An Experimental Investigation of Quadrotor Variations using NASA’s Multirotor Test Bed

An Experimental Investigation of Quadrotor Variations using NASA’s

Multirotor Test Bed

Sarah Conley Carl Russell Dorsa Shirazi Aerospace Engineer Chief, Aeromechanics Office Aerospace Engineer Kristen Kallstrom Carlos Pereyra Stephen Wright Aerospace Engineer Aerospace Engineer Aerospace Engineer NASA Ames Research Center Moffett Field, CA, 94035, USA ABSTRACT Generating multiple high-quality sets of rotor performance data is necessary to validate Vertical Take-Off and Landing (VTOL) aircraft performance prediction codes across a broad range of vehicle configurations. Many aircraft companies are actively pursuing multirotor vehicle configurations, which has created a need for validation data for multirotor systems. The NASA Multirotor Test Bed was designed to accommodate a broad range of reconfigurable multirotor systems and to measure rotor performance and loads in a wind tunnel environment. This paper presents results from the second wind tunnel entry of the test bed, which was completed in August 2022. This wind tunnel test focused on a quadrotor configuration, with variations in rotor placement, blade number, and rotor phasing, across a range of wind tunnel test conditions. This paper describes the test methods and provides and discusses a sample of the quasi-steady and dynamic loads data that were collected during the test program.

* NOTATION INTRODUCTION Ĉ resultant calibration matrix coefficients High-quality test data are a critical component to the C thrust coefficient T development and validation of software tools used for C /σ blade loading T Vertical Take-Off and Landing (VTOL) rotor performance dz vertical difference between front and back rotors [ in ] predictions. These data are needed for tools at varying levels ෡ F approximated loading force [lb] of fidelity, from simple prediction tools up through time- F force reading from load cell in x - direction [ lb ] x accurate high-fidelity Computational Fluid Dynamics (CFD) F force reading from load cell in y - direction [lb] y simulations. Up until around the last decade, wind tunnel F t hrust force reading from load cell [lb] z testing for VTOL rotor systems focused almost entirely on M roll moment reading from load cell [in - lb] x single main rotor, tandem, or tiltrotor configurations. With the M pitch moment reading from load cell [in - lb] y development of the electric VTOL market over the past M torque reading from load cell [ in - lb ] z several years, the design space for VTOL rotor configurations N number of blades has expanded significantly, especially in the Urban Air p n umber of multivariate parameters Mobility (UAM) domain. Correspondingly, there is now a P induced power [ lb - ft/s ] i need for validation data to support simulations of these new P profile power [ lb - ft/s ] o rotor configurations.

q dynamic pressure [psf] R radius of the rotor blade [ in ] The Multirotor Test Bed (MTB) was developed for the t distribution used for confidence interval calculations purpose of testing a wide range of multirotor systems on a u uncertainty, 95% of predictive interval pi,95 single test platform. The development of the MTB hardware u total uncertainty tot was first described in [Ref. 1], and the first wind tunnel test V voltage [V] of the MTB, referred to as MTB1, was completed in the U.S.

v input voltage [V] 0 Army 7- by 10-Foot Wind Tunnel at NASA Ames Research VTOL Vertical Take - Off and Landing Center in 2019 [Ref. 2]. The MTB test rig allows for flexible σ blade solidity placement of up to six rotors with diameters up to about 24 σ variance term i inches, with full capabilities of the MTB described in [Refs.

st Presented at the Vertical Flight Society’s 81 Annual Forum & Technology Display, Virginia Beach, VA, USA, May 20-22, 2025. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

1,2]. In addition to allowing for variations in rotor placement, systems at model- and full-scale. The third MTB wind tunnel the pitch angle of the entire rig is adjustable, and each rotor test entry (MTB3) is planned to take place in the National has its own tilt actuator that allows for independent variation Full-Scale Aerodynamics Complex (NFAC) at NASA Ames of the rotor tilt angle. Additional details are provided in later in 2026 and will provide the ability to measure noise in an sections. The primary measurements collected by the MTB anechoic facility. MTB3 will have previous model are the quasi-steady and dynamic rotor loads. These loads are capabilities and a new hub with ground adjustable collective.

collected by six-axis load cells located under each rotor. The The blades used in MTB2 will be tested along with new MTB in its test configuration for the second wind tunnel test blades, both with 24.5-inch diameter. Future testing after (MTB2) described here is shown in Figure 1. The following MTB3 will focus on a larger multirotor system that will subsections provide brief descriptions of the MTB1, MTB2, provide research data on the effects of rotor size scaling.

and the upcoming MTB3 test.

Prior MTB Publications Multirotor Test Bed Entry 1 There have been several prior publications on the MTB, listed The first wind tunnel test of the MTB (MTB1) served as a in the references section and above, but this is the first shakedown test of the new test rig, with a wide-ranging test publication that presents the corrected wind tunnel test data matrix that was mainly intended to exercise all the different from the MTB2 wind tunnel test. References 1 and 11 cover mechanical and measurement hardware systems. Data the design and loads and stress analysis of the MTB.

collected during that test have already been used for Reference 2 gives a description of the MTB1 test and presents validation studies for various simulation tools including some of the data. This paper will present a selection of the RotCFD [Ref. 3], CHARM [Ref. 4], CAMRAD II [Refs. 5,6], data from MTB2 with updated calibrated load cell matrices.

and OVERFLOW [Ref. 7]. The rotor used for the MTB1 test Another paper presented at this venue, Reference 12, was an off-the-shelf KDE-CF245-DP with 24.5-inch presents comparisons of the MTB2 data to CHARM and diameter. The MTB had the ability to adjust rotor RPM, rotor OVERFLOW simulation results, identifying best practices tilt, full rig pitch, and number of rotors.

