NASA Contractor Report 175092

Analytical Determination of Propeller

Performance Degradation Due

to Ice Accretion

(NASA-CR-175Q92) ANALYTICAL DETEEMINATION N86-23577

OF PROPELLER PEBFGRHANCE DEGRADATION DUE TO

ICE ACCRETION Final Eeport (Sverdrup

Technology, Inc.) 138 p HC A07/MF A01 Unclas

CSCL 01C G3/03 05976

Thomas L. Miller

Sverdrup Technology, Inc.

Lewis Research Center

Cleveland, Ohio

April 1986

Prepared for

Lewis Research Center

Under Contract NAS 3-24105

NASA

National Aeronautics and

Space Administration
TABLE OF CONTENTS

Pa_ge_

LIST OF SYMBOLS . . . . i i i

CHAPTER 1. INTRODUCTION . . . . 1

CHAPTER 2. SUMMARY OF PREVIOUS WORK 5

A . Early Work

1. Experimental Effort 5

2. Analytical Effort 7

B. Recent Work

1. Experimental Effort 1O

2. Analytical Effort . 12

CHAPTER 3. CODES EMPLOYED 17

A. Theodorsen Transformation 17

B. Droplet Trajectory Code 19

C. Aerodynamic Coefficient Correlations 22

1. Gray Correlation 30

2. Bragg Correlation 32

3- Flemming Correlations 34

4. Miller Correlation 36

D. Propeller Performance Code 37

CHAPTER 4. PERFORMANCE DEGRADATION CODE ASSEMBLY .... 39

CHAPTER 5. RESULTS ...... . 44

A. Bragg 48

B. Gray 49

C. Flemming .... . 51
Page

SUMMARY AND CONCLUSIONS 54

REFERENCES . . 57

FIGURES ..... . ...... . 62

TABLES OF EXPERIMENTAL & ANALYTICAL DATA . . . . . . . .60

APPENDIX 1. PROGRAM FLOWCHART 85

APPENDIX 2. USER'S GUIDE ... ...... . 88

APPENDIX 3. SAMPLE CASE . 100

ii
LIST OF SYMBOLS

a speed of sound

Ac accumulation parameter

b propeller section chord

B number of propeller blades

BMP propeller power absorption

c airfoil section chord

C . section drag coefficient

C section lift coefficient

C. propeller power coefficient = P_

. 3.5

Pn D

C

T propeller thrust coefficient =

-P . /,- propeller diameter

E total collection efficiency =

Fr Froude number = U

-PnV

g gravitational constant

h airfoil project height

I airfoil drag constant

J propeller advance ratio =

nD

2

K inertia parameter•= c & U

18cu

k/c particle roughness height

K modified inertia parameter = K(l +' .O967 (R )°'6397)

o u

M, M local Mach number

m
n, N propeller revolutions per minute

r leading edge radius of curvature

R droplet Reynolds number = Plu - DIU&/U

5 airfoil surface arc length

t/c airfoil thickness to chord ratio

T freestream temperature

u local air velocity

U, V freestream velocity

w liquid water content

x propeller radial location in fraction of tip radius

Y initial droplet y-coordinate

of. airfoil section angle of attack

«f. induced angle of attack

6 impingement efficiency = dy /ds; propeller twist

angle

&max maximum local impingement efficiency

& droplet diameter

C

D propeller efficiency = J T

C

P

T) local droplet velocity vector

p. absolute air viscosity

P air density

Pice ice density ....

ff droplet density

ff section solidity = Bb

'P . . ~~

JID

IV
T icing time

+ resultant advance angle
CHAPTER 1

INTRODUCTION

The accretion of ice on the lifting or propulsive

surfaces of an aircraft is a phenomenon which can have severe,

if not diaaatroua, consequences if it is not dealt with

properly, and in a timely fashion. In many cases, this

accretion may produce a serious reduction in lift and increase

in drag, requiring more power than is available and resulting

in a aerious departure from the mission profile. Although

>measures and devices exist which generally prevent this worstcase scenario from happening, ice accretion on airfoils is

still a common occurrence in certain atmospheric conditions

and aa such merits further study because of the significant

negative effect which it has on airfoil and aircraft

performance. It is the objective of this thesis to provide a

single computer code which will accurately predict the degree

of performance degradation, primarily with respect to drag

increment, which will result from the exposure of an airfoil

to some set of atmospheric and flight conditions conducive to

ice formation.

Two basic types of ice are found to occur as a result of

exposing an airfoil in forward motion to aupercooled water

droplets in a sub-freezing environment (Fig. 1). The type of

ice which will form may be determined by a variety of factors

including freestream velocity, liquid water content of the

cloud, droplet size distribution, and freestream temperature.

Based upon an investigation of the data currently available.
. the two latter factors appear to be the moat influential in

determining the resulting ice type. The first kind of ice,

known as rime ice, occurs at relatively low velocities, low

•- r • •..«' . • ' - • • liquid water content values (typically O.5 to l.O grams per

cubic meter), and temperatures well below freezing. Due

primarily to the very cold temperatures associated with rime

ice formation, the droplets tend to freeze on impact to form a

fairly smooth 'addition to the leading edge of the airfoil. At

some point with respect to the combination of flight and

'atmospheric conditions present, ice type transitions from'rime

to glaze ice. Not only is the crystalline structure of these

ice types different, but glaze ice is also produced by higher

'" freestream velocities, higher' liquid water content values (on

the orde'r of 1/5 to 3.0 grams per cubic meter), and

temperatures- near, but below, freezing. Again, due chiefly to

"the warmer temperatures involved, the water droplets impacting

the surface tend not to freeze on impact but rather to strike

the airfoil or existing ice formation and run back somewhat in

a chbrdwise direction before freezing.

Both types of ice cause significant performance

"degradation of*the airfoil. When compared to the aerodynamics

of an airfoil in the clean, or non-iced,; configuration, the

iced airfoil will virtually always exhibit a decrease in lift,

an increase in drag, and a change in pitching moment which

'will yield a detrimental effect on aircraft stability.

Examination of the available icing data base indicates that

the degree of performance degradation, specifically with
respect to drag increment., la generally more severe for the

glaze ice condition. Thia may be attributed to the more

draatic alteration of the leading edge of the airfoil aa a

reault of glaze ice formation, aa compared to the typically

smoother and leaa obtruaive rime ice formation. Increases in

drag coefficient in exceaa of 1OOX or more are not unusual for

either type of accretion.

Both rime and glaze ice act to negatively influence

airfoil performance by physically altering the shape of the

airfoil, thereby changing the flowfield around the airfoil.

In computing this flowfield for the propeller caae, the

rotational and induced components of velocity, as well as the

forward component, must be taken into account aa exhibited in

Figure 2. The reshaping of the airfoil surface by the ice

accretion and the rough peaka and surfaces commonly preaent in

ice accretions, especially in the glaze ice caae, aerve to

induce premature tranaition and often separation of the flow

around the airfoil, thua spoiling ita deaigned aerodynamic

characteristics. The associated ice roughness also acts as an

energy loss device. For the propeller configuration dealt

with in this thesis, these effects may occur along the entire

span of the propeller and have the same effect on propeller

aerodynamics as they are found to have with reapect to fixed

wing aircraft. Ice accretion on a propeller may then

tranalate for example into an increaae in power required to

maintain a given flight condition when ice is allowed to form

on the propeller bladea. As a pilot, passenger, or other
concerned party it would therefore be desirable before

undergoing an icing encounter to have aome idea of just how

much power would be required to maintain a flight condition

with ice accreting on the propeller and other aircraft

components, so that some decision could be confidently made

regarding the safety of undergoing or avoiding such an

encounter. In addition, information provided by this code may

be used in establishing propeller ice protection system

specifications, as well as potentially in future icing

certification efforts.
CHAPTER 2

SUMMARY OF PREVIOUS WORK

Much work haa already been done in att.empt.ing to better

.understand ice accretion and ita effect on aircraft

performance. However, due to the very complicated phyaica

which govern the ice accretion process, many questions remain

unanswered in this area and it ia atill difficult with preaent

technology to accurately predict the degree of performance

degradation which will reault from an arbitrary icing

encounter. Several recent developments have made the

prediction of performance degradation, especially in terms of

drag increase, more reliable and have expanded the range of

conditions over which relatively accurate predictions can now

be made. Yet much of the groundwork for these developments

was laid thirty to forty yeara ago. This initial work

involved both experimental and analytical inveatigatlona of

ice accretion, and much of the icing data used in current

correlation development work was actually collected during

this.early period, from roughly the late 1940'a to the late

1950's.

A. Early Work

1. Experimental Effort

Early propeller performance degradation data waa

gathered using both eimulated ice and actual natural icing

encounters. Coraon and Maynard (1) in 1946 uaed aimulated ice

on propeller bladea and measured average efficiency loaaea on

the order of three percent, with maximum loasea of fifteen
percent, noted. In 1948, Preston and Blackman (2) undertook a

flight, test program in which they also noted average decreases

of roughly ten percent in propeller efficiency due to ice

formation, as well as the associated increase in drag. This

study waa of special significance due to the fact that an

attempt was made to examine the effects of ice accretion on

all major components of the aircraft. Possibly the most

complete and informative work relative to ice accretion on

propellers was performed and documented by Neel and Bright (3)

in 195O. In a flight test program in which efficiency loss

was measured during actual natural icing encounters, they

observed losses of roughly ten percent in most cases, with

maximum losses on the order of twenty percent. The

performance degradation data of Neel and Bright is still used

by present researchers to develop or verify analytical

propeller performance degradation codes.

Also of note with respect to experimental investigations

of airfoil icing are a series of test programs undertaken in

the Icing Research Tunnel at the NASA Lewis Research Center

and documented by a variety of NACA personnel in the early and

mid-195O's. Gray and von Glahn (4,5) looked at the effects of

ice on the performance of NACA 65AOO4 and 65-212 airfoils,

and lesser increases were noted for both airfoils with rime

ice accretions. Brun, et. al. (6,7,8) and Brun and V/ogt (9)

produced a series of reports dealing with experimental
measurements of performance degradation of NACA 65AOO4, 65,-

*2O8, and 65.-212 airfoils due to ice formation. These reports

focused on the impingement characteristics of these airfoils,

which in turn relate directly to.drag increment and decreased

performance. Included in their investigations were the

effects of airfoil thickness and angle of attack on droplet

V. "..'•- . " ' . • ' . • • •

impingement values, noting that thickness tends to increase

the volume of water collected and decrease the rearward limit

' •

 :

of droplet impingement, and as expected total impingement

increases with increasing angle of attack.

Gelder, Smyers, and von Glahn (1O) in 1956 investigated

"j ".•:•" • . . '

droplet impingement properties on several airfoil sections of

various thickness and concluded in part that the total and

*•••'• ' . -

maximum local collection efficiencies were strong functions of

first of all the modified inertia parameter, a parameter which

takes into account factors such as freestream velocity,

droplet density and diameter, airfoil chord, absolute air

viscosity and air density, and also of thickness ratio and

angle of attack.

These early experimental programs not only provided

valuable insight into the process and effects of ice

accretion, but also established a data base from which

analytical ice growth and performance degradation predictions

could be developed or verified.

2. .Analytical Effort

In the report by Neel and Bright (3), the authors

attempted to predict analytically the degree of propeller
performance reduction to be expected as a reault of ice

accretion. Using blade element theory as the basis for their

analysis, and by relating the change in airfoil drag/lift

ratio to efficiency loss, they predicted efficiency losses

which agreed at leaat to the same order of magnitude with the

experimentally obtained values.

Bergrun (11) in 1951 offered a method for determining

droplet impingement characteristics on an airfoil by solving a

set of simultaneous differential equations which described the

particle dynamics of a water droplet moving in an air stream.

This same principle forms the basis for present droplet

trajectory codes also. Along with Lewis in 1952 (12), Bergrun

also investigated using probability analysis the atmospheric

factors responsible for ice formation and identified with a

quite limited data base the three parameters still felt to be

of primary importance in the ice accretion process: cloud

liquid water content, water droplet size, and ambient

temperature.

In 1958, Gray undertook an icing study of the NACA

65AOO4 airfoil (13) and attempted to develop a drag

coefficient correlation which would relate ice nature and

droplet impingement rates to the associated aerodynamic

penalties for this airfoil. Using experimental icing data, he

obtained a dimensional correlation which he found to be

accurate at all but angles of attack greater than four

degrees, presumably due to the flow separation occurring at

the higher angles of attack. Gray then published in 1964 a

a
report. (14) in which he examined available .aerodynamic icing

data for other airfoils and modified his correlation to make

it applicable to these other airfoils as well. He

accomplished this through the introduction of the factor *r*

. which represents the airfoil leading edge radius of curvature

in percent of chord. This modified correlation represented

,the only available icing drag coefficient correlation at that

time, and saw widespread use for several years. Only recently

.has its validity as a general icing correlation been

questioned, and it will most probably remain in use until a

suitable replacement is offered.

The formulation of Gray's drag coefficient correlation

represented the last ma3or development with respect to ice

accretion effects for several years. The advent and use of

the ;jet engine and turbofan on the propulsion scene then

deemphasized the use of the propeller as a propulsive device

.••<•.•- . -

and subsequently drew much attention away from the problem of

ice accretion, which was of lesser importance for the large

commercial transports and military aircraft of that time.

However, with recent increased fuel costs and a renewed

interest in commuter aircraft and all-weather helicopters, new

interest in ice protection systems and a need to better

understand the phenomenon of ice accretion have again come

about.
B. Recent Work

1. Experimental Effort

Researchers involved in the renewed study of ice

accretion recognized the need to expand the quite limited

experimental data base, especially to include tests of ice

accretion on the newer airfoils designed for use on current

general aviation aircraft, propellers, and helicopter rotors.

Shaw, Sotos, and Solano in a 1982 report (15) discussed the

results of one such program in which aerodynamic performance

degradation data was obtained for a NACA 63 -A415 airfoil.

Glaze and rime ice formations were studied in both cruise and

climb configurations and significant performance degradation

was noted for all cases. Also evaluated was the effect of aft

frost growth on airfoil performance, and this phenomenon was

found to significantly increase section drag coefficient.

This project was also of importance because it provided new

data with which to test Gray's drag coefficient correlation.

The authors found that the correlation was as accurate in most

cases for the new data as it was for the old data upon which

the correlation was developed, but it became poorer in

accuracy for higher liquid water content values. This

conclusion again pointed out the need for a better, more

accurate drag coefficient correlation.

Also in 1982 at the Ohio State University, Bragg and

Gregorek (16), along with Zaguli (17), used simulated ice

shapes to investigate various aspects of the ice accretion

problem. In one test a simulated rime ice shape was applied.

10
.with and without surface roughness, to a NACA 65A413 airfoil

and the ensuing performance degradation waa measured. Surface

roughness was determined to be an important factor in

modelling ice shapes, affecting drag coefficient and C,

max

In the second test, they also demonstrated the feasibility of

using wood shapes to model ice accretions on a NACA 63.-A415

airfoil in order to ascertain the effects of the ice shape on

the aerodynamic flowfield.

Flemming and Lednicer in 1983 (Id) tested a series of

scale models of helicopter airfoils to investigate the effects

of artificial ice accretion on airfoils at high speeds.

Aerodynamic performance degradation of all the airfoils waa

noted, with the authors citing drag coefficient increases of

up to roughly 300* in some cases. Also accomplished in this

•'. s ."" ' ':

teat were better definitions of the boundaries for ice growth

and ice type in terms of static temperature, Mach number, and

liquid water content.

Motivated by a desire to find a relatively simple,

economical means of collecting performance degradation data

relative to rotating systems, Korkan, Cross, and Cornell

(19,2O) and Korkan, Cross, and Miller, (21,22) in 1984

undertook a test program utilizing a model helicopter with a

53.375-inch diameter, 2.5-inch chord NACA 0012 main rotor with

a simulated ice shape attached and measured main rotor

performance degradation. Trends identical to those previously

seen on larger or full-size airfoils and rotors were noted.

11
with increaaea of up to 30OX in torque coefficient found to be

required to maintain a given thrust coefficient after the

addition of the aimulated ice to the rotor blades. The

aenaitivity of the tip region of the rotor to the adverae

effecta of ice formation was alao seen, with an increaae in

torque coefficient required to maintain a given thruat

coefficient of aa much aa 150* measured when the aimulated ice

waa extended from the 85x rotor radial location out to the

10OX- location.

Juat prior to thia model helicopter teat, the iaaue of

Reynolda number effecta on aerodynamic data waa alao addreaaed

by the same authora <2O,22). In a 2-D airfoil teat uaing a

NACA OO12 airfoil section with a aimulated ice formation

i

geometrically identical to that uaed in the model helicopter

teat, the authora collected aerodynamic data for the airfoil

in both clean and iced configurations over a Reynolda number

range which included the operating range of the model

helicopter rotor tip. Reynolda numbera effecta appeared

aignificant only at the highest Reynolda number tested,

3.4 x 1O6.

2. Analytical Effort

Much has been learned in recent years aa a result of

theae experimental programs, and a major contribution of theae

teata haa been in the expanaion of the icing data baae to

provide more current data with which to develop and evaluate

analytical methods for prediction of icing-related performance

degradation. Aa in the experimental area, many analytical

12
advances have also been recently made. These advances have

taken the forms of both better methods of predicting droplet

impingement characteristics as well as better aerodynamic

performance degradation correlations.

Bragg et. al. recently developed a computer program to

calculate water droplet trajectories and thereby determine

airfoil impingement efficiencies and theoretical ice shapes

.(23). Development of this code represented a major step

toward the goal of analytical prediction of airfoil

performance degradation due to ice accretion and the code la

now often used for this purpose. The code itself will be

discussed in more detail in a later chapter as it is one of

.. the major components of the code development which is the

subject.of this report. Along with this droplet trajectory

code, Bragg and Gregorek have also formulated a drag

coefficient correlation for the rime ice condition (16). In

this correlation, the change in drag due to ice is given as a

function of several variables related to flight and

atmospheric conditions, airfoil geometry, and duration of ice

.accretion. This correlation has seen widespread use since its

development and has only recently been studied in any detail

to better define its range of applicability. An unpublished

Investigation performed by this author shows the correlation

to in several cases significantly overpredlct drag increment

, for icing data which appears to be rime-oriented.

. Cansdale and Gent in a 1983 report (24) detailed the

development of another two-dimensional airfoil icing code.

13
Unlike the Bragg code, the effects of compressibility, kinetic

heating, and water runback are taken into account in this

code, thue making it applicable to both rime and glaze ice

conditions. Designed to be applied to helicopter

configurations, the code employs a heat balance analysis to

calculate the kinetic heating and runback effects. The

authors have reported good agreement between predicted and

experimentally obtained ice shapes, temperature distributions,

and icing threshold conditions.

Flemmlng and Lednicer (25) have used experimental icing

data to formulate new rime and glaze ice drag coefficient

correlations. In addition, this data was also used to

formulate separate lift and moment coefficient correlations.

These correlations, recently published in final form (25),

have shown some promise in preliminary evaluations and are

discussed in more detail in a later section.

Using Bragg's droplet trajectory code, Korkan, Dadone,

and Shaw (26) have developed a method for predicting

performance degradation of rotating systems under the

influence of ice accretions. Limited currently to the rime

ice condition, the effects of ice formation on helicopter

rotor or propeller thrust coefficient, torque coefficient, and

efficiency may be calculated. Originally restricted to the

helicopter hover mode, extension of the method to include

forward flight calculations has been performed and documented

in a recent AIAA paper by Korkan, Dadone, and Shaw (27). The

method essentially involves first obtaining non-iced values of
angle of attack and Mach number as a function of radial

location, then determining impingement efficiency and

accumulation parameter for a given set of icing conditions for

, each radial location, and finally determining the resulting

drag increment at each radial location. An existing propeller

or helicopter performance code with the iced drag increment

input .then will produce values of iced performance which may

be compared with,known or calculated clean values to ascertain

.the. degree of performance degradation which results from the

.given icing encounter. Good agreement between theory and

experiment has been obtained for both the propeller and

.helicopter rotor configurations.

Korkan et. al. have also developed a method of averaging

, JC27) to compute rotor or propeller disk performance in which

angle of attack and Mach number are first averaged around the

, disk. From these averaged values, collection efficiency,

accumulation parameter, and finally drag increment are

calculated for given icing conditions. This procedure has

been shown to be virtually as accurate as the previously

described method but provides a significant reduction in the

number of necessary calculations and hence computer run time.

Miller, Korkan, and Shaw in 1983 (28) attempted to

develop a drag coefficient correlation for the glaze ice

condition using statistical analysis of icing data as a basis

of the correlation development. Although a resulting

correlation was presented, it represented only the state of

the study at the time and showed a need for much further

15
modification and analysis. Feasibility of using such an

analysis as the basis for correlation development was

demonstrated, but the results of such an analysis must be

interpreted correctly and in tandem with physical observations

of. the associated phenomenon to make the method truly

beneficial.

Bragg (29) has also recently documented a study in which

he predicted airfoil performance with both simulated rime and

glaze ice shapes. Various codes were examined for possible

use in calculating pressure distributions on an airfoil with

glaze ice attached. The potential flow code of Bristow was

determined to be suitable for this purpose and provided good

agreement between predicted and experimental pressure

distributions. Bragg also investigated the effects of surface

roughness in the laminar boundary layer on drag increment and

offered promising results for predicting drag increase by this

method.

16
:, CHAPTER 3

CODES EMPLOYED

A. Theodoraen Transformation

The firat step In the performance degradation

determination proceaa ia computation of the flowfield about

the airfoil aectlon being investigated. The method used in

this code ia a Theodoraen technique of conformal mapping which

translates the airfoil coordinates to a circle plane and from

that plane determines the velocity distribution about the

.airfoil. The calculations involved in this method make the

assumption of potential flow, in which no viacoua effects are

considered. This haa been found to be an acceptable

assumption, allowing the method to yield accurate results, due

to the fact that viscous effects existing in the boundary

layer near the leading edge of the airfoil have little effect

on droplet trajectory for all but the smallest of droplet

sizes. The magnitude of the Inertia force associated with the

larger dropleta greatly predominatea over any viscous

deflection or interaction phenomena in this region.

This particular flowfield calculation technique ia - ......... . • _

limited to incompressible flow, which ia acceptible aince

compressibility effects on droplet trajectory have been found

to be negligible up to the airfoil section critical Mach

number for all but the smallest of drop sizes. In recent

joint studies between NASA and the Royal Aircraft

Establishment (RAE) (3O), back-to-back comparisons were made

between the impingement efficiency values generated using the

17
incompressible Theodorsen method at NASA and those calculated

i •

using the compressible flowfield code of Garabedian and Korn

for supercritical airfoil sections at the RAE. Good agreement

was observed between the two methods, thereby deemphasizing

any compressibility effects and validating the use of the

Theodorsen transformation in computing the flowfield about

airfoil sections exposed to icing.

Theodorsen'a method makes use of the Karman-Trefftz

transformation to relate the airfoil geometry to a near circle

plane. This particular transformation is used because it has

been found to yield a better near circle for airfoils with

finite trailing edge angles by avoiding any cusp atthe

trailing edge. It is given by the formula

H = nb <z -»-b> * (z -b>

where z is a vector which may define some profile such as an

airfoil section, and z is a vector from the origin, O, to

some arbitrary point on the circle. Here, b represents a

vector directed along.the positive x-axls with length OB',

where B' is a point at which the circle and x-axls intersect.

The value of n is typically just less than two, and it may be

observed that for n=2, the Karman-Trefftz transformation

simplifies to the more familiar Joukowski profile, given by

z = z+ b

2

1 <2>

Finally, an iterative procedure calculates the Fourier

coefficients in the Theodorsen mapping to the exact circle.

