The measured geometries of the NR640 (Clark Y, NACA Report 640) and DA4002/DA4022 (SDA1075 section) propellers, imposed on Heliciel in reverse engineering, and their C_T, C_P and efficiency compared with the University of Illinois measurements, within the domain where the comparison makes sense.

Validation: Wageningen B-series
Reverse engineering
Reading Kt, Kq and J
Heliciel MCP connector

The Wageningen B-series lets Heliciel be compared with marine propellers tested in a towing tank. For aircraft propellers, no series is as standardized. There are, however, propellers whose geometry and measured performance are both known. This page compares two families of them, both measured in a wind tunnel by the University of Illinois with their geometry surveyed:

• the NR640, a 3D-printed replica of the Navy 5868-9 with Clark Y sections, a 10-foot propeller tested by NACA in 1938 (Report 640) (sections 1 to 7);
• the DA4002, a rectangular blade designed at the University of Illinois, with a single published section, the SDA1075, along the whole blade, tested at four pitch settings, and its wider variant, the DA4022, tested with 2, 3 and 4 blades (sections 9 to 13).

Each time, Heliciel is given the surveyed geometry and computes the performance over the whole advance ratio sweep; the computed curves are laid over the measured points. Section 8 delimits, for both families, the domain of interest: the J values where the comparison makes sense.

1: The question, and what it does not cover

The question is the same as for the B-series: with an identical geometry, does Heliciel's BEM (Blade Element Momentum) model reproduce the measured coefficients? The comparison covers a sweep in J, not a single point.

What it does not cover:

• the measured model is a small, low Reynolds number propeller: 6,000 to 46,000 depending on the element and the speed (section 5). This is the domain of drones and scale models, not of an aircraft propeller. The comparison therefore tests the low Reynolds polars as much as the BEM itself;
• the model is 3D-printed, and its measured geometry departs from the design: 16.36° instead of 15° at 0.75 R, rounded blade tip. Heliciel was given the measured geometry;
• the full-scale propeller of Report 640 is not compared here. It ran in front of an engine nacelle, its published thrust is an effective thrust (thrust minus the change in nacelle drag) and its efficiency that of the propeller-engine unit: these are not the isolated propeller quantities that Heliciel computes;
• a single configuration is run: 2 blades, 15°, 9 inches, at two speeds. The database also holds 3- and 4-blade versions and a 5-inch model, not run so far.

2: The measured reference

The measurements come from the UIUC Propeller Data Site, volume 2, compiled by R. W. Deters (applied aerodynamics group of M. S. Selig, University of Illinois). For each propeller the database publishes the surveyed geometry (chord and pitch angle along the radius), the static coefficients and, in the wind tunnel, C_T, C_P and efficiency against J at several speeds. It states that its latest wind tunnel correction method is applied. The original propeller is described in NACA Report 640 (Hartman and Biermann, 1938). Linking the NR640 to that report rests on its name and on the agreement of its design geometry with figure 2 of the report: nearly constant pitch, P/D 0.63 between 0.6 and 0.75 R, maximum chord of 0.153 R near mid-radius.

Two speeds are selected for the 2-blade 9-inch model: 6,000 rpm (runs 6004 and 6068 of the database, 27 points from J 0.10 to 0.68), the highest Reynolds number available, and 3,000 rpm (run 3023, 9 points from J 0.21 to 0.64), for the Reynolds effect. On these same measurements, the maximum efficiency goes from 0.544 at 3,000 rpm to 0.641 at 6,000 rpm: the same propeller loses 10 points of efficiency when the Reynolds number is halved.

3: The geometry imposed on Heliciel

The model's surveyed geometry file has 18 stations, from 0.15 to 1.00 R. Heliciel receives them in reverse engineering mode: 228.6 mm diameter, 2 blades, 8 elements, a chord law tabulated on the 18 stations, and pitch angles read on the same table at each element root radius and at the tip. The interpolation is monotone (PCHIP): it passes through every station without oscillating between them. The table below reads back what Heliciel actually applied; chord and pitch angle match the table to the hundredth.

