Jen-Ching Tsao

Ohio Aerospace Institute, Brook Park, Ohio

Richard E. Kreeger

Glenn Research Center, Cleveland, Ohio

Further Evaluation of Scaling Methods for

Rotorcraft Icing

NASA/TM—2012-217418

May 2012

11ICE-0033
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Jen-Ching Tsao

Ohio Aerospace Institute, Brook Park, Ohio

Richard E. Kreeger

Glenn Research Center, Cleveland, Ohio

Further Evaluation of Scaling Methods for

Rotorcraft Icing

NASA/TM—2012-217418

May 2012

11ICE-0033

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

International Conference on Aircraft and Engine Icing and Ground Deicing

sponsored by the SAE International

Chicago, Illinois, June 13–17, 2011
Acknowledgments

The authors acknowledge the support of the Subsonic Rotary Wing project under Fundamental Aeronautics at NASA Glenn 

Research Center. The authors also wish to thank the NASA Glenn Icing Research Tunnel (IRT) personnel for their excellent and 

committed technical support.

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Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.
NASA/TM—2012-217418 1 

Further Evaluation of Scaling Methods for Rotorcraft Icing 

Jen-Ching Tsao 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Richard E. Kreeger 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The paper will present experimental results from two recent icing tests in the NASA Glenn Icing 

Research Tunnel (IRT). The first test, conducted in February 2009, was to evaluate the current 

recommended scaling methodsfor fixed wing (Refs. 1 and 2) on representative rotor airfoils at fixed angle 

of attack. For this test, scaling was based on the modified Ruff method with scale velocity determined by 

constant Weber number and water film Weber number. Models were un-swept NACA 0012 wing 

sections. The reference model had a chord of 91.4 cm and scale model had a chord of 35.6 cm. Reference 

tests were conducted with velocity of 100 kt (52 m/s), droplet medium volume diameter (MVD) 195 m, 

and stagnation-point freezing fractions of 0.3 and 0.5 at angle of attack of 5 and 7°. It was shown that 

good ice shape scaling was achieved with constant Weber number for NACA 0012 airfoils with angle of 

attack up to 7. The second test, completed in May 2010, was primarily focused on obtaining transient 

and steady-state iced aerodynamics, ice accretion and shedding, and thermal icing validation data from an 

oscillating airfoil section over some selected ranges of icing conditions and blade assembly operational 

configurations. The model used was a 38.1-cm chord Sikorsky SC2110 airfoil section installed on an 

airfoil test apparatus with oscillating capability in the IRT. For two test conditions, size and condition 

scaling were performed. It was shown that good ice shape scaling was achieved for SC2110 airfoil at 

dynamic pitching motion. The data obtained will be applicable for future main rotor blade and tail rotor 

blade applications. 

Introduction 

Aircraft and component manufacturers must thoroughly test new products to determine the effect of 

icing on their performance. This testing is performed both during the design process and for certification 

purposes. Flight-testing is necessary but expensive and can only be done when atmospheric icing 

conditions exist. Furthermore, it can be very time consuming to find in nature the extremes in the cloud 

drop size and liquid-water content (LWC) envelope required for certification testing. Icing wind tunnels 

can simulate natural icing with water-spray and refrigeration systems and provide control of cloud 

conditions, temperature and airspeed to permit safe, convenient and relatively inexpensive testing. 

Because of test-section blockage limitations, many components cannot be tested full size in an icing wind 

tunnel. Furthermore, facilities that simulate natural icing can provide only limited ranges of air speed, 

cloud drop size, and LWC. An icing scaling method is a procedure to determine the scaled test conditions 

to produce the same non-dimensional ice shape results as exposing the reference model to the desired 

cloud conditions. When the reference (full-size) model is too large for a given facility, model-size scaling 

is applied, and when the desired test conditions are outside the facility operating capability, test-condition 

scaling is required. Constraints may also prohibit strict geometric scaling of sub-scale models. 

Scaling methods consist of a set of equations that are used to determine the necessary scale test 

conditions, given the reference conditions, model size, and geometry that need to be simulated. Unlike the 

fixed-wing case where extensive research efforts to develop appropriate scaling methods (Refs. 1 and 2)
NASA/TM—2012-217418 2 

have begun as early as in the 1950’s and continue to the present, there is no single method that has been 

systematically developed and evaluated for rotorcraft icing scaling applications. The scaling parameters 

have not been adequately verified (Ref. 3), in part because there is no publicly available research-quality 

database with which to assess the validity of these methods in a rigorous manner. Scaling methodologies 

also play an important role in obtaining data for icing code development and validation (Ref. 4). 

Previously, icing tests were performed in the NASA Glenn Icing Research Tunnel and scaling results for 

0° and 5° angles of attack were presented by Tsao and Kreeger (Ref. 5). Evidence from ice-shape 

comparison has shown that for NACA 0012 airfoils the ability to simulate a reference ice shape by 

scaling was not affected by the angle of attack in the range tested. Also, for the limited conditions of this 

study, there was no evidence of any difference in the fundamental formation mechanisms of either feather 

growth or horn formation on airfoil models at finite angle of attack. However these tests were made with 

velocities of 76 and 100 kt, and these conclusions may not be valid for higher velocities. Similar concern 

for larger static angle of attack should also be considered. Recently, two icing test programs were 

conducted in the IRT to help identify the limiting conditions and to evaluate other potential alternatives of 

scaling methods for such application to improve the current scaling knowledge and capability for 

rotorcraft icing. 