for the simulation tools and identifying suggestions for the Multirotor Test Bed Entry 2 future MTB wind tunnel tests. There will be some overlap The second wind tunnel test entry of the MTB (MTB2) was between the experimental data presented in this paper and completed in August 2022, in the same facility, the U.S. Army those presented in Reference 12. However, this paper will 7- by 10-Foot Wind Tunnel, with the test configuration shown present more experimental data, go into greater detail in Figure 1. MTB2 was intended to focus on a scaled-down regarding the trends in the experimental data, and will not be version of the NASA Revolution Vertical Lift Technology comparing the data to results from simulation tools. The (RVLT) Project concept quadrotor vehicle configuration MTB2 data report, Reference 13, has a more detailed [Ref. 3] with variable height of the back rotors to investigate overview of the test and lists all the data tables. The data effects of rotor-rotor interference. The RVLT concept report only shows a few plots and focuses mainly on the test quadrotor is one of several concept vehicles that were setup, execution, data tables, etc., and does not draw any developed by the RVLT Project to focus research on a set of conclusions from the data. However, this paper presents objective aircraft that are realistic, non-proprietary several plots, identifies some trends in the data, and aims to representations of the broad range of eVTOL aircraft currently under development. The different RVLT concept interpret the results.

vehicles are described in References 8 and 9. In the MTB2 test entry, the MTB was tested in three quadrotor configurations of varying vertical separation between the front and back rotors, denoted as dz/R , including dz/R =0, 0.33, and 0.57. Note that dz/R =0.33 represents the rotor separation of the RVLT concept quadrotor. In addition to the variable rotor heights, the MTB2 test included the ability to control the azimuthal phase angle between rotors. Rotor phase angle control has been proposed by various researchers as a method to improve overall vehicle performance and to reduce noise and vibrations [Ref. 10]. The main structural hardware modification for this test was the installation of new, more robust actuators that had negligible backlash. Additionally, the rotors, discussed more thoroughly in later sections, were custom designed to facilitate public distribution of the rotor geometry.

Multirotor Test Bed Entry 3 Figure 1: Front view of the MTB2 in the U.S. Army Additional MTB tests are planned for the future, one of which 7- by 10-Foot Wind Tunnel.

will focus on the evaluation of noise produced by multirotor TEST DESCRIPTION U.S. Army 7- by 10-Foot Wind Tunnel Like the first MTB test, the 2022 test (MTB2) described in this paper was carried out in the U.S. Army 7- by 10-Foot Wind Tunnel at NASA Ames Research Center. This is a closed-throat, single-return wind tunnel with a 14:1 contraction ratio, and a test section of 7.0 x 10.0 x 15.0 feet.

The MTB was mounted on a strut and secured to the turntable in the center of the test section. The cabling was routed underneath the tunnel floor through the opening at the strut (secured to the strut with the yellow tape in Figure 2) and was either routed directly below the turntable or through the floor to the control room. Also shown in Figure 2 is the skylight on the ceiling of the test section, above which a strobe light Figure 3: 7- by 10-Foot Wind Tunnel control room with and camera were placed, which allowed for verification of the MTB2 operator positions identified.

rotor phase angle. Additional details regarding the wind tunnel can be found in the data report, Reference 13. Test Matrix For the quadrotor layout tested here, there were three primary rotor configuration variables that were studied – vertical spacing, phasing, and solidity – in addition to the typical variables of dynamic pressure (wind speed), rotor rotation rate, model pitch angle, and rotor tilt angle. These variations were chosen based on results from previous computational studies indicating a need for additional validation data.

Descriptions of each of the rotor variations, along with the computational studies that inspired each experimental investigation are given below: 1) Rotor vertical spacing study: The height difference of the back rotors to the front rotors expressed as a function of rotor radius, dz/R , was tested at three different values: dz/R =0, 0.33 and 0.57 (the concept quadrotor has a dz/R =0.33). The effects of dz/R on rotor performance were studied in- depth through OVERFLOW simulations in Reference 14.

2) Rotor azimuthal phasing study: The relative phase angle of the rotors was varied from 0 to –90 deg, using a custom electronic speed controller built by Launchpoint Electric Propulsion Solutions that allowed for on-the-fly adjustment of the phase angle. The effects of rotor phasing on vehicle vibratory loads are particularly of interest and have been studied with the RMAC Figure 2: Test section ceiling and test crew working on comprehensive analysis code in Reference 10.

model.

3) Rotor solidity study: Three different rotor hubs were used for testing, For the MTB2 test, operations typically involved five people: allowing for 2-, 3-, and 6-bladed versions of the rotor Tunnel Operator, Test Engineer/Director, Safety-of-Flight with identical blades. Rotor solidity has long been a (SOF) Monitor, Model Operator, and Data Operator. The design variable in rotorcraft sizing studies and was control room setup is shown in Figure 3. All functions of the recently explored in Reference 15, which looked at model and the tunnel were controlled from within the control multiple iterations of the RVLT Concept Vehicles.

room, and test section conditions and video of the model were As can be seen from Table 1, the test matrix is quite extensive displayed on the large monitors at the front of the room.

and there are multiple test variables that allow a plethora of testing configurations. This table is a condensed version of the MTB2 Test Matrix and is not all-encompassing. For the complete MTB2 Test Matrix, see the MTB2 data report [Ref. 13]. For brevity, not all testing conditions are discussed and shown in this paper.

Table 1. Condensed MTB2 test matrix. Note that this coordinate system obeys the right-hand rule and may differ from other reported wind tunnel experimental or dz/R 0.33 0.00 0.57 flight data.