Three choices had to be made for lack of data, and they must be stated:

• section: the UIUC database only publishes chord and pitch angle. The section is the Clark Y of the original propeller, taken here as a single profile of Heliciel's database, clarky_turbulent, over the whole blade. Yet the design thickness ratio goes from 37 % at 0.30 R to 8 % at 0.95 R: the blade root is represented by a much thinner section than the real one;
• hub: no file gives its radius. The blade root is set at 0.155 R (17.7 mm), just above the first measured station;
• fluid: the air of Heliciel's aircraft propeller model, 1.012 kg/m³. The C_T and C_P coefficients do not depend on density; the Reynolds number does depend on the viscosity of the fluid used.

The reverse engineering grid after application: radii, chords, forced section, pitch angles and pitch ratios of the 8 elements, plus the tip

Blade outline and element stations, from the root (17.7 mm) to the tip (114.3 mm)

4: The 3D model, a visual check

The 3D model is built by Heliciel from the imposed geometry. It serves as a visual check: narrow blade, maximum chord near mid-radius, strong twist from root (41.5°) to tip (9.4°), tip rounded by the surveyed chord.

Front view	Side view: the twist
Three-quarter view	A single blade

5: The J sweep at 6,000 rpm

Speed is held at 6,000 rpm and the advance speed swept from 2.29 to 18.3 m/s in 25 points, i.e. J from 0.10 to 0.80, in off-design mode: the imposed geometry is never recomputed. C_T and C_P are recomputed from the thrust, power, density, speed and diameter read in Heliciel's table, and agree with its own columns. Element Reynolds numbers, read at J = 0.437:

The sweep in Heliciel's multiple analysis window, marine reading K_T, 10 K_Q and efficiency (K_T equals C_T here)

Blue dots: UIUC measurements. Orange line: Heliciel. Same propeller, same speed

Point by point, Heliciel being interpolated at the J of each measurement:

Up to J 0.37, deviations stay between −5 and +6 % on C_T and C_P, and efficiency is matched within 0.017. The computed curve then does not bend down as fast as the measurement: at J 0.52, Heliciel gives 30 % more thrust, and thrust vanishes later (J 0.742 against 0.674). The computed curve is smooth from end to end. Near zero thrust, the ratio of two small quantities makes relative deviations meaningless: they are marked n.s. when the measured C_T is below 0.005.

6: The same sweep at 3,000 rpm

At 3,000 rpm the Reynolds numbers are halved (table of section 5). Same protocol, advance speed from 1.14 to 8.0 m/s.

Blue dots: UIUC measurements, run 3023. Orange line: Heliciel

Agreement holds only up to J 0.31, then the overestimate grows faster than at 6,000 rpm: +40 % on C_T at J 0.43, against +9 to +12 % between J 0.42 and 0.44 at 6,000 rpm. Heliciel reproduces the direction of the Reynolds effect: its maximum efficiency drops from 0.690 to 0.637 when the speed goes from 6,000 to 3,000 rpm. It does not reproduce its magnitude: a computed drop of 0.05, against 0.10 measured. At 3,000 rpm the elements work between the only two polars the database holds below a Reynolds number of 50,000, at 12,000 and 50,000: interpolating between them cannot restore what neither of them describes.

7: What can be said, and what remains open

What is established

• On this propeller and at these Reynolds numbers, Heliciel matches the measured C_T, C_P and efficiency within a few percent over the lower half of the sweep, where the propeller is loaded: J ≤ 0.37 at 6,000 rpm, J ≤ 0.31 at 3,000 rpm.
• Beyond that, it overestimates thrust and power, more so as J increases and as the Reynolds number drops. The computed efficiency is then too high: +0.05 at maximum efficiency at 6,000 rpm, +0.09 at 3,000 rpm.
• The computed geometry is indeed the measured one: the applied chords and pitch angles reproduce the table to the hundredth, checked element by element.
• The computation is reproducible: the 6,000 rpm sweep, run twice, returned two tables identical to the bit.