18
Using a Newton root-finding scheme, the point in the circle

plane corresponding to a particular point on the airfoil may

be determined and from this the flow velocity at that point

may be obtained given the section angle of attack.

B. Droplet Trajectory Code

'"'.••':'•.'.'.'.' ' '

The droplet trajectory code employed in this analysis

was developed by Bragg (31) in 1980. Using basic theory and

equations developed several years earlier as its foundation,

the code extends the earlier work to include the results of

more recent studies as well as much improved computer

technology. Essentially, the code is used to compute single

droplet trajectories and points of impingement on a given

airfoil, and from these calculations it is able to determine

both-'total and maximum local collection efficiencies as well

as a predicted ice shape if desired.

;.; Again, the initial step in the trajectory calculation

process requires a computation of the potential flowfield

about the airfoil under investigation. This flowfield

information, calculated using the Theodorsen transformation

method described in the previous section, is passed to the

trajectory calculation portion of the code in the form of the

aforementioned Fourier coefficients, which yield the flow

velocity at any given point in the airfoil flowfield for a

specific angle of attack. With this flowfield information

available, droplet trajectories may then be computed.

The trajectory calculation requires solving a

differential equation which results from the application of

19
Newton's Second Law to a water. droplet moving in an air

stream. This equation is given aa : . .

KD =

 CDR <u-i)> i- 1 q

24 Fr8 g <3>

where K and Fr are nondimensional parameters known

respectively aa the inertia parameter and Froude number. They

are given by

18cw (4)

and

Fr= U

. ^g (5)

From Equation 3 a set of four simultaneous first order

ordinary differential equations result, which when solved

yield the droplet trajectory. •

Once the droplet trajectories are known, impingement

efficiencies may then be calculated. Airfoil local

impingement efficiency, &, physically represents a ratio of

airfoil surface droplet mass flux to freestream mass flux, and

is

* « ?LL

da <6>

Here, y. is the initial particle y-coordinate and S is

the airfoil surface arc length from the leading edge to the

point of impact. Figure 3 illustrates graphically the

calculation of &, and Figure 4 shows a typical &-S curve. If

yo is plotted versus S, it may be seen that & is simply the

slope of the yo -S curve at a given point. Total, or overall,

20
collection efficiency of an airfoil ia also an important icing

parameter and is defined by

?':•.. t. "•• --7..E = - 0

(.7)

where ,YQ is -the distance between the initial y-coordinate of

the upper and lower droplet tangent trajectories and h

represents the maximum airfoil projected height. Total

"- V.i. •'.-••••; . ! ' •' • ' • . . -. '..

'collection efficiency is then a ratio of the amount of water

'mass'.collected by the airfoil to the amount in the freeatream

sector which is swept out by the airfoil. Figure 5 exhibits

typical variation of collection efficiencies with radial

(location, .and Figure & is an example of the radial variation

of local angle of attack and Hach number.

Other capabilities exist within the droplet trajectory

code, perhaps most significantly the ability to develop a

theoretical rime ice shape using a time-stepping routine, but

this function is not necessary in the present study and will

not be employed or further discussed here. Although it is

true that the formation of an ice shape on an airfoil will

indeed alter the flowfield about the airfoil, and hence the P

curve for that airfoil, this phenomenon is not considered in

.this analysis because the values of & and E used in later

calculations are taken for the clean airfoil. The importance

of the collection efficiencies will be manifested in the

following section dealing with aerodynamic coefficient

correlations.

21
C. Aerodynamic Coefficient Correlations

Prior to the initiation of the present study, an effort

was made to identify all of the dimensionless parameters

relevant to an icing encounter using Buckingham's Pi Theorem,

with the goal of identifying and/or justifying the use of

certain variables in empirical correlations. The Pi theom of

Buckingham, presented first in 1914, provides a means of

creating a dimensionless variable set from an Initial group of

dimensional variables. The theorem states that any function

of N variables, of the form

f(Pi 'P

a'P3'"-PN

) = °

may also be given in terms of (N-K) dimensionless Pi products,

such that

£<Pi1.Pia....PiI|_K) = O

Here K represents the number of dimensionally independent

quantities necessary to fully express the dimensions of the N

variables, and each Pi term is a dimensionless combination of

an arbitrarily chosen set of K dimensionally independent

variables. The Pi theorem will be used here to

nondimensionalize parameters relevant to an airfoil icing

encounter.

The procedure is initiated by first listing all of the

suspected relevant dimensional parameters. In an icing

encounter, these are taken to be as given in Table 1.

Table 1. Dimensional parameters considered in the ice

accretion process.

22
Symbol . Denotes Units

vc ;,-, T temperature at which ice t

:.. f •-• • .

 ia formed

T reference temperature t

T icing time T

w liquid water content ML

d droplet diameter L '

V freestream velocity LT

•./•:: .:••..'.:<<••:•: •••» . f-. . . -.: •' ice density ' • ' ML~S

ice

P air density ML-~5

' • 31 IT • '

;-.,'ft u. absolute air viscosity ML"1?"1

' ; . c airfoil chord L

-s' o . <t=temperature, T*=time, M = mass, L=length)

Here, ten dimensional variables (N) and four fundamental

dimensions OK) are given. Therefore, N-K = 10-4 = 6 Pi

products will result. It should be noted that although other

parameters such as total and local collection efficiencies are

also thought to be important parameters in an icing encounter,

they are not included in the above variable set because they

are already dimensionless and would not be affected by the Pi

theorem which deals only with dimensional quantities. They

can, however, be added to the final list of nondimensional

variables which will result from the use of the Pi theorem.

Certain other physical characteristics of the airfoil

which may affect ice accretion and resulting aerodynamic

23
performance losaea, namely leading edge radius of curvature,

airfoil thickness, and camber, are not included in the above

variable set even though they are dimensional quantities.

This is because the only seemingly meaningful way to

nondimenaionalize these terms is with respect to airfoil

chord, so that for the purposes of this analysis it will be

assumed that these parameters are all initially

nondimensionalized by chord and hence are hot Included in the

variable set. Instead they may be added to the list of

nondimensional variables at the conclusion of the application

of the theorem if desired.

It may be noted that the chord term makes its influence

felt in the nbndimensionalization of these airfoil geometry

terms, and has also been included in the dimensional variable

set* to allow -for the possible development of dimensionless

terms which will be consistent with or similar to

dimensionless quantities already in existence. For example:

V wT

AC = O (Accumulation Parameter)

.

 PiceC

 .

KQ = f<K,Ru> (Modified Inertia Parameter)

where

18cW

R = Vaird

u

u.

The next step in the procedure is to formulate a K set

of four (equal to the number of fundamental dimensions)

24
dimensionally independent, variables, from which .the Pi

products .will be developed. To form the set, any four

variables may be chosen from the dimensional variable list,

with the restriction that they may not themselves combine to

form a dimensionless combination. A K set consisting of

K = <T, T, w, Vo >

is initially chosen. With this K set, the six resulting Pi

products are;

Pii = f (T, T, w, Vo , To >

f ' •..-•'.•-• Pifi = .£ (T, T, w, Vo, d> • • . -

Pi. = f (T, T, w, Vo , P. ) ' 3 ice

PiH = f<T, T, w, Vo,

,PiB = f (T, T, w, Vo , W)

Pi4 = f (T, T, w, Vo , c)

To create nondimensional terms from these sets, the

following procedure, as illustrated by an example using Pi ,

is employed. The Pi product is first written as a product of

all of its terms, each raised to some power.

Pij = (T) <T)a <w)b <Vo)C (To)d

It is then rewritten in terms of the fundamental dimensions

involved:

Pi = (t) <T)a <ML~3)

b<LT~1)C(t)d

25
For this product to be nondimensionalized, all of these '

dimensions must go to zero, i.e., the exponents on each '

dimension must sum to zero.

t: 1+d =0

T: a-c = 0

M: b = o

L: -3b+c = O

This set of equations is then solved for a, b, c, and d.

d=- l b= O c= 0 a = O

The Pi product is then rewritten with these values included.

Pit = (T) (To)'1 = ( T ) .

To

which is the first dimensionless quantity.

Likewise, the other Pi products are found to be

v T Pia

w

. P .ice

Pair

Pis = wVo8

M.

Pi&

The resulting set of dimensionless variables as

determined by the Pi theorem is then

f<t/To, VoT/d, w/P. , wVo8/U, VoT/c) = O,

ice

26
or in the case of predicting drag coefficient change due to

these variables,

f (T/To , .... .... . . . . , Vo T/c) = ACT,

d

At this point, any other dimensionless variables such as

collection efficiencies or airfoil geometry terms may be

included in the equation of desired. The user may then apply

some correlation development technique to determine the exact

relationship between these dimensionless variables and the

associated dependent variable(s).

It may be demonstrated that the resultant set of

dimensionless variables is dependent on both the set of

dimensional variables which is used and on the K set which ia

Initially chosen. Since there are a finite number of ••

dimensional variables and a finite number of K sets which can

'.'.-!••- .

'be chosen, there will be a finite number of dimensionless

variables which will result for a given problem. However, not

all of these variables will necessarily be produced by one K

set. For the icing encounter problem discussed here, this can

be illustrated by choosing a second K set:

K a ( T, w, c, Vo )

This particular K set is especially noteworthy for the icing

encounter problem since it contains parameters which are

thought to be of primary importance in the ice accretion

process: temperature, liquid water content, freestream

velocity, and airfoil chord length. The Pi products for this

set are:

27
Pit = f<T, w, c, Vo , To)

Pia = f<T, w, c, Vo , T)

Pi3 = f <T, w, c, Vo, d)

- PiH = *<T, w, c, Vo.,. Pice>

PIS = f<T; w, c, vo, Pair>

Pi4 = f(T, w, c, Vo, ix > "

Following the procedure previously outlined for

nondimensionlizing these products, the resultant set of

dimensionless variables is:

f<T/To, VoT/c, c/d, w/P. , w/P . , wcVo/W) = 0,

. , . ice air

which differs somewhat from the set produced by the other K

set used. So for any given problem it is necessary to

consider all of the possible K sets to obtain a complete list

of dimensionless variables which may be produced. Knowledge

of the physics of the problem under consideration should then

provide a starting point in the analysis of these variables as

they relate to the given dependent variable(a).

In the icing encounter problem, it was desired to use

the Pi theorem to provide some justification for the use of

the terms AC and Ko, previously defined, in the development of

a glaze ice drag coefficient correlation. Although the Pi

theorem does not produce these terms directly, it does provide

the following dimensionless terms:

28
< 1) Vo T/.c

<2) w/P

ice

(3) PiceV0d

<4) d/c

M.

. -i .... . • .• . '

; •/.:- -i- it may be noted that AC is simply the product of terms

(!') 'and '(2). Ko is a function of K, the product of terms (3)

and (4) , and R , which is identical to term (5) , e.g. ,

-

AC = OT w

4ice

-.-.-.. .--. -; :--p.i . V d P V d

K = ice O d_ = ice 0

H

1 c M>c

(3) (4)

R = PairVAd

u o

•';'•' • ' ' : P.

(5)

; : Should the reader wish to verify that these terms are indeed

obtainable from the original set of dimensional variables,

they can be found as follows:

. (1) - from K set (T, T, w, Vo)

(2) - from K set (T, T, w, Vo)

(3) - from K set (T, d, Vo, P. > ice

(4) - from K set (T, w, c, Vo>

(5) - from K set (T, d, Vo, P >

d 1 IT

29
It can be seen that the Pi theorem does indeed provide

some justification for the use of the variables AC and Ko in

developing a correlation, and any correlation which does

result will be in terms of dimensionless variables obtainable

by Buckingham's Pi theorem.

At present, the only means available for analytically

determining performance degradation of an airfoil in terms of

its .aerodynamic coefficients is through the use of empirical

correlations. As previously indicated, several individuals

have attempted development of one or more of these

correlations and generally have met with only limited success

in terms of accuracy and range of application. Incorporated

into the present study are the two correlations currently most

widely used to predict drag increment, as well as a aeries of

new correlations. These empirical correlations represent only

an interim solution to the problem of assessing aerodynamic

performance losses due to ice formation. A potentially more

precise solution technique currently under development

involves a Navier-Stokes solution for the flowfield around an

iced airfoil (32).

1. Gray Correlation

The first correlation, formulated by Gray (14) roughly

twenty years ago is of the form

AC=[8.7 x 10~S Tu WB <32-To)°"J] (1+6 {l + 2.52r°-i sin1* 12*)

D c~ max

30
sin2

 C543 w < E )i /J - 81 * 65.3 ( 1 - 1 )3

... 32-To 1.35*1 1?35*

^0.17 sin* Ilex) > (8)

;: , r • ' '

where here AC . represents the actual numerical value of drag

coefficient increment; i.e., AC, = C.(iced>- C,(clean). As

" • • ' • • a a a ..

can be seen, this correlation involves combinations of various

dimensional parameters, and the dimensionlesa total and local

-collection efficiencies calculated in the droplet trajectory

code'previously discussed also appear. This correlation also

has the capability of computing drag coefficient increment at

'angles of attack other than that at which the ice was formed,

through the use of the ex and ex terms. Here et. represents the

angle of attack at which the experimental data was taken, or

the angle at which the effects of the ice accretion are to be

evaluated, and o< represents the angle of attack at which the

ice was formed.

The dimensional variables have not in all cases been

grouped so as to form dimensionless quantities, and this has

evoked some criticism by various persons since the

correlation's development. This criticism is based on the

idea that any correlation which involves dimensional

'•••>• •

quantities will be to some extent a function of the data set

from which it was formulated. Thus, if the correlation was

applied to some other set of data in which the range of one or

more of the relevant parameters differed from that of the

original data aet, the variable affected may have an undue

31
effect on the prediction which waa not accounted for in the

original, limited data set. Indeed, aa ia aeen in Figure 7,

Gray'a correlation haa been found to predict quite poorly for

much of the recently generated NASA glaze ice data, which ia

typefied by significantly higher liquid water content valuea

than are found in the data aet uaed by Gray in developing hla

correlation. Nevertheless, since no other glaze ice drag

coefficient existed until quite;recently, Gray'a correlation

still sees widespread uae and haa been included in this

program aa an option available to the uaer.

Because Gray's correlation accounts for only changes in

drag coefficient, modification of C haa been added to take

into account the decambering effect of ice accretion.

max

resulting in a ahift in the C -at curve and a decreaae in C

i

due to flow separation on the airfoil upper surface. Trial

valuea teated by the author have indicated that reducing C to

95X of its clean configuration value yields an acceptable

approximation for iced C . This factor is incorporated into

the present study for both Gray's and Bragg's correlations.

2. Bragg Correlation

A correlation has been developed by Bragg (16) for the

rime ice condition. It has the form

AC_, = O.01 (15.8 ln(k/c) «• 28000 A E * I) (9)

d . • c

where Ac is accumulation parameter, given by

Ac = uwf

4 c (1O)

ice

32
,,, and I repreaenta a drag constant which variea according to

airfoil type ae shown in Table 2.

Table 2. Conatanta in Bragg Drag Coefficient

Correlation

Airfoil Type Drag Constant. I

NACA 4 and 5 digit 184

NACA 63 aeriea 218

NACA 64 aeriea 232

NACA 65 aeriea 252

NACA 66 aeriea 290

•-•• ' *•'•',-'., ' " " ' ' • ' ; ...

In thia correlation, AC . repreaenta a fractional change

d

in, rather than an actual numerical value of, drag

••# - T- . •.. - v , . , . .

coefficient. Here AC, may be uaed to find the iced airfoil

drag coefficient uaing

Cd = (lfACd>Cd (11)

iced clean

'•' - 3. . 5 . Previoua studies of thia correlation applied to NACA and

NASA 2-D icing data have indicated a atrong tendency for the

correlation to overpredict drag increment. Because the

predictiona are commonly off by a relatively conatant

percentage with reapect to the Neel and Bright propeller

performance data, a factor waa Introduced which reducea the

degree of drag coefficient increase calculated by the Bragg

correlation. Replacement of the initial conatant in the

equation, O.01, by O.OOO8 produced much more acceptable

predictiona and waa therefore incorporated into the preaent

analyaia.

33
Bragg has also recently proposed a new, modified form of

his correlation (33) which has also been included in the

present study. This new form of the correlation given below,

appears to work well for the cases examined to date, but it

has not yet been applied to the 2-D NACA and NASA icing data

with which the other correlations were tested.

AC. = O.O1 (15.81n(k/c) + 1171 AcE •* I) (12)

d

3. Flemming Correlations

The third correlation, or more precisely set of

correlations, are those developed by Flemming (25). Whereas

Gray and Bragg dealt strictly with drag coefficient

correlations, Flemming has also formulated correlations for

lift and moment coefficients for both glaze and rime

encounters. These correlations are of the forms:

For a glaze ice encounter,

AC_, = KD..C.OO686 Ko ( t/c) * "S (<*+6) - .O313(r/c)2 «-KD( .OO6)M2 "H ] d »

[WTC,(_C >°'2/(_c )* *2] C1-8AC / (Vhelo)] (13) £j

.1524 .1524 278

For a rime ice encounter,

AC., = C.1581n<k/c)*175< V )«T E + 1.7Q] (<*•••&) d . — c

P4 c 10

ice

[1-8AC '(Vhelo)3C . (14)

278 clean

and for both glaze and rime encounters,

AC. = <-.6i335Ko (t/c) [<x+2 + KL, < .OO555) (<x-6) 8]KL] CWT

i 1 C

(_c__)° • 2/(_c__) 1 '2] (15)

.1524 .1524

34
and . , .

ACm = [<.00179-.OO45M> (.O0544>Ko*/<t/c>2 '7 +

.OO383M<l-63.29r/c>3 (16)

EU)T < c

c

.1524 .1524

'where Ko la the modified inertia parameter, given by

Ko = KC1+.0967 R •

&I97> (17)

and KL, KL4 •', and KD, and KD4 are functions of temperature and

angle of attack and are defined within the subroutine.

These correlations were developed using data obtained in

a series of tests conducted in the Canadian National Research

Council's High Speed Icing Wind Tunnel in late 1982. The ten

airfoil scale models tested, with typical chords of roughly

six inches, were designed primarily for use in helicopter

applications and cover a wide range of helicopter airfoil

shapes. For correlation development purposes this range

should enable the resulting correlations to adequately account

for airfoil geometry as a factor in aerodynamic coefficient

increments due to icing.

The correlations are, however, dimensional in nature and

again were developed using model data for high speed

applications. The full effects of these two items on the

range of applicability of the correlations remains to be seen.

The correlations have been found in a recent study to

underpredict AC . in many cases however. In spite of this,

35
Flemming'a correlations still hold promise and do in fact work

well in many cases.

4. Miller Correlation

A fourth general drag coefficient correlation

development has been attempted by Miller, et. al. Described

in detail in Reference 28, this effort used as the basis for

the correlation formulation the method of statistical analysis

as applied to a set of experimentally obtained icing data.

Although a correlation was presented in Reference 28, it

represented only a status report and not a final result.

Further study and modification of this correlation is

, necessar,y before it may be deemed useable, and no

modifications made to date have proven satisfactory. The

method of statistical analysis is a powerful tool in

correlation in development and should yield greater success at

some future date, but because the present form of the

correlation is not acceptable in terms of accuracy of

prediction it will not be incorporated into the code.

•-,'"'•/--. . . •

So there are presently available three correlations or

sets of correlations which are integrated into the code. They

provided values of drag, lift, and/or moment coefficient

increment for both glaze and rime ice encounters. These

increments may then be passed to a propeller performance code,

described in the following section, to evaluate the ensuing

propeller rotor performance degradation.

36
; D. Propeller Performance Code • -

 r ' • • . . 7 : - " 1. . :-

The, propeller performance code which is integrated into

the performance degradation program ia based upon a linearized

inflow propeller strip analysis, developed by Cooper (34) in

1957,. Strip analysis involves the calculation of aerodynamic

forces at selected spanwise blade locations for a, given

operating condition and propeller geometry. From these

differential forces, given in terms of thrust and torque

coefficients by

dCT = k £ M 8 (C. COS4--C .sin*-) (18)

, - D x A d '

where k= 9OOa8 b (19)

N»D»

and

dx 2 dx C. cos*- C .sin*

* d

thrust and torque coefficients may be obtained by integrating

these terms along the blade. Propeller efficiency and power

absorbed may then be calculated by

p \f p D = j :u_ = <__) IT _ <2i)

C nD 21TC

p Q

and

BMP =

 Cp Pt)?D' (22)

550

Cooper's propeller performance analysis is unique due to

the fact that it assumes, or actually approximates, a linear

induced flow distribution on the propeller blade. Typically

37
an iterative process is required to obtain the induced angle

of attack and" lift coefficient at a specific radial location

since they are interrelated. However, Goldstein (35) has

solved for the radial distribution of circulation for a

lightly loaded propeller having a finite number of blades and

has established the relationship between ff C, and ot . Cooper

has then approximated the 9 C. - e* curves by straight lines

and has plotted the slopes of these lines versus advance ratio

for various spanwise locations. From these plots, and using

available aerodynamic data, it is then possible to determine

values for an induced angle of attack. When experimental and

analytical results obtained using this method were compared,

agreement to within three percent was seen for over ninety

percent of the cases investigated.

38
CHAPTER 4 ,

PERFORMANCE DEGRADATION CODE ASSEMBLY

• •.,- In order to integrate each of the codes involved. into a

single performance degradation code, heretofore known as

ICEPERF, several .phases of modifications were required. These

modifications were relatively minor in that they did not

change the basic functions, operation, or logic of any of the

codes but rather served to make the transition from one

section to the next more simple and automatic. This

automation then eliminated the necessity of any user

.intervention in the run stream.

The user-friendly nature of the code was a primary

objective of this effort, and although several files are

necessary to run the code very few changes are required from

one run to another, for the same airfoil. The various

components of the code were selected on the basis of

availability and accuracy of results. Each component was run

and tested separately and extensively to demonstrate its

capability to consistently function properly, and all

displayed good performance in these runs. Also of importance

in the component selection and modification was a desire to

maintain a high degree of modularity in the code, such that a

different flowfield computation, new correlation, different

propeller analysis, etc. could be inserted with a minimum of

changes to the code. This also permits the code, now applied

to propellers, to be relatively easily extended to a

39
helicopter configuration. A flowchart denoting the current

major elements of the program is provided in Appendix 1.

The firat phase in the code integration process involved

combining the flowfield and droplet trajectory codes

previously described. Because the droplet trajectory code was

designed to operate using much of the output from the

Theodorsen transformation code, this step was relatively

straightforward. The modified code has been set up to handle

a maximum of four input propeller radial locations, and

current runs of the code have been made with four input

stations, at the 3O, 5O, 7O, and 9O percent radial locations.

An investigation of the benefits of using more input stations,

offset by the additional cost due to the extra run time

required, has not yet been performed.

Next, a set of subroutines was created to predict drag

increment due to ice accretion, given the appropriate

impingement efficiency values output from the trajectory code.

The AC. correlations of Gray, Bragg, and Flemming are included

in the subroutines, with Flemming'a correlation also being

capable of determining lift and moment coefficient increments.

The user may select any of these correlations in each run of

the program, and the choice of correlation should be dependent

on the type of ice formation expected for a given input

condition.

The correlations of Gray and Bragg use values of total

and maximum local collection efficiencies in computing drag

coefficient increment. One value for each of these parameters

40
is generated for each radial location input, so that a maximum

of four sets of collection efficiencies are available as

output from the trajectory calculation section. However, it

is best when using the propeller performance code to include

considerably more input radial locations in the calculations

(eleven stations are used in the analysis of a propeller

utilizing double-cambered Clark-Y airfoil sections which

follows in Chapter 5). In order to obtain values for drag

coefficient increment at each of these locations, the

collection efficiencies at these stations must be known.

