APC THIN ELECTRIC PROPELLER ANALYSISW B GARNER, November 2012

INTRODUCTIONAPC makes a line of propellers, the Thin Electrics, designed specifically for planes driven by

electric motors at fairly high rpm. They are thinner than the Sport line, making them lighter. They alsohave different pitch and chord distribution characteristics to make them perform better at lower rpm.Diameters range from about 5 inches to more than 14 inches. Pitch to diameter ratios range from about0.4 to 1.0.

The QPROP formulation is used to analyze these propellers, based on a modified version of the1

VBA programs developed for the Sport propellers . The pitch distributions and chord distributions aredifferent. The Cl and Cd functions were modified to account for some of the observed differencesbetween measured and calculated Ct and Cp results.

PITCH DISTRIBUTIONS

The normalized pitch distributions as a function of normalized radius are similar for allpropeller sizes in the measured data base. Figure 1 is a plot of the pitch distributions for a number ofpropellers. The profiles are normalized relative to their name plate pitch values.

APC Thin Electric Prop Normailzed Pitch

1.4

1.2

1

p9x4.5p9x6

p10x5p10x70.8

0.6

0.4

0.2

0

p11x7p11x8p11x5.5p11x8.5p11x10p14x12average0 0.2 0.4 0.6 0.8 1 1.2

r/R

Figure 1. Comparison of APC Thin Electric Pitch ProfilesThese propellers all have nearly constant pitch for r/R between about 0.25 and 0.9. Most show

decreases in pitch near the tip radius. Because these props have such close tracking, the analysis uses asingle average fit polynomial to represent all of them.

1 APC Sport Propeller Performance Program, W B Garner, February 2012

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CHORD DISTRIBUTIONS

Normalized chord distributions are a function of propeller diameter, not pitch. The chorddistribution is essentially the same for propellers with diameters of nine inches are less. Thedistributions become thinner with increasing diameters greater than nine inches. Figure 2 plots thenormalized chord distributions for diameters of nine inches or less. Figure 3 is a similar plot fordiameters of nine inches or more for comparison.

APC Thin Electric Props, Normalized Chordsy = 0.367x3 - 1.3058x2 + 0.9789x + 0.0116

0.25

0.2

8x4 or 50.157x59x6

averagePoly. (average)0.1

0.05

0

0 0.2 0.4 0.6 0.8 1 1.2

r/R

Figure 2. Normalized Chord Distributions, Diameter <= Nine Inches

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Selected Representative APC E Normalized Chords

0.25

0.2

c/R9x60.15

0.1

c/R10x5c/R11x8

c/R14x12

0.05

0

0 0.2 0.4 0.6 0.8 1 1.2

r/R

Figure 3. Normalized Chord Distributions, All DiametersFigure 2 indicates that the chord distributions for the 7, 8 and 9 inch propellers are similar. The

7 inch shows the greatest deviation. It was not part of the UIUC data base,being measured manually bythe author. The differences may be a result of measurement error.

Figure 3 compares 9, 10, 11 & 14 inch normalized chord distributions. As the diameterincreases the relative chord decreases. It was determined that the decrease is linear between 10 and 14inches over the whole radius range. The 10 inch distribution was selected as a reference and scalingwas done using that reference. Figure 4 shows the results. The scaling matches the measured valuesvery closely.

Comaprison of Measured & Scaled c/R. Reference 10"c/R 10" = -0.2017x4 + 1.1395x3 - 2.057x2 + 1.1685x - 0.0063

0.25

0.2 c/R10x5c/R11x8

0.15

0.1

0.05

0

c/R14x12c/R rel10

c/R rel11c/R rel14Poly. (c/R10x5)

0 0.2 0.4 0.6 0.8 1 1.2

r/R3 Of 15

Figure 4. Comparison of Measured and Scaled Chord Distributions

ANGLE OF ATTACK ADJUSTMENTSThe angle of attack, Alpha, is computed using the QPROP formulation, then applied to the

assumed Cl versus Alpha function. Comparison of measured and calculated results indicated that Alphaneeded to be adjusted as a function of pitch to diameter ratio to bring Ct estimates into betteralignment. The Sport program started the adjustment at p/D ratios of 0.5 or greater while this programstarts the adjustment at p/D of 0.7 or greater. These adjustments decrease Alpha with increasing p/Dratios, effectively decreasing the corresponding Cl and resulting Ct.