What remains open

• Low Reynolds polars. The elements work at Reynolds numbers between 6,000 and 46,000. The upper part of the sweep corresponds to low angles of attack, where the polars of a thin section at low Reynolds number are the most delicate, and that is where the overestimate appears. Below 100,000, the clarky_turbulent profile has only two polars, at 12,000 and 50,000: Heliciel interpolates between them, but nothing describes what happens in between. A trial with the free-transition Clark Y of the database, clarky, matches C_T within ±8 % up to J 0.575 at 6,000 rpm, but loses 7 % at low J and 23 % at 3,000 rpm, where the 10,000 polar weighs in: neither transition hypothesis alone describes this propeller, and it is indeed between the two, through a laminar bubble, that these sections work at these Reynolds numbers. The lead is therefore the computation of Clark Y polars between 20,000 and 40,000, under both hypotheses.
• A single section for the whole blade, whereas the real thickness varies from 37 to 8 %. The blade root carries little load, but its effect is not quantified here.
• The hub radius, set at 0.155 R for lack of data.
• The 3- and 4-blade configurations, the 5-inch model and the full-scale propeller of Report 640 remain to be run. The last one requires taking the nacelle and the effective thrust into account.

8: The domain of interest, or what the comparison can judge

Heliciel's polars are computed by XFoil over the positive lift range, up to stall. Beyond stall and in negative lift, Heliciel applies a flat plate model. This is a design choice: an element that enters it works outside the operating range of its section, a situation that propeller design avoids, and accuracy is not sought there. A comparison with measurements therefore only makes sense as long as the elements stay in positive lift.

This domain was surveyed point by point. Every 0.05 in J, the Cl of each of the 8 elements was read; it is the mean between its root and the root of the next element. The table gives the first J surveyed at which this Cl is negative or zero, i.e. where the element entered the flat plate zone:

• Element 1 is the first to enter the flat plate zone, around J 0.45 to 0.55, on every surveyed part. It covers the hub fillet, from about 0.15 to 0.26 R, where, on the DA4002, the reference paper states that the SDA1075 section does not apply. It carries little load: the deviations on this page are therefore given on the domain of elements 2 to 8, the last J at which all of them are still in positive lift.
• NR640: at both speeds, this domain extends to J 0.65. The thrust overestimate observed between J 0.37 and 0.65 (sections 5 and 6) is therefore inside the domain: it does not come from the flat plate zone. The computed zero thrust, at J 0.742 against 0.674 measured, falls on the other hand beyond the domain and does not judge the model.
• DA4002 and DA4022: the domain extends from J 0.40 to 0.90 depending on the pitch setting. Beyond it, on the DA4002, the computed thrust drops faster than the measurement and zero thrust comes too early (J 0.78 against 0.89 at the 6.75 pitch). This is the expected effect of the flat plate model, not a deviation of the BEM computation.

9: The DA4002, a simple blade with a published section

The DA4002 was designed at the University of Illinois for a study of Reynolds number effects on small propellers. Its blade is rectangular, with a constant chord c/R = 0.18 and a constant pitch P/D = 0.75 (17.7° at 0.75 R), and carries a single section along its whole length, the SDA1075 (12 % thick, trailing edge left open for 3D printing), whose coordinates are published. The blades are mounted on four hubs that change the pitch setting by −10°, −5°, 0° and +5°, i.e. pitches of 2.85, 4.76, 6.75 and 8.95 in at 9 inches. The DA4022 is the same blade with a 0.23 R chord.

Sources: R. W. Deters, G. K. Ananda and M. S. Selig, Reynolds Number Effects on the Performance of Small-Scale Propellers, AIAA 2014-2151 (geometry, SDA1075 coordinates in appendix A, XFOIL polars of the section); measurements and surveyed geometries in the UIUC Propeller Data Site, volume 2.

The SDA1075 was imported into Heliciel's profile database from the published coordinates, and its polars computed by XFoil with Reynolds number steps of 10,000 below 100,000. The published table runs from x = 0.000280 to 1.000137: the chord was rescaled to run from 0 to 1, a mere scaling by 1.00014 that does not change the shape.