The test (1) was a follow-up study of Reference 5 in which the static angle of attack of NACA 0012 

airfoil models was further extended from 5° to 7°. Also in the study another potential scaling parameter, 

Wef, was evaluated for velocity scaling in super-cooled large droplet (SLD) glaze icing conditions. The 

test (2), conducted in collaboration with Sikorsky, Boeing, Bell Helicopters, and the Georgia Institute of 

Technology, was a detailed aerodynamic, ice accretion and thermal icing study of oscillating SC2110 

airfoils in various icing conditions. Size and condition scaling were performed for two selected cases 

(Ref. 6), NRC Run 453 and NRC Run 585 as reference conditions. The resulting ice shapes and some 

corresponding load measurements (lift, drag, and pitching moment) will be briefly compared with data 

from Reference 6 to provide a quick check on the current scaling method capability in applications to 

rotorcraft icing. 

Nomenclature 

Ac Accumulation parameter, dimensionless 

c Airfoil chord, cm. 

d Cylinder diameter or 2  leading-edge radius of airfoil, cm 

hc Convective heat transfer coefficient, cal/sec m2

 K 

hG Gas-phase mass-transfer coefficient, g/sec m2

K Inertia parameter, dimensionless 

K0 Modified inertia parameter, dimensionless 

L Length proportional to model chord, cm. 

LWC Cloud liquid-water content, g/m3 

MVD Water droplet median volume diameter, m 

n0 Stagnation-point freezing fraction, dimensionless 

p Pressure, Pa 

pw Vapor pressure of water in atmosphere, Pa 

pww Vapor pressure of water at the icing surface, Pa 

Re Reynolds number of water drop, dimensionless 

t Temperature, °C 

tf Freezing temperature, °C 

ts Surface temperature, °C 
NASA/TM—2012-217418 3 

T Absolute temperature, K 

V Air velocity, kt 

WeL Weber number based on dimension L and water properties, dimensionless 

Wef Weber number based on water-film thickness, water properties and film velocity, dimensionless 

α Angle of attack, deg. 

 Collection efficiency, dimensionless 

0 Stagnation-point collection efficiency, dimensionless 

 Droplet energy transfer parameter, °C 

 Drop range, m 

Stokes Drop range if Stokes Law applies, m 

f Latent heat of freezing, cal/g 

v Latent heat of vaporization, cal/g 

 Air viscosity, poise

 Air energy transfer parameter, °C 

 Air density, kg/m3

i Ice density, kg/m3

w Liquid water density, kg/m3

 Surface tension of water against air, dyne/cm 

 Accretion time, min 

Subscripts: 

R Reference 

S Scale 

st static 

tot total 

Similarity Parameters 

The current recommended scaling methods (Refs. 1 and 2) for unprotected surfaces on fixed wings 

under Appendix C and SLD icing conditions would be a good candidate to begin the development of 

scaling method for rotorcraft icing study. These two references provide a detailed explanation of the 

rationale and derivations of the equations used to describe the similarity parameters involved in traditional 

fixed-wing aircraft icing. It also includes some validation data. A very brief summary of current 

understanding and practice of scaling methods is given here, and the reader is referred to these references 

for a more comprehensive discussion. 

For traditional fixed-wing aircraft icing, various icing scaling studies over the past 50 years have 

shown that there are four most important similarity parameters affecting ice shape. They are: 

(1) Accumulation parameter 

LWC V c

i

A

d

  

 (1) 
NASA/TM—2012-217418 4 

(2) Stagnation-point collection efficiency 0, for example Langmuir and Blodgett (Ref. 7) had shown the 

0 for small water drops across a cylinder of radius d to be a function only of the modified inertia 

parameter, K0, 

0.84

0

0 0.84

0

1 1.40

8 β

1 1+1.40

8

K

K

       

      

 (2) 

This K0 was defined by Langmuir and Blodgett to describe the inertia of drops in an air stream flowing 

around a body: 

0

Stokes

1 1

8 8

K K            

In Equation , K is the drop inertia parameter, 

2 MVD

18

w V K

d

  

 (4) 

where d is the radius for cylindrical models or twice the leading-edge radius for airfoils. Also in 

Equation  /Stokes is the drop range parameter, defined as the ratio of actual drop range to that if Stokes 

drag law for solid spheres applied. It is a function only of the drop Reynolds number, Re

 δ

MVDρ Re

μ

V = (5) 

Langmuir and Blodgett tabulated the values of their calculated range parameter. For convenience, those 

data had been curve-fitted to the following expression: 

1

δ

0.8388 0.001483 Re λ δ

λStokes 0.1847 Re =

   

 

 

 (6) 

(3) Stagnation-point freezing fraction, n0. From Messinger’s (Ref. 8) surface energy balance, the 

stagnation-point freezing fraction is 

,

0

0

p ws

f

c

n

b

         

 (7) 

The individual terms in this expression are , the water energy transfer parameter, 

2

st

,

φ 2 f

p ws

V

t t

c  (8) 
NASA/TM—2012-217418 5 

the air energy transfer parameter, 

tot

2

st tot st

s st

tot

tot st

θ

2 1

.622

ww w

G v p c ww

p pp

V h T Tp tt r Λ

c h p p

T T

      

    

  

 

 (9) 

and b0, the relative heat factor, introduced by Tribus, et al., (Ref. 9) At the stagnation line, it is: 

0 ,

0

LWC p ws

c

V c

b

h

  (8) 

Equation Error! Reference source not found. from Ruff (Ref. 10) includes compressibility effects. A 

simpler form without compressibility was used by Charpin and Fasso (Ref. 11) and others. Ruff’s 

expression for  was used in the calculations for all this work, but values found without compressibility 

are not significantly different for most icing conditions. 