COEFFICIENT OF DRAG ADJUSTMENTS

The Thin Electric series of propellers have higher propeller power coefficients (Cp) than do theSport props. This is primarily caused by the difference in pitch distributions. The thin props have moreof the blade in stalled conditions for a given set of operating conditions, increasing the drag andrequired prop input power. This program compensates by applying a multiplier to the drag coefficientthat is proportional to p/D ratio.

COMPARISONS OF MEASURED AND CALCULATED Ct COEFFICIENTS

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Figures 5 through 12 are example plots showing measured and calculated Ct as a function ofadvance ratio, J, for several propellers. Overall the matches are satisfactory.

apc thin e 8x6apc thin e 8x4

0.14

0.12

0.12

0.10.1

0.080.08

0.06

0.04

0.02

0

0.06

0.04

0.02

0

Ct meas.Ct calc

Ct meas.

Ct calc

0 0.2 0.4 0.6 0.8 1-0.02

-0.040 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.02

J J

Figure 5. 8x4 Ct Figure 6. 8x6 Ct

apc thin e 9x4.5 apc thin e 9x9

0.12 0.16

0.1

0.08

0.06

0.04

0.02

0

0.14

0.12

0.1

Ct meas.Ct calc

0.08

0.06

0.04

0.02

0

Ct meas.Ct calc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70 0.2 0.4 0.6 0.8 1

-0.02 -0.02J J

Figure 7. 9x4.5 Ct Figure 8. 9x9 Ct

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apc thin e 10x 5 apc thin e 10x7

0.12

0.1

0.12

0.1

0.08

0.06

0.04

0.02

0

0.08

0.06

0.04

0.02

0

Ct meas.Ct calc

Ct meas.Ct calc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.02 0 0.2 0.4 0.6 0.8

JJ

Figure 9. 10x6 Ct Figure 10. 10x7 Ct

apc thin e 11x5.5 apc thin E 11x8

0.1 0.12

0.10.08

0.06

0.04

0.02

0

0.08

0.06

0.04

0.02

0

Ct meas.Ct calc

Ct meas.

Ct calc

0 0.2 0.4 0.6 0.8 1-0.02

-0.04

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.02

J J

Figure 11. 11x5.5 Ct Figure 12. 11x8 Ct

COMPARISON OF MEASURED AND CALCULATED POWER COEFFICIENT, Cp

Figures 13 through x compare measured and calculated values of the power coefficient, Cp, forseveral propeller sizes and p/D ratios.

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apc thin e 8x4 Cp apc thin e 8x6 Cp

0.05

0.04

0.03

0.02

0.01

0

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

Cp meas.

Cp calcCp meas.Cp calc

0 0.2 0.4 0.6 0.8 1

-0.01 0 0.2 0.4 0.6 0.8 1J J

Figure 13. 8x4 Cp Figure 14. 8x8 Cpapc thin e 9x4.5 Cp

apc thin e 9x6 Cp

0.05 0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

0.04

0.03

0.02

0.01

Cp meas.Cp calc

Cp meas.Cp calc

00 0.2 0.4 0.6 0.8 1

-0.01 0 0.2 0.4 0.6 0.8 1J J

Figure 15. 9x4.5 Cp Figure 16. 9x6 Cp

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apc thin e 10x5 Cp apc thin e 10x7

0.05

0.04

0.03

0.02

0.01

0

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

Cp meas.Cp calc

Cp meas.Cp calc

0 0.2 0.4 0.6 0.8 1

-0.01 0 0.2 0.4 0.6 0.8 1

J J

Figure 17. 10x5 Cp Figure 18. 10x7 Cp

apc thin e 11x5.5 apc thin e 11x8.5 Cp

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

0

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

Cp meas.Cp calc

Cp meas.Cp calc

0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1J J

Figure 19. 11x5.5 Cp Figure 20. 11x8.5 Cp

Generally there is good agreement between measured and calculated results. There are exceptions asillustrated in Figure 16, the 9x6 graph. The greatest deviations occur for the higher p/D ratios, a resultof the uncertainty of the drag and lift coefficients over the stalled portion of the blades.

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