Two geometries were imposed. First, the measured geometry of each part, 18 stations from 0.15 to 1.00 R. The measured pitch angle exceeds the design by 1.1 to 3.0° depending on the hub, and the paper notes that the scanner used underestimates the actual twist. The measured tip station (chord 0.015 R, pitch angle 2.1°) is most likely an artefact of the instrument on the tip edge; it was not touched up. Second, the design geometry: c/R 0.18 constant from 0.30 R to the tip, with the design pitch angle. Which of the two better describes the tested part is not known: both are published.

The measured DA4002 geometry (6.75 in pitch) in the reverse engineering grid, SDA1075 section forced on the 8 elements

DA4002, front view	Side view: the twist
Three-quarter view	Blade outline: constant chord, hub fillet

10: DA4002 at 6.75 in pitch, at 5,000 and 3,000 rpm

Same protocol as for the NR640: speed held, advance speed swept in 25 points from J 0.10 to 0.95, off-design mode. Reference measurements: runs 5028 and 5064 at 5,000 rpm, run 3030 at 3,000 rpm. At 5,000 rpm and J 0.5, the elements work at Reynolds numbers between 11,800 and 62,000; at 3,000 rpm and the same J, each element's Reynolds number is 0.6 times its 5,000 rpm value.

The 5,000 rpm sweep in Heliciel's multiple analysis window, measured geometry, marine reading

Blue dots: UIUC measurements. Orange line: Heliciel, measured geometry. Green dashes: Heliciel, design geometry. Grey zone: outside the domain of interest

Same propeller at 3,000 rpm, run 3030

At 5,000 rpm, the design geometry gives the smallest deviation: −6 % on C_T and −7 % on C_P on average, efficiency within 0.02. The measured geometry gives −14 % and −12 %, efficiency within 0.01. At 3,000 rpm, both geometries strongly underestimate thrust, by 33 to 41 % on average; the SDA1075 polars could not be checked at these Reynolds numbers (section 13).

11: The same blade at four pitch settings

Each hub makes a different propeller, whose part was surveyed. Heliciel is given the measured geometry of each, at 5,000 rpm.

One colour per pitch setting: dots, UIUC measurements; lines, Heliciel

With the measured geometry, the C_T deviation ranges from +1 % (4.76 pitch) to −14 % (6.75 pitch), and efficiency is matched within 0.03 everywhere. At the 8.95 pitch, the design geometry falls to 0 % on average, the measured geometry to −13 %. The last two rows use the design geometry shifted by −10° and −5°: they deviate a lot, but they do not represent the parts, whose measured pitch angle exceeds that shift by nearly 3°. They are given for the record.

12: The DA4022, the same blade widened, with 2, 3 and 4 blades

Three-blade DA4022 in Heliciel, measured geometry

Dots: UIUC measurements. Lines: Heliciel. One colour per blade count

On the DA4022, Heliciel overestimates thrust and power by 13 to 28 % on average, where it underestimates the DA4002 with the same section and pitch. Efficiency stays within 0.02. The next chart isolates the difference between the two propellers: at the same J and speed, the ratio of the measured C_T of the DA4022 and of the DA4002, and the same ratio computed.

With a 28 % wider chord, the measured thrust gains only 0 to 17 %, and loses beyond J 0.4 at 9 inches; Heliciel predicts 31 to 38 %

At static thrust, the measured DA4022 gives 11 to 16 % more thrust than the DA4002. Heliciel translates the chord increase into a thrust gain close to the chord ratio, whereas the measurement shows much less. The imposed geometries match the surveyed files. The cause of this deviation is not established.

13: The SDA1075 polars against the published XFOIL

The reference paper publishes the XFOIL polars of the SDA1075 at Reynolds numbers of 40,000, 60,000 and 100,000 (its figure 30). The chart compares the lift that Heliciel actually used, element by element during the sweep, with these curves read from the figure.