Phase [deg] 0, –30, –60, –90 0, –90 0, –90 a a # blades 2, 3 , 6 2 2 Hardware b c c c # rotors 1, 2 , 2 , 4 1, 2 , 4 1, 2 , 4 The MTB was designed to be an extremely versatile and Tilt [deg] 0, –3 0, –3 0 reconfigurable system. It can have up to 6 rotors, though for this test only up to 4 were tested, and the rotors can be Conditions for all dz/R configurations repositioned along the x, y, and z axes with individual tilt q [psf] 0, 0.48, 1.90 rotation available via the linear actuators. Figure 5 provides a Pitch [deg] 0, –1, –3, –5, –10 CAD image of the MTB in the quadrotor configuration, with RPM 2000, 2500, 3000 the rotor numbers labeled. Table 2 provides a list of the capabilities and range of the test stand as it was during the Notes: a Not all 3- and 6-bladed runs were performed for all testing MTB2 Test Campaign.

conditions for the dz/R=0.33 configuration given in this table; b c A stepper motor under the main strut turns a jack screw inside, Side-by-side; Tandem.

moving a lug on the strut up and down. There is a linkage connecting that lug to the strongback (the backbone of the Coordinate Systems MTB) which allows the full rig to pitch up and down.

Figure 4 shows the Balance Coordinate System and the Hub Coordinate System. These axes are identical to each other except that they are displaced a distance of “HUB_DIST” along the z axis (2.783 inches). This is the distance from the moment center of the Balance Coordinate System, the top of the load cell, to the center of the hub in the rotor plane. The Hub axes are defined as follows: Fx_H downstream Fy_H toward control room Fz_H up Mx_H positive roll left My_H positive pitch up Mz_H positive torque CCW (as viewed from above) Figure 5: CAD image of the MTB2, isometric view.

Table 2: MTB2 capabilities and limits.

Characteristic Range Rotor diameter 24.5 inches (same as the KDE-CF245- DP rotors of MTB1) Max. rotor RPM 4,500 Lateral spacing 24.7–38.7 inches, adjustable in 1-inch increments (2-inch increments if symmetr ic about the centerline) Longitudinal spacing 25.5–72 inches, adjustable in 1.5-inch increments Vertical position 9 inches of travel, adjustable in 1-inch increments Individual rotor tilt – 90 deg forward to 5 deg aft, adjustable in arbitrary increments Full MTB pitch – 30 deg forward to 10 deg aft, adjustable in arbitrary increments Max. wind speed 40 ft/s, higher if vibratory load limit is Figure 4: The load cell forces and moments in the not reached Balance and Hub Coordinate Systems.

While the configuration of the MTB is easily reconfigurable, Table 3: MTB2 as-built (APC modified) blade geometry.

the system was designed with very rigid materials (high Property Value strength stainless steel) which both increased safety factors and decreased structural deflection in the strongback, lateral Root cutout, % R 0.22 support beams, and vertical support beams that hold the rotor stacks. The MTB was designed to minimize deflections, Rotor radius 12.245 inches keeping the total angular displacement of the rotors less than Chord length 1.54 inches 0.1 deg in any direction with reference to the ground for all planned test conditions. To be approved for the wind tunnel, Airfoil Eppler 387 a minimum safety factor of 3 on yield strength and 4 on Blade twist – 16 deg, linear from root to tip ultimate strength is required. A blade out analysis was performed, and all parts showed a minimum safety factor of 1 Built-in collective pitch 6.7 deg at 75% radius on yield for blade out conditions. For more details about the Trailing edge thickness ~0.020 inches design and the loads and stress analysis of the MTB, see Sharp corners at tip rounded to Reference 11.

radius of 0.020 in Blade Geometry Ultimately, due to manufacturing constraints, some The MTB2 test incorporated non-proprietary, custom designed rotor blades. Some characteristics of the MTB1 rotor modifications to the airfoil geometry (such as thickening the blades were retained, primarily the blade radius and the rotor trailing edge) were required by the manufacturer, Advanced solidity. The MTB2 blade has a constant chord with the Precision Composites (APC).

Eppler 387 (E387) airfoil – chosen for its performance characteristics at low Reynolds numbers [Ref. 1616]. Testing Procedure The intent of the MTB2 test was to measure steady and A design study was performed in the CAMRAD II rotorcraft vibratory forces and moments as a function of dynamic comprehensive analysis code [Ref. 55], to determine desired pressure (wind speed), attitude, MTB configuration, rotor settings for the blade’s linear twist distribution and built-in phase, and rotor RPM. The general strategy for testing was to collective pitch. Assessments of two performance metrics, vary RPM for a given combination of dynamic pressure power defined as profile power ( P ) + induced power ( P ), and (tunnel speed), model pitch angle, rotor phase, and o i configuration. The model pitch was then changed, and RPM blade loading ( C /σ ), were used to determine the desired T values for twist and built-in collective pitch. A linear twist was varied again for multiple rotor tilt angles. Depending on sweep was simulated in CAMRAD II with C /σ trimmed to how long a pitch and RPM sweep took at a given wind speed, T 0.09 (a chosen design point matching the concept multiple wind speeds could be tested in a single test run.

quadrotor). Simulations were run for 40 ft/s, 2000 RPM, and Because the tunnel operator and test director set on a dynamic for –5 and –10 deg rotor tilt, operating conditions which were pressure of 0.48 psf and 1.90 psf +/- 0.02 psf, some of the wind tunnel speed values may deviate more from 20 ft/s and deemed representative of the eventual wind tunnel test conditions. Figure 6 shows the results of the twist sweep with 40 ft/s. Setting on dynamic pressure allows for better 2000 RPM, 40 ft/s, and –10 deg rotor tilt. The optimum twist, comparison of the data since it takes the humidity and air -16 deg (the red line in the figure), and the corresponding temperature into account.

built-in collective, 6.7 deg, were selected for the blade. The overall MTB2 blade geometry is detailed in Table 3. Aerodynamic and weight tares were performed throughout the test campaign and were used for postprocessing of the data. R-Cals were performed at the beginning and ending of each run to verify the health of the load cells. Repeat points were taken at the beginning and end of each run to help account for any hysteresis or load cell offsets caused by temperature fluctuations. These were referred to as “housekeeping wind off” and “housekeeping wind on” points and were taken at 2000 RPM, 0 pitch, 0 tilt, and wind tunnel speed of either 0 or 20 ft/s (~0.48 psf dynamic pressure).

