception
For an analyeie nd interpretation of the teat r esult1 it will be helpful to
h ve a comparable theoretioal standard value available.
The t·igure that seems to be moat helpful in this reepeot 11 the total inter­oeption
of all the ter content in the epaoe ewept by wing. Thia figure will
be called ''avail ble interception" in this report.
The available interception on a surface element or on the total wing le equal
to: 1mter oontent in unit air volume x resultant velocity of wing motion and
rainfall x projection of wing eurfaoe element (total wing) on plane perpendic­ular
to direction ot re1ultant velocity.
This figure is dependent on rate of rainfall. drop aize--and connected dth
the drop size, velocity of fall of the drops--wing speed, wing aeotion, wing
eize, engle of att ok of wing again t flight path, inclination of flight path
aga1net horizontal plane.
The ter content in the volume unit ia equal to rate of rainfall divid ed by
falling velocity of drops. For a given rate of rainfall, the water oont ent .
per volume unit inorea1ea with decreasing drop size.
The available ioe thickness, in inches per I!li.nute, 1& iven by:
n_ • hatm [v . oo · \Y + ( vdrop + v•1 · •· f . 1~ sin ol.. - t. x)
thminx 60 • vdrop 1
where hwthm.i • available ioe thioknees formation, inohe1 per minute. at
nx point x of wing eurfaoe;
hatm • rate of rainf'all in 1nohe1 per houri
v • airplane velocityJ
Vdrol • falling velocitJ Of rain drop•;
!.f •angle of flight path against horizon;
ol • anLle of attack of wing , reference xis againet flight pathi
~ ~ • angle between wing surface at point x and wing reference
axis.
The angle oL of Fig. 2 is equal to tan-1 Tdrop
T •
The drop velooitiee used in the computation of Fig. 2 are taken from the ourve
plotted in Fig. 1.
f.ffept pf Sbgrt Span of )tin~ pn Teat Resul tp
The teate on the whirling arm are made with wings of square wing area, i . e.,
of spnn equal to the chord. Thia wing outline wae chosen because, on the one
hand, it was desirable to use the l rgeet possible wing chord and highe1t
1peed possible with the whirling arm of the Institute, llhioh condition re­quired
a small Qrea of the wing, i.e., 1mall apan when the chord s to be
large . On the other hand, a chord-space ratio of 111 on the basis of exist­ing
literature. seemed to be the largeat possible one that would still give
flow conditione near the span center similar to that of long epan 1rlng1.
4
Two te t 1eriaa wer made to check tho influenc or th short aspect ratio or
tho ing model upon the desired ini'ormation on dro~ lntoroeptions
a) tho aerodynnmio pre ure distribution along the center chord of the
25012 n with nd without slots ..ae m eured for a number of nglea;
b) the drop interception on n wing with nnd without end pl tes
measured.
T at reeults of eerie e) arc shovm here in ~1 • 3a, 3b nnd 4 and aun:utarily
in Fig. 5. The me sur monts indicate that the oir flo !/ about the center of
tho short span wine on the ,._1irlir1 arm ie equivalent to thot about a long­•
P n airplane win at smaller anglos of attack.
Aerodyn mioally, n an le of 10° of the wing on the whirling arm corresponds
to about 4° of an aver ge modern airpluno win .
Teat r eult ot aerie• b) are given in Fi e. 6 , 6b, eo.
me Eurement of thie eer1ee is, cle rly, that there ie no
in the interoeption, when end platoe are ttachod to the
inareaae or tho effeoti-vo span ie brou ht about.
iho result or the
perceptible ch nge
n n~ and t ereb~ an
The end platee ~hiol were e.ttached to the wing would chcneo tho air foroes on
the win so that they would occur bout at th s mo an le of attack ne for
nor.am! airpl n win • Fig. 5 indicates the resultant norIDCll force ooefficients
onw • ? or lift ooef'f1cienta o • L for variou win outline •
q•S q•S
N • nor 1 foroe, aotin 1 crpendiaular to ~in referenoe axia; value
obtained by integration of preeeuro distribution
L • lift foroe, ~erpondicular to 111ght velooity
q • velocity head of flight v~locity
S • inc; area
• 1 • 008
ot . an lo of attack • Dgle between inb xi nd fli ht velo"ity.
Fig. 5 indic t s that the att~o'hment of end pl te hown in Fig. 7 and Fi • 8
brin about more than a doubling of tho foroe coeffioient • Ir. nevertheleee,
igc. 6 , 6b and 60 sho no ehange in the droplet interception, tho indio tion
1• ol rly thut, t least for theee rtioular drop ei es, tho lift-oonneot d
part of the ir flow ie Vlithout important influence on the drop intoroeption,
but th t tho droplet interception ttern depends mainly on tho geonetrio
angle of th win nd of the velocities of dng und falling drop •
Speo1fio Test Re ulte
fo~ typical potential ioe acoumul tion curves hove bcon civen in previoue
report1.
1 • 9 indio tee the present soope of the inveetig tion.
In view of the fnot thot the toste ao:npletoly ovalunted to date do not permit
drawiDg of fin 1 conclusions. there are included here only .ew ~igure1
(Fi e. lOa and lOb) indicating the offeot of epeGd on the tot~l in~orception.
5
The trend is generally a deoreaee of the ratio of interoeptad to available
rain with inoreaae in speed.
This result ie opposite to the theoretical prediot1on b~ Ritz. However,
there ie no error in the teet arrantement npparent that would briDg ubout a
talae result in this direotion and there are strong theoretical reaeona to
expeot that for the drop sizes ueod in thie investigation the thooretioal
reeulte by Rltz--not further explainerl in his roport--are not valid.