Between Reynolds numbers of 40,000 and 60,000, the lift used by Heliciel follows the published XFOIL

Between 40,000 and 60,000, the lift computed by Heliciel reproduces the paper's within ±0.06 on Cl, with one exception: below 1.5° angle of attack, element 4 (Re 46,000) exceeds by 0.08 to 0.11 the 40,000 curve, which shows a laminar bubble dip near 0°. The deviations of the DA4002 at 5,000 rpm therefore do not come from a lift polar differing from the reference. Drag was not compared. At 3,000 rpm and J 0.5, the elements work at Reynolds numbers between 7,100 and 37,200: the figure does not go below 40,000, and no comparison is possible there.

14: What the whole set allows us to say

What is established

• Efficiency. On the DA4002 and DA4022, at 4,000 and 5,000 rpm and within the domain of interest, Heliciel matches the measured efficiency within 0.03 on average; on the NR640, up to J 0.37, beyond which the computed efficiency is too high (section 7).
• Thrust and power are matched within a few percent for the NR640 up to J 0.37, and for the DA4002 at the 2.85 and 4.76 pitches with the measured geometry and at the 6.75 and 8.95 pitches with the design geometry. At 4,000 and 5,000 rpm, the other cases deviate by −14 to +28 % on average.
• The domain of interest is known, element by element. The thrust collapse at high J belongs to the flat plate model chosen for negative lift; the NR640 overestimate between J 0.37 and 0.65, however, is inside the domain.
• The SDA1075 polars computed by Heliciel agree with the published XFOIL between Reynolds numbers of 40,000 and 60,000.
• The imposed geometries reproduce the surveyed tables to the hundredth, and the computations are reproducible to the bit.

What remains open

• The effect of chord. With 28 % more chord, the measured DA4022 gains almost no thrust at 9 inches; Heliciel predicts 31 to 38 %.
• Very low Reynolds numbers. At 3,000 rpm, the DA4002 is underestimated by 33 to 41 % and the NR640 overestimated beyond J 0.32; at these Reynolds numbers, the XFoil polars are not checked.
• The reference geometry. Between the measured and the design geometry, the pitch angle differs by 1 to 3°, and depending on the case the better agreement comes from one or the other.
• The NR640 leads of section 7 (Clark Y polars between 20,000 and 40,000, single section, hub) remain open.

15: Reproducing these comparisons

The reference data are public, in volume 2 of the UIUC database:

• NR640: nr640_9_15deg_geom.txt (surveyed geometry), nr640_9_15deg_0782rd_6004.txt, nr640_9_15deg_0783rd_6068.txt and nr640_9_15deg_0778rd_3023.txt;
• DA4002: da4002_9x6.75_geom.txt, da4002_9x2.85_geom.txt, da4002_9x4.76_geom.txt, da4002_9x8.95_geom.txt (surveyed geometries), da4002_geom.txt (design), and the measurement runs cited in the tables;
• DA4022: da4022_9x6.75_geom.txt and its 2-, 3- and 4-blade runs.

The SDA1075 coordinates are in appendix A of paper AIAA 2014-2151. In Heliciel, the "Aircraft propeller" model is loaded and put in reverse engineering mode. Through an assistant connected to the local MCP connector, the sequence is:

• charger_modele_projet, then a first design_helice at a diameter of 228.6 mm;
• appliquer_geometrie_relevee, which applies the stations, the section (clarky_turbulent for the NR640, SDA1075 for the DA4002 and DA4022) and the hub, and enters reverse engineering mode;
• analyser_point_fonctionnement at the desired speed, then calculer_retro_conception twice;
• generer_courbes_analyse_multiple over advance speed, off-design mode, then lire_tableau_analyse;
• for the domain of interest: analyser_point_fonctionnement every 0.05 in J, then lire_element_pale on the 8 elements.

In the interface, the reverse engineering grid takes the pitch angles; the surveyed chord law is applied through the connector.

Related pages: validation on the Wageningen B-series · reverse engineering an existing propeller · Kt, Kq and J · computation method