Data Collection and Instrumentation Both quasi-steady and dynamic data were recorded for the load cells for this test. The quasi-steady data were mean values from unfiltered dynamic channel measurements. The dynamic data were recorded following the quasi-steady point and represent a time history of the loads sampled over 5 Figure 6: Power and collective pitch vs twist, wind seconds. Data were recorded and stored in multiple files with speed=40 ft/s, rotor tilt= –10 deg.

low-speed channels (tunnel parameters) sampled at 10 Hz and high-speed channels (load cells and accelerometers) at 4 kHz. The additional details of MTB2 data collection can be found All load cell data underwent zero subtraction and temperature in the Multirotor Test Bed Wind Tunnel Test data report corrections, detailed in the post-processing section. The [Ref. 13].

primary data acquisition used for this test was a LabVIEW- based interface called the Standard Data Acquisition System Post-Processing and Data Correction (SDAS). The SDAS uses a flexible architecture to acquire Each load cell was calibrated post-test to determine a more data for several channels. The various instruments used for accurate model for calculating forces and moments from the this test are summarized below. load cell readings. Additionally, the post-test calibration data was used to establish an understanding of the uncertainty Load Cells: The primary data of interest for this test were quantification in the load cell response. A pool of post-test quasi-steady and dynamic loads, which were measured using calibration data was gathered from a sequence of known Interface model 6AR70A-S11 six-axis load cells. The six loading cases, in which the loads and moments were applied channels from each load cell were routed to a junction box, in both positive and negative directions up to a maximum of where the signal was amplified and filtered with a 1 kHz low- 50 lb (resulting in 142 in-lb moments) in combined loading pass filter. The signal was stored in both engineering units and cases and 120 in-lb in the pure moment cases. These data raw voltages. The signal was also sent to Safety of Flight for were gathered in discrete intervals of 5 lb and applied in loads monitoring during testing. The excitation at the load cell triangular loading / unloading schedules. This cycle was was adjusted to match the calibration excitation, and then an repeated three times, providing ample data for cross- R-Cal was taken at the beginning and end of each run to validation.

monitor the health of the gauges.

The calibration data were partitioned into a training set and a RPM Sensors: The RPM was measured using a 1/rev Hall validation set, using an 80% and 20% ratio respectively. A sensor which was mounted under the motor, sending signals weighted least squares model was used to determine the to the control system and data storage for both real-time and optimal multi-dimensional linear set of conversion † recorded RPM values. coefficients (the 6x6 conversion matrix), whereby its performance was quantified by residual variance on the Thermocouples: Temperatures of the load cells and power bus testing set. Note, upon inspection of the load cell channel were measured using thermocouples. The thermocouple responses per each loading configuration, it was determined signals were sent unamplified to the MTB Control System that channels were interdependent. This is reflected in the fact Data Acquisition System where they were filtered and that the linear calibration matrices are not strongly diagonal.

averaged. They were then sent to the SDAS via an RS-232 The variance is impacted from coupling of the load cell gage line. Due to the lack of amplification, the thermocouple signals. The uncertainty quantification is discussed in the next signals were very noisy while the motors were running, so section.

only the starting and ending temperature measurements proved to be useful. Before converting the raw voltages into engineering units, the data was first tared or zero-subtracted from its baseline point.

Accelerometers: Tri-axial 5g accelerometers were used to The zero or baseline points were taken at the beginning of measure acceleration of the load cell mounting plate. The each run. This took out any initial load on the model. After signals were transmitted to an amplifier, filtered, and then the raw voltages were tared, they were converted into recorded directly in the dynamic raw storage without zero- engineering units via the calibrated model. These were the subtraction. initial load values. Then a series of post-processing steps were taken to account for load cell drift (skewness), aerodynamic Inclinometer: An analog inclinometer was used to measure drag, inertial loading of the motor, and weight influences. At the pitch angle of the MTB strongback. The inclinometer was the start and end of each run static points were taken, in which calibrated in-place, with a linear conversion for signal no load was applied (all testing parameters set to zero). These processing. points, called static points, served as measures of bias and linear drift through comparing the beginning and ending static Rotor Tilt: Rotor tilt was controlled indirectly by an analog points for each run. Aerodynamic and weight tares were voltage sent to the linear actuators for the different rotors. recorded in the tunnel during the test entry and were applied There was an in-place calibration performed for each actuator to the data to remove their effects. The process of to determine a polynomial conversion of actuator analog input implementing the data corrections is further explained in the to rotor tilt. data report [Ref. 13].

† Optimal in the sense that the chi-squared distribution is minimized for the linear set of dimensions.

෠ መ Uncertainty 𝐹 = 𝑉𝐶 ± 𝑢 ( 𝑉 ) ( 3 ) ௧௢௧ This section explains how the variances (denoted by 𝜎 ) and ௜ ෠ where 𝐹 is the (approximated) loading force yielded by the the total uncertainty values ( 𝑢 ), shown as error bars in the ௧௢௧ መ linear model terms 𝑉𝐶 (voltage times the 6x6 matrix plots, were calculated. The error distribution of the load cell coefficients) bounded by the total uncertainty. Since the responses depends highly on the nominal load values and the uncertainty depends on a specific load value, the equation is load configuration. This error is assumed to be normally expressed as a function of voltage, V .

distributed. Placing an interval of upper and lower bounds on the mean loads can be computed by the 95% predictive interval, 𝑢 . The equation to calculate the 95% predictive RESULTS AND ANALYSIS ௣௜ , ଽହ % interval, is shown below.