Rather than running the Theodorsen transformation and droplet

... trajectory codes eleven times to obtain collection efficiency

values at each of these stations however, a curve fit routine

is employed which takes the values computed at each of the

four input radial locations and fits a curve through them.

Flemming's correlations compute values of collection

efficiencies empirically, so that it is not necessary to run

the Theodorsen and droplet trajectory sections of the code if

Flemming's correlations are to be employed.

In this code, a cubic spline fit routine is used to fit

separate curves for total maximum local collection

efficiencies between the 30H and 90* radial locations, or

between the two most extreme sections input by the user. This

method has been found to yield good results due to the fact

that the .collection efficiencies are both smooth, continuous

.functions or propeller radial location. Due to the nature of

the spline fit routine, it is applicable .only between the

41
innermost and outermost radial locations input. Outboard of

the outermost input station, and inboard of the innermost

station, some other technique is required to compute values

for the collection efficiencies as a function of radial

location. In this analysis a linear fit, computing the slopes

at the endpoints of the spline fit and extending straight

lines inboard and outboard of these endpoints, is used to

approximate the curves where the spline fit is not. applicable.

With this method, values for both total and maximum local

collection efficiencies are available for any radial location.

Cooper's propeller performance code has been utilized to

calculate values of propeller thrust, torque, and efficiency

for a given condition. The previously mentioned drag

increment subroutines have been incorporated into the

propeller performance code to modify the drag coefficient and

values used by the code in computing iced propeller thrust and

torque. In Equations 18 and 2O, the C. and C. terms are

A d

modified by the factors (1 + AC,) and (1 + AC .) respectively, such

that

C = C (clean)- <1 +AC ) (23)

* ft A

and

C =CJ<clean) *(1 +AC.) (24)

d d d

so that iced propeller thrust and torque coefficients as well

as propeller efficiency may then be computed. The code first

calculates clean, or non-iced, values for these quantities,

and then calculates using the user-selected aerodynamic

42
coefficient correlation the iced valuea for theae aame

parameters. Varioua input parameters have been altered or

omitted from the original code to make it more conducive to

the purposes pf the present program, but the esssence and

mechanics of the code remain unchanged. ..

The entire code then operates by first.computing clean

propeller performance values for one advance ratio. Next, the

Theodorsen transformation is performed, or previously

calculated results^ are read for the first input radial

location. The droplet trajectory section then computes

impingement efficiency values for the radial location using

the flowfield from the Theodorsen transformation and a section

angle of attack computed in the propeller performance section.

Impingement efficiencies are then calculated for the remaining

input radial stations following the same procedure. The code

spline fits the impingement efficiency curves and computes

using these values and the selected aerodynamic coefficient

increment correlation the iced propeller performance data.

This entire procedure is then repeated for each additional

advance ratio input.

43
CHAPTER 5

RESULTS

In the Neel and Bright teat, a C-46 twin-engine aircraft

was used to obtain propeller efficiency losses as a result of

ice formation. Ice was allowed to form on the propeller of

the right engine while the left engine propeller was kept

clean. Following this procedure, data was recorded for twelve

natural icing encounters and typical efficiency losses of four

to ten percent were noted. The propellers on the C-46

utilized double-cambered Clark-Y airfoil sections, for which

airfoil coordinates used in ICEPERF were obtained from Borst

(36) .

The Neel and Bright experimental data provided a data

base with which to evaluate the ICEPERF iced propeller

performance code. For ten of the twelve encounters documented

in the test program report (Table 3), calculations were

performed for the propeller in both clean and iced

configurations. Results and comparison of analytical and

experimental performance values are here presented for each of

the three correlations employed, specifically those of Bragg,

Gray, and Flemming. It should be noted that in all

performance calculations presented in this report,

consideration was given to the radial extent of icing such

that no ice was allowed to accrete analytically outboard of

the experimentally observed radial icing extent. These

results therefore differ from previous calculations shown by

44
this author (37) in which.no restriction was placed

analytically on the radial extent of icing.

The results presented in this paper may also be compared

directly with calculations performed by Korkan, et. al (27).

Their work involved generation of propeller performance

predictions for the Neel and Bright data as well, using the

Theordorsen transformation flowfield code, Bragg droplet

trajectory code, and Cooper propeller performance codes

separately. In this initial study by Korkan, et. al.,

pressure altitude was input and the standard atmospheric

pressure, temperature, and density were then used in the

calculations rather than the experimentally obtained values

for these parameters. The use of actual flight conditions, as

employed in all calculations presented in this report, was

found to alter the computed thrust and power coefficients by

roughly one percent. Potential differences in blade angle

specification from study to study may also have a significant

impact on the predictions. Finally, the initial constant in

the original Bragg correlation was decreased in both studies

%

in an attempt to produce reasonable performance values. This

then introduces additional variation between the corresponding

iced calculations.

Clean performance predictions were found to agree well

with the experimental data for all of the encounters

investigated. (Tables 4-6 summarize the analytical and

experimental data for Encounters 2, 7, and 12 respectively.)

In all cases, calculated thrust and power coefficients were

45
found to agree with the corresponding experimental values

within an average of 12.5 percent. C_ and C for a given

encounter and advance ratio tended to be underpredicted by

roughly the same percentage, so that resulting propeller

efficiencies compared with experimental measurements to within

six percent. Since propeller efficiency is essentially a

ratio of thrust coefficient to power coefficient however,

errors of similar magnitude in C_ and C should then cancel so

that the resulting efficiency values would be much less

sensitive to error in performance calculations and would not

be as good an indicator of analytical prediction accuracy.

Therefore statements herein relate primarily to thrust and

power coefficient calculations rather than propeller

efficiency.

The results shown in thia report all involved use of the

actual blade angles as measured and reported in the

experimental test program. It was found however that by

increasing the reported blade angle setting by 0.7 degrees,

much better agreement between theory and experiment could be

obtained for all encounters. Figures 8-10 are illustrations

of the effect of blade angle variation on clean thrust and

power coefficients for Encounter 2. This anomaly could be an

indication of a deficiency in the performance calculations,

but because a constant increase in blade setting produces much

better correlation with experiment for several encounters over

a range of flight conditions, it more likely signifies the

existence of a bias error in the experimental measurement of

46
blade angle. Theae calculations serve also to indicate the

sensitivity of propeller performance predictions to propeller

geometry.

The code was found to often overpredict the clean

propeller efficiency at the higher advance ratios.. Typically,

performance predictions agreed with experiment to within a.few

percent at the lowest advance ratios and gradually worsened to

the point where they were often off by roughly twenty percent

at the highest advance ratios investigated. It is postulated

that this may be due to an inability of the code to adequately

account for compressibility effects, which become more

significant as advance ratio increases (via increased forward

velocity for a fixed rpm>. This effect should be studied

further in subsequent efforts.

When the restriction on radial icing extent was imposed

in the present study's calculations, better agreement with the

experimental data was obtained than was previously presented.

Currently there is no mechanism in the code for determining

the actual radial icing extent. Rather, the user must specify

the desired or assumed radial location inboard of which iced

calculations are to be performed. In this study, approximate

radial icing extent for each encounter was reported by Neel

and Bright and these values were then input for the iced

performance calculations. The following discussion details

results obtained by each correlation for the several

encounters investigated.

47
A. BRAGG

Two forms of Bragg'a basic rime ice correlation are

available in ICEPERF, aa discussed in a previous section. The

first of these is a modified form of Bragg's original

equation, in which the leading constant was changed from O.O1

to O.OOO8 in an effort to produce more realistic drag

coefficient increments. This change was made after initial

runs of the code indicated that the original equation was

producing quite unreasonably large performance changes due to

ice formation, as a result of inordinately large predicted

AC values. The O.OOO8 constant was arrived at by bestfitting the correlation's performance predictions to Encounter

2 data and was then found to perform acceptably for the other

encounters as well. Future use of the correlation may suggest

additional modifications of this constant.

This modified form of Bragg's original correlation was

then applied to all of the available Neel and Bright data

regardless of assumed rime or glaze ice type, as was Bragg's

new form of the correlation. Reasonably good agreement

between experiment and theory was obtained using both

correlations for all encounters. In all cases the original

but modified Bragg correlation produced more accurate results

than did the newer correlation, but the differences were

generally small. The fact that the newer, unmodified

correlation gave results almost as accurate as those of the

older form which was specifically modified to better fit the

propeller data indicates that the changes made by Bragg in

48
forming the new correlation improved the quality of the

correlation significantly. Both correlations handled the lesa

severe icing encounters (icing extents below 60* > well (i.e..

Encounter 7, Figures 14-16), much better than did the Gray or

Flamming correlations. In the most severe case however

(Encounter 12, Figures 17-19) both correlations seriously

overpredict the degree of degradation, especially in terms of

C , and produce C -J curves which inflect upward at the lower

P P

advance ratios rather than downward as would be expected.

It should also be noted that Bragg'a equations are for

AC. only. Lift coefficient will also generally decrease as a d •• . '

result of ice formation at the leading edge as the flow there

is spoiled to some extent, but this is not accounted for in

the Bragg equations. A factor was therefore introduced to

provide a simple representation of this phenomenon by

assigning the iced section lift coefficient a value equal to

95* of its clean value. Although this seems to be a

reasonable typical value for AC., it would be desirable to

incorporate a more discriminating form of determining AC. in

future calculations.

B. GRAY

As was the case with the Bragg correlations, the Gray

correlation also provides its most accurate performance

predictions when radial icing extent is small. It is

difficult to make any Inference regarding the quality of the

correlation under such conditions due to the fact that the

49
propeller Is loaded moat heavily at the tip and its

performance will be moat sensitive to geometry changes (i.e.,

ice accretions) in the tip region. Farther Inboard, even

"quite severe ice growths will have much less effect on the

overall performance and consequently any correlation,

regardless of how great its predicted AC. values may be, will

appear to work well in low radial icing extent cases. Thus

the true measure of the quality of these correlations comes in

the more severe icing encounters such as Encounters 2 and 12.

In these two encounters, as can be seen in Figures 11-13 and

17-19, the Gray correlation fails to accurately predict the

iced performance, yielding values which overpredict the degree

of degradation. Indeed, upon examining the actual AC . values

predicted by Gray for Encounter 12 it was found that this

correlation was predicting drag coefficient increases of

typically 3OOH at lower advance ratios to as much as 6OOOX at

the outer stations at high advance ratios. The Gray

correlation, like that of Bragg, also predicts only drag

coefficient increment, so the same five percent reduction in

C. for the iced configuration was again employed when Gray's

correlation was used. The Gray correlation itself was

unmodified for use in this study, and it is likely that

introducing some constant into Gray's equation to affect a

constant percentage decrease in its calculated AC , values, as

was done with the original Bragg equation, would greatly

5O
improve its ability to calculate iced drag coefficient

increment and hence iced propeller performance.

C. FLEMMING

The Flemming correlations were applied twice to each

encounter, once with icing restricted by the user-input value

and then allowing the Flemming correlations to predict the

radial icing extent. The second runs were performed to check

the no-icing capability of the correlations and to ascertain

.whether this capability would properly reflect existence of

ice. under the influence of 3-D, rotating forces (kinetic

heating and shedding). Instead of properly predicting radial

icing extent however, this feature dictated no icing in the

first 30* of propeller radius for any encounter, and then

overpredicted the radial icing extent outboard of the 30x

station for eight of the ten encounters (Table 7).

In the case of the user-input icing extent, the no-icing

problem manifests itself in an underpredictlon of the

propeller performance degradation for all encounters. As the

figures illustrate, many of the Flemming-predicted iced thrust

and power coefficient values are identical or virtually

identical to the clean values, indicating analytically little

if any degradation. While these results may appear reasonable

at first glance in cases where the actual degradation ia

minimal, they actually serve only to mask the underlying

problem and reason for the negligible degradation prediction.

It should also be noted that in Figures 11 through 19, in

cases where the clean theoretical curve is not easily visible,

51
it has been hidden by the Flemming correlation curves which

are often virtually coincident with the clean data curve.

When no restriction is imposed upon radial icing extent,

Flemming's correlations still tend to underpredict the degree

of iced performance degradation in several cases. This occurs

even though Flemming's correlations predict more extensive

icing radially than was seen experimentally, which would

indicate that the percentage decreases in thrust and power

coefficients predicted by Flemming are actually smaller than

the experimental values. For the encounters in which the nonrestricted Flemming correlations do predict C_ and C well,

the predicted radial icing extent is always greater than the

measured extent, sometimes by as much as 60%.

It would therefore appear that the Flemming correlations

have two significant deficiencies. The first of these is the

no-icing calculation which has failed in this study to

properly indicate either ice existence or icing extent. In

fairness to the correlations it should be pointed out though

that various forces not stressed in the 2-D correlation

development (i.e., centrifugal forces leading to ice shedding)

may have a significant effect on the radial icing extent, and

in only one out of ten encounters did the Flemming

correlations actually underpredict the extent of ice. The

second apparent shortcoming of the correlations is the

underprediction of section drag and possibly lift coefficient

increments. This same trend toward underprediction of section

C has also been seen in application of the Flemming

52
correlationa to available NACA and NASA 2-D icing data in a

separate study (38).

53
SUMMARY AND CONCLUSIONS

Application of the ICEPERF code to the Neel and Bright

experimental data baae has provided much insight into the

code's performance prediction capability for both clean and

iced configurations. The code has been shown to run properly

and to produce realistic thrust and power coefficient values,

especially when radial icing extent is known and input. As a

result of this study several areas of future development and

potential improvement, discussed in the following paragraphs,

have been identified.

Currently restrictions and simplifications exist within

the code which, if removed or modified, should yield better

performance evaluations. Development of a AC correlation to

be used in conjunction with the Bragg or Gray correlations

would provide a more precise and complete representation of

the effects of ice formation on section aerodynamics.

Secondly, incorporation of some computational mechanism of

predicting the transition from rime to glaze.ice, or vice

versa, on the blades would enable the code to use the proper

correlation at each radial computational station, rather than

assuming all rime or all glaze ice in any given encounter.

Because of the generally moderate radial icing extent and only

slight degree of ensuing degradation, this change will

probably have only a very minor effect on the predicted

propeller performance. This is in contrast to the helicopter

rotor icing situation in which radial icing extent and the

54
related performance degradation are typically more severe for

a given icing condition.

Another potential area of improvement liea in the

accuracy of the experimental data used for comparison with

analysis. One such area with respect to the Neel and Bright

data is the actual radial icing extent for each encounter. As

specified in the report, the true extent is somewhat unclear

and may possibly vary by as much as 2Ot. Values of radial

icing extent presented in this report represent a best

estimate of the extent as interpreted from the Information in

Neel and Bright's report.

The present study has also provided insight into the

type and accuracy of experimental data which would be

desirable in future test programs. Additional propeller icing

data of any type would be useful in further validating and

analyzing the code at the present time. Future tests though

should include, in addition to flight and atmospheric

parameters and icing time, specification of icing extent as

accurately as possible. Also desirable would be some

photographic or other indication of the ice type so that the

proper correlation could be applied at each radial location.

Finally, sensitivity of propeller performance to blade angle

setting also has indicated the need for quite accurate blade

angle measurements. Certainly it is desirable to have a high

degree of accuracy in the thrust and power measurements as

well.

55
With respect to the empirical lift and drag correlations

used in this code, results obtained in this study concurred

with previous work done involving these correlations in

indicating deficiencies which exist in each correlation.

Overall, 'the Bragg correlation(s) produced the moat reasonable

iced propeller performance predictions but overprediction of

drag coefficient increment by Bragg'a correlation(s) remains a

problem, as illustrated in the more,severe icing encounters.

Overprediction also remains a problem with Gray's correlation,

whereas Flemming's correlations typically underpredict the

aerodynamic coefficient increments. It is evident then that

much more 2-D validation of all these correlations is

necessary before iced propeller performance can be predicted

consistently using this method and before results of this

analysis can be fully evaluated. It should be realized that

any ultimate analytical treatment of ice accretion on rotating

systems will potentially involve much less empiricism than is

currently required and that the use of these correlations

represents an interim approach to the problem, which will

continue to be used until more aophiaticated analytical

procedures such as Navier-Stokes or interactive boundary layer

analyses of iced airfoil flowfielda become available.

56
REFERENCES

1. Corson, B. W. and Maynard, J. D., "The Effect of

Simulated Ice on Propeller Performance," NACA TN 1O84,

1946.

2. Preston, C. M. and Blackman, C. D., "Effects of Ice

Formation on Airplane Performance in Level Cruising

Flight," NACA TN 1598, May 1948.

3. Neel, Jr., C. B. and Bright, G. L., "The Effect of Ice

Formations on Propeller Performance," NACA TN 2212,

October 1950.

4. Gray, V. H. and von Glahn, U. H., "Effect of Ice and

Frost Formations on Drag of NACA 65t-212 Airfoil for

Various Modes of Thermal Ice Protection," NACA TN 2962,

June 1953.

5. Gray, V. H. and von Glahn, U. H., "Aerodynamic Effects

Caused by Icing of an Unswept NACA 65AO04 Airfoil," NACA

TN 4155, Feb. 1958.

6. Brun, R. J., Gallagher, H. M., and Vogt, D. E.,

"Impingement of Water Droplets on NACA 65i-208 and 65i -

212 Airfoils at 4 Degrees Angle of Attack," NACA TN 2952,

May 1953.

7. Brun, R. J., Gallagher, H. M., and Vogt, D. E.,

"Impingement of Water Droplets on NACA 65A004 Airfoil and

Effect of Change in Airfoil Thickness from 12 to 4

Percent at 4 Degrees Angle of Attack," NACA TN 3047,

November 1953.

57
8. Brun, R. J., Gallagher, H. M., and Vogt, D. E.,

"Impingement of Water Droplets on NACA 65AOO4 Airfoil at

8 Degrees Angle of Attack," NACA TN 3155, July 1954.

9. Brun, R. J. and Vogt, D. E., "Impingement of Water

Droplets on NACA 65AOO4 Airfoil at O Degrees Angle of

Attack" NACA TN 3586, November 1955.

10. Gelder, T. F., Smyera, Jr., W. H., and von Glahn, U. H.,

"Experimental Droplet Impingement on Several TwoDlmensional Airfoils with Thickness Ratios of 6 to 16

Percent," NACA TN 3859, December 1956.

11. Bergrun, N. R., "An Empirical Method Permitting Rapid

Determination of the Area, Rate, and Distribution of

Water-Drop Impingement on an Airfoil of Arbitrary Section

at Subsonic Speeds," NACA TN 2476, September 1951.

12. Lewis, W. and Bergrun, N. R., "A Probability Analysis of

the Meteorological Factors Conducive to Aircraft Icing in

the United States," NACA TN 2738, July 1952.

13. Gray, V. H., "Correlations Among Ice Measurements,

'Impingement Rates, Icing Conditions, and Drag

Coefficients for Unswept NACA 65AOO4 Airfoil," NACA TN

4151, February 1958.

14. Gray, V. H., "Prediction of Aerodynamic Penalties Caused

by Ice Formations on Various Airfoils," NASA TN-D 2166,

February 1964.

15. Shaw, R. J., Sotos, R. G., and Solano, F. R., "An

Experimental Study of Airfoil Icing Characteristics, AIAA

82-O282, January 1982.

58
16. Bragg, M. B. and Gregorek, G. M., "Aerodynamic

Characteristics of Airfoils with Ice Accretions," AIAA

82-0282, January 1982.

17. Bragg, M. B., Zaguli, R. J., and Gregorek, G. M., "Wind

Tunnel Evaluation of Airfoil Performance Using Simulated

>•

Ice Shapes," NASA CR 16796O, November 1982.

18. Flemming, R. J. and Lednicer, D. A., "High Speed Ice

Accretion on Rotorcraft Airfoils," AHS A-83-39-O4-OOOO,

May 1983.

19. Korkan, K. D., Cross, Jr., E. J., and Cornell, C. C.,

"Experimental Study of Performance Degradation of a Model

Helicopter Main Rotor with Simulated Ice Shapes," AIAA

84-0184, January 1984.

20. Korkan, K. D., Cross, Jr., E. J., and Cornell, C. C.,

"Experimental Aerodynamic Characteristics of a NACA O012

Airfoil with Simulated Ice," to be published in AIAA J.

of Aircraft.

21. Korkan, K. D., Cross, Jr., E. J., and Miller, T. L.,

"Performance Degradation of a Model Helicopter Main Rotor

in Hover and Forward Flight with Generic Ice Shape," AIAA

84-0609, March 1984.

22. Korkan, K. D., Cross, Jr., E. J., and Miller, T. L. ,

"Performance Degradation of a Model Helicopter Rotor with

a Generic Ice Shape," AIAA J. of Aircraft, Vol. 21, No.

1O, October 1984, pp. 823-83O.

59
23. Bragg, M. B., Gregorek, G. M.', and Shaw, R. J., "An

Analytical Approach to Airfoil Icing," AIAA 81-0403,

January 1981.

'24. Cansdale, J. T. and Gent, R. W., "Ice Accretion on

Aerofoils in Two-Dlmensional Compressible Flow - A

Theoretical Model," RAE TR 82128, January 1983.

25. Flemming, R. J., and Lednicer, D. A., "High Speed Ice

Accretion on Rotorcraft Airfoils," NASA CR 391O, August

1985.

26. Korkan, K. D., Dadone, L., and Shaw, R. J., "Performance

Degradation of Propeller Systems Due to Rime Ice

Accretion," AIAA J. Of Aircraft, Vol. 21, No. 1, January

1984, pp. 44-49.

27. Korkan, K. D'. , Dadone, L., and Shaw, R. J., "Performance

Degradation of Helicopter Rotor Systems in Forward Flight

Due to Rime Ice Accretion," AIAA 83-O028, January 1983.

28. Miller, T. L., Korkan, K. D., and Shaw, R. J.,

"Statistical Study of a Glaze Ice Drag Coefficient

Correlation," SAE 83O753, April 1983.

29. Bragg, M. B., "Predicting Airfoil Performance with Rime

and Glaze Ice Accretions," AIAA 84-O106, January 1984.

30. Shaw, "R. J., Private Communication, NASA Lewis Research

Center, Cleveland, Ohio, August 1984.

31. Bragg, M. B., "Rime Ice Accretion and Its Effect on

Airfoil Performance," NASA CR'l65599, March 1982.

32. Potapczuk, M. G. and Gerhart, P. M., "Progress in

Development of a Navier-Stokes Solver for Evaluation of

Iced Airfoil Performance, AIAA 85-0410, January 1985.

60
33. Bragg, M. B., Private Communication, The Ohio State

University, Columbus, Ohio, December 1985.

34. Cooper, J. P., "The ^Linearized Inflow' Propeller Strip

Analysis," WADC TR 56-615, March 1957.

35. Goldstein, S., "On the Vortex Theory o£ Screw

Propellers," Proceedings of the Royal Aeronautical

Society (London), Ser. A, Vol. 123, No. 792, April 6,

1929.

36. Borat, H. V., Private Communication, Henry V. Borat and

Associates, Wayne, Pennsylvania, June 1984.

37. Miller, T. L., "Analytical Determination of Propeller

Performance Degradation Due to Ice Accretion," AIAA 85-

0339, January 1985.

38. Sanchez-Cantalejo, P. G., Private Communication, NASA

Lewis Research Center, Cleveland, Ohio, September 1985.