(4) Weber number 

2

We w L

V d  

 (9) 

With scale model size selected, by matching scale and reference values of WeL the scale velocity can be 

determined from 

1/2

R

S R

S

d V V

d

      

 (10) 

Another approach presented by Feo (Ref. 12) involved matching simultaneously the water-film thickness 

and a Weber number that used the water-film velocity and water-film thickness: 

2

We f f w

f

V h   

 (11) 

By equating shear stresses at the air-water interface, the water-film velocity can be written as 

1/2 Re f

f

h

V V

d

      

 (12) 

When Equation (12) is substituted into Equation (11) and letting scale and reference values of (hf /d) be 

equated while matching Wef,S = Wef,R, the expression becomes 

ReWe ReWe L L    S R  (13) 

From Equation (13) the scale velocity from the constant Wef method is 
NASA/TM—2012-217418 6 

2/3

R

S R

S

d V V

d

      

 (14) 

By matching 0 the scale MVD can be found. References 1 and 2 also showed that the effects of 

temperature and LWC are not independent, but interact through the freezing fraction. This is effectively the 

conceptual base of the Olsen method (Ref. 13) for condition scaling. With scale LWC (or temperature) 

selected by user, the scale temperature (or LWC) can be calculated by matching n0. Finally the scale time 

can be established by matching Ac. For the scale model test, then, only temperature (or LWC), velocity, 

MVD and time have to be calculated from the known (reference) values of the similarity parameters. 

While some of those similarity parameters are based on conditions that apply anywhere on the model, 

0 and n0 are specific to the stagnation line of a clean model. Therefore, strictly speaking, scaling methods 

only apply at the stagnation line of a clean model. These parameters vary with chord-wise location and 

change as ice accretion modifies the geometry. Consequently, two assumptions are implied for scaling to 

be valid. The first is that with similar model geometries and similar flows around both reference and scale 

models, if  and n match at the stagnation point, they will tend to match everywhere on the model. This 

assumption has been verified for collection efficiencies in Reference 2. As for other airflow related issues: 

transition and roughness, for example, may not scale, and Re effects are assumed to have a minor 

influence on the final ice shape. Second, if the scaling is done successfully, the scale ice shape normalized 

by the model size will consistently agree with the reference for any accretion time starting with the clean 

model. Thus, scale  and n will continue to match the respective reference values, even though those 

parameters are changing with time. 

As for rotorcraft all the similarity considerations for fixed-wing aircraft icing should apply. In 

addition, compressibility and dynamic effects due to blade rotation must be considered. Also flow-field 

similarity requires matching of advance ratio and pitching settings as well as geometric similarity of the 

rotors. While future studies need to demonstrate scaling when aforementioned effects are present, it is 

necessary for the development of the appropriate scaling methods to begin with a much simplified flow 

and model configuration as a baseline and proceed with additional physical effect of importance one at a 

time in testing. This could allow us to evaluate the significance of various physical effects unique to 

rotorcraft icing independently and reduces the complications from scaling testing. 

Therefore we begin with the main rotor to address scaling, and the baseline is a two-dimensional flow 

over a generic rotor blade airfoil at a prescribed angle of attack that can simulate local flow conditions 

along the blade at various radial locations. In test (1), the symmetrical NACA 0012 airfoil models of 

different chord size were used. The prescribed angle of attack is fixed in time. However in test (2) an 

oscillating SC2110 airfoil section was used with a range of oscillation amplitude and frequency for 

unsteady angle of attack simulation. 

Test Description 

The icing tests were performed in the NASA Glenn Icing Research Tunnel (IRT). The IRT is a 

closed-loop, refrigerated, sea-level tunnel with a 1.8 by 2.7 m rectangular test section. The icing cloud is 

generated by operating 10 spray bars, a configuration in use since 1998. The IRT cloud calibrations for 

both Appendix-C and SLD conditions used for test (1) were performed in the summer of 2008. The LWC 

measurements were made using icing blade method as reported previously (Ref. 14). The MVDs reported 

in this paper are based on an analysis of the MVD calibration data completed in February, 2006. In 

addition, because only a few specific MVD-LWC combinations at speeds of 100, 150, 200, and 250 kt 

(51, 77, 103, and 128 m/s) have been calibrated to date in the SLD regime, additional LWC 

measurements for SLD conditions were made in the IRT on September 22, 2008 with an icing blade. 

Therefore SLD tests are constrained to these particular conditions. As for test (2), the IRT cloud 

calibrations for both Appendix-C and SLD conditions used were performed in April 2009. 
NASA/TM—2012-217418 7 

Figure 1.—NACA 0012 models installed in IRT test section. 

Test 1: NACA 0012 Airfoils at Fixed Angle of Attack in Glaze Icing 

In February 2009, a 5-day test entry was conducted in the NASA Glenn Icing Research Tunnel to 

examine currently existing scaling methods on rotor blades at larger angles of attack. The scaling methods 

were applied to NACA 0012 airfoil models at angle of 5 and 7 through icing conditions that covers a 

range of MVD’s, air speeds and LWC’s, i.e., a number of stagnation-point freezing fractions. 

The models used were NACA 0012 airfoil sections with chords of 91.4 and 35.6 cm shown in 

Figure 1. The 91.4-cm-chord airfoil was a full-span, fiberglass model and served as the reference model. 

The 35.6-cm-chord scale model was of 61-cm span and made of aluminum. It was mounted vertically 

between splitter plates at the center of the IRT test section. The supports allow changing the angle of 

attack via IRT turntable control. Although no angle-of-attack sweeps are planned for this test, models 

need to be rotated to align with airflow using external pressure belts wrapped around the model leading 

edge at specified chord-wise locations along the tunnel vertical center plane. For AOA of 5 and 7 both 

reference and scale models were rotated to align with the airflow by matching the corresponding cp curve 

using the external pressure taps on the models. Horizontal lines at the leading edge indicated tunnel center 

and 2.5 cm from the center as visual guides for locating ice tracings. Both SLD and Mod-1 nozzles were 

used. Also because of the quick start capability of the current IRT spray system, the models were not 

shielded during the initiation of the spray. 