This section presents a subset of the results from the MTB2 test. The objective of this section is to demonstrate the types ் ் ି ଵ 𝑢 = ±𝑡 𝜎 ට 1 + 𝑣 ( 𝑉 𝑉 ) 𝑣 ( 1 ) of results that can be analyzed from the data and to discuss ௣௜ , ଽହ % ௡ି௣ , ଴ . ଽ଻ହ ௜ ଴ ଴ possible discrepancies in the data collection abilities. The individual quasi-steady rotor loads and uncertainty studies Given some input voltage 𝑣 taken during experimentation, ௢ will be presented and discussed first, followed by the the possible regions of load values may be heuristically multirotor quasi-steady loads, and ending with the dynamic determined from Equation 1. Here, 𝑡 ≈ 1.96 ௡ି௣ , ଴ . ଽ଻ହ loads.

represents the 95% quantile of the 𝑡 -distribution. Two key pieces of information saved from calibration are the variances ୘ ି ଵ Individual Rotor Quasi-Steady Loads and Uncertainty ( ) 𝜎 , and the covariance 𝑉 𝑉 of the calibration voltage ௜ Studies readings. These values are then used to determine the upper First, the individual rotor thrust and torque values are and lower bounds of the mean load predictions. The variances analyzed to help determine potential differences in the shown in Table 4 are used in Equation 1 and are a measure of measurements between rotors and load cells. Theoretically, the mean deviation between applied and model predicted each individually tested rotor should yield the same forces and loads across all load schedules.

moments for each test condition, and any observed Table 4: MTB2 Load Cell Variances.

differences between the loading values could be due to load cell differences, rotor geometry differences, and/or test stand Load 𝝈 𝝈 𝝈 𝝈 𝝈 𝝈 𝑭𝒙 𝑭𝒛 𝑴𝒙 𝑴𝒛 interference. Note that the dynamic pressure ( q ) 0.48 psf and 𝑭𝒚 𝑴𝒚 Cell (lb) (lb) (in-lb) (in-lb) (lb) (in-lb) 1.90 psf is equivalent to about 20 ft/s and 40 ft/s, respectively.

In the data, the q values can vary +/- 0.02 psf. Rotor 1 is LC1 0.93 0.19 0.32 0.65 0.82 0.64 denoted by R1, and the other rotors are denoted similarly. In LC2 0.08 0.04 0.29 0.14 0.31 0.56 the force and moment plots, the back rotors are denoted with a dashed line. Additionally, the error bars shown in the plots LC3 0.37 0.21 0.08 0.16 0.13 0.08 represent the uncertainty in the measurements. The method LC4 0.09 0.08 0.07 0.29 0.22 0.11 for obtaining the error bars is described in previous sections.

Figure 7 shows the rotation direction and position of the rotors in the quadrotor configuration for the rotors phased with 0 deg As seen in Table 4, it is observed for load cells 1 and 2 that separation. The blue line represents blade 1. Rotors 2 and 3 variance in the thrust directions is nominally higher than in were phased with respect to rotors 1 and 4. The rotors were load cells 3 and 4 and thus may yield higher regions of not phased for the single rotor runs.

predictive intervals (larger error bars). While higher order models were investigated with the hopes of reducing co- linearity (between load cell channels) and consequentially reducing variance, the mean load predictions were quite similar to the linear model used. The uncertainty was also calculated for the nonlinear, higher order model but yielded very similar values for thrust and torque. Since the linear model had been more thoroughly examined and reviewed, it was decided to remain with the linear model. Equation 2 calculates the total uncertainty for a specific load in a particular configuration by combining the uncertainty from the predictive interval with the mean dynamic uncertainty.

ଶ ଶ 𝑢 = 𝑢 + 𝑢 ( 2 ) ට ௧௢௧ ௣௜ , ଽହ % ௗ௬௡ Finally, incorporating 𝑢 into Equation 3 gives the upper ௧௢௧ and lower error bounds on the loads and is what is shown in Figure 7: Schematic of rotors phased with 0 deg the error bars on the plots.

separation.

Figure 8: Individual rotor runs, thrust values for Figure 9: Individual rotor runs, torque values for different dynamic pressures and rotor speeds as a different dynamic pressures and rotor speeds as a function of pitch angle, with dz/R =0.33 and tilt=0 deg. function of pitch angle, with dz/R =0.33 and tilt=0 deg.

Figure 8 presents thrust from the single rotor runs at different As mentioned before, R-Cals were performed on the load tunnel speeds and RPMs. R1 and R2 show very similar thrust cells at the beginning and ending of each run, to assess the values at all conditions with R2 thrust being slightly higher health of the sensors. Because the R-Cals always passed their than R1 thrust at lower tunnel speeds and the opposite being checks, it is unlikely that the load cells were misused. Again, true for higher tunnel speeds. The thrust from R3 is below that when looking at the data from multirotor runs, the of R1 and R2, with the difference between them increasing discrepancy between the CW and CCW torques should be with higher tunnel speeds and lower RPM. The thrust from considered. It should be noted that the conditions in Figures R4 is the lowest of all, with the difference to the other rotors Figure 8 and Figure 9 were also checked for a tilt value of –3 increasing with increasing tunnel speed and increasing RPM. deg. The resulting plots showed that tilting had very little When looking at the data from multirotor runs, it is important impact on the thrust and torque, and thus those plots were to note that R4 may be reading slightly lower thrust values excluded from this paper for brevity.

than the other rotors not because of an aerodynamic phenomenon, but because of a potential difference in load cell Figures Figure 10 and Figure 11 show an uncertainty study measuring capability or rotor geometry. Overall, all the rotors with R1 and R4 and load cells 1 and 4 (LC1 and LC4) for showed that higher tunnel speeds resulted in a greater thrust and torque, at different tunnel speeds and rotor RPMs.