61
rime

glaze

FIGURE 1. The two basic ice types

thrust

freestream

rotational

FIGURE 2. Velocity components of propeller section

62
8

- I

00s

I

tflI<J«J .gs

63
1 oO

O c 8

UJ

LU

CD

0.-6

o

CD

0.2

O o O

ENCOUNTE R 2

y

l o O -'0.7 -Oo f -Oo l 0. 1 Oo f Oo 7

SURFAC E AR C LENGT H

FIGURE 4. Variation of local impingement efficiency with

airfoil surface arc length; r/R = 0.9, J = 1.18

1 oO

64
O o9

O o6

O o3

o

D

ACCUMULATIO N PARAMETE R

TOTA L COLLECTIO N EFFICIENC Y

MAX . LOCAL COLLECTIO N EFFICIENC Y

ENCOUNTE R 2

oO 0 o 2 0 o 4 Oo6 Oo8

RADIA L LOCATIO N

FIGURE 5. Radial variation of accumulation parameter, maximum

local collection efficiency, and total collection

efficiency for Encounter 2, J = 1.18

1 oO

65
1 0

CD

LU

Q

CJ

<t

8

CD ,

_J

<£

O -

o

D

ANGL E OF ATTAC K

MACH ND:c

;

ENCOUNTE R 2

I 0 o 2 Oof Oo6 0 o 8

RADIA L LOCATIO N

FIGURE 6. Radial variation of local angle of attack and Mach

• no. for Encounter 2, J = 1.18

c\j

o

O- O

CO

O "

o

CO

o

o

66
.0*

.05

.M

O

a

40«/s*c

51

40

40

51

51

it

SPREAD IN NACA DATA

L5gm/ra3

1.5

2.9

1.5

1.5

134

FIGURE 7. Comparison of experimental results with Gray's

predicted AC, values

67
25

20

LU -

»—i ;.

O ic

^ o 1 5

u_ ?•

u_

LU

O

O

o 1 0

05

O Cbo8

o

a

CLEAN * EXPT.

ICED * EXPT,

CLEAN s BLDSET=13«7 5

CLEAN s BLDSET=13o0 5

DEG c

DEG.

ENCOUNTE R 2

O o9 -1 o 1 1 o2 1 o3

ADVANC E RATI O

FIGURE 8. Effect of propeller blade setting on predicted

thrust coefficient, Encounter 2

1 o5

68
30

LU

UJ

o

CJ

UJ

3

O

CL

1 8

12

06

o

o

CLEAN s EXPT,

ICED * EXPT.

CLEAN. BLDSET=13o7 5

CLEAN s BLDSET=13o0 5

DEG.

DEG.

ENCOUNTE R 2

°%o 8 Oo 9 1o O 1o 1 1. 2 1. 3 1 c

ADVANC E RATI O

FIGURE 9. Effect of propeller blade setting on predicted

power coefficient, Encounter 2

1.5

69
1 .3

1 o 1

O o 9

LU

O o 7

Q.

CD

O o 5

O

o

LEAN p EXPT.

CED» EXPT c

CLEAN * BLDSET=13.75

CLEAN * BLDSET=13c0 5

DE6.

DEG c

ENCOUNTE R 2

°°%o 8 Oo 9 0 1 o 1 1 o 2 1 o 3

ADVANC E RATI O

1 0 1 O 5

FIGURE 10. Effect of propeller blade setting on predicted

propeller efficiency, Encounter 2

70
30

LU

u_

LJ_

LU

CD

O

CO

18

12

06

o

a

CLEAN 9 EXPT c

ICED s EXPT c

CLEAN » THEOR Y

BRAG G

N E W BRAG G

GRA Y

FLEMMING s

FLEMMING p

ENCOUNTE R .2

UNRESTRICTE D

RESTRICTE D

o

O o 9 0 1 o 1 1 o 2 1 o 3

ADVANC E RATI O

1.5

FIGURE 11. Variation of thrust coefficient with advance ratio,

clean and iced (iced to r/R = 0.7), Encounter 2

71
o o 3

o

o

LU

3

O

O_

O

Q

s"

CLEAN * EXPT,

ICED * EXPT o

CLEAN * THEOR Y

BRAG G

N E W BRAG G

GRA Y

FLEMMING s

FLEMMING s

ENCOUNTE R 2

UNRESTRICTE D

RESTRICTE D

%.8 • 0.9 1 oO 1 o 1 1.2 1.3'

ADVANC E RATI O

1.1- 1.5

FIGURE 12. Variation of power coefficient with advance ratio,

clean and iced (iced to r/R = 0.7), Encounter 2

72
1 oO

O o 9

>-

o

z

LJU

°0o 8

0 - 7

UJ

Q.

D

O c 6

o

D

CLEAN. EXPT o

ICED. EXPT c

CLEAN. THEOR Y

BRAG G

N E W BRAG G

GRA Y

FLEMMING s

FLEMMING .

ENCOUNTE R 2

UNRESTRICTE D

RESTRICTE D

°°%o 8 Oo9 loO Id 1 ,,2 1..3 1.1- 1.5

ADVANC E RATI O

FIGURE 13. Variation of propeller efficiency with advance ratio,

clean and iced (iced to r/R = 0.7), Encounter 2

73
20

16

o

08

S

o

CLEAN *

CLEAN *

BRAGG

N EW BRAG G

GRA Y

FLEMMING p

FLEMMINGs .

EXPT o

THEOR Y ENCOUNTE R 7

UNRESTRICTE D

RESTRICTE D

O

O

O

o 7 0 o 8 0 o 9 1 o 0 1 o 1 1.2. 1 c 3

ADVANC E RATI O

FIGURE 14. Variation of thrust coefficient with advance ratio,

clean and iced (iced to r/R = 0.4), Encounter 7

1 of

74
20

GJ o 1 5

10

D

CL

05

CLEAN * EXP T

CLEAN *

BRAGG

N EW BRAG G

GRA Y

FLEMMING p

FLEMMING p

THEORY ENCOUNTE R 7

UNRESTRICTE D

RESTRICTE D

O

O

O o 8 0» 9 1. 0 1. 1 1. 2

ADVANC E RATI O

1 »3 1 of

FIGURE 15. Variation of power coefficient with advance ratio,

clean and iced (iced to r/R = 0.4), Encounter 1

75
o

2

LU

i—i

O

i—i

u_

u_

LU

CZ

LU

O o9

O o6

LU

Q_

o

O o 3

0

o

D

CLEAN s EXPT.

1CED9 EXPT c

CLEAN * THEOR Y

BRAG G

M E N BRAGG .

GRA Y

FLEMMING * UNRESTRICTE D

FLEMMING s RESTRICTE D

ENCOUNTE R 7

. I

Oo8 Oo9 1.0 1 o 1 1,2

ADVANC E RATI O

1 .HFIGURE 16. Variation of propeller efficiency with advance ratio,

clean and iced (iced to r/R = 0.4), Encounter 7

76
c30

CD

CJ

(/) 12

06

S

1CED » EXPT.

CLEAN* THEORY

BRAGG

N E W BRAG G

GRAY

FLEMMING * UNRESTRICTE D

FLEMMING p RESTRICTE D

ENCOUNTE R 12

nnU L_ ' i i i 1 '— to7 Oo8 Oo9 1 oO 1 o 1 1 ,2

ADVANC E RATI O

1 o3 1 of

FIGURE 17. Variation of thrust coefficient with advance ratio,

clean and iced (iced to r/R = 0.9), Encounter 12

77
LU

o 3

o

o

Q.

S

ICED 9 EXPT.

CLEAN * THEORY

BRAG G

N EW BRAG G

GRA Y

FLEMMING * UNRESTRICTE D

FLEMMING p RESTRICTE D

ENCOUNTE R 12

Oo8 0«9 1 oO 1 .1

ADVANC E RATI O

o3 1 of

FIGURE 18. Variation of power coefficient with advance ratio,

clean and iced (iced to r/R = 0.9), Encounter 12

78
1 ,,2

a:

LU

O o 6

LU

Q.

D

0,3

0

T T

o

O

S

CLEAN s EXPT o

ICED » EXPT.

CLEAN * THEORY

BRAG G

N EW BRAG G

GRA Y

FLEMMING *

FLEMMING p

ENCOUNTE R 12

UNRESTRICTE D

RESTRICTE D

O

7 Oo8 0»9 1 oO 1 o 1 1.2

ADVANC E RATI O

1 of

FIGURE 19. Variation of propeller efficiency with advance ratio,

clean and iced (iced to r/R = 0.9), Encounter 12

79
4

J41 ^a0i<o•>*•

c0t,ustj®wI!CH

oo o o in tf> t-> m

rH CN N 0* <N rt Tt

Bv.m

oooooooo

a t.

co0

Ca•

<N| CM NI

ho00^4«auj,41 £,aa0e0•ocac.

-rt ^U.* CO0&h-

"

0a<t 0a0•oo-HCDh

»-«0a0a

c•H•k. ea•H1-01cuM,^Jo3•H*>»H<9•o•, oclOfs0ijc0O) czaue^-<0aoa.ac30ueUl

O*H*H0^0^0^OOOOI

^oco t-iCM^cow

o o o o o o o o o o O O O O O O O O O O O ^ ^ ^ 0^ CO t^ CM 01 0

1

<-i N

co«<Jja)«)flOa)a)«OO

•HinHintHinminmco

COCMCOOICOfMOICtCSCN

uiinininininininmm

ooooooooo^

»HrfrHrtiHrt»Hrtrt«-l

< CU < CO

(NCOrt^^'l/lvfl^flOOl

«-l 8

0
k.

41

*J

C

0

0

Ul

a

V4

ai

a

o

0

a

o

•H

"0

a

o

u

TJ

U

0 0>

•H C

ll -1

U.

c

•H

(1

-H

•o

41

U

-H

tJ C

os m co in N\o «

3 -H

u.

c

0

H

vD vfl (N CO (N CO

>• \Q co co ^ «-* cn

a •-< CN vo <H (N v0

o

al

14

u

M( ci o** v£ co in co v0

jo> in m in * H vo

41 « «H(Ntf ) .-iCNvf l

CO

T)

41

•H

"o u> tnoc o o^o^i n

OOi \0 ? <-i * O H

6 « rH(Nv O rH CN |S

•o co

O

4J

-H

CO

41

41

Z

U

flc ^* p^ o r^ ^* on

in (^ M en in O vO

Q< fH CN VjD tH CS S

o

1 "

ul 01

•H

h T* P* <Q .

CO ^ O ^

Cfl rH (N t^

&

V

z

n a n a

U U P OO P

o o

•-> on o

^r^o t inco^ 1 coo^t o 1 0 ^ ^ * (j^cnt o

(*) r** 01 «Hiov o o^v)c o <o (N tx* if) o^ co

fH fH CQ *H *H CO O *"• w O «H <0 OO< 0

oio o p^r^ w WH ^ * H «D f ( N r^o o

«H in N o ^* vfl cnco< o <o CD o^ in <r co

tH«HC O «H«H< 0 O^*C O O »H CO O O CO

r*» co (N ^ co oo (N o^ ^ o^ 10 N ^ ^8* ^

04 cO V O ^' ^ 0^ ^ ^ f** CO ^ (0 O 0^

*H tH f\ ^4 <H ^ O *H ^ O *H 1^ O ^ ^D

0*1 co v o ^ co en ^f co 1% w r^ ^* o ^

T^«^I S «H«Hf s O*^r ^ O«Ht ^ O*H W

<T^ H co c^o^^X ) trt H n) 04 ^ ro ^*s0 ^

C^ <D CO «H lO (N ^ ^" j CO W 5 lOO^c O

fH <H |S «H «H CO O *~* CO O*4C O O- O IN

•j'Ot Q Is* (7^ if) 0^ xO O

CO CO O CN t^ ^ OlOs O

*HtHCO*H*H<OHHC O

(O 0^ O (^ 0^ If) 0"t O ^ ^ If) ^J* 0^ CO ^

CO 1^ CO **4 if) vO ^ ^* CO CO 04 0^ tO Cft CO

«H<HC O H«-4C O OrHC O O «H 00 O O CO

THHS D CO CO O rH (P If) 00 ^ f^ 1^^*1 0

«HtHC O iH<-*C O «H«H< 0 OHC O O«rtC O

na na na H a H a O O P oo e OO P OO P OO P

O CO if) Q O

*-4 H OJ CO ^

81
ORIGINAL PAGE IS

OF POOR QUALITY

i

0

*>

c

3

O

u

c

UI

0

*H

01

u

a

•

o

>«

b

01

a

e

^H

01

a

0

a

c

4J

C

01

.5

a

X

0)

•o

c

•o

01

u

•H

TJ

0)

a

^0

c

o

(0

b

a

aml

O

U

,

in

0

,Q

0

^TM

u o>

-H C

*i a

sw w«

c

-«4

U

•H

•o

0

+1

u

fc O"

*J C

a -i

0 • fc a

C 01

3 H

U.

C

-H

u

i*

>.

i' 3t 0)

41 g,

C

t.

M

a>

01

Vl

"O O*

0 tn

s a

•a co

o

*>

o>

^i<

CO

»H

01

0

z

b.

a

a

o

, M 5

UI JJ

J £

Ui (7i

v4

t.

00

c«

z

^

S S S8 o S S gi S3 5? S° « S? 3 8S S S

HI «H (X'H H) COO O CQO O COO O COO O COO O *•&

^» if) \Q w r^ coco ^o ^o (N *H ^* o *"* co ^ «H sotpc o co

(N C4 CH O O tf) CO 0>Nc O (T> <0 f*» CO 0^ ^ tf CO H O CO

*Hr4N«HHCOOOCOOOcOOO<OOOcOOO<J )

S S g8 § g§ 1 B3 g-5 S 8 S9 J 9K X 8

rt ,-icx ^ rt oo o o oo o o oo o o «oo o r» o 'o «o

(M (N 0"* O O ^* cO 0^ vD cO 0^ r** uD CO t** ^ ^ 10 ^ O 07

o in o

^ \fl vO

• • •

v to ^ (N r^ co co ^ ^ N ^4 ^* o HI co en *H ^ o^ o co

rtvH(x^irtflOOOoOOO«DOOaOOoSoO^

(Mco^'r^^'cn^'^'in^ocsoioocMr^i n

o

1

) oo o^^ (X'^f o ••* ^o^ r>< ^9t o co\o r^ tfi

rt rl f^rt rH'CO' H «-« flOO rt COO H COO O 5)

f- a H a c-a (-a t-a (-a i-a

O U PO O PO O PO O PO O PO O PO O P

m m

o o in co M o o

00 C* 0* 0* O «^ (N

O O O O «-< «H «-i

82
(N

""*

L,

41

C

3

0

U

c

UJ

^

0

<«

4)

U

C

o

e

0

V*

a

b

4)

*-«

0

a

0

a

a

c

e

•H

b

41

a

X

•o

c

e

•o

41

U

•o

41

CL

<«

4J

U

fc C

a •

O f*

m

14 41

Oi U.

C

•H

u

•H

•o

«

*J

u

•H

fci (71

•U C

a -i

41 •

I* S

C 41

3 -t

U.

c

•H

u

a

o

Ul

u

3 C7*

4i a

C

i.

M

a

•o

41

>«

•H

*D (7*

o a>

e a

•o co

^H

0

4J

W

j,

CO

41

41

f o^NocomtDHiflcriaiovoijcoctiot N

2 2 S 2 i2 fS ^ 2 S2 2 SS ^ «o o «o o P

.. >

(N^ >coin<-)in^ |cooivo^C4cnc)\i)<-ifflt0o>co<- i

in (T* (NCO vD'inn CO (MO N ^*aO «H \D^) CD NN ^J1 Is

*<Hino*o*a»<r>o<ococor^r*< i*incNO(Nc o

«-iCMin'-»(Nino«-'ino«H*o<H^ io«"ic |>o«' |o

(0 H(N< N CN S O (*• O <S in S S (0 ? S O co2 h> -H

>H(<)coi-t(N*»H«H>x)O'-i(flOHvooHinooci i

in tof^in o Ovor* * o^ ^ r4 «HC40 i H^ * in^v 4 \O« H

co omN H coo ^ o o* in r^cof t otf) o< CON W«H

!-((<)<<)H<Nin«-i«-'»OO»'lvDOHfsOO3oO *

•H O C1) (N CO (7*

•H •* CH O M N

a

a.

8

0

U,

a

ui

a

u

o

ig

0> J> 9> «

r» N * r»

03 o o rv

a

o

•H

to

ID

O

rH

CO

m

o o

( - a t- a i - a H A t- a i- a

U o PO o PO o PO o PO o PO o '

o

ca

o

o

8

83
Table 7. Experimental and predicted (Flemming correlationa) radial

extent for each encounter.

Encounter 2 3A 3B 4A 4B 66 7 8 12

r / R ETE T ETE T E T E T E T E T E T E T

.20 V V V V V V V V V V

. 2 5 VVVVVVVVV V

.30 V V V V v V V V V V

. 4 0 V R V G V G V R V R V R V G V V R V R

. 5 0 V R V G V G R R -/ R V G V R V R

.60 V G G G G G G G V R

. 7 0 V G GGGG G V R

. S O G GGG G V R

.90 G G G V R

.95 G G G R

.975 G G G R

E - experiment T - theory

V - iced G - glaze

R - rime

8A
APPENDIX 1

PROGRAM FLOWCHART

f START J

1 t

READ USER INPUT

READ PROP

PERFORMANCE INPUT

ARE

ADVANCE

RATIOS

INPUT? HAVE

J VALUES

ALREADY

BEEN CALCULATE J FROM

INPUT Vg, RPM

READ J VALUES

CALCULATE CLEAN PROP

PERFORMANCE FOR GIVEN J

WRITE RESULTS

85
IS

FLEMMING

CORRELATION

TO BE

SED'

HAS

THEODORSEN

ALREADY

BEEN RUN FOR

GIVEN

r/R?

READ TRANSFORMATION

RESULTS FROM FILE

.DO THEODORSEN

TRANSFORMATION FOR

GIVEN r/R

STORE RESULTS

IN FILE

READ DROPLET

TRAJECTORY INPUT

FOR GIVEN r/R

00 DROPLET TRAJECTORY

CALCULATIONS FOR r/R

STORE COLLECTION

EFFICIENCY VALUES

IN ARRAYS

86
NO

SPLINE FIT COLLECTION

EFFICIENCIES FOR ALL r/R

ICED PROP PERFORMANCE

CALCULATIONS FOR GIVEN J

NEXT r/R

87
APPENDIX 2

USER'S GUIDE

ICEPERF has been designed auch that user Intervention In

the run stream has been eliminated and the amount of user

input is minimized. Still, with the wide scope of work and

calculations which the code must perform, a substantial degree

of input is required of the user. This information is

provided through several files which are read at various

points in the program and which are separated such that each

contains input data relative to a particular phase of the

program and to a particular radial location. As previously

mentioned, the code handles four input radial locations, and a

complete set of input data is required at each radial

location.

The actual parameters in each file are described in the

Comments section of the code listing which will follow. They

are redescribed here to provide the user with a better idea of

how to specify and use each variable.

Files 1 through 4 contain airfoil coordinates and other

information related to the airfoil geometry at each radial

location. These files are used in computing the flowfield

about the airfoil. File 1 contains information for the most

inboard radial station input, with files 2 through 4

containing input data for progressively more outboard

stations.

Card 1 of files 1 through 4 contains the title for the

Theodorsen transformation input. This title is printed at the

88
beginning of the airfoil section geometry output for the

particular radial location input. It may typically read

similarly to, "CLARK-Y COORDINATES AT 30X STATION".

Card 2 contains five variables: LPT, ITAU, IZ1N, TAU,

and XZ1N, input in the format <3I5,2F1O.O).

LPT represents the number of harmonics which the user

desires in the exponential transformation of the airfoil to

the circle plane. A value of 5O to 60 is typically used for

LPT to attain a satisfactory degree of accuracy.

ITAU is a flag which indicates whether or not the user

wishes to input the trailing edge angle of the airfoil

section. A value of 0 indicates that the trailing edge angle

is not known or will not be input, and any value greater than

0 indicates that the user will input the section trailing edge

angle.

IZ1N is a flag which indicates whether or not the user

will input the nose singularity coordinates. An IZ1N value of

0 means that the nose singularity will not be input, and IZ1N

should be set to any value greater than 0 to input the nose

singularity coordinates.

TAU is the trailing edge angle in degrees, to be input

if ITAU is greater than O.

XZ1N and YZ1N are the x- and y-coordinates of the nose

singularity, to be input if IZ1N is greater than O.

Card 3 contains the variables NU and NL, which are the

number of upper and lower surface coordinates to be input,

respectively. This card has the format 215.

89
'. Cards 4 through the last contain the airfoil section

coordinates, nondimensionalized with respect to chord. Eight

values are listed on each line in format 8F1O.O. Upper

surface x-coordinates are all listed first, followed by upper

surface y-coordinates, lower surface x-coordinates, and

finally lower surface y-coordinates. i

-This then completes the input required to map the

airfoil sections to the circle plane.

File 8 contains input parameters which are used to

compute droplet impingement values for the airfoil. The same

File 8 input data is used for each input radial location.

Card 1 of file 8 contains the title for that particular

radial location, and would typically read similarly to "30*

STATION TRAJECTORY INPUT." This title is printed at the

beginning of the droplet trajectory section at each radial

location.

Card 2 contains the variables IPRINT, MSPL, XFIRST,

XLAST, and EPS.

IPRINT is a print option, with a value of O used for the

shortened version of the trajectory summary output, and a

value of 1 producing the complete printed output. The

shortened version will print only the general input to the

trajectory section, the tangent trajectories, and the

impingement efficiencies. The trajectory tabulation and

summary and surface impingement values are not printed when

IPRINT equals 0.

90
MSPL ia a variable which ia uaed to aelect the method

deaired to calculate the impingement efficiency curve.

Setting MSPL equal to O requeata the program to aelect the

beat of three methoda poaaible for calculating the curve. An

MSPL value of 1 causea the program to uae a simple cubic

apline routine to calculate the curve. An MSPL value of 2

inatructa the program to uae a cubic apline but to piece in a

linear fit where the cubic spline faila. An MSPL value of 3

causes a quadratic apline to be uaed, in which the

coefficienta are aelected to optimize the fit of the curve.

Setting MSPL equal to O haa alwaya produced satiafactory

results in all cases run for thia inveatigation.

XFIRST ia the x-coordinate after which each atep ia

checked for droplet impingement on the airfoil. A value of -

0.05 ia typically uaed for XFIRST.

XLAST ia the x-coordinate at which droplet trajectory

calculationa are terminated. Thia value typically rangea from

0.5 to l.O, and if the uaer lacka a good feel for the

impingement characteriatica to be expected for a given case, a

value of 1.0 should be used for XLAST to ensure that no

trajectoriea are terminated prematurely.

EPS is the maximum error allowed in the step integration

process. A value of l.xlO ia generally used for EPS.

Card 3 contains the variables XO, UDO, YO, VDO, and FR,

in format 5F1O.5.

XO ia the initial droplet x-coordinate. Thia is the xvalue of the point at which the trajectory inveatigation ia

91
begun, and it ia typically given a value of -5.0, representing

a starting point five chord lengths in front of the airfoil.

UDO ia the initial droplet x-velocity with reapect to

freestream, and is commonly set equal to 1.

YO is the initial droplet y-coordlnate. Thia ia the

starting point for the first trajectory calculation only, and

ita value will depend on the section angle of attack. For a

positive angle of attack, it is suggested that to maximize the

chance of initial droplet impingement a slightly negative

•value of YO be used, perhaps approximately -0.05.

VDO is the initial droplet*y-velocity with respect to

freestream, and ia generally equal to O in the undisturbed

flowfield five or more chordlengths in front of the airfoil.

PR represents Froude number. This parameter may be aet

equal to 0 to ignore the force of gravity on the droplet

trajectories, and this is commonly done.

Card 4 contains four variables, DYO, CON, ERRY, and HGT,

in the format 4F1O.6.