Test 2: An Oscillating SC2110 Airfoil in Icing 

In May 2010, a 10-day test entry of an oscillating rotorcraft airfoil was completed in the IRT. The 

model used was a pressure and thermally instrumented helicopter airfoil section of 38.1-cm chord shown 

in Figure 2. The main objective of this test was to obtain ice accretion and detailed aerodynamic 

measurements for two-dimensional clean and iced oscillating airfoils undergoing both steady and 

transient behavior. It should be noted that the IRT has made some change on nozzle arrangement during 

the April 2009 calibration. As a result, SLD clouds were generated by Mod-1 nozzles. 

In preparing for a test, the temperature and airspeed in the test section and the air and water pressures 

on the spray manifolds were set. When these conditions had stabilized, the spray nozzle valves were 

opened to initiate the spray. The spray was timed for the required duration, and then turned off. The fan 

was brought to a full stop and the researchers entered the test section to document the ice shape with hand 

tracings. Close-up photographs were also taken with a hand-held digital camera. To record the ice shapes, 

a thin slice was first melted through the ice normal to the model surface. A cardboard template was then 

91.4-cm-chord full-span reference model 35.6-cm-chord 61-cm-span scale model 
NASA/TM—2012-217418 8 

Figure 2.—Sikorsky SC2110 model installed in IRT test section. 

placed into this slit and an outline of the ice shape traced by pencil, giving a two-dimensional cross 

section of the ice. For test (1), tracings were taken at the vertical center of the tunnel (91 cm from the 

floor) and at 2.5 cm above the center. For test (2), tracings were taken at stations of 71.1 and 121.9 cm 

from the floor. The ice shapes so recorded were digitized using an automated line-following feature in the 

image-analysis software, SigmaScan Pro (Ref. 15). Since the ice shape differences between the two 

tracing locations were not significant for test (1), only centerline shapes will be reported. As for test (2), 

the 121.9-cm station ice shapes will be reported. 

Uncertainty Analysis 

Estimates of the uncertainty in the reported average conditions were made by considering inherent 

errors of instruments, temporal fluctuation and spatial variation of the instrument readings in the test 

section, and uncertainty in tunnel calibration of MVD and LWC. Recorded air temperature was believed 

to be accurate to 0.2°C, although variations during the period of an icing spray increases the uncertainty 

for reported average temperatures to about 0.5°C. The uncertainty in air velocity was estimated to be 

2 kt. For Appendix-C conditions the net uncertainty in MVD was estimated at 12 percent. For SLD 

conditions it may have been as much as 20 percent. These uncertainties are not referenced to an absolute 

value of MVD, which is unknown. Repeatability and scatter in the LWC calibration data suggests the 

uncertainty is about 12 percent for both Appendix-C and SLD conditions. The test-parameter 

uncertainties were used to estimate the following uncertainties in the similarity parameters for the test (1) 

the uncertainties were: 2 percent in 0, 12 percent in Ac, 10 percent in n0 and 3 percent in WeL and for the 

test (2) the uncertainties were: 3 percent in 0, 12 percent in Ac, 13 percent in n0 and 2 percent in WeL. 

Test Results 

Test 1: NACA 0012 Airfoils at Fixed Angle of Attack in Glaze Icing 

In planning the test matrix, reference test conditions were chosen so that both reference and scale 

conditions would fall within the IRT operating envelope. Due to very limited IRT test time available for 

the scaling evaluation this study is only focused on the SLD droplets. A preliminary evaluation of two 

velocity scaling methods at finite angle of attack was shown in Figures 3 to 6. Those figures compared the 

non-dimensional reference and scale ice shapes obtained using the constant WeL method (part (a) of each 

figure) with those using the constant Wef method (part (b) of each figure) at  = 5 and 7, and for 

stagnation-point freezing fraction of 0.3 and 0.5 at reference velocities of 100 kt. For each figure, 

reference ice shape was shown shaded, while a solid line indicated the scale ice shape. 
NASA/TM—2012-217418 9 

 

Date/Run c, 

cm 

tst, 

°C 

ttot, 

°C 

V, 

kt 

MVD, 

m 

LWC,

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

Wef, 

10-16

(a) 02-03-09/1 91.4 -9.1 -7.8 100 199 1.08 14.0 96 1.75 1.68 0.31 1.17 0.74 

 02-05-09/6 35.6 -9.4 -6.2 156 88 1.37 3.02 96 1.94 1.86 0.28 1.11 3.26 

(b) 02-03-09/1 91.4 -9.1 -7.8 100 199 1.08 14.0 96 1.75 1.68 0.31 1.17 0.74 

 02-05-09/1 35.6 -7.1 -2.6 186 86 0.54 5.61 96 1.68 1.62 0.31 1.57 0.72 

Figure 3.—Velocity scaling with WeL and Wef matched. NACA 0012 airfoils with  5; n0, 0.3; VR, 100 kt. 

 

Date/Run c, 

cm 

tst, 

°C 

ttot, 

°C 

V, 

kt 

MVD, 

m 

LWC,

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

Wef, 

10-16

(a) 02-04-09/1 91.4 -9.1 -7.8 99 198 1.08 14.0 96 1.74 1.67 0.31 1.16 0.75 

 02-06-09/6 35.6 -9.5 -6.2 159 88 1.35 3.05 96 1.96 1.89 0.29 1.15 3.14 

(b) 02-04-09/1 91.4 -9.1 -7.8 99 198 1.08 14.0 96 1.74 1.67 0.31 1.16 0.75 

 02-06-09/1 35.6 -7.3 -2.7 188 86 0.53 5.65 96 1.68 1.62 0.32 1.61 0.70 

Figure 4.—Velocity scaling with WeL and Wef matched. NACA 0012 airfoils with  7; n0, 0.3; VR, 100 kt. 