dependency of thrust on pitch, with thrust increasing as the Three different cases are compared to each other: rotor 1 on pitch approached 0 deg. load cell 1 (R1 on LC1), rotor 4 on load cell 4 (R4 on LC4), and rotor 4 on load cell 1 (R4 on LC1). For the last case, R4 on LC1, the hub that was in position 4 (back port) replaced Figure 9 shows torque vs pitch for the same conditions as in the hub in position 1 (front starboard). The figures show that Figure 8. The clockwise rotating rotors, R2 and R3, showed the thrust of R1 on LC1 was very similar to the thrust of R4 much higher torque than the counter-clockwise rotating on LC1, with R4 on LC1 being slightly lower. This could be rotors, R1 and R4, for all conditions. From the previous due to a slight deviation in rotor geometry between R1 and figure, it is shown that R3 and R4 yielded less thrust, so it R4. This difference in thrust decreased with increased tunnel would make sense for R4 to have lower torque, but R3 having speed but increased with increased RPM. More notably, the higher torque with lower thrust suggests that there could be thrust of R4 on LC4 was significantly lower than the thrusts an inefficiency present – potentially a less efficient motor, of R1 on LC1 and of R4 on LC1. This indicates that LC4 was friction in the motor bearings, less efficient blades, etc. The reading lower thrust values for the same condition with the beginning and ending load cell temperatures for several runs same rotor. This could be due to the load cell measuring were checked, and the load cell temperatures were all within capability, or the wake being influenced by the test stand. It is about 1 deg of each other.

unlikely that these differences could be due to tunnel flow quality since a flow quality study was done a few years prior in 2019 [Ref. 17] and yielded very uniform readings.

When observing the data, it should also be taken into consideration that the error bars for R1 and R2 are higher than those for R3 and R4. This is due to the variance of the individual load cells and is explained in the Uncertainty Section.

Multirotor Quasi-Steady Loads In this section, several multirotor studies are presented. The figure captions for each study state which configuration is being observed: quadrotor, side-by-side, or tandem; dz/R =0, 0.33, or 0.57. Recall that the dz/R =0.33 condition is the RVLT concept quadrotor configuration and the dynamic pressure ( q ) 0.48 psf and 1.90 psf is equivalent to about 20 ft/s and 40 ft/s, respectively. The studies were done with two-bladed rotors with rotors in phase with 0 deg separation unless otherwise stated. For the quadrotor runs, often only the starboard rotors are shown for brevity.

During testing, several runs were performed with 2-, 3-, and Figure 10: Thrust uncertainty study between R1 and R4 6-bladed rotors. Figure 12 shows some results from that and LC1 and LC4 as a function of pitch angle, dz/R =0.33 quadrotor solidity study. The subplots show the blade loading and tilt=0 deg.

on each individual rotor. Blade loading is the highest for the 2-bladed rotors across all rotors. The front rotors show higher Similar observations can be made for the torque values blade loading than the back rotors for all solidities.

presented in Figure 11. R4 on LC4 yields the lowest torque value, with R4 on LC1 coming in second, and R1 on LC1 being the highest. The differences in torque values between the three curves are much smaller than those for the thrust values in Figure 10. R4 on LC1 torque is closer to R1 on LC1 for lower RPMs and is in the middle of the two curves for higher RPMs. Increasing tunnel speed did not show much effect on the differences between the curves. Additional uncertainty studies are planned for future MTB tests to facilitate identifying sources of error.

Figure 12: Blade loading vs pitch for different quadrotor solidities for dz/R =0.33, q =0.48 psf, RPM=2000, and tilt=0 deg.

Figure 13 shows the effect of tilt on thrust and torque for the starboard rotors, R1 and R3, in the dz/R =0.33 configuration for different tunnel speeds and RPMs as a function of vehicle pitch. Only the starboard rotors are shown, and as expected, the front rotors show higher thrust than the back rotors.

Consistent with the results discussed in the previous section, Figure 11: Torque uncertainty study between R1 and R4 R3 shows higher torque than R1. The difference in thrust with and L1 and L4 as a function of pitch angle, dz/R =0.33 tilt is more noticeable at higher tunnel speeds, Figure 13 (b), and tilt=0 deg.

for R1 and for R3 between pitch of –3 and 0 deg, with the –3 deg tilt yielding lower thrust values. All the other subplots coming in slightly higher than 0.57 for both the 2000 and 3000 show that tilt does not have a large effect on thrust and torque. RPM cases (plots c and d).

In Figure 13(d), the torque tends to increase slightly for tilt of –3 deg for both rotors between pitch of –3 and 0 deg.

Figure 14: Starboard rotors dz/R comparison for thrust and torque for quadrotor configuration at q =0.48 psf, Figure 13: Starboard rotors tilt comparison for thrust and RPM=2000 and 3000, and tilt=0 deg.

torque for the quadrotor configuration at dz/R =0.33, q =0.48 and 1.90 psf, and RPM=2000.

Figure 14 shows the impact of dz/R on R1 and R3 in the quadrotor configuration for various RPMs and the lower tunnel speed of 0.48 psf. Again, only the starboard rotors are shown for brevity. Thrust for the front rotor, R1, was not significantly affected by configuration. However, thrust for the back rotor, R3, was greatly affected, with the dz/R =0.33 yielding the highest thrust, dz/R =0.57 coming in second, and dz/R =0 coming in far below. Subplots c and d show the configuration did not greatly affect torque for R3, as they all yielded similar values. This indicates that the dz/R=0 configuration was very inefficient compared to the others, since it yielded much less thrust for about the same torque, and that the dz/R =0.33 was the most efficient for R3. R1 had slightly higher torque values for dz/R =0.33, then dz/R =0, and finally dz/R =0.57 being the lowest. Thus, the dz/R =0.33 configuration may be slightly less efficient for the front rotors, but it is significantly more efficient for the back rotors.

Figure 15: Starboard rotors dz/R comparison for thrust Figure 15, shows the same conditions as Figure 14, but at a and torque for quadrotor configuration at q =1.90 psf, higher tunnel dynamic pressure of 1.90 psf. Some of the same RPM=2000 and 3000, and tilt=0 deg.

trends are observed, mainly that the back rotor is significantly less efficient for the dz/R =0 configuration. Figure 15 (d) Figure 16 shows a similar case to that in the previous figure shows that the dz/R =0 case for the back rotor yields but for the tandem configuration instead of the quadrotor significantly higher torque than the other configurations for configuration. The differences between the dz/R all pitch angles for higher RPM. Another difference from the configurations are less pronounced for the tandem than for the lower tunnel speed condition is that the back rotor, R3, yields quadrotor case, meaning the curves shown in Figure 16 similar thrust values for the dz/R =0.33 and the dz/R =0.57 (tandem) are closer to each other than in Figure 15 configurations. Additionally, the dz/R =0.33 and 0.57 (quadrotor). Additionally, some of the trends for the torque configurations yield similar torque values at –10 deg and then branch out as pitch gets closer to 0 deg, with dz/R =0.33 values in the tandem configuration are different than those for between them, did not change much as tunnel speed was the quadrotor configuration. increased. The –90 deg phase configuration appears to be slightly more efficient at higher tunnel speeds for the tandem rotor case.