DYO is the increment in YO used by the program to vary

the beginning droplet y-coordinate. Valuea of DYO are

commonly on the order of .001 to .Ol. The code has been set

up to assign a value for DYO if the user inputs a value of 0

for this parameter. The internally assigned value will change

with section angle of attack. If the user inputs a DYO value

however, this value will be used regardless of the section

angle of attack. When internally assigned, DYO ia given a

value of O.OO3 for section angles of attack less than or equal

92
to 4.6 degrees and is set equal to O.OO5 for section angles of

attack greater than 4.6 degrees.

CON is a multiplication constant for the impingement

efficiency curve output. It is generally set equal to 1.

ERRY is the maximum error acceptable in total collection

efficiency. A value of 2 (in percent) has commonly been used.

HGT is a reference height in the y-direction used to

compute total collection efficiency. If this parameter is set

equal to 0 the code will calculate and use for HGT the

projected height of the airfoil section.

This then completes the droplet trajectory section

input.

Files 12 through 15 contain binary flowfield information

which is output by the flowfield computation section of the

code when airfoil coordinates (files 1 through 4) are input.

Since this flowfield information is independent of angle of

attack and velocity, it is necessary to run the code with

airfoil coordinates input only once for a particular geometry.

In subsequent runs using the same geometry, the flowfield

information calculated and stored in the initial run is read

and used by the code, thereby eliminating the need for

recalculation of propeller flowfield information in each run.

The user must only set up the computer job control language

(JCL) appropriately to exercise this option. For example, in

the initial run of a particular geometry, units 12 through 15

must be set up to have the binary flowfield data written to

them. In subsequent runs these files must be established as

93
existing data files from which data is to be read. When

previously computed airfoil flowfield information is used, it

is not necessary to input airfoil coordinates, and the

flowfield calculation section of the code will be bypassed.

File 16 contains input data for the propeller

performance calculations. This file contains data for the

entire propeller, so no duplicate files are required for

different radial locations. Data for a maximum of 15 radial

locations may be input.

Card 1 of this file contains the flight and atmospheric

variables VO, TO, DD, W, TAUM, and ALTUDE in format 6F1O.4.

VO is the freestream velocity in miles per hour.

TO is the freestream temperature in degrees Fahrenheit.

DD represents the volume mean droplet diameter of the

icing cloud in microns.

W is cloud liquid water content in grams per cubic

meter.

TAUM is the icing exposure time in minutes.

Finally, ALTUDE is the pressure altitude in feet at

which the icing encounter occurred.

Card 2 contains the variables NUMBLD, NUMSTA, INCOMP and

NUMADV/ in format 415.

NUMBLD represents the number .of propeller blades.

NUMSTA is the number of radial locations to be input by

the uaer (maximum is 15.)

INCOMP is a compressibility check flag which provides

the uaer with the option of obtaining either a compressible or

94
incompressible solution. If set equal to O, a compressible

solution is obtained and if set equal to 1, an incompressible

solution is computed. Recall however that the flowfield

around the various propeller sections was computed using a

method which assumes imcompressible flow.

NUMADV is the number of advance ratios to be input. Set

equal to 0 if advance ratio is to be calculated using input

RPM and freestream velocity. NUMADV may have a maximum value

of 1O.

Card 3 contains the variables RADHUB, BLSET, RPM,

CPDESI, DESIHP, and DIVIS in format 6F10.5.

RADHUB is the propeller hub radius in feet.

BLDSET represents the propeller blade setting in

degrees. If either CPDESI or DESIHP are assigned values other

than O, the program will derive a BLDSET value based upon

these input parameters.

RPM is the number of propeller revolutions per minute.

If specified, RPM will be held constant. Otherwise RPM will

be calculated based on the input freestream velocity and

advance ratio. Either RPM or advance ratio must be specified

in the input.

CPDESI is the design power coefficient. If set equal to

O, power coefficient will be calculated based upon the input

value of BLDSET.

DESIHP is the design horsepower, and if it is input as

0, a value for DESIHP will be calculated based on the input

BLDSET value.

95
DIVIS la a convergence aid variable for the design mode

in which a BLDSET value must be computed. It is generally

assigned a value between .OO1 and 1. When BLDSET is

specified, the DIVIS variable is not employed.

Card 4 contains the variables CORTIP, RADIUS, STUBLT,

CDINT, and CORHUB in format 5F10.5.

CORTIP is the propeller tip chord in feet.

RADIUS is the propeller radius in feet.

STUBLT is the propeller stub length in feet.

CDINT is a blade shank correction factor which takes

into account interference from the blade shank. If a value

for CDINT is unknown, a value of O.567 should be used.

CORHUB represents the propeller hub chord in feet.

Card 5 is a title card which denotes the variables on

the card to follow exactly as shown in the code input

comments:

R/RAD= BLDANG= CHORD= T/C= ALPHAO= CLD=

VDIS= RC=

Cards 6 through NUMSTA contain values for these

variables, in format 8F1O.6.

XPR is the nondimensional radial location to be input.

BLDANG is the propeller blade angle in degrees of this

section. Generally this is just.the twist distribution built

into the propeller.

CHORD is the propeller section chord in feet.

TC is the section thickness to chord ratio.

96
ALO la the angle of attack for zero lift. In degrees,

referenced to the longest chordline.

CLD is the section design lift coefficient.

VDIS represents the velocity distribution seen by the

section, taking into account nacelle effects. This parameter

equals the local velocity divided by that of freeatream.

Finally RC is the section leading edge radius of

curvature, nondimensional with respect to section chord.

The final card(a), in format F1O.6, with one value per

card, are ADVRAT values.

ADVRAT ia the propeller advance ratio, and as many as 1O

values of ADVRAT may be input by the user, with performance

calculations performed by the code for each advance ratio. If

NUMADV is set equal to 0, such that advance ratio ia to be

calculated by the code given RPM and freestream velocity, no

ADVRAT values should be input.

This completed the propeller performance section input.

File 17 contains input for options available to the

user, including choice of aerodynamic coefficient correlation

to be used as well as print options.

Card 1 is the title card for the run. This title is

printed at the beginning of each section of calculations

within the program and so should be general in nature, such

as, "ENCOUNTER 2 FROM NEEL AND BRIGHT REPORT."

Card 2 contains the variables NCD, RADEXT, IREAD,

IPRCOR, and NSECT in format 15,F10.5,315.

97
NCD ia the aerodynamic coefficient correlation selector.

A value of 1 for NCD calls for the use of Bragg'a rime ice AC ,d

correlation. A value of 2 calls for the use of Gray's glaze

ice AC, correlation. A value of 3 calls for the use of

d

Flamming'a AC, and AC correlations for rime and glaze ice.

RADEXT is the fractional radial extent of icing.

IREAD is a flag which determines whether or not the code

will calculate the flowfield at the input radial locations.

The option is to use previously calculated and stored

flowfield data. For each radial location input, the code will

write the flowfield information to a file if it has not been

computed in a previous run. Set IREAD equal to O to calculate

the flowfield, or set it equal to 1 to use the previously

computed data. The user must also be sure that the

corresponding JCL for each of these files is set up correctly,

i.e., if IREAD equals 0 the JCL must be write-oriented, and if

IREAD equals 1 the JCL for these files must be read-oriented.

IPRCOR is a flag which indicates whether or not the user

wishes to have the airfoil coordinates at each of the four

input radial locations printed. An IPRCOR value of O

instructs the code to not print the coordinates, and an IPRCOR

value of 1 causes the coordinates to be printed.

NSECT is a variable which indicates the number of radial

locations to be input, with a maximum of four possible.

Cards 3 through 7 contains values for the variable RSTA

in format F1O.5.

98
RSTA is the nondimenaional radial location at which

flowfield calculations are to be performed. A maximum of four

radial locations may be input. These radial locations must

for the current version of the code be the aame as any four of

the radial locations input in the propeller performance

section.

It may be shown that the curves of total and maximum

local collection efficiencies are relatively smooth functions

of radial location, ao that four points should provide a

reasonable representation of the variance of these impingement

efficiencies with radial location. However, it is obvious

that the fewer points one uses to fit these curves, the less

accurate they will tend to be. It is recommended therefore

that whenever possible, no less than the maximum of four

stations should be input to maximize the available accuracy in

the impingement efficiency calculations, which then affect the

propeller performance computations for the iced configuration.

This then completes the required input to the code.

99
APPENDIX 3

SAMPLE CASE

The following output was produced for Encounter 2 at an

advance ratio of 1.18. The Iced calculations were performed

uaing Bragg'a older, modified correlation. This same format

la output regardleaa of the user's choice of correlation. Uae

of the Bragg or Gray correlations will generate output similar

In appearance to that shown here. When the Flemming

correlations are used, no flowfield or droplet trajectory

information is printed out.

The code requires approximately 57OK of computer memory.

Typical run times are roughly five minutes (CPU time) on an

IBM 370 and 33 seconds on a CRAY-IS for one advance ratio

using either the Bragg or Gray correlations. Use of the

Flemming correlations significantly reduces run time because

the flowfield and droplet trajectory calculation sections of

the,code are bypassed, resulting in typical run times for the

Flemming runs of 8.4 seconds on the IBM 37O and O.57 seconds

on the CRAY-IS.

100
ooooooo r>. os ifi 10 o in <*• ooooooo CMO <*• rv ro so CM

o o o o o o o CM CM "cf" ro eo si- sj* o o o o o o o CM r^ os «ct- cr» os o

inoooooo so CM I-H s*-in 10 in inoooooo in so os i— eo os r*

CMoininmino o so si- oo oo o» r- cMominmino in o >a- o oo oo 10

O r» CM CM CM CM Cs CM rH 00 OO m O> O a f» CM CM CM CM OS rH sO r» rs. in IO O

O O CM sS- SO OO OS OrHrHrHrHOO O O CM sf sO 00 OS OOOOOOO

O O O O O O O OOOOOOO O O O O O O O OOOOOOO

I I I I I I I

ooooooo oooocMCMor- ooooooo eo r~ eo cb so o siooo^ooca r*»ooosorovT*os o^^caooo r^cosj-osirtooin

O O O O O O O Sf SO SO h- sf rH in OOOOOOO 00 O IO CO sO CM OS

CMOOOOOO CO f> CO O IO OS s^ CMOOOOOO IO CO >d-rH O CM SO

OsOOOOOOO rH^r^CT*sOC3rH OsOOOOOCO rHinr^r^sOsfO

O O CM sT SO eO C7> O rH rH i-l rH r-H C3 O O CM st* sO CO Os C3 O O O O O O

ooooooo ooooooo ooooooo ooooooo

I I I I I I I

OOOOOOO r*»9»IO!OC^rHrH O^C^OOOO ^tninrHIOC^r^ 'S~

**^ r^ f^ f^ f^ ^^ fy ^^ ^Q t^ fs. r^ r^ ^^ o ^^ C) ^3 C3 ^3 C3 ^^ 1^ P^» CM O *G 00 ^^

inoOOOOO O rH s*- sT CO CM sf in O O O O O O Os OS CM Os K) CM <7»

r-i o in in in in o so eo »H CM r- oo rn rn o m in in in o rH srro CM CM m os •

*-^ m ^^ ^^ r*^ r**» r^ rH os r*»» ^N so *H CM' ^3 in r^* r*^ r^ r** f*» cs in r** fs* *Q *f ^^ '

C>OrHIOinrs-Os OCDrHrHrHrHCD CdCOpflOinr^OS OOOOOOO ^

OOC3OOOO OC3OOC3OO O C3 O C3 O O C5 OOOOOOO "~ O

I I I I I I I E -

ooooooo so CM p~ in so ro rH ooooooo eo rH eo sr so sr os J8

ooooooo CM s*- sr si- eo si- in ooooooo so rH so r> co os sr ° ^

I-HOOOOOO lOr^CMIOrHsDsf rHOOOOOO OSrHrHIOIOr»in

rH oo so cr> r>-CM ro o si-m in in in in o in r»-rs. so •*• rH +•* '

o o I-H 10 in r^ o> ooooooo TO <"

I/)

0)

ooooooo ooooooo ooooooo ooooooo ~ "^

I I I I I I I ,0 W

ooooooo ^rHrocMior»« ooooooo in CT> so >o <o CM rin ca o o o o o oo ro so r--(\J o-j3 inoooooo in o rH t» f> er> eo ~ *f

r*oooooo in rH ro >o in o eo p^oooooo CM 10 «a-<a-10 ^-<*•

 -tJ

 ^ ooinininmin rH in rn 10 in o- cr- oommininin oo ^o o» >a- in o rH "•

O IO CM CM CM CM CM i-H r- in O« !>. rO >*• O IO CM CM CM CM CM O «S" •£> t~~ O in CM '— c

OOOOOOO ^ *r"

^ g

K) OOOOOOO CO rH IO rH IO CM O» OOOOOOO

. o o'o o o o o 10 in ro in in vo o ca ca o o o o o

o inoooooo \oinincj>oa»o» inoooooo

II cso^^ooc^ o^or^CMO^orO ^ocao^oo

Qi OCMOC3OOO ^ sO IO O> P~ Si- >O OCMOO^OCS C3 IO >O P- >O Irt CM

X O^rHIOinr~Cf> OOrHrHrHrHO O^rHIOini>-C> O C3 O O O O O C\J ro

^^^CDOC9O O^^^^^^ OOOOOOO • ^^^OO^CJ 1

 ...... s I

UJ OCDCS^O^O SO O CT- CT< 00 CO O O O O O O O C3 >OC»IOIOCOIOin ' - ^~

r- inoooooo lO^vjeo-a-'OeO inescsoooo CMr^eOMTioooO '/~

«t CMOOOOOO rH 0» O rH <J- IO f-> CMOOOOOO IO 1^ \O CM rH tf. CM *" JjJ

z- oooinmmm r>-i-ir-irHCMr--<o cscaoinminm <d-a>^-moo>*'rH QJ

i—io cDrH^r^-f^r^r^ ^^±100^00*^^ ^rHO^^-r^r^r^ CDCM^SI — >omio ^~ "^

Q O O O CM sT -O 00 OOrHrHr-lrHO O C3 O CM \3" SO OO OOOOOOC9 O TO

Q£ ....... ....... ....... ....... £-

O OC3OC3OC3O O^OOC^^O OOOOOOO OOOOOOO H->

 >r

~

o ..... ' ' 2 "?

Ooi^ i « in cs o o o o o o o CM o o o r-. r»- >a- in o o o o p o o o o 10 CMin CM m<3- oo *- ° O O

^ es in o o o o o o i— i o» ro oo in ro oo o o mo o o o oo o.-HCMinc>r- in o

c£ CT> r^ o o eo inin in in o o CM CM oo oo in 00,0 o o oo inmin in o o CM -or»>o in 10 o

<X in in O CD O CM *J* ^ 00 O ^ O rH rH r-* »— I O O O O O CM *tf" O OO O O O O O O O O O

_i ................................

O O O CD C3 O O O i-H O O O O O O O CD O CD O CD CD CD CD rH

101
II ooooooooooo

O

Xooooooooooo

of.

omoooinoiniomc*

M

rH

o

• O O f\J K> CO m CO CM C\J O so rH

o • o» sr c* o CM o- oo •£• 10 CM (M

o 1-1 r»> r»- vo ^ in tf- 10 10 ro ro 10

o ii ...........

o o

o o 10 oo o (O rs. o oo m es I-H «*• O*

• .1-1 o* CT> rH *a CM rH ro 1-1 <M I-H o*

o out cn-rN. in rH r«. K> o eo rx r«. \o

r-l .11 ...........

I I I I I I I

or-, in o o in o in oo irt o m <o

o o r-i in r-- cy- t\i •-! o r-^

o ^ . II \orOCM r-l r-i^ C3 o oo o O

I-H

UJ

CLO OCM ro in in N 0> OO CM CM 00 OO vO Of

z • « • i-i r>- r«» o CM i^ r^ »o CM <r»d- o

MOO mo in >o r- o> CT> eo r^ so in K> CNJ o

i-l CM II ...........

ui o a . oo

O rH ft! O

z o t

< i a:

C o o a

Of i-l i-H .

oo mm a> CM r>. oo o «M 10 oo *> <M^ « o

UL • orx ........... < m

et*-i • . ii cMr^r-itMMOor^^inin i— CM

UJ K> \O O in <*• <f K) CM CM CM i-H rH i-l i-H 4

O. OrH Z Q

< ..

r- <M Q H- I-

=3- 1 3

a. ae to a. o

0. Of Z UJ rH Z r-I

Z I— r-H (— CDrHinO O O C3 £3 O CD O O OC3 in I-H Of ^ • • • •

r-l O Z > rHWO O in O O O O O O O in l>- (Q OOOOO

r— SO Z3O C9s±ll CM CM IO <* in »O !•> 00 "> O"» O> r~ *

00 UJ rH O mCMQ ........... rH oB

_i o <a- • .4 o •-<

ui a. >o ui z oocg o ui _i

_i OrH m • _i LU x * —i UJ

rHJOfl O rH Q£ O M UJ

U. O U. UL Z

102
tn

OfU.

o

• M O

O Eo

Z

»H 00

>- coo

O 1-lrH

E O II

< —I II UJ

of. o of a

O Z UJS

o a: t-tOf O UJl-l

O. UJ >0 Ett- CO <t _l

cn x M<

X h-l Of O. CO Q

x co UJ => r-i uj

x >- _i of. v h-<*

_l _l Q (NJ UJ=>

U. < I-H QJ —ICO

a: z E uj Q.<n

UJ < > UJ OUJ

Q. cn i— of of

UJ O _l < QO.

o z «« o

i-i i-i OL

O t- >- 3

X l-l I— U. •

X >- I-H h- Z

x oi co cn co .1-4

uj of. ^ OH

_J UJ _l UJ

-I > QO

UJ l-l O

Q. Z O •

O 15 O O

Of TH

Q. E rH

M E:

cn UJHH

<t OilX =>

uj i-o

LUO

D-I-H

UJ

UJ

a:

o

o

o

o

a:

CO

<

h-

<

o

t-H O

pa of <t<to

III III -^ ^«l

o« X Of

103
II io r^ 10 ro ro i^ vJ-tf-CM o oo

O CD o \o CM -o (M o c* o* C" oO

X 00 iri rO CM I-H •-! •-! o o o ca

Of 00000000000

II OOOOOOOOOOO

to o in oo o in omro mo»

n in r» in o in r«- c* oo <»• <** <*

Q in O» CM in O r~ 00 C7» O» O» O»

z

o

o *

LU

to *

O

t-t Q

to o

UJ X

Q I—

Ul

O £

z

<c. to

l-l—UILLI

UJLU

U.U. v^

UJ

tno CM

rs.in.i-i •

UJ

o

z

<t

a:

o

UQf

UJ

a.

a:

Ul

UJ

a.

o

a:

Q.

CO

z

•t.

CO

II

o

o

z

to

O Of

1-4 Ul

to to— i

I-H UJLU

a: a a. I-LU

UJ <t OCQOQ.

I- ~IO£=>UJO

o eao.x«/)a:

<t o_

of U.U.U.U.

•< ooooi—

o

UJ

a.

o

to

o

II OOOOOOOOOOO

Q O CM rO CO in 00 CM CM O O •-(

_J €7» <J- O> O CM ••»• CO >*• K> CM CM

O f» f^ vO vO IT! %*• K) IO IO IO K>

<->

CM

>K

u.

X

CM

9K

II O>. <T> t-l SO CS) rH IO i-l (M r-l

o

X (O K> ro KJ CM CM CM r-l rH i-l rH

0. I I I I I I I I I I I

ii mo omo in oo mo m «o

o

X

I— «otOPJ i-H t

OOC3C3OOOC3C3OO

o oo o o

-o

O

o

to

o

IO

HH

Of

Ul

IO—

Of

X

o

o ^t

UJ H-U-ZlDUJ

to UJ X M * UJ

X LU ca vent*

U. -^ ^ <t >-• LU

^ Of Q

o in ^ CM ^^

m o r-» m

CMinorooroo

,Der>. •ooo>d-in

in \O O -CJrHO

• o oin -o •

r*. 1-1 o to r-i o to

O • O rH -£> • rH

CM O r-i rH <d- ^

II II II II II II II II II

UJ

z a o

o 3 z

-HLLJH- M LL

o

o.

(O

o

z

z

UJ

O Of(-_l=3UU3O

OIUJH< t— IOOO

uj«io_ii— i— LULU a:

II

Q

O. Of

O X

OC3OC3OOOOOCOC3

OOOOOC3OOOOO

Oo

ui

o.

o

Of

a.

LUUJ

OfOlUJUJH- QQQ

O-LULULU

t— tO LU t-t l-l n »-l

.

UJLU I— UJHZO'O'O'

OfQf-IOfUJUJUJLIJU.-

(O

U

to

o

tf.

Of

o

>-

z

UJ

»-

o

104
111

II CMO i-i 00 ° r^ ro oo sj-si-o

Q CM <f i-s- o in ro os ro r-s. o CD

O to oo 10 oo r~ oo to r-- so 1-1 r>-

X—i «*• oo PS, in PS. r-i r-t in trs tr> o*

O ro sr in sr ro CM i-i

II

3:

O

El

00 s> l-s. i-H O SO <M i"H in O rH

P-. m e»s c\j ro in ro CM o ro 1-1

so m ro •-! .-i ro ps. CM so <MO

CM r\j CM M ro s*- ui in so so s/>

CDOOOCDOOCDOOO

II

Q

O

CM O

o o o o o o o o o o

-JLL

o

UJ

o

a:

u

a.

I

D.

in in in PS. in 1-1 ps. o cisps. CD

cr> CO ro so ro co s> o» in so «3-

00 CM ON ro rH ro \f ir> i

II

_J

o

) CD i-i CM ro ro

> rH rH i-l i-l rH rH

mo m

> (M in CM sO OO ro CM vS- CO CO «J- r~.

CD • oo CT* • • • *tf- \o r*^ crx to r^ r*«

o in • • in oo «o FN. ro CM oo r^ CM eo

O CM in 00 CM (7> CM rH CD CM so rH CM >O

Z

o

II CMo o CM coo o o r-i ro to

» o o o^ ox ro sr c\j pj tn oo rO

UJ

a

OC3OOOOOOOOO

C5 O CD O CD <

it in iri 10 in m m m in in in in

<t o> c\j i—co c> CM ro oo \D CT> r^

II CM l"» CTN CO i-l vD LO CD i-l r-. O

M ^-t rO CD CD CMT1 O CM CO CM •*>

r-^ ro r~- CM iri o m cf- r~- in ro

t-i CM CM ro ro <r >a- v*- in o r>-

S

o£.

CD IO

CM CM ro \j- in \o r~ co o» v a*

u

O CD CD CD O CD CD CD CD CD CD in

OincDOCDCDCDOCDinr^

CM CM ro <j- in o r~. co o c* cf>

...........

CD O CD CD CD CDCDCD CD CD O

uj

o

a;

UJ

Qa.

O

W

O

II

O

M

<

Of

UJ

%_» r-- so sr

rHCM CM

II II II II

OO

r— 1—

OO

«s<t

sOrHOOOCDCDCDCD

II II II II II II II II II

y

oz

HOZ

r-rHO

OH-M

UJOrCkfUJO

>-OOiC^

Q oooo;

UJr-r- Z OO

CQZZr-UJX O

oc

o

O

^^

U.

z

o

o

z

U^J

—J

0

o

u.

UJ

o

ZE en 3 o i-i i-i uj o I-H t- x

5> O- r- r- a: Qi OQ t-i »-( O U. 3M

O • r-i n x O <t U. U. h-i U- . 3

<XQtC=>2>r-h- U.U.U.UJU. .

r-ll-H QiUJUJLL. UJU. •

ai ttr t— i— oi ct: uj o o LJJ oi o LU u.