(a) WeL = c 

(a) WeL = c (b) Wef = c 

(b) Wef = c 
NASA/TM—2012-217418 10 

 

Date/Run c, 

cm 

tst, 

°C 

ttot, 

°C 

V, 

kt 

MVD, 

m 

LWC,

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

Wef, 

10-16

(a) 02-03-09/3 91.4 -15.3 -14.0 100 199 1.08 14.0 96 1.75 1.69 0.52 1.17 0.75 

 02-05-09/8 35.6 -15.9 -12.3 159 88 1.31 2.90 96 1.81 1.74 0.51 1.16 3.04 

(b) 02-03-09/3 91.4 -15.3 -14.0 100 199 1.08 14.0 96 1.75 1.69 0.52 1.17 0.75 

 02-05-09/5 35.6 -10.6 -5.90 188 86 0.53 5.60 96 1.67 1.61 0.53 1.61 0.70 

Figure 5.—Velocity scaling with WeL and Wef matched. NACA 0012 airfoils with  5; n0, 0.5; VR, 100 kt. 

 

Date/Run c, 

cm 

tst, 

°C 

ttot, 

°C 

V, 

kt 

MVD, 

m 

LWC,

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

Wef, 

10-16

(a) 02-04-09/3 91.4 -15.3 -14.0 100 198 1.08 14.0 96 1.75 1.68 0.52 1.16 0.76 

 02-06-09/8 35.6 -15.8 -12.4 159 88 1.31 2.92 96 1.83 1.76 0.50 1.16 3.03 

(b) 02-04-09/3 91.4 -15.3 -14.0 100 198 1.08 14.0 96 1.75 1.68 0.52 1.16 0.76 

 02-06-09/5 35.6 -10.5 -5.9 188 86 0.53 5.64 96 1.68 1.62 0.53 1.61 0.70 

Figure 6.—Velocity scaling with WeL and Wef matched. NACA 0012 airfoils with  7; n0, 0.5; VR, 100 kt. 

 

(b) Wef = c 

(a) WeL = c (b) Wef = c 

(a) WeL = c 
NASA/TM—2012-217418 11 

The table below each figure gave the test conditions and similarity parameters for each pair of reference 

and scale tests. The conditions given were the average conditions recorded over the duration of each test, 

which can sometimes differ slightly from the planned set points. The parameters in the tables were 

calculated from these average conditions. 

Stagnation-Point Freezing Fraction of 0.3.—Figures 3 and 4 showed reference and scale ice shape 

comparisons for the constant WeL and constant Wef methods at  = 5 and 7 respectively. The reference 

model size, velocity and MVD were 91.4 cm, 100 kt, and 195 m. The scale model size was 35.6 cm. The 

coordinates of the ice shapes were all normalized by the corresponding model chord. 

In Figure 3(a) the scale and reference values of 0 matched well but Ac, 0Ac, and n0 were just within 

10 percent, and WeL matched within 5 percent. This was because the averaged reference LWC value was 

reduced to 94 percent of the planned value (i.e., 1.15 g/m3

 instead of 1.08 g/m3) and the scale LWC was 

increased by 7 percent from its planned value (i.e., 1.28 g/m3

 instead of 1.37 g/m3) based on the IRT 

calibration. This disagreement explains the difference observed in the leading-edge ice thickness for this 

pair of shapes. However the scale ice shape did closely simulate the reference main ice shape and feather 

region, even including smaller feathers further aft on the surface. In Figure 3(b) the scale and reference 

values of 0 and n0 matched well and Ac, 0Ac, and Wef were also agreed within about 4 percent. The size 

of the reference ice was simulated fairly well by the scale test in the leading-edge region. The scale ice 

shape also captured pretty well the upper horn structure however it had a rather distinct lower horn 

structure that was not observed in the reference ice shape. 

In Figure 4(a) the scale and reference values of 0 and WeL matched well but Ac, and 0Ac were just 

within 12 percent, and n0 matched within 6 percent. This was because the averaged reference LWC value 

was reduced to 94 percent of the planned value (i.e., 1.15 g/m3

 instead of 1.08 g/m3) and the scale LWC 

was increased by 5 percent from its planned value (i.e., 1.28 g/m3

 instead of 1.35 g/m3) based on the IRT 

calibration. This disagreement again explains the difference observed in the leading-edge ice thickness for 

this pair of shapes. However the scale ice shape captured the reference main ice shape and feather region 

fairly well except the scale upper horn was a bit thinner than the reference one has shown. 

In Figure 4(b) the scale and reference values of 0 matched well, Ac, 0Ac, and n0 were also agreed 

within about 3 percent, and Wef matched within 7 percent. The size of the reference ice was simulated 

fairly well by the scale test in the leading-edge region. The scale ice shape however did not simulate the 

overall reference horn structure very well. 

Stagnation-Point Freezing Fraction of 0.5.—Figures 5 and 6 showed reference and scale ice shape 

comparisons for the constant WeL and constant Wef methods at  = 5 and 7 respectively. In Figure 5(a) 

the scale and reference values of 0 and WeL matched well and Ac, 0Ac, and n0 were just within 3 percent. 

This was because the averaged reference LWC value was reduced to 94 percent of the planned value (i.e., 

1.15 g/m3

 instead of 1.08 g/m3) and the scale LWC was reduced by 2 percent from its planned value (i.e., 

1.34 g/m3

 instead of 1.31 g/m3) based on the IRT calibration. This difference might explain the overall 

size of the scale ice shape appears to be a bit larger than the reference. Still the scale ice shape did 

simulate the reference main ice shape and the feathers well, though a few large feathers in the aft region 

of scale ice shape were not observed in the reference ice shape. 