Figure 16: Starboard rotors dz/R comparison for thrust and torque for tandem configuration at q =1.90 psf, RPM=2000 and 3000, and tilt=0 deg. Figure 17: Starboard rotors phase comparison for thrust and torque or tandem configuration at dz/R =0.33, q = The front rotor torque values are lower for dz/R =0 than for the 0.48 psf and 1.90 psf, RPM=3000, and tilt=0 deg.

other configurations for both RPMs for the tandem case, whereas for the quadrotor case, dz/R =0.57 was the lowest.

Also, for the tandem case, the dz/R =0.33 torque for the back rotor, R3, is higher than for the other cases, which is also different from the trends observed in the quadrotor configuration. Previously, for the quadrotor case, R3 torque was highest for dz/R =0. This suggests that the configuration trends for varying rotor height may be different between the front and back rotors for a quadrotor versus a tandem. It is likely that the aerodynamic interactions from R2 and R4 in the quadrotor configuration affect the performance and characteristics of R1 and R3.

Figure 17 shows the trends between 0 and –90 deg phase for the tandem configuration for 3000 RPM at different tunnel speeds. Figure 18 shows a schematic of the quadrotor configuration with R2 and R3 phased with –90 deg separation, with the dark blue line showing blade 1 in the Figure 18: Schematic of rotors phased with –90 deg phased position. Note that “R1: -90 deg phase” refers to the separation for R2 and R3 with respect to R1 and R4.

configuration for which R3 is phased -90 deg with respect to R1 where R1 is still in the 0 deg phase position. “R1: 0 deg Figure 19 shows the phase comparison of thrust for each rotor phase” refers to the configuration in which all the rotors are in the quadrotor configuration for dynamic pressure (tunnel phased with 0 deg separation. The thrust values for the rotors speed) 1.90 psf and 3000 RPM. Figure 20 and Figure 21 show in the 0 deg phase configuration yielded slightly higher thrust schematics of the rotors phased with –30 and –60 deg values for lower tunnel speeds for both rotors, but that separation for R2 and R3. There is not a very significant difference decreased as tunnel speed increased, with similar difference in the rotor thrust for the different phase values; thrust values at different phase angles. However, the back however, for all the rotors, –90 deg phase yielded slightly rotor, R3, still yielded slightly higher thrust for the 0 deg lower thrust for pitch angle of –10. For the back rotors, the 0 phase configuration. For both tunnel speeds, the torque values deg phase thrust values were higher also for the -10 deg pitch were higher for both the front and back rotor for 0 deg phase.

angle.

The torque values themselves, as well as the difference Figure 21: Schematic of rotors phased with –60 deg separation for R2 and R3 with respect to R1 and R4.

Figure 19: Phase comparison for individual thrust for quadrotor configuration at dz/R =0.33, q =1.90 psf, RPM=3000, and tilt=0 deg.

Figure 22: Phase comparison for total thrust for quadrotor configuration at dz/R =0.33, q =1.90 psf, RPM=2000 and 3000, and tilt=0 deg.

Figure 23 shows the power for the same conditions as given Figure 20: Schematic of rotors phased with –30 deg in the previous two figures: quadrotor, dz/R =0.33, q =1.90 psf.

separation for R2 and R3 with respect to R1 and R4.

The –90 deg phase has the lowest power for both RPMs and all pitch angles. The differences in power are much harder to Figure 22 shows plots of the total thrust from all four rotors see at 2000 RPM. At 3000 RPM the 0 deg and –30 deg phase for the same configurations and conditions given in the yield similar power with –60 deg coming in slightly less and previous plot. When all the thrust values are added together, –90 deg yielding the lowest. The –90 deg phase may be both RPM cases show that the 0 deg phase case yields higher slightly more efficient between –5 and 0 deg pitch.

total thrust for –10 deg pitch. Additionally, at –10 deg pitch, the –90 deg phase yields the lowest thrust. When the pitch goes to 0 deg, this trend reverses and –90 deg phase yields the highest thrust and 0 deg phase yields the lowest, but the differences are much smaller.

Figure 23: Phase comparison for total power for the quadrotor configuration at dz/R =0.33, q =1.90 psf, RPM=2000 and 3000, and tilt=0 deg.

Dynamic Data Results Figure 25: Dynamic plot – Tandem configuration, phase comparison for rotor 3 at dz/R =0, q =1.90 psf, RPM=3000, pitch=0 deg, and tilt=0 deg.

The plots presented in this section show the dynamic data for F , M , F , and M as functions of frequency. Each plot shows x y y x the 0 deg and –90 deg phase as a solid and dotted line, respectively. Only R1 and R3 from the quadrotor runs are shown for brevity. R1 is shown in magenta and R3 is shown in bright green. Note that all plots are for 3000 RPM; thus, the 1/rev frequency is 50 Hz, the 2/rev frequency is 100 Hz, etc.

Figure 24 and Figure 25 show dynamic data results for R1 and R3, respectively, for 0 deg and –90 deg phase for the tandem configuration for dz / R = 0 at 1.90 psf, 3000 RPM, 0 deg pitch, and 0 deg tilt. For all forces and moments shown, the 2/rev harmonic content is significantly lower for R3 than for R1.