LUUJ o o UJ uJ3 o o o LU o o LL

O _ I OUJ

ia_r— UJ — i r—

if)

UJ

o

Z

105
o

in

eo

ro

ro

CM^r-IOOCDOOOOOOOOOOOOO

otroooooooooooooooocpo

C7>CMOOOOCDOOOOOOOOOOOO

inOCDCDOOOOOOOOCDOCDOCDCDCD

i— looesoooooooococaoeaeacao

OOOOOOC3OOC3OOOOOOOOO

ooooooooooooooooooo

OOC3C3OOOOOOOC3C3OOC3C3C3O

at

o

o

10

* »-l

K (/)

* >-

C* Z

uj <r

QLU O

O Z

l-l l-l

O

'* l-l

*

* as

LU

Q.

O

Of.

LU

o

o

_i

o

z

Q

fti

UJ

>

00

I I

I-HTKMOOOOOOOOOOOOOOOO

sD

00

00

X

CM

<

r—

Q

00

00

CM

ro

O-OOCDCDCDOOOOOOOOOOOCDO

I-IOOOOOOCDOCDOOCDOOOOOO

OOOOOCDOOOOOOOOOOCDOO

OOCDOOCDOOOOOCDOOOOOOO

OOOOOOOCDOOOOOOOOOOO

OOOOOOOOOOOOOOOOCDC3O

I I I I I I I I I

SO

in<

r*.

Mt

>-

« in in

LU

> O

r-. O

O LU

•o o

om

u

io.

in<MCDOOC3OCDOCD<

OCMOOCDCDOCDOCDCDOOOOCDOOOO

00<

rH<

OCDOOCDCDOOO O O CDC3CDOOCDCDOO

CDOOOOCDOOOOOCDC3OOOOC3OO

X

UJ

oo

>O

0 (NJCMQ.

CM o» o LU

CM

r~ o

Z

O

LU

O

o

o

0£

ta

II

O£

X

00ES

IO=0 .

RDIN

A

O

C£

ca

LU

RACO

iu>-

o i

oa

xc

1 1

CMOOOOCDCDOOOCDCDOOO O CD CD O O CD

r^OCDCDCDCDCDOOCDCDCDCDOOOCDCDCDO

r-ICDCDCDOOCDCDCDOOCDCDOOOCDCDCDO

\DCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDC3

CDOCDOCDCDOCDCDCDOCDCDCDOCDOC9C3CD

OOC3OC3C3OCDOCDOOOOCDOCDOOCD

II III I II I II

rOOtni

XNinu j »Q__I

oxxoa;iuo

o

«n

i—

z

LU

hH

O

hH

U.

u.

LU

O

O

Qi

LU

r—i

o:

o

l>.\rCDC3CDCDCDOCDCDCD«

inCKOCDCDCDCDOOCDOCDOOOCDCDCDCDCD

<ffCDCDCDCDOCDC3CDCDC3CDCDCDCDOCDCDCDCD

CDCDOCDCDCDCDCDCDCDCDCDCDOOCDCDCDOCD

OOCDOOCDOOOCDCDCDOCDCDCDOOOO

CDOOCDCDCDCDCDCDCDCDCDCDOC3OOC3CDCD

r^OOOO'-HCDCDCDCDOC3C3CDCDCDC3OOCDCDO

i—ItnmcDOCDCDCDCDCDCDOCDCDCDCDOCDCDCD

\OCI«OCDCDCDCDCDC3CDCDC9CDCDCDCDC3CDCDC3

incDCDOCDCDCDCDCDCDCDCDOCDCDCDCDCDCDCD

incDOOCDCDCDOCDCDCDCDCDCDCDCDCDCDCDCD

CDCDCDCDCDCDCDOCDCDCDCDCDCDCDCDCDCDCDCD

OCDCDCDCDCDCDOCDCDaCDCDOCDOOCDCDCD

106
<

_1

X

M

o

Q

II

(-

O

u.

o

o

O

*

*

DC

UJ

O.

UJ

o

<t I-H

Z

<t

O

O

z

X

O

u

ui 3

-I «*

_l O

(*:

UJ

>

</>

O

* h-l

** of

UJ

UJ

a.

t- >-

• I-

>- M GO «n

01

UJ

>

>o

CO

X

CM

UJ

!-

<

a

ft.

en

a

o

o

o

u

Of.

U.

U.

Q

II

>-

of.

0£

UJ

>-QQQQQQQOOClQaQQQQQQQQ

O O O OOOO O OOOO OOOO OO O O

X

UJ

HI II I III III III II I III III III HI III I If II I II I 111 III II I II I ILI II I

Qf m in m in in in in HI in m iii in i»i in in in in in in

U.OOOUOOUOOOOOUOOOOUOO

I l-l »H H W H »H H

(-

<t

_l

UI

ft/

ft/

o

o

o

o

O^f

03

<t

L^

^TM

a

HX

o

HI

Of 0

O3 K)

•

00 O

.

_l II

UJ Of

UJ S

Z ft£

o

^

o

II

O

HI

Ha^

:

U)

o

z

^>

a

<t

0-

z

HI

_J

<c

ftX

UI

UJ

o

z

o

hTM*

<

3

0

J

•^

U

^_

ft/

o

to

UJ

^<t

Of

1-

Ha.

z

HI

>-

Ot^

^~

o

UJ

~5

<x

ft/

H-

^.

UJ

_J

ft.

o

ft/

Q

II

_J

ft.

(/)

3^

r-l

II

1-

z

HI

Of

a.

HI

II

<

3C

a.

_j

<c

in

o

1

Q

o

o

rH

•

O

II

</)

ft.

UJ

II

o

Q

^5

^

0

O

0

o

•

in

n

o

X

n

II Z

&l O

< o

0

^ o

in o

o in

(7^ o

in o « •

CM 0

II

II 0

O >-

of o

OOOC3OC3OOOC3OOOC3C3OOOOC3

OOOC3C3C3OOC3OOOC3OOC3C3C3OC.

aaaaaQaaaaaaaaaaaaaa

OC7C3C3C3OOC3C3C3OOOOOOOOOO

l-lfHrHi-lrHr-liHi-Hi-li-irNJCM(M(M(MCM(NJ(MCMCM

QQQQOQQClQQQQQClQQQCaQQ

Xooo ooo oooo ooo oo oo ooo

oooooooooooooooooooo

C3C3OOOOOOOC3C3C3OOOC3OOOO

OOOOC3OOOOCJOOC3C3OC3C3C3C3O

inininininininminininininininminintnin

107
CD sj- CO sD f> CM ro 00 ro OO &> o \o <T oQ rO 00 rO t-t CM -O

mr-. co oo r-< »o ro CM o o CM r^ in in r*. o r-i o in vj- o

»— » a* a* o so co r^. CD I-H <r ro CD in CM •— * CD o r-« r-i «tf- o

CM CM o* o v± CT* i— i r>. CD s^- ro o1* m m CM r-- in (**• m, ro m

m ro r-i «-H m co CD r^. in CM o oo co o* CD i— i ro m oo CM oo

K> in CM rH rH \O lO rO vj- in +O *O r*. CO rH rH rH rH rH CM CM

CD CD CDCDOCDCDCDCDOOOCDCDOCDOCDCDOCD

I I I I I I I I I I I I I I I I

CM

CD

OO

ro

\o

QQQQQQQQQQQQQQClQClQQ

ro to <y* o •-* r-i >j- ro csi -j- •<}• i— i "S* r^ o* r^ *- 1 oo co

O

Q

ti— II— l(\IC3O<\JOONj'OOOs'Or**^rHOO CNJ

t-HI-. >»• O» >J- (M 00 TO t^ O> e-H CM ^^• IT) \O r~ CO O O C3 ^

>3- m l>- O> CO i-H r-1 »-l i-H CM CM CM CM CM CM CM CM rO IO IO

OOOOOOOOOOOOOOOOOOO ^

O

Q

xJ*

CNJ

OO QOQQOQOQQQ QQQQQOQQ Q

oo o i^ 10 in r^ ro (M <?• oo >3- o so r>. r^ cr> vo i-H o

to o in co o>. oo in <T> r-. oo o <»• vo CM CM ca a> >j- CM

•— * >o r^ m cO >~*

l CM CM CM CM rO 10 >3-

in in in in in in in in in in in in m in tn in in in in

O

r~

vD

in

O

C3O OOCDOOOOOOOOOrHrHrHCMrHrHrH

OO OOOOOOOOOOOOOOOC3OOO

I I I I I I I

ao oaoaaonoaaaaaoaaaaa

r*. ro o^ NO ro o ro vo rH o <»• in »o

in \r \5- ro ro ro CM CM rH I-H rH rH r^ <r CM CM CM \r \o

OOOOOOOOOOOOOOOOOOO

I I I I

OOOOOOOOOC3OOC3OOOOO O

O

I

aa

O sO

rHCO

ro sis3- ON

>OsO

oa oa a a a a o a a a o a QQ a aa o o

CM cj cs rn so C3 \r rH o ro ON oo ro i— i ro in CO r^ NO in o

so %a* r^ c/s ro r-^ ro in ro \o -d- so CM oo iri in rH ro in CM cr*

o o ro CM CM so \1- os in ro oo r^ >3- a« ro rH I-H oo o ro CM

r^ o osom I-H o rH r^sj- rom o> s3- cMCMm CMO o sio oo so s3- ro ro ro ro ro sfin so r~ crs 1-1 ro in 00 CM in CM

COO

I I

oo

C3C3COOC3C3OC3OCDC3OC3C3C3OC3OO

I I I I I I I I I I I I I I I I I I

aaaoaooaaaaaaaciaaaa

I

o

OOOCMCMOsj-ooOrHsOsrCMrooosOsorooOosrHorOrHOroooin

cMs3-

s3- o CMCMr^soroor>-s3-osoCMr^roosinrH03so

iCMr-iCMinrHCMC\)ros3-s3-ininsOsors.ooooosr

»LlJ<UJLLl

>tnC3(ni/)

en i I i I I i i i i i i i i I i i en I tnin

O_CLD_rHrHQ_CMCMrOrOrOCMCMCMrHrHrHrHr-lrHrHr-HOOOO_Oa.a_rH

CDO C3C3C3OC3OC3OC3OOOC3C3C3OOC3CD CD O

tULJJLU I I UJ I I I I I I I I I I I I I I I I 1X1 LULIJ |

_l_J_IQQ_lQQQQQQQQOQQQQQaQQQQ_lQ_l_lQ

OOOCMoOr^cOOsrCMCMC\lC\losrHCMrHrOinos1-s3-rOroOCMOOi-H

r— sOs3-CMininrOrHs3-rHs3*rOs3-CDrHOsO

OOOOOOOOOOOOC3OOOOCD O

oooaoaaoooooaoaaooaoaaooaoaaQa

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

OOOOOOOOOC3OOOOOOOOC7C3OOOOOOOOOO

C3CDCDC3CDCDCOCDCDCDC3CDCDC3CDCDCDC3C3CDC3CDC3CDC3C3CDCDC3CD

OOOOOOOOOCDOOOOOOOCDOOOOOOOOOOOO

CDC3C3CDC7C3CDCJCDCDCDCDC3CDCDCDCDC3C7C3COCDCDCDCDCDC3C3CDCD

inininininininininminminininininininininminminininintnin

CDCDC3CDCDC3CDCDCDCDCDCDCDC9C3CDCDCDC3CDCDCDCDCDC3CDCDCDCDCD

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

OOOOOOOOOOC300000C3000000

00000000000000000000000

sTOOOOOCDOOOOOOCDOOOOOOOOin

CO

>-

O£

O

rO

UJ

o r^ in CD in CD in <=> tn CD in o m o in CD in o m c? m o in CM

>- CM CM CM rH rH CD CD Os Os OO CO I — f^* so sO in ITi s3" s± K> rO CM CM

s3" s3- >3- s3- s3- s3" sj- ro ro ro ro rO ro ro ro ro ro ro ro ro ro lO ro

.......................

00 O O O O OCD CD OCDO 00 O O O OOCDO O O

I I I I I I I I I I I I I I I I I I I I I I I

O CD CD O CD CD CD CD rH rH rH rH rH rH rH rH CM CM rH r-H rH rH rH

I I I I I I I I I I I I I I I

aa a no a a oa a aa a aa aa aa aa aa

r^ so CM rH ro oo ro oo s3- so CD as oo ro oo ro CM ro so oo CD s3- s3-

rO CD s3- rH rH CD CD rH CM in CD rO S3" rH CD r^ OO sO C3 Os i— I OS l^.

U- oo m ro in r^ in r~ CM in in as ro si- o r^ r-i as s3- o as CM CM so

COinOOCMCOtnrOrHCDOscOOOCDCMinr^CDOOinrHrHinrOrO

rO CM CM rH rH rH rH rH CO f^ SO SO in s3- IO rO SO rH rH CM rO in 00

OOOOOOOCDOOOOOOOOOOOCDOOO

I I I I I I I I I I I I I I I I I

108
OOOOOOOOOOOOOOOOOOOOO

O

'..

If)UJh- 1

Of. 0r—OUJ ->^fV1—(—ZLUOz<t (—

)0 SF(UPPER)= 0.8367040-01 QinmmCM(Mto• CD1II

r-* Of UJ 0-o. — ^ s^CD>-

JO SFUOWER)=-0.35S337D 00 Q\^ON*o

t^ta

CMVf.o1II

**\ C£UJ 2j o^j v^CD>-

0.105139D 00 uf^Of UJ30_)

S^l CD>- ^%n*UJQ. Q. "^s^O>-

CD

CDQCMONCDtoont—IrHUJ3: QUJh-OUJ — 7 oD£Q. _l nOU. 0^rH<t

CD

CDQrHCMtoCDIIUJ£ozUJ rHOrHU. U. UJZonh-OUJ ^J_Joo

0.107891D 01 PERCENT uUJzrH

ftr* O

tto

:

UJ

-^y~rHXE^l

CDQrH00CM°IIt-zUJ yUJC3ZrHQ. y~rHy^3yhHX<E

iHO1Qmi— i SOtoCD1IIXu. 01oCDQ

s^-

pN.

CD

CTN

into* CD|II

r*i Xy~s^O>-

VALUES >- zUJ z: UJozrHQ. EnUJOu. a: 3

vo eo m in so vr •-> CM cr> 1-1 r- r- in CM oo <r NO CM o in o cr> r-~ (si CM in ^ oo

mcr'i-4^mr^

o •-< cr> CM t\i tM r^ o (

>ooooooooooooooo

OOOOOC3OOOOOOOOOOOOOOOOOOOOOOOO

o rH cis CM CM CM r~ o CM to in p^ eo o rH to in so co o CM •* \o r^ ON rH CM <r in r-

)rHi—lrHrHrHrHCMCMCMCMCMCMfOIOfOtOtOtO^-srv3-\J-<J-

O O CD O CD CD CD CD CD CD CD CD CD rH rH i-^ rt r— I i— 4 I—I

OOOOOOOOOOOOOOOOOOO

I I I I I I I

fOfOIOtOCMCMCMCMOOi— l rHC^C»>«XOCOCOO

O

^CDCDCDCDCDCDCDCDCDCDCDCDOOOCDCDCDCDCDCDCDOCDCDOCD^CD

QOQOQOQQQQQQCiaaQClOQQCinClClQClQQQQ

*mC3>Ct'(NJCDCD>CCDCJ^incDi—IsOfOOp—ItOtO

i—ICDlTl^CD*tf-r^CDC\JvDCDCMCf»CMCDi—100"-^

I I I I I I I I I I I I I I I I I I I I

109
OOOOOOOOOOOOOOOOOOOOOOOOOOOO

oooooooooooooooooooooooooocso

f^ in ^* in ix o csj to o o* »—* to «A o^ r^ oo ^ ^ ^o ft- o* oo f^ ^ *~i

OOOOOOOOOOOOOOOOOOOOOOOOOOOO

oo orH to in r^ cr« rn <M «s- in r^ r^ r^«-< pj<Njt\ic\)CM^-ic>«^r^ into

rj<NJ<M^<a-|^

C3CDC3^)OOCOOOOOOOC3t»O

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

<JIII) .

OC3OOOOOOOOOC3OOOC3OOOOC3C3OOOOOOOC3OOC3OOO OOOOOOOOOOOOOC3OOO

I I I I I I I I I I I I I I I I I I I I I I I I I I I I

110
OOOOOOOOOOOOOOl—li—* r-» •—I »—I f-* r-4 (M O

OOOOOOOOOOOOOOOOOOOOOOO

I I I I I I I I o

00000000000000000000000

*O OO CNJ 00 ^O r^ *~* *^~ CNJ '•H ^" CT* 1^^ OO CO "O C5 ^3 \O 00 SO CT» *~*

I I I I I I I I O

00000000000000000000000

C3OC3C3OC3OOC3OOOOC3C3C3OOC3OOCD

C30OOOOOOOOOOOOOOC3C3C3OC30O

I I I I I I I I I I I I I I I I I I I I I I I

00000000000000000000000

QQQQOQQQQQQ O Q aOOaOOOOOO

C3C30OC30OOOC3C3

I I I I I I I I I I I

111
o

CM

CO

SO

If)

ooooooooooooooooooo

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

Cg

O

O

eg

Qto

* M

* (/>

* >-

U- <

eg Z

LU <(

LU O

o z

K4 1-1

o

111

Of

Q.

eg

UJ

o

_l

o

z

x

o

LU sO

r- 00

O. CO

eg

a

Cg

UJ

>

«/>

>- W

CQ «/>

o;

UJ

e«

<C

<ft

X

CM

UJ

I-

<t

a

a.

3

I-

(ft

00

m

ooCM1-1

sO

O

O

CMrOOOOOOOOOOOOOOOOOO

iniOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOO

CslOOOOOOOOOOOOOOOOOO

I-HOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

III II II II II I

so

CM

•a00

sO

to

o <^

s*- o

to in o I-H in LU

O iH O

O O s^>

CD m

HO CD in

o mo

f- into

SO C7> sOtt.

r-. inooLU

in

n

i—

o.

insfOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOO

II II 1 1

Z

O

UJ

eg

o

o

o

o

<t

Q

O

eg

OQ

LU

in

II

eg

x

eg

OUJ

in

oo• •-« m • + r-*o o incM

CMCDCD sO <

ooooco 31

O -COCM D_

OOCO • —I

o i in (si <

O i-H I II s^

o o> z

CO • rH ~M

C3I-H O LU tO

^> toe

(\JsOfOOOOOCPC3OC3OOOCDOOCDCDCD

CMsTCDOCDCDOCDCDCDCDCDCDOOO^CDOCa

C3OOOOOOOOOCDC3OOOOC3C3OO

P3

K

CD

CD

CD

CD

O

CM I —I

CO fO M

CM 01—Q.

O OLU

00-J

sO I OO

II O

OCg

MO

<CO

eg

.. so

ZCM .

M .'• CM CgO

MOO 'LUCM

» >• sjZ •> U.-H

rl O

•• M N

<X X LUCM

Q. •

o

If)

LU

O

. M

OCM U.

ULU

O

o O

z

zcg

. n

« r-l r-l Z Q- tft

XMmuj «o._i

oxxoegLuo

UJ

l-l

eg

o

oooooooooooooooooooo

II II III I II I

Oinsl-ooooooooooooooooo

Ulr-IOOOOOOOOOOOOOOOOOO

inOCDCDC3C5OOC3CDCDOOC>OOOCDOCD

roooooooooooooooooooo

oooooooooooooooooooo

oooooooooooooooooooo

oooooooooooooooooooo

oooooooooooooooooooo

I I I I I I I I I I I

CMinr^ooooooooooooooooo

OsOr-IOOOOOOOOOOOOOOOOO

CftrHOOOOOOOOOOOOOOOOOO

CDCDCDOOCDOCDCDOCDCDCDC3CDOCDC3CDO

CDOC3OOC3CDOC3OOOOOOOOCDC3O

^-OOC3OC3OOC3OCDOOC5OCDOOOO

CDOC5CJC3OOOC3OOOOOCDOOOOC5

OOOOOOOOOOOOOOOOOOOO

oooooooooooooooooooo

I I I II I I I

112
I I

U-X

QCMin

sj-

roco

QQOQQQQQQQ

CO si- so rO CO I** 00 CM o rH

O O> CO 00 so si- rH 00 <*> so

so ro 00 so si- in o o oo in

o o in o- CM si- so r~ rs eo

in rH rH tH CM CM CM CM CM CM

oCDCDO

LL

IIoQ

orO

QQQQQQQQQa

CM CJs o in r-t \O CM so K) 00 00

00 «^ ro in ri os p4 in ro sj- es

in >*• si- <*• in in r- oo o CM in

CD O O O O OOO it rl i-«

m m m m m m m in m m m

o oooooooooo

*xt Q. uj o

oO

tea

.

in

tH10ozO

* rH

*x e

gHI Q. OOf a.

>-

ca

ozoOzXOLUO_ rsS>10

(-4

in

u. Q

soCOs00CMUJa0-in<£

O O O O O O OO Oit it

o oooooooooo

I I

a aaaoaaaaaa

os in so in CM ro r-> CM so oo so

r«- r^ si- CM ri sj- ro in os cs CM

in so so CM r-. m r^ in o >s- r-^

IH oo m o CM o ro CM in r^ **•

sT sT K) IO CM CM iH rH rH 00 sO

O OOOOOOOOOO

OOOOOOOOOO

oooooooooo

inCDOIIIh-in

0 00

o o o • CM O CD I II u u or o of. at >- U. UJ

u.OZ5

QoorOrHroCMOSQQ QQQQQQQQ

i>. in co CM m o< <r CM os in

iH SO CM rH in sj- CO O si- SO

SO CM rO CM O 00 r» s3- rH sl-

oo si- so C3 ro rH si- os in CM

OOOOOOOOOO

rH CMrOCMrHrHrHrHrHrHrH

C3 OOOOOOOOOO

I I I I I I I I I I I Q QQQQQQQQQQ . O rH f<. OS CTS 00 rH

rOsOsl-CMOOCMso

oooooooocsocMsooinmroinsosoro

OQOQGQBQCQeQCQCQrHCQCMsOrHinCMsDOOOOCM

o oo r«- si- o in os ro r^ CM so

LJJ LU LU LLJ LLJ UJ LU LU • UJ

miniOl/>iniOtniOC3(/)

trun 10 «n in in in in in

i i i ii i

X

ZoOf Of ooooto•> <t-Q0£to_i n UJ 0£ uj s

roII

II < _i I a. o. in —i z: <

inOS

si-

oooIIzoo

LU LU LU UJ UJ UJ UJ LU I UJ I I I I I I I I I I

ULOOOOOOOOinOrHinmOSrHrHsl-sl-SOO>

0.0>CMininoOrHsOOsrH

C3OOOOC3OOOC3OOC3C3C3OOOOO

IIoUJoz

LCULATION GEN <£0>-

oe. oi—oLU-><1—

JECTORY INPUT O^f r-rLLJ _l O. 0ora

rHII1-zrHnsa. n

inCD|OoCDrH• CDIIina. LU

CD

CD

CD

CD

CD•

iniuCDX

<TS COomin• roorHII—^ a:

Oooinoo» oIICD>-Q

C7 O> O O ^ C3 C3 CD CD O O CD CD CD CD CD O O O CD

CDOOOOOOOOOOOOOOOOOOOO

>"CDOOOOOOOOOOOOOOOOOOO

oooooooootninoinoinomoino

rHrHiHrHrHrHrHrHrHrHrHrHrHCMCMCMCMCMCMCM

CD O O O O CD O O O CD O O CD CD CD CD O CD O O

I I I I 1 I I I I I I I I I I I I I I I O O O O CD O CD CD O O O CD CD CD CD O O O O O

QQQQQQQQOOQClQQaClQQQQ

C3CDC3OOCDCDCDCDCDOCDCDCDCDCDCDOOOO

XOO^^^CDOO^CDOCDCDCDOOO^O^

^CDOCDCDCDCDCDOOOCDCDCDCDCDOOCDO

CD O O O CD CD O CD CD O CD CD CD CD CD CD O O CD O

OOOCDCDCDCDOCDCDOCDCDCDOCDOCDOO

ininminininininininmininininininininin

CD O O O O O CD O O O O CD CD CD O O O CD CD CD

I I I I I I I I I I I I I I I I I I I I

113
CO CM s3- sO ro t> OO

in CM O* r-H CD \O 00

l~ CM \O CM

i-H sj- CO rO CD CM --H

i-H i-H rH t\) fO s±- O»

O O CD CD O CD CD

QQQQQQQ Q

O sj- r-t CO s3" ro CM 1-^

sj- CM so in sr 1-1 sj- m

co m oo ss- os in vr s±

r- i so CD xt- r^ I-H r-^ in

CM CM ro ro rO IO CM CM

. CD CD CD O O CD O O

QOQQQQQ Q

CTs Cs 00 CTs sO in L"l CD

stf- F-H sj- r^ r^ s}- co x±

CM rH Ox CD s± CM r* s±

00 CM O ro »—i so I-H CM

rH CM CM rO vT ""> r-l i-l

. i-H i-H CM r-l r-l i-l •-! i-H

C3C3OC3C3OCD C3

IO I-H CM «*• r~ ro O O

>o r~- oo eo 10 r~ 10 o

<O •-< >o

o >s- rvl- CM i

OC3C3C3OOO o

I I I I I

QQQQQQ Q Q

r^. r^ oo >o CD oo »— i o

CM O CM >J- to o CM

CM>j-os£>mcor^

»j- in r^ eo <=> fO •-<

CD

Q

osoocMincDinxj->-oo>->-

osrHinrorOrHasQsoQQ

so ro in in CO ro ro CQ

CD in CD sO rO in rH

s3-sj-inmsor--i—ico

LU . LULU

CDOCDCDCDOCDCOOCOC/}

I I I I I I I CO I </) tO

LU UJLJJ

QQQQQQD—1Q—I—I

rHrHrHCMCMsrOsQ-OsCUDO CD CD O CD CD CD O

o

CM

II

r>

Of.

a.

o.