In Figure 5(b) the scale and reference values of 0 matched well and (Ac, 0Ac), n0 and Wef were also 

agreed within about 5, 2, and 7 percent respectively. This was because the averaged reference LWC value 

was reduced to 94 percent of the planned value (i.e., 1.15 g/m3

 instead of 1.08 g/m3) and the scale LWC 

was reduced by 10 percent from its planned value (i.e., 0.59 g/m3

 instead of 0.53 g/m3) based on the IRT 

calibration. This difference might explain the overall size of the scale ice shape seems to be smaller than 

the reference. The scale ice shape captured the reference main ice shape fairly well, though the simulated 

upper horn structure appears to be smaller than the reference. 

In Figure 6(a) the scale and reference values of 0 and WeL matched well but Ac, and 0Ac were just 

within 6 percent, and n0 matched within 4 percent. This was because the averaged reference LWC value 

was reduced to 94 percent of the planned value (i.e., 1.15 g/m3

 instead of 1.08 g/m3) and the scale LWC 

was reduced by 2 percent from its planned value (i.e., 1.34 g/m3

 instead of 1.31 g/m3) based on the IRT 
NASA/TM—2012-217418 12 

calibration. This disagreement might explain the difference observed in the leading-edge ice thickness for 

this pair of shapes and also why the overall size of the scale ice shape appears to be a bit larger than the 

reference. However the scale ice shape captured the reference main ice shape and feather region fairly 

well except in the lower horn area where the scale ice shape has a thicker structure than the reference one 

has shown. 

In Figure 6(b) the scale and reference values of 0 matched well, Ac and0Ac were also agreed within 

about 4 percent, n0 matched within 2 percent, and Wef matched within 9 percent. This was because the 

averaged reference LWC value was reduced to 94 percent of the planned value (i.e., 1.15 g/m3

 instead of 

1.08 g/m3

) and the scale LWC was reduced by 10 percent from its planned value (i.e., 0.59 g/m3 instead 

of 0.53 g/m3

) based on the IRT calibration. This difference might explain the difference observed in the 

leading-edge ice thickness for this pair of shapes and also why the overall size of the scale ice shape 

seems to be smaller than the reference. The size of the reference ice was simulated fairly well by the scale 

test in the leading-edge region but the scale ice shape did not simulate the overall reference horn structure 

very well. 

Test 2: An Oscillating SC2110 Airfoil in Icing 

In planning the test matrix, there was consideration to run some icing conditions from previous rotor 

airfoil icing test and compare the results with data from Reference 6. Two cases, NRC Run 453 and NRC 

Run 585, were chosen as reference conditions. The model used for those conditions was a 15.2-cm-chord 

NACA 0012 airfoil but the present test utilized a Sikorsky SC2110 airfoil section of 38.1-cm chord. 

Figure 7 showed the cross section profiles of both airfoils near the leading edge. In spite of the high-lift 

camber of SC2110 airfoil, both airfoils have rather similar leading edge characteristics in terms of their 

nose radius of curvature and maximum thickness to chord size ratios. Therefore it was decided that for 

calculating the scale test conditions the NACA 0012 airfoil of 35.6-cm chord was used as the scale model 

and the 15.2-cm-chord NACA 0012 airfoil as the reference model. 

Figure 7.—NACA 0012 and SC2110 airfoil section profiles. 
NASA/TM—2012-217418 13 

 

Date/Run c, 

cm 

M ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac n0 WeL, 

106 , 



∆,



, 

Hz 

NRC Run 585 15.2 0.59 -10. 370 20 1.03 0.75 92 1.99 0.68 2.68 -0.1 4.5 5 

NRC Run 585m 15.2 0.40 -10. 250 20 1.03 0.75 91 1.35 0.66 1.23 -0.1 4.5 5 

5-27-10 Run 60 38.1 0.25 -9.2 158 43 0.65 4.70 91 1.35 0.66 1.23 -0.1 4.5 5 

Figure 8.—Size scaling with WeL matched for NRC Run 585. 

Condition Scaling for NRC Run 585.—Figure 8 showed reference and scale ice shape comparison for 

the case NRC Run 585 in which the airfoil was oscillating at  = –0.1 with moderate amplitude and 

frequency. When calculating the scale condition, it was concerned that the scale velocity would be still 

high (235 kt) so the reference velocity was reset to 250 kt (i.e., M = 0.4 instead of 0.59) for calculation. 

Taking into account the potential velocity change effect on the reference ice shape, for instance some 

increase in horn angle and some reduction in the size of ice shape, the scale ice shape did simulate the 

reference main ice shape quite well. Distinctive feather regions on the scale ice shape were completely 

missed from the reference ice shape. It was very possible with such a short spray (45 sec only) that the 

reference ice shape did not even have any large enough feathers behind the horns to be penciled in on the 

tracing templates. This is the difficulty and challenge often encountered in icing scaling study: i.e., “how 

good is good enough”. Conceptually the scaling method should work for all scales in size and time but 

practically there is always limit on how much detail can be included. Therefore when reference and scale 

ice shape comparison was made one often needed to bear this in mind. 

For this case, condition scaling methods were also applied to the 5-27-10 Run 60 to generate an 

alternative scaling condition in which the user can utilize better LWC and MVD values within the IRT 

operational envelope. It was previously reported in Reference 2 that the Olsen method can be used to 

scale LWC over a limited range at least in the IRT for both Appendix C and SLD condition. Furthermore 

if the scale test was only interested in simulating the main ice shape but not the icing limit; a 

recommended procedure for MVD scaling can be used as well over the range of 25 to 195 m. Interested 

reader is referred to this reference for a more comprehensive discussion. 