Additionally, for all loads, for both rotor phase angles, the 2/rev signal is significantly higher than any other signal. This is to be expected; generally, for a rotor in forward flight, the dominant harmonic is the N /rev, where N is the number of rotor blades per rotor (in this case, 2). For this tandem case, the phasing of the rotors does not have a very large impact on the harmonic content of the individual rotor loads/moments.

Figure 24: Dynamic plot – Tandem configuration, phase comparison for rotor 1 at dz/R =0, q =1.90 psf, RPM=3000, pitch=0 deg, and tilt=0 deg.

Figure 27: Dynamic plot – Quadrotor configuration, Figure 26: Dynamic plot – Quadrotor configuration, phase comparison for rotor 1 at dz/R =0, q =1.90 psf, phase comparison for rotor 3 at dz/R =0, q =1.90 psf, RPM=3000, pitch=0 deg, and tilt=0 deg.

RPM=3000, pitch=0 deg, and tilt=0 deg.

With –90 deg phase, the 2/rev of both rotors is approximately Figure 26 and Figure 27 show the same conditions as the previous two figures (Figure 24 and Figure 25), but for the the same. 0 deg phasing causes a significant decrease in the 2/rev F for the back rotor, but this reduction is not as dramatic quadrotor configuration. Thus, the previous two figures can y be compared to Figures Figure 26 and Figure 27 to assess for the front rotor. Additionally, the front rotor has significant 3/rev F for –90 deg phase, but none for 0 deg phase. The differences between the tandem and quadrotor configurations y for dz / R =0. Like for the tandem configuration, the 2/rev signal opposite is true for the back rotor.

for the front rotor, R1, in the quadrotor configuration, is significantly higher than the other signals. This trend does not Figures Figure 28 and Figure 29 show similar results to those of the previous figures, but for a front to back rotor separation hold for the back rotor in the quadrotor configuration, where other harmonics sometimes were the most significant, of dz/R =0.33 in the quadrotor configuration. Comparing the plots with dz/R =0.33 to those of the dz/R =0 quadrotor depending on specific load and phase condition. This inconsistency could be due to the more chaotic aerodynamic configuration, one notable observation is that for R3, the back rotor, the 1/rev M , F , and M signals are significantly lower environment experienced by the back rotors. Additionally, y y x the 2/rev signal for R1 F is higher for tandem than for for the dz/R =0.33 configuration.

y quadrotor. R1 and R3 also show more higher frequency signals for the quadrotor configuration than for the tandem, Similar to other cases, for dz/R =0.33, for a given phase, the particularly for F . For -90 deg phase, the 4/rev R3 F signal x x 2/rev signals are higher for the front rotor than for the of the quadrotor was more than double that of the tandem.

back. This may be due to differences in the aerodynamic operating environments of the front and back rotors, with the Focusing on Figure 26 and Figure 27, for R3 F , the 4/rev x front rotor encountering relatively undisturbed air compared frequency is nearly doubled by phasing the rotor –90 deg; to that encountered by the back rotor. The air going into the however, this phasing reduces the signals of other harmonics, back rotors may have a slight downward trajectory, affecting such as the 3/rev and 5/rev. For F , there are some notable y the vibrations seen by the back rotors.

dissimilarities between the front and back rotors (R1 and R3).

Figure 28: Dynamic plot – Quadrotor configuration, Figure 29: Dynamic plot – Quadrotor configuration, phase comparison for rotor 1 at dz/R =0.33, q =1.90 psf, phase comparison for rotor 3 at dz/R =0.33, q =1.90 psf, RPM=3000, pitch=0 deg, and tilt=0 deg. RPM=3000, pitch=0 deg, and tilt=0 deg.

An additional observation is that the 2/rev F and M are x y relatively unaffected by the rotor phasing, for both R1 and CONCLUSIONS R3. This is not the case for the 2/rev F and M , where a y x significant dependence on rotor phase is observed for both The Multirotor Test Bed Entry 2 (MTB2) wind tunnel test, rotors, with the 2/rev F significantly increased by applying conducted in August 2022, was summarized and described.

y The main focus for the MTB2 test was obtaining forces and –90 deg phasing and the corresponding 2/rev M values x moments for the quadrotor configuration for back rotor significantly decreased by applying that same –90 deg heights of dz / R =0, 0.33, and 0.57, where dz / R =0.33 phasing.

represented the RVLT conceptual quadrotor. Additionally, this test allowed for rotor phasing and solidity studies for 2-, 3-, and 6-bladed rotors. Quasi-steady and dynamic data from the MTB2 wind tunnel test were presented and discussed.

Some of the discrepancies observed in the data are as follows: - The single rotor runs and the runs associated with the uncertainty analysis showed that the back rotors yielded lower thrust for the same conditions, potentially due to a load cell discrepancy.

- The CW spinning rotors yielded higher torque values than the CCW spinning rotors, likely due to a load cell or motor discrepancy.

- There could be a slight deviation in measurement from rotor to rotor (independent of the load cell) (observed between front starboard rotor (R1) and the Willink, Lead of the Ames Aeromechanics Mechanical back port rotor (R4)), potentially due to slight Systems Team, for helping with the design process of the deviations in rotor geometry. MTB. The NASA Machine Shop Team, led by Robert Kornienko and Vincent Derilo, machined the parts of the Some of the results observed in the quasi-steady data are as MTB and provided guidance and helpful suggestions during follows: the design process. And as always thank you to William Warmbrodt for his outstanding leadership and to Tom - Blade loading was the highest for 2-bladed, then 3- Norman for invaluable guidance and assistance. Thank you to the reviewers of this work, Lauren Weist, Dorcas Kaweesa, bladed, and then 6-bladed rotors.

and Sesi Kottapalli. A more complete list of - The influence of tilt on thrust and torque was more acknowledgements of all individuals who helped in acquiring pronounced at higher tunnel speeds.

the MTB2 data is given in the data report [Ref. 13].

- For the quadrotor configuration at both low and high tunnel speeds and RPMs, the back rotors were less efficient for dz/R =0 (front and back rotors at the same height), yielding low thrust and high REFERENCES torque values.

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