QQQQQQClQQQQ

CMCMCMCMCMCMCMCMCMCMrH

CDOCDCDCDCDCDCDOOO

I I

OOCDCDCDOCDOCDCDO

QQQQQQQQQQQ

O CD CD O CD CD CD CD CD CD CD

CDCDCDCDCDCDCDCDCDCDCD

CD CD CD CD CD CD CD CD CD CD CD

CDCDCDCDCDCDCDCDCDCDCD

CDCDCDC5CDCDOCDCDCDCD

ininminminminminin

CDCDCDCDCDOCDCDCDCDO

II

at

<t

10

>-

oi

o

hO

CDCDCDCDOCDCDCDOCDCDCDCDCDCDCDOOCDCD

CDCDCDCDCDCDCDOCDCDCDCDCDCDCDCDCDOOCD

QQQQQQQC3QC1QQQQQQQC1QQ

CNCDCDCDOCDCDCDCDCDCDCDCDCDCDCDCDCDCDOO

^CDCDCDOCDOCDCDCDCDCDCDCDCDCDCDOOCT^

r-HCDOCDCDCDOCDCDCDCDCDCDCDCDCDCDOCDxO

CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMr

OCDCDCDOCDOCDOCDCDCDCDCDCDCDCDOCDCD

I I I I I I I I I I I I I I I I I I I I

CDCDCDCDOCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

I I I I I I I I I I I I

QQQQQQQQQQOQQQQQQQQQ

CDCDCDCDOCDCDCDCDCDCDCDCDOOCDCDCDCDCD

I I I I I I I I I I I I I I I I I

Q

ro

i—i

m

•3-

ro

II

f^

a:

i

a

CD

in

co

co

o

CM

03

CM

a

CM

ii

LU

z

LU

O

CD

Q

Q

CO

CO

m

oo

<r>

LU

n

Oi

0

^

O

LU

—>

<C

a:

>—

iz

LU

0

Z

<t

tQ

CO

Cfs

sO

cys

rH

•

O

1

II

S-*

Of.

LU

a.

a.

rj

s^

CD

>-

Q

CTs

sT

rH

CO

CM

•

o

1

II

*~s

C£

LU

3

O

_l

s^

0

>-

^-s

O£

LU

2

O

s^

CD

>-

1

r^

at

LU

Q.

OL

3

s^

CD

>-

LU

X

Q

LU

O

LU

— >

O

or

Q.

— I

rH

O

Lu

C£

rH

<I

O

z

LU

rH

O

LU

LU

LU

Z

O

rH

1—

O

LU

— 1

_J

O

o

II

LU

Z

HH

a:

o

C£

a:

LU

E:

3

Jt

rH

X

<

E

CM

CD

I

O

CM

o

•aCD

I

II

^>

X

<:

^^

U.

10

o

o

O

I

II

X

O

>-

114
O1

11)

tu

n

UJ

o

O.

z:

LU

O

u.

a:

IS)OO|—lrHrHrHr—lr-f»-4OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

I I I I I I I

Odd!

O O>OM

yK o oo f"H

 r

^ *~H 00 ^" *tf" ^ r** fO to sj* cr» sj* o CM I-H t

3E • sD IO l/^ IO C\l CM »O <t" f^ IO IO O^ >o o C* o in r^- K) »—1 CM f* >O CM t**- CM s^ IO O^ JO «O ^ IO O*« ^ o r—1 r^ O^ Ifi r^ «rf* *^ iO & C7^ r-i rH 00 00 O r

o

oooooooooooooooooooooooooooooooooooooooooooooo .00000*

OC3C3C3C3CDC>C3OCDCDC>OC3OC3C>OC>O<r>C>OOOOC3C>C>C>C>C3CDC3C>C3OOO(=>CDC3OC3OC3C3C><=)OC>C=><

O I I I I I I

<

X

l<

C3

)^i-iCMrO

O

IOi-li-Hr-l^>-sOr^OO'

(r-li-lrHCMCMCMCMCMCMCMCM

OC3C3OC3C30OOOOCJC30OOOOC3OOOC3C3OOOC3OC3C3OOOOC3OOOC3OC3OC3OOCOOC3DOC3O

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

QQQQQC

<oom

)i-HrHCMr'JI')rHinO<i'OOCMeOr^>O

0 o <

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

IOC3OOC3C3OC3I

aoaooc

X> SOC3 CO O vj

3-vj-roo^moc

OCMvOO^rOsT

O IOCM"-I rH G

3 OO C3 O G

MCMCMCMCMC N

O^^C3C3OCOOO^OC3OOC3^OC3OOOOOC3OOOC3OOC3O^CDOO^C

1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

115
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I I I I I I I I I

116
o

o

o

CM

O

o

(MinOOOOOOOOOl

OQi-HOOOOOOOOOOOOOOOOO

sJ-OOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

I I

UJ

Q.

LU

O

JK

X

*

O

O

tD*_

to

rH Of

(O UJ

>- -I

—I _l

< H

Z S:

«t

O -I

z

O

LLl

Q.

O

>-

CO

o

UJ

a:

Q

<*

>-

IM

</>

o>

UJ

z:

ee

to

<

X

00

x

to

N

CNJ

UJ

r-

<r

Q

Q.

CM

10

CM

r--

o<

o

o

so

00

SO

o O

CM UJ

r~- Q

ca in ^>

o o

1^ • iH CM

•4T o ea ro

n

ia.

oo o r>-o

«o o co

so CMOOQ.

OsO

Z

O

UJ

Of

Of

o

u

o

CQ

<

IQ

oa

<*

_i

UJ

r-.

siCM CTo r^ • +

CMOO OrH

CMOO 00 < oosj-ers x

o -so so a.

VfOrHOOOOOOOOOOOOOOOO

OOC3C3OC3OC3C3C3OOOC3OOOC3C3

OOOOOOOOOOOOOOOOOOO

C3C3C3OC3C3OOOOC3OOC3C3C3OC3C3

I I I I I I I I I

CMOrHOOOOOOOOOOOOOOOOO

OOOC3C3OOOOC3C3OC3OOOOOOOO

9^ rH *""s C3 ^3 ^3 C? O O ^3 C^ *"^ C9 ^9 ^3 *~* **^ **"* ^^ C9

SDC3OC3C5OOOC3OOC3OOOC3OC5OO

ITIOCDC3OOOOOOOC3OOOOC3CJOO

oooooooooooooooooooo

oooooooooooooooooooo

oooooooooooooooooooo

oooooooooooooooooooo

I I I I I I I I I

sOOOr-HOOOOOOOOOOOOOOOOO

CMr^-oooooooooooooooooo

oooooooooooooooooooo

inooooooooooooooooooo

CMC3OC30C3OOOC3OC9OC3OOOOOO

C3OC3C3OOOOC3C3OOOC3C3C3C3C3OO

IOC3OOOC3OO

III I

I II

N

o:

• Z

I-H X

_l

IO >H

sol— a.

CMU.

CM-I

a> i sj-

• z

O KH

II Q

OK

MO

<o

UJ

za:

QO

O s±

O (O

o in

o o

so

•-H in

••so

ZCM

NoO

>- NoNtO

« >- >*•

z » u.in

rH O OrH

•• N N

•«X X UJCM

0_ » _l

«tr- " O

^rH .. Q Z

*NrHrH •• <

3>-lOOh-s^

*t «>-a:rH

H-l— -I-IO II

-rHrHZ OL C/1

ZNJlOUJ -O I

OXXOQJUJO

«t rH

s- +

Z «

•^

s^

<x

II

sOrHOOOOOOOOOOOOOOOOOO

o

10

I—

z

UJ

t-i

o

u.

til

o

o

LU

O

u.

OOOOOOOOOOOOOOOOOOOO

oooooooooooooooooooo

oooooooooooooooooooo

oooooooooooooooooooo

III III I I I I

>oooooooooooo

r*-CMrHOOOOOOOOOOOOOOOOO

CMOOOOOOOOOC3OC3C3C3OC3OC3OC3

OOOOOOOOOOOOOOOOOOOOO

VJ-OOOOOCDC3OC3OOOC3OC3C3OOO

OOOC3C3OOOC3OOC3OOOOOC3C3O

C9 ^9 C3 CD ^3 C3 C3 ^3 ^3 ^7 C3 C3 ^3 CD C3 <*^ ^3 ^3 ^3 **^

OOOOOC3OC3OOOC3OC3OOOOOC3

I I I I I I I I

117
to

CM i-H

SO SO r-H CM tO %J- SO OO r-t r-t t-i r

OC3OOOOOOC3OOO

I I I I I I I I I I I I

o

o

o

o

o

II

CD

Q O

x

to

in

10

o

CM

o*

CM

o

in

000000000000

tooco«— it

OOOC3OC3C3C3OOOO

CDOCDCDOCDCDCDO

C3OOC3C3C3CDI—Ii-Hi—IC

inininininininLninininm

o;

UJ

OLU

O

x

*

o

o

lien

O

Z

cm

LU

o

z

O

_J

O

z

X

o

LU

a

n:

LU

>

01

o«

>-

«0

\

to

V.

<M

UJ

Q

a.

o

o

o

I

II

I-

<n

X

II II Oi

a a: K

>- U- LU

Q.

O

a:

to en in

rv ^

z>

s:

c«

X

LU

•a

oo

O>

O

I

a

O C3 O O O

OC3OOOOOOOOOO

C3OOOOOC3OCDC3OO

OOC3OOC3C3CDC3OCDO

OOC3CDOOCDOOOO O

I I I I I I I I I I I I

ooaoaooooaoQ

O OOOOOOOOOC3OO

LULU LULU LULU I LU I I I I I I I I I

_l_l-l_l_J_lO_JQQQQQQQOQQQQ

O

I—I

I—f.

a:

o

o

o

o

<x

a:

(Q

<t

a

x

o

a:

co

LU

LU

Z

m

sD

u

00

oo

Q_Q-CL.Q_O_D_IOCur^CSJf^rHCNJtOlTir>-Or-*i— ti— I

II

z

o

•a:

at:

LU

o

z

<t

O

O

LU

u

C£

X

Q.

Z

>-

Oi

o

o

LU

a.

o

a:

o

CD OOOOOOOOC3OOC3

I

OC3OOC3C3CDOOOC3C3OC3OC3OC3OO

aoooooooaoooooQaoaao

ICNJCMCNJCMCJ

o

o

o

a.

U.'

o

o

in

i

n

CD

X

10

CO

vD

to

II

3

a:

o

o

m

II

O

OC3C3C3C3C3CDC3C7C3C3C3C3C3C3OOC3OCD

I I I I I I I I I I I I I I I I I I I I

OOOOC3C3OCDC3C3C3OC3C3OC3C3C3C3C3

QQQQQQQQQQQQQOQOQQQQ

C3C3C3OOC3C3C7CDOCDOC3OC3C3OOCDOO

C3C3OC7OCD C3.O O C3 O O CD O O

C3OOOOC3OC3OOCDC3OC3C3C3OOC3O

C3C3OC3CDCDC3CDOOC3OC3C3C3C3C3OOCD

OOC3OCDC3C7CDOC3CDOCDOOCDOOC3O

I I I I I I I I I I I I I I I I I I I I

118
oooooooo

I I I I I I I I

OOOOOOOO

QQQQQOQQ

I

Odd

OOCMvJo in oo

o> co m

i-lfOOO

IOCMOO

OOOOOOOO

QQQQQQQQ

(sjoOCMino.-liniO

OOCMOOsJ-CMrHlMCO

CM ro ro sj- in, >o r-. 00

inininminminin

QQQ

COO 00

CMrHf>.

r~ fO ro

os o o

in in in

rHf-HCMCMf-lr-lf-lr-l

OOOOOOOO

I I I I I I I I

OaOQQQQO

i i i i l

O O O CD CD

OOOOOOOO

QQQQQQQQ

OOOOC3OOO

QQCI

ro si-Hi

inr- i-i

CO <7>i-l

C3 O C3

I

OC3 O

O CO O

QQQ

CMOOO

osj- in

co <a- r^

CO<J- CO

CDCMf— I

I I I I I I I I

QQQQQQQQ QQQ

O O C3 O O

LULU I I LU

QQQQQQQQ—1_IQQQ_I

I

Q

in

vD

to

in

(M

(M

a.

a.

QQQQQQQQQQQQQQ

QQQQQQQQQQQQQ Q

OOOOC300000C30OO

OC3OC3OOOOOOOOC3O

OC30C3OC300OC30C3C3O

inininininminininininininin

ct:

<t

H

a:

o

o

LU

a:

OOOOOOOOOOOOOCTJOOOOOOOO O

C3OOOOOOOOC3C3OC3OC3OOCTC3C3C3OO

QaaQQQQQQQQQQQQQQUQQQQQ

«OOOOOOC3OC300C3C3C3C30C3

\OCDCDCDOC3^CDOC7CDC3^C3C3OC3

fO CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD

tMomoincDincDincDincDinomoinoincDinor^

\o>oinin>j->a-ior<iCMCMi-ii-icDCDCf>c^oooor^r-.\DvOin

COPJCMCMCJCSJCJCMCMCOCSlCMtMCMrHi-lrHrH^-Hr-tr-Hr-li-l

CDCDOOCDCDCDOCDCDCDCDCDCDOCDCDCDCDCDCDCDO

I I I I I I I I I I I I I I I I I I I I I I I

OCDCDCDOC3CDCDCDOCDC3CDCDCDOCDOCDCDCDCDCD

I I I I I I I I I I

QQQQQQQQQQQQQQQQQQQQQQ Q

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDOCDCDCDCDCDCD

I I I I I I I I I I I I I I I I I I I I I

«n

LU

O

LU

LU

O

o

Q

in

CD

I

II

ct

LU

DOQ

00

in

OS

K)

vD

ao

II

^a^:

3

O

in

Q

SO

sO

K1

(M

sO

(M

<*

LU

3

o

Q

CM

CM

m

CD

rH II

O

II l-l

r* LU

fV 1"

LU

3 Q

O LU

_l Is^ O

o LU

~ Qoi

LU _l

CL. l-l

3 LL

s«> oi

CD l-l

LU

O o

ro

Cf. Q

rH 00

O» CO

o CM

r^ in

o

o o

II O

LU

O

Z

LU

l-l

O

M

LL

LL

LU

Z

O

o

LU

O

O

II

LU

Oi

O

LU

X

119
CJ

o

0

•do

to

o

I

II

X

o <£

Q U.

CO

CD

t-t

O»

o

o

II O

Iz o

UJ O E ^ UJ r~

O r^

Z vO

•-I I

II

E ~

3 X

S -4

W E

X «^

<t o

z: >-

CO

L'J

LU

O

UJ

o

Qi

3

CO

^O^C3OOOCD^^^^O^O<

OrHi-lr-HrHi-li-li-Hi-Hi-li-lt-IOOOOCDOOOOOOOOOCIOOOOOOCDOOOOOOOOOOOO

C3OOOC3OOOC3C3OOCDOOCDC3OOOC30OC3OOOOOOOOC3OOOOC3UOOC3OOOO

I I I I I I I I I I I

QQQQQQQQQQQ

mr^ooiocMinsocsr^^oo

r-4r^>CMo*oocjoocMirtOK)

i-icMio\i-ir(insDr^r~cO''k

OOC3OOC3OOOCDOOC3OOOCDOOC3OOOOOOOOOOOC3C5OC3OC3C3OC3OC3OOOO

I I I I I I I I I I I I I I I I I I I

aQQQQQQQQQ

:DovfT**i-isrf-NOC^<rtr>

OsDO^CMIOrOCO'OsrO

«oo»t\)irtoO'Ooo»l"'-"^«*'<Mo*f>.mK>^i<

O^C3OC3O^^OCD^O^OOOCDO^O^O^^^^OOCD^lOO^OOC3^CDOOC3CDOCD<DC3

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

OOOOOOOCDOOOOOOOOOOOOOOOOOOI

OC3OOO^C3OOOOC3CDOCDCDCDOOC3OOCD(

QQQQOQQQQQQQQClQQQQQClClQQl

CMCMCMCMCMCMCMCNINCMCMCMCMCNICMCMCMCNICMCMCMCMrMCMCMCMCMi-lr-li

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

120
OOOOOOOOOOC3OOOO

OOOOOOOOOOOOOOC3OOOO

>OOOOOOOO

>OOOOOOOOOC3OOOOOOOOOOOOOOOt-l>-ti-lf-Hi-<r-li-<CMO

>OOOOOOOOOOOOOC3OOOOOC3OC3OOOOC9OOOOOOOOOOO

I I I I I I I I O

r*H s^ CM C7 O^ Q* ^ CSJ O >O fx C3 «^ IO ^ 00 O

CM rH O O P^ CM O O r

~* CM IO »^ <^ If) ^ »O f^ 00 O* <^ O i— I i— < CSJ

OOOOC3OOOOOC3O

OOOOOOOOOOOO

121
in

CM

o

z

CMO^OOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOO

rOOOOOOOOOOOOOOOOOOO

SJ-OOOOOOO O.O OOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOO

Of

o

o

O

O

—I

O

z

z

o

LU O

r- eo

X

a. eo

OCMOOOOOOC

in oo o ooo <

co oo o

oooooooo

OOC3C3OOOO

00000000

to

x I-H aj

X CO UJ

X >- _i Oi X

_i _i a CM

(* z LU <t

a.

LU o

o z

rH H

O

> uj

<n i-

<

o» a

O.

>- 3

SIC V rH Hx at: ca <n in

LU Q£ < _l UJ _l

•dso

CM

O

ooo

in

oo

oo

oo

OOOOOC3C3O

O OO O O

C3OOOOOOO

OOC3OC3C3OOOC3C3C5OC3C3C3C3CSO

in

II

Ia.

SDrHOOOCSOOOOOOOCSCaOOCiOO

LU

a.

O

Of

a.

l-H

z

<n

x

LU

II

Qi

en

z

o

a:

at:

o

o

o

o

CQ

<

o <to

M Of

oc >-

CO LU I

o:*:

otl ZOC

LU

Z

in ro LU

>S-o o 00 •

>J- > CO «

m o f-io

es so oco

OO O Oi-HQ.

SO vD OOOOLU

CD in oo \r

• O r-H • -f

OOO Oi-4

CMOO r-H <

.ooinoo z

O -o vT O.

O ^ Os • -J

O Si" r-H <I

O t-l | II ~

O CM Z

oooooooooooooooooooo

OOOOOOOOOO)OOOOOOOOOO

oooooooooooooooooooo

oooooooooooooooooooo

I I I I I I I I I

inaOrHooooooooooooooooo

\oirioooooooooooooooooo

eo

x

t-4 X w

O O CM H

O CM OOt-CL

13 C3 COLL

rH tOrH X

CMOOOOOOOOOOOOOOOOOO O

C3OOC3OC3OC3OOOOC3C3OC3C3C3C3e3

C3OOOOOOOOOOOOOOC3OC3OO

CJ C- 3OOOC3C3e3OOC3OOOCDC3OOC3

.II I II I I

i— IsJ-sDOOOOOOOOOOOOOOOOO

inooooooooooooooooooo

1— IOOOOOC3CJC3C3OOOOC3OOOC3C3

C3OOC3OC3OC3C3C3OOOC3OC3OC3OO

OOC3C3OOOOC3C3OC3OOOC3OC3C3C3

a

K

rHO

••«o so I

ZCM

rH • •• CMQfO

ISJOO -LUrH

>- NoNin

« >- in

z - ILIO

rH O OrH

.. M rsj

<tX X LUCM

O. - —I

oo

-rHrHZO.(/>

zNiniu »Q.

OXXOQfLUO

o

Z

LU

O

u.

o

o

o

LU

OOOOOOOOOOOOOOOOOOOO

I I I II I .111 1 I

I— 1OOC3OOC3OOC3OOOOOOC5C3OC3

K)OOOOOOOOOOOOOOOOOOO

C3OC3OOC3OCJOC3OC3C3OC3C3C5OCDO

CSOOC3OC3OC3OC3OOOOC3OC3OOC3

I I I I I I I I I

122
cM ON si- ON «o t^-i 10 oo ON si- o* o oo in c\)

os so ON so in s-f- f—i in NO i—i i—i sj- r*-- ro i—i

CM CM ON si- s-T so O in CM O CM sj- so ON CM

SO r-l SO iH CJ rO ITI sO 00 r-» •

OQQQQQQOOaQQQQ

r— ICMOSfMoOCMO

i— 1CMCMCMCMCMCMCMCMCMCNJCMCMCM

OOOOOOOOOOOOOO

o o Q OQQClQQQ QQQQQQQ

,_! • O O rH ON i-l in i—11-- so IO CM rO CM IO so siO 1— O r^ CM ^ r-l in r-l O O CM sO rO rH rH sill CM I-H CM ro Nfin r--ON r-i ro in oo rH si-r-s.

|_ O OOOOOOOrHi-HrHi-HCMCMCM

to n n m m m m in in in m m m m m m in m

«t O r—

_| Q O O OOOOOOOOOOOOOO

X > X

0 O 000000 000 1-HrHrHrHrH

z O OO OOO O O CD O OO O O O

rH I I I I I

Q QQQQQQQQQQQQQQ

.. U. !»• rONOOCMOOsOrHOOinrHrHCMCM

^ Q CM i-H 00 O O i-H in O IO 00 si-si-•"<• IO 00

e- o 00 r--rH CM oo ON CM i-» ro I-H ro ro ON ON siS _l rH r-. N»-rH 00 sO U1 ro CM i-H ON 00 r*.!-». 00

c2 O IO CM CM CM rH rH rH rH rH rH ON 00 C-« SO in

O X ° OOOOOOOOOOOOOO

Of O o

(X. UJ so o

1 QQ r-^ **N ^-> ^-) ^3 ^3 ^3 CD* c"j o cr** ^3 o cm f3 ^3 o

t n N o o —

* M Of O. 0 0 inOO O

* tO UJ 3 rH 000 0

X >- _i Of X . o o o U.