Figure 9 showed the reference and scale ice shapes obtained from aforementioned condition scaling 

calculations. The 5-27-10 Run 60 was considered as the reference and the 5-27-10 Run 59 as the scale 

condition. With a LWC of 0.5 g/m3

 and a MVD of 22 m while maintaining the velocity and model size 

the same, the temperature and spray time for the new scale condition were calculated by matching the 

reference n0 and 0Ac. As expected with smaller MVD, the scale ice shape captured the reference main 

ice shape and large feathers on the upper surface fairly well. The only thing missed by the scale ice shape 

was the region of very small feathers covering most of the lower reference model surface. For this ice 

shape, the authors actually have examined the tracing templates and discovered that though there was no 

pencil tracing but a note was there describing about the very small feathers in that region. 
NASA/TM—2012-217418 14 

Date/Run c, 

cm 

M ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106 ,



∆, 



, 

Hz 

5-27-10 Run 38.1 0.2 -9.2 158 43 0.65 4.7 91 1.3 1.22 0. 1.23 -0.1 4.5 5 

5-27-10 Run 38.1 0.2 -6.1 158 22 0.50 6.9 80 1.5 1.22 0. 1.23 -0.1 4.5 5 

Figure 9.—LWC and MVD scaling application for 5-27-10 Run 60. 

For icing scaling studies, it had never been able to obtain the aerodynamic load measurement and the 

ice accretion at the same time. The load measurements such as CL, CD, and CM certainly provided 

invaluable information on how airflow interacts with ice shape during the accretion. It helped one to 

assess how similar the iced aerodynamics was for the reference and scale ice shapes and how sensitive the 

aerodynamic responses to any discernible difference between the reference and the scale ice shape. 

Figures 10 to 12 showed and compared the time history of CL, CD, and CM measurements for two 

geometrically similar ice shapes obtained from condition scaling, i.e., 5-27-10 Run 59 and 60. Although 

those load measurement were raw data and have not been properly reduced for detailed load analysis 

purpose, it was considered adequate for this study to help evaluate how aerodynamically similar those two 

ice shapes were. It was observed that: 

1. Both CL and CM of the scale ice shape simulated fairly well the reference CL and CM curves. This 

implied the overall large scale reference ice shape features such as the main ice shape and large 

feathers were duplicated fairly well by the scale ice shape. Aerodynamically speaking, the 

inviscid air responses of these two ice shapes were similar. 

2. The CD curve of the scale ice shape though followed the general trend of the reference CD; it 

seemed to under represent the reference drag value. This suggested that the small ice shape 

features did matter to the overall drag through the interaction with the airflow boundary layer, and 

so far as the drag was concerned, the scale ice shape did not capture those smaller ice feathers of 

reference ice shape well enough to have similar drag characteristics. 

These findings were consistent with the current understanding of the effect of various ice shape features 

on the ensuing aerodynamics of an iced airfoil. 

Condition Scaling for NRC Run 453.—Figure 12 showed reference and scale ice shape comparison 

for the case NRC Run 453 in which the airfoil was oscillating at  = 6 with moderate amplitude and 

frequency. Size and condition scaling calculations were performed to determine the scale test conditions. 

Since this was a rime ice accretion, it permitted one to choose the scale V, LWC, and MVD, and the 

temperature and spray time were calculated by matching reference n0 (=1) and 0Ac. Certainly the scale 

temperature could have gone colder than the value obtained from the scaling calculation for just rime. It 

was a good practice for the researchers to set the temperature just cold enough to have rime to 
NASA/TM—2012-217418 15 

independently validate the tunnel’s LWC calibration. For any researcher to develop confidence in the 

tunnel operation capability, it was recommended to include some rime ice test conditions to check on the 

facility whenever possible. 

Considering the apparent effect of model geometry on rime ice accretion, the scale rime ice shape of 

5-26-10 Run 52 did simulate well the reference NRC Run 453 rime ice shape except the overall size 

appeared to be a bit smaller than the reference. 

(a) 

Figure 10(a).—The time history of lift coefficient (CL) 

measurement for 5-27-10 Run 59 and 60. 

(b) 

Figure 10(b).—The time history of drag coefficient (CD) 

measurement for 5-27-10 Run 59 and 60. 

 
NASA/TM—2012-217418 16 

Figure 11.—The time history of pitching-moment coefficient 

(CM) measurement for 5-27-10 Run 59 and 60. 

 

Date/Run c, 

cm 

M ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 , 



∆, 



, 

Hz 

NRC Run 453 15.2 0.40 -10.0 250 20 0.3 1.0 91 0.52 0.48 1.0 6.0 4.5 5 

5-26-10 Run 52 38.1 0.25 -10.3 158 22 0.5 2.7 80 0.60 0.47 1.0 6.0 4.5 5 

Figure 12.—Size and condition scaling for NRC Run 453. 

Summary/Conclusions 

Two rotor airfoil icing tests were performed in the NASA Glenn Icing Research Tunnel, and some 

size and condition scaling results from airfoil models at fixed angle of attack and dynamic pitching 

motion were presented in this study. Evidence from ice shape comparison for NACA 0012 airfoils 

showed that the ability to simulate a reference ice shape by size scaling was not affected by the angle of 

attack in the range tested. Also limited evidence from ice shape and load measurement comparison for a 

Sikorsky SC2110 airfoil suggested that the ability to simulate a reference ice shape by size and condition 

scaling was not affected by the dynamic pitching motion in the range tested. 

Good ice shape scaling was achieved by matching scale and reference values of the parameters 0, Ac, 

n0, and WeL for NACA 0012 airfoils with angle of attack up to 7. Model size ratio was 2.6:1 and freezing 

fractions covered the range from 0.3 to 0.5. The present SLD reference tests were made with velocities of 

100 kt, and these conclusions may not be valid for higher velocities. Additional testing in the IRT is 

needed to document the limiting conditions for such application to improve the current scaling knowledge 

and capability for rotorcraft icing. 
NASA/TM—2012-217418 17 

From the load measurement of two similar ice shapes obtained from condition scaling it was shown 

that the CL and CM of reference and scale ice shape would be similar if the main ice shape and large scale 

feather features were kept via the scaling calculation. However for the CD similarity, the smaller reference 

ice shape features (in the order of the boundary layer scale) would also have to be captured by the scale 

ice shape via the scaling. 

Developing an experimental method for rotorcraft scaling will help industry users (domestic or 

international) to standardize the scaling test procedure as well as its credibility as a means of compliance 

for certification. As a result it will shorten the time and resource required for the certification process. It 

will also enhance NASA’s own core capability to conduct relevant icing test in an icing research tunnel 

(i.e., its ability to simulate the actual in-flight icing condition and its effects) as well as increase our 

knowledge of relevant icing physics involved. 

References 

1. Anderson, D.N., “Manual of Scaling Methods,” NASA/CR—2004-212875, March 2004. 

2. Anderson, D.N. and Tsao, J.C., “Ice Shape Scaling for Aircraft in SLD Conditions,” NASA/CR—

2008-215302 and DOT/FAA/AR-07/55, September 2008. 

3. “Rotor Blade Electrothermal Ice Protection Design Considerations,” SAE Aerospace Information 

Report 1667, Rev. A, September 2002. 

4. Flemming, R., Britton, R., and Bond, T., “Role of Wind Tunnels and Computer Codes in the 

Certification and Qualification of Rotorcraft for Flight in Forecast Icing,” NASA TM 106747, 

October 1994. 

5. Tsao, J.C. and Kreeger, R.E., “Evaluation of Scaling Methods for Rotorcraft Icing,” AHS Forum 

65, May 27-29, 2009 and NASA/TM—2010-215801, March 2010. 

6. Flemming, R.J. and Lednicer, D.A., “High Speed Ice Accretion on Rotorcraft Airfoils,” NASA 

Contractor Report 3910, August 1985. 

7. Langmuir, I. and Blodgett, K.B.: “A Mathematical Investigation of Water Droplet Trajectories,” 

Army Air Forces Technical Report No. 5418, February 1946. 

8. Messinger, B.L., “Equilibrium Temperature of an Unheated Icing Surface as a Function of 

Airspeed,” J. Aeron. Sci., vol. 20 no. 1, January 1953, pp 29–42. 

9. Tribus, Myron, Young, G.B.W. and Boelter, L.M.K., “Analysis of Heat Transfer Over a Small 

Cylinder in Icing Conditions on Mount Washington,” Trans. ASME, vol. 70, November 1948, 

pp 971–976. 

10. Ruff, G.A., “Analysis and Verification of the Icing Scaling Equations,” AEDC-TR-85-30, vol 1 

(rev), March 1986. 

11. Charpin, F. and Fasso, G., “Essais de givrage dans la grande soufflerie de Modane sur maquettes a 

echelle grandeur et echelle reduite,” L’Aeronautique et l’Astronautique, no. 38, 1972, pp 23–31. 

English translation published as “Icing Testing in the Large Modane Wind-Tunnel on Full-Scale 

and Reduced Scale Models,” NASA TM-75373, March 1979. 

12. Feo, A., “Similarity of Water Film Weber Number and Film Thickness in Icing Scaling,” 

AE/TNO/4420/264/INTA/01, Instituto Nacional de Técnica Aeroespacial, October 2001. 

13. Olsen, W. and Newton, J., “Experimental and Analytical Evaluation of Existing Icing Scaling 

Laws,” unpublished draft of NASA Technical Memorandum, 1986. 

14. Ide, Robert F. and Oldenburg, John R., “Icing Cloud Calibration of the NASA Glenn Icing 

Research Tunnel,” AIAA-2001-0234, January 2001. 

15. SigmaScan Pro, image-processing software, ver. 5.0, Systat Software, Inc., Point Richmond, CA. 
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Further Evaluation of Scaling Methods for Rotorcraft Icing 

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6. AUTHOR(S)

Tsao, Jen-Ching; Kreeger, Richard, E. 

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WBS 877868.02.07.03.03.01 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The paper will present experimental results from two recent icing tests in the NASA Glenn Icing Research Tunnel (IRT). The first test, 

conducted in February 2009, was to evaluate the current recommended scaling methods for fixed wing on representative rotor airfoils at 

fixed angle of attack. For this test, scaling was based on the modified Ruff method with scale velocity determined by constant Weber 

number and water film Weber number. Models were un-swept NACA 0012 wing sections. The reference model had a chord of 91.4 cm and 

scale model had a chord of 35.6 cm. Reference tests were conducted with velocity of 100 kt (52 m/s), droplet medium volume diameter 

(MVD) 195 μm, and stagnation-point freezing fractions of 0.3 and 0.5 at angle of attack of 5° and 7°. It was shown that good ice shape 

scaling was achieved with constant Weber number for NACA 0012 airfoils with angle of attack up to 7°. The second test, completed in May 

2010, was primarily focused on obtaining transient and steady-state iced aerodynamics, ice accretion and shedding, and thermal icing 

validation data from an oscillating airfoil section over some selected ranges of icing conditions and blade assembly operational 

configurations. The model used was a 38.1-cm chord Sikorsky SC2110 airfoil section installed on an airfoil test apparatus with oscillating 

capability in the IRT. For two test conditions, size and condition scaling were performed. It was shown that good ice shape scaling was 

achieved for SC2110 airfoil at dynamic pitching motion. The data obtained will be applicable for future main rotor blade and tail rotor blade 

applications. 

15. SUBJECT TERMS

Icing; Scaling; Rotorcraft 

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