_l _l Q CO o o o o Q

U. If hH Of I rH O • =}

of z z: ui • • CM H i * f S > 11 1 MO O

O_ . cr> r- I— I "^ 00 oo 00 00 00 CO 00 00 00 00 00 00 00 oo

QJ(r » I ^ IO II ' ' "

O Z 0« Q O£ >- ° O C3 O C3 O O C3 C3 O O C5 CD O O

hH M • O. rH M II 0£

O»->- 3 U-OOfO f ,_,,_,,_,,_, , H

^ j_ ,_, ^_ O OOOOOOOOOOOOOO

ca to

a:

I I I I I I I I I I I I I I

aaaaaaaaaaaaaa

Q.

O

_ UJUJUJUJ

S tn tn en en o in o o o o o o o o o o o o o o

<j totntotn to i i i i i i i i i i ••• •

<,- O OOOOOOOOOOOOOO

N> UJUJUJUJ I UJ I I I I I I I I I

'N ^ _ , > ( i ^^ i ^% ^^ ^^ ^-^ s^ ^\ ^^ f~* r**

r— o K) C3

O SO O

U-OOOOlMOsOr- i

eo

r~isOsj-r-.rs-eor^ooooONt-ONro

r-l O .si- O

Z •• . . j- o

O r— 1^ rH

r H 3 0 r H r H

I— Q. U

<t Z II <

_J tH _J I II II

UJ Q- Q- o M Z oooooooooooooooooooo

^ _j in —J Q N^ o oooo o oo ca o c-> cr> oo o ooo o o o

O f5 *" "* ^ ** ° QQOQQQQQQQQQQQQQQQCIQ

O UJ OO C3 O C3 C3OO O O O OO OO OO O O O

z )_ c-s caca ea o o o oca o o o ooo oo o o o o

O uj -3 >- o ca e--» o o o o o o o o oo o o oo o o o

ry -y ^-4 rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH I—I rH CM CM CM

GO O

O I—I >- OOOOOOOOOOOOOOOOOOOO

„ o r- Of I I I I I I I I I I I I 1 I I I I I I I

< ON <t O

<( o 3 O ^^o o o o oea o o o oca o o o o o o o

° O . " -> m o QQQQQQQQQQQQQQQQQQQQ

T- |_ ^ iv | r^ (SJ ^ X^^<-

?c-'^^c>^o<^c3c9c

-

>

^^cdO^CD^

O <t r— QOONi n ______ _ _ _ _ _ _

>_! Of >- O O K) O CDC3 O OO O OO O <

Of

03

«0

_1

UJ

UJ

z

C5

ON

•

o

II

rv*

N

UJ

o

z

<

•>

Q

<

<v

O

Ho

UJ

-»

<t

1—

rLU

_j

Q.

O

Of

Q

rH

II

1-

z

n

Of

Q.

rH

O

rH

•

O

II

to

Q.

UJ

O

t

m

i

M

0

X

i-H

•

rH

r^

i-H

II

-^

Of

o

•

o

II

o

>-

Q

ininmininininininininininininininminin

C3CJOOC3OOOOOOOOC3C3C30OOC3
OOOOOOOOOOOO

I I I I I I I I I I I I

OOOOOa000000 OOO

inoo^so^CMOi-HOCT^o^J " in oo f

oo o CM in o r-i ^ co vo CM r^ oo 00-3-00

-O OO in O CO CM CM » CO .-I r-l O O" >O >JinsoooooCMi-oro^r-or^cT' o in r--

OOOO-OOOOOOOO I—I O O"

CM CM CM CM to IO IO to IO rO IO rO »O CM rH

000

OQQQOOOOOOOO OOO

»rn r— <o oo o -J- ^H inini-i

CM CM CM

000

m in m in in m in in m in in in soinin

oooooooooooo ooo

I— li— l^ti-H^-ICMrOCMf-HrHrHi— I

C3C3C3OC7OOOOOC3O

I I I I I I I I I I I I

QOQQQQ OQQQQO

co o> vo ^ >3- <r rt CM x

CT^csc^socT^CMinsDr

•-< to r~- so r^ •-! o CM o in r^ CM

sJ-r~*OOvO

f— iCMCMro

OC30 O 00 O O 00 O O

I I I I I

oooooooooooo

oooooooooooo

oaoooaooooao

^ CM r^ o> CM <a vi- p^ CM eo \o i-^

oococooooooooooocooooooo

I

QQQ

coooo

CMr-oo

rooto

CM ^ rCT^CMCM

toioro

000

I

ooo

ooo

o

HH

I—

<t

—I

3

O

_l

•<

I I I I I I I I I I ooaooQoooaao

OCMCM

OC3C3

I I

oaa

a

UJ

i-Hr-itni— ir^coco

uj . . .ILI

I I I I I I I I I I I I tn I in

C3C>OOOC3C3C3C3C3CDOQ_C3CMCMQ. Q^

^C3C3^C3OC9COC3OC3C3 OOO

UJ i i uj in

OOOOOOQOOOOO—IOOO-1 1-1

000 O

Oooooooooooooooooo Q£

OOOOOOOOOOOOOOOOO h—

X

00000000000000000 uj

0=>OOOOOOOOOOOOrOCMfH

a:

<c

CMCMCMCMCMCMCMCMCMCMCMCMCMCM^H^-lr-l

I I I I I I I I

C3C3OC3C3CDOOOC3C3OOOC3C3OOOC3OOOC3C9OC3C3O

OQQQQQQQQQQQOQQQQQOQQaQQCaQQQ Q

OC3C3C^(OC3CDC>OOC3OC3C9C?OC?C3OOC3OOC^C3OOC?r-l

inooooooooooooooooooooooooooosjOf.

in

UJ

OQQQQQQQQQQQQQQQQ

OC7OC3C3C3C3C3OOC3OC3CDOC3O

OOC3OC3OC3CDC3CDC3C3C3OOOC?

on

o

^^C3C3C3^^^CDC3C3^C3^^C3^^^i—Ir—It—IrHf—tr-<CMCMCMf—I

OC3C3C3C3C3C3C3OC3^OC3C^C7OC9C3C3C3C?C=>OC3C3OOC3O

I I I I I I I I I

OOOOOOOOOOOOOOOOO

inininminininininininmininininin

I I I I I I I I I I

oi-HCMro^inNOr^-cocy*!

CMCMCMCMCMCMCMCMCMCM

X

X

X

OOOOOOOOOOOOOOOOOOOOOOOOOOOOO

I I I I I I I I I I I I I I I I I I I I I I I I I I I

o

KO

<t

en:

uj

o

124
PPER)= 0.167705D- 3^^u. 01CDOO

iH

N^" NOPS10

IH• CD1II

/•s

<V/ LUQ. 0_

N-* CD>-

QCMNOOONT

rl ONCD1II

LIJ3O_Js^

LL.

(/) CDOQCDinpsto

ps.

CM• CD1II^N

ft/ LU3Os^CD>-

CD

CDoONCDrHNO10

rl• CDII^\

fiSLU30_J N^CD>-1r\

0£.

LU0. Q. N^CD>-

0CDtotoCDinw— 1• oII1—a: 0

h~l

LUXQLUh—OLU— •) 0fVO. — 1

IHO1 1 HH<t

O0Q0NOmmoON• OIILU*>- OZLU

IHOt— 1 LLU. LUZO

»-H

(—OLUIJOo

D 01 PERCENT 00CMmNOmi— i• CDIILUZnC£OfVenLUz: HX^cCD

CDO

Nl"

NO

fx.

00

00

CD

IIh-ZLUyLUOZnQl-l >C£XE

CMCD

iHrH00toCD1IIXJ£s^

LL.

01

CD

CD0intoCM

^}-

1-1.CD1II

**%X5

.

o>-

</>LU3_l >(—ZLUELUOZnQ. £

ll LUO

LL. &01

rH tO CNJ CD in CN NO O in in NO

'j-\DCMr^>ioinoN\i-in

OOQOOOOOOOOOOQQOOOQOQOOQQOOaoOQQQO

CDCDCDCDCDCDCDCDCDCDOOOOCDCDOCDOCDCDCDOCDCDCDCD

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

CDCDCDCDOOCDCDCDCDCDCDCDCDCDCDCDOOCDCDCDCDOCDCDCDCD<

CDCDCDOCDCDCDCDCDCDCDCDCDCDCDCDOOOCDCDCDCDOCDCDCDt

OaOQOQaQQOOQOQOaQOQaOQOQOaQQOQOOQQ

CD in CD 00 CD CD CD tO CD r— I CD f*s CD ON CD 00 O NO CD 00 CD NO CD \O CD ps CD

CM CMCMCM CM CMCMCMCM CMCMCMCMCMCM CM CJCMCM CM CM CM CM CVJCMCMCM CM CM CM <M CM rHtH O CD I I

125
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOC9OOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOOOOOOOOOOC3OOOOOOOOOOOOOOOOOOOOOOOOC3OOOOOO

ro»oeO'Hioi^

I I I I I I I I I I I I I I I I I

r^rslCNIf^NCSICNirvlCJCSIrOrOlOtOrOrOCSIN

>C>C3CJC5C>C3C3C>OC3C>C5C3e3C>C>C3C3C>C3£3C3C3C5C3C>e3C3C3C>C3C3C3C3

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

>ooooooooooooooooo<

I I I I I I I I I I I I I I I

>oooooooo

I I I I I I I

126
OOOOOOOOOOOOOOOr-4i-Hr-li-li-4in

QOOOOOOOOOOOOOOOOOOOrH

I I I I I I 000000000000000000000

OCDOOOOOOOC3OOOOCJOOC3OOO

OOOOC3C3OC3OOOC3C3OC3i-li-lrHi-lr-lin

OOOOOOOOOOOOOOOOOOOOr-1

I I I I I I

CNJCSKMCMr-HrHi-li-trHi-lr-tr-Hi—Ir

I I I I I I I I I I I I I I I I I I I I I QoaaaoaooooooaoaaaQoo

QQQQOQOQQQQQQQOQQOQQO

OrorotororotoiOioiorororoiOroroioiOMMKI

ooooooooooooooooooocao

I I I I I I I I I I I I I I I I I I I I I

127
z

o

z

o

z

o

z

o

z

o

z

o

z z z

o o o

Ul

C£

Oi

O

o

o

0

<r

>v

03

0

Z

in

3

K>

00

00

0

II

0

O

1

LU

Oi

Oi

o

o

o

0

<c

Oi

CO

0

z

in

=

IO

vD

00

0

II

Q

O

1

LU

Of

Oi

o

o

o

0

^Oi

03

O

Z

in

=>

m

CM

^

o

II

Q

O

1

Ul

Q£

Oi

o

o

0

o

•et

Oi

CO

o

z

co

=5

l^

sjI-H

I-H

II

Q

O

1

Ul

Of

Of

0

o

o

o4

Oi

CO

O

z

in

=>

m

\^in

-«

n

o

o

1

Ul

oi

oi

o

o

o

o

<c

Of

ea

0

z

in

3

CM

0

CM

CM

II

O

O

1

Ul

Of

Of

o

o

0

o

<t

Oi

CO

o

z

in

3

i-H

f-s

CM

.0

II

Q

O

1

LU

Of

Of

O

o

o

o

<c

Oi

CO

o

z

in

=9

vO

SO

O

m

n

Q

o

1

Ul

oi

Oi

o

0

0

o

<t

Oi

03

o

z

in

=5

00

00

*»•

>•

II

O

o

1

Ul

Oi

Oi

o

o

o

0

<t

Oi

00

o

z

in

=>

m

CM

ao

rH

II

O

O

1

LU

Q£

Oi

O

o

o

o

4

Oi

CO

o

z

in

=>

rH

00

<»•

00

r-l

II

0

O

1

LU

Q

0

o

CM

C3

II

Of

X

Oi

LU

O

0

in

CM

0

n

Oi

X

Oi

Ul

Q

o

o

(0

o

II

Oi

X

Oi

Ul

o

0

o

•*

o

II

Oi

X

Of

Ul

Q

0

to

in

o

M

Oi

X

Oi

Ul

o

a

0

sO

O

II

Oi

X

Oi

Ul

Q

0

o

f^

0

II

Oi

X

Oi

Ul

Q

o

0

00

0

II

Oi

X

Of

Ul

o

0

o

0*

o

u

Oi

X

Oi

LU

0

0

in

o>

o

n

Oi

X

Oi

LU

a

m

^0

o

II

Oi

X

Of

128
ii to r~ io io K> t-» •* <»• CM o co

O O O vO CM so (M O O> O CT> CO

S CO m O CM r-l r-l •-! O O O O

Of OOOO O O OOOO O

OOOOOOOOOOO

II OOOOOOOOOOO

tn o moo o mo in>oincr>

1-1 in r-s in o in r- os co 0s °* o*

Q m cr» CM m vo i-» oo o* f» <^ o»

> CO CO O» O* <T> O» «7» CM^O" «*•

OOOOOOOOOOO

o

HI

in

o

i-i a tn o

LU X

a tLLI

O £

< Iff

HH

UJ CO

O >-

Z _l

UJ

UJUJ UJ

LULU U.

LULL —

m -o

r-i <amo CM

II II II

II II

of

o

u.

tx.

LU

o.

Qo

a:

a.

<

a.

10

n

o

<c

a:

o

z

V)

u a:

n UJ

i- _i ZLU

i/> 40 _j

H LULU

a: do- i—LU

LU <COOQOQ_

t- _JQiZ5LUO

o <aa.x
a:

< oQi U.U.U.U.

•< ooooi—

LU

iO

<t

X

o

O

UJ

to

Of.

UJ

o.

O

o:

D.

M

O

O

II

Q

0£

O

II

o

<

a

II

Q

<t

of

S

a:

o o o o o o a o oo o

o (M to oo LO co CM CM <=> -o .-•

O- >3- O* O CM \± 00 -»• IO CO CM

r~ rs. »o vo in st- f*> 10 »o K> K>

I I I I I I I I

ii in o o in omco in o in o

I/I I— \OIOCMrHi-IOOOOOO

o

n o o o o o o o o o o o

OOOOOOOOOOO

(OlT>lTIC\JOCOCNJCMOOCOvO

invor^a-c^eor^-omrocM

O O C5 O O O O O O

o o o oca o o o in

X

^ CM

CM X

X X

•~ 3K ^>O— >

O ~h- UILUc/1

UJ V-U.ZC1LU

I/I LU S M X UJ

N

in or-, in oo

CM1DO Kioroooo

-C3rHCDC5O

(M CM ro v*- in vO P^ 00 <*• <*• O*

O O O O CD O O O O C3 O

O

to

CK

LU

O

Of

LU

O.

o

I J

Lk.

O

of.

a.

f^ r-l O rO r-H O K1 C3

O -O i-H >O • i— I •

CMOi-lrH.3-0 O

II II II II II II II II II

Z Q O

o => Z

>- -MLUH- M LU

t-Ol-QnUJl-QiUHZOf-Qt— LULU

o o;i-_iz3LU3o

oxLui-i««i-tr»oo

C5

LU

I-I

LL

n

UJ

a.

10

LU

X

LULU

t£KLUUJt- QQQ

I— >- Q Of •<>- UJ LU LU

<r»f> => 3 & t— of of of

I— in LU n 1-1 n M

LU LU M 10 a. in 3 3 o LLJ LU t- LU £ z cr <y <y

u_ u. < a. t- a oi a: of

10

o

0£

LU

t—

O

<t

of

<t

O

>-

z

<r

u,

I-I

LU

Io

z

129
ii so >n r*. o in to co in m r-i os

Z o in so so in rH P-H r^ in to r«.

>- in rs. os to so co co so in CM rs.

UJ

II in O si-so r-l in CO 00 sT S3-O

O oo r-i r^ r-i CM «*• in to r*. o o

N

_j CM os to sj- r. os •»• tn ox os os

O r-ICMCMi-l r-l

n

O

Q

O

x

r-l

Q

O

h» r-s 10 1-1 in r-i 1-1 o o o o

cMCMininincMi-ioooo

00 sO CM sj-s»-O r-s-O O O O

00 CO O* «-l m fM C\» O O O O

o

ZI

00 <* 1^ rH O O CSJ rH IT1 O i-t

r>. in o» CM M in to CM o« to 1-1

«o m ro i-i ^i 10 r-- PJ *o o* in

CM c\i<\i ro to vr m m >o ^c so

OOOOOOC3C3C3OO

O

O ooooooooooo

ooooooooooo

ooooooooooo

in m m inminmo o^o

II

O

O

X

rH O O O O O O O rH r-l r-l r-l

_J

O

II

•<

o.

_)

<

in in m r^ in -< rs. o CTS r^ o

CT> 00 >O vO IO 00 ON CMA \O sT

00 CM O IO rH O •* in f-«T* >D

_IIl O OOOs Os Oso rH CM f) IO

O rH rH rH O O O r-l rH rH rH rH

II

o

in o o

ooococ

^HOOvD

CM i-4 r-l i-l fl CM CM IO •* in O>

...........

O O O O O C3 O C5 C3 O C3

I/I

O

CK

UJ

II

<I

(—UJ

CO rH O fO r-- G r-. -J- VD O 00

co »o >o in r^ in »-i oo >i- •-< ro

CM rH IO CM &• CO CO m CO CM fv

II «J- >a- -^ IO CM fO sD O r-l K) IO

cy K> oo in »a- 10 >r oo CM in co r^ o vi- vo ca o i— i oo CM

UJ

Q

o oo o o oo o o

...........

ooooooooooo

OOC3OOC3OOOOO

O

<t

Qi

I

O

UJ

O

II

ZQ_

in .-i >J- oo in c\j CT- r- o vo

II Os Os so so in Os sO in sO CM O

I— r»-os o oo m CM os r-i CM so in

O Q rO sO O SO CM in K) OS K> rH

_J O O O rH rH CM CM tO tO K) CM

UJ

O OOOOOOOQOOO

n os in o r^ oo o co co co r-i to

X in m in so i-i o o to oo r>. r-i

«t sj- 00 CM OS in OS rH r-l Os CO CO

K SO sO r«- f>» CO CO OS Os CO 00 CO

CQ

OOOOOC3OC3C3CDO

UJ

a.

o o o ooo ooo o o

ii in in m in in in m in in in m

<£ o* CM r^ co o CM >o oo so o> t~

CQ sO so m sj-sj-to tO IO CM CM CM

II

rH rHtOOOOsinOsCMOOCMsO

ui r>. to r^ CM m o in os i-^ tn (o

> rH CM CM fO IO si- si- sfr in SO rv

ii so os to in so in CM so so o CM

ui si- osin CM r-i oo o> os in CM in

CMIOlOsS-insOI>.COOsOsOs

OOC3OOOO OC3O C3

UJ

—1

UJ

o

0.

Q oooooooooom Q

<t o in oo ooo ooinr- <f

a£ CM CM to sj-in so r< co os os os o£

N X

0£ «3OO O O«3 O O OOO 0^

OOOOOOOOOOO

ooooooooooin

CM CM ro sj-in so r-oo os os os

ooooooooooo

II

Q

<:

or

x

OOOC5CJC3C3C3C5OO

ooooooooooin

o m o o o o o o o mr^

CM CM to sj- in so r~ oo os os os

...........

ooooooooooo

130
to

_J

Ml—

_JUv^ s^

<i-r^ co

o • oo <y- • • • sr co o» r^ >a- o in

o tri • • o* »o co o to ^ >—isorOi—i if)

<=> CM LTl CO CO sD O r-H O CM \D rH CSJ >£> HCT> o r^ vo IM 1-110 O

•rHCNJ

II II II II II II II II II II II II II II LU

o

oz o

HOZ I-H

(-MO

h- OI-M Hi

3 O UJOt- Q

O. l-l QiLUO Z3

H- I— QJOr Ck^QJUJ —I

Z> <£ OO >-OO£Q^ O

O CX. t-H- Q OOOC* Z

oo aii— i— z oo M ILI ILI <i<t CQZZI-UJJ: o

O O • U. U. H- LU Oi UJ UJ Z M I— X tf>

z z E:

t-n n o u_ 3 i-i LU

or Q • i-i ** n: o <t U- LU M u_ • 3 i— O <IQf»l— I— U-U-LLLULL. •

LL. 1-0-H (^LULULL LULL • LU

a: Q: a; t- 1— QJ o; uj o o LU a: o LU u. >

LU . LU LUO OLULU3OO O LU O O U- O

Q_ — 1 — I <I <t — J — I O O -J O LU CQ

a: LU LU —i LU uj LU LU <n =} a: LU en r^ •

LU O. O. <t Q D_ D- CD 3 O- UJ Q_ 3 LU Q_ LU

_l Qi (XO— Jl^o: OI OOQi 3COQi I—

a.

O LU

o: i0- O

z

131
1. Report No.

NASA CR-175092

2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

Analytical Determination of Propeller Performance

Degradation Due to Ice Accretion

5. Report Date

April 1986

6. Performing Organization Code

7. Author(s)

Thomas L. Miller

8. Performing Organization Report No.

None

10. Work Unit No.

9. Performing Organization Name and Address

Sverdrup Technology, Inc.

Lewis Research Center

Cleveland, Ohio 44135

11. Contract or Grant No.

NAS 3-24105

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

505-68-11

15. Supplementary Notes

Final report. Project Manager, Robert J. Shaw, Propulsion System Division, NASA

Lewis Research Center, Cleveland, Ohio 44135.

16. Abstract

A computer code has been developed which 1s capable of computing propeller

performance for clean, glaze, or rime Iced propeller configurations, thereby

providing a mechanism for determining the degree of performance degradation

which results from a given U1ng encounter. The 1nv1sc1d, Incompressible flow

field at each specified propeller radial location 1s first computed using the

Theodorsen transformation method of conformal mapping. A droplet trajectory

computation then calculates droplet Impingement points and airfoil collection

efficiency for each radial location, at which point several user-selectable

empirical correlations are available for determining the aerodynamic penaHtles

which arise due to the 1ce accretion. Propeller performance 1s finally computed

using strip analysis for either the clean or Iced propeller. In the Iced mode,

the differential thrust and torque coefficient equations are modified by the

drag and 11ft coefficient Increments due to 1ce to obtain the appropriate Iced

values. Comparison with available experimental propeller 1c1ng data shows good

agreement 1n several cases. The code's capability to properly predict Iced

thrust coefficient, power coefficient, and propeller efficiency 1s shown to be

dependent on the choice of empirical correlation employed as well as proper

specification of radial Icing extent.

1 7. Key Words (Suggested by Authors))

Propeller 1c1ng; Performance degradation;

Analytical prediction

19. Security Classif. (of this report)

Unclassified

18. Distribution Statement

Unclassified

STAR Category

20. Security Classif. (of this page)

Unclassified

- unlimited

03

21. No. of pages

137

22. Price'

A07

*For sale by the National Technical Information Service, Springfield, Virginia 22161
National Aeronautics and

Space Administration

Lewis Research Center

Cleveland. Ohio 44135

Offld«l Business

Penally (or Prtrato Uw 1300

SECOND CLASS MAIL

ADDRESS CORRECTION REQUESTED

Postage and Fees Paid

National Aeronautics and

Space Administration

NASA-451

NASA