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AN ASSESSMENT OF ELECTRIC STOL AIRCRAFT

Christopher B. Courtin and R. John Hansman

This report is based on the Masters Thesis of Christopher B. Courtin submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of

Master of Science at the Massachusetts Institute of Technology.

Report No. ICAT-2019-13 August 2019

MIT International Center for Air Transportation (ICAT) Department of Aeronautics & Astronautics

Massachusetts Institute of Technology Cambridge, MA 02139 USA

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AN ASSESSMENT OF ELECTRIC STOL AIRCRAFT

by

Christopher B. Courtin

Submitted to the Department of Aeronautics and Astronautics on August 22, 2019, in partial fulfillment of the

requirements for the degree of

Master of Science in Aeronautics and Aeronautics

A

BSTRACT

Distributed electric propulsion (DEP) is an emerging set of technologies which enable new vehicle configurations by allowing the efficient distribution of many smaller propulsors around the airframe. One application of this technology is to greatly enhance the short takeoff and landing (STOL) capability of a fixed-wing aircraft. STOL aircraft may have advantages over vertical takeoff and land (VTOL) configurations being considered for urban passenger transport missions due to lower risk associated with the certification process and improved performance or reduced weight due to smaller required propulsion systems. To be useful for these missions, STOL vehicles require short-field performance competitive with vertical lift configurations.

One pathway to achieving this is by placing many electric motors and propellers along the leading edge of the wing, an arrangement referred to as a DEP blown wing. This arrangement increases the effective lift of the wing through interaction of the propeller slipstream with the trailing edge flap.

Previous blown wing concepts, based on large propellers or turbine engines, were mechanically complex and adopted only for specialized applications. A DEP blown wing offers a simpler and potentially more efficient way to enhance the high-lift capability of a wing, but the performance is not reliably predictable using existing theoretical or empirical methods.

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A wind tunnel test of a representative 2D blown wing section was undertaken, and section lift coefficient values up to 9 were measured at moderate power settings. The results of this wind tunnel testing were used to predict the takeoff and landing performance of reference vehicles with wing and power loading representative of modern GA aircraft. The results of this analysis suggest that a DEP blown wing may enable takeoff and landing ground rolls of less than 100 ft. Landing distance over a 50 ft obstacle is identified as the likely driver of runway requirements for a super-short takeoff and landing vehicle.

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A

CKNOWLEDGEMENTS

This work was supported by Aurora Flight Sciences, especially Tony Tao, Brian Yutko, and Alex Mozdzanowska, as well as the FAA Joint University Program for Air Transportation Research under Grant#16-G-011. The authors are also grateful to Prof. Mark Drela, and the students of the Fall 16.82 class for their efforts in the wind tunnel testing.

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Contents

1 Introduction 21

2 Background 25

2.1 Blown Lift Overview . . . 25

2.1.1 Mechanisms of Blown Lift . . . 28

2.2 Thin Airfoil Theory Model of a Blown Wing . . . 29

2.3 Key Flow Parameters . . . 32

2.4 3D Corrections . . . 35

3 2D Wind Tunnel Testing 39 3.1 Experimental Overview . . . 39

3.1.1 Experimental Procedures . . . 41

3.2 Key Results . . . 43

3.3 Comparison With Theory . . . 46

4 Performance of STOL Aircraft 49 4.1 Approach . . . 49

4.2 Takeoff and Landing Modeling . . . 52

4.2.1 Takeoff Equations . . . 52

4.2.2 Landing Equations . . . 54

4.3 3D Polars . . . 55

4.4 Expected Takeoff Performance . . . 57

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4.4.2 Takeoff Over a 50ft. Obstacle . . . 62

4.5 Expected Landing Performance . . . 64

4.5.1 Landing Ground Roll . . . 67

4.5.2 Landing Over a 50ft. Obstacle . . . 69

5 Conclusion 75 A Electric Aircraft Certification 79 A.1 Certification Pathways . . . 80

A.2 Emerging Electric Aircraft Architectures . . . 83

A.3 Preliminary Emerging Hazard Assessment . . . 88

A.3.1 Common Mode Power System Failure . . . 89

A.3.2 Battery Thermal Runaway . . . 96

A.3.3 Battery Energy Uncertainty . . . 98

A.3.4 Fly-By-Wire System Failure . . . 100

A.3.5 High Level Autonomy Failure . . . 103

A.3.6 Bird Strike . . . 104

A.4 Summary . . . 106

B Wind Tunnel Testing of a Blown Flap Wing 109 B.1 Abstract . . . 109

B.2 Nomenclature . . . 109

B.3 Introduction . . . 111

B.4 Blown Airfoil Theory . . . 112

B.4.1 Physical Mechanism . . . 112

B.4.2 Vortex Sheet Model . . . 112

B.5 Methodology . . . 115

B.5.1 Test Parameters . . . 115

B.5.2 Test Rig . . . 116

B.5.3 Wing Section . . . 117

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B.5.5 Data best-fit functions . . . 120

B.6 Results . . . 123

B.6.1 Force and Moment Coefficients . . . 123

B.6.2 Wake Characterization . . . 125

B.7 Discussion . . . 125

B.7.1 Force Coefficient Polars . . . 125

B.7.2 Effect of Motor Axis Angle . . . 126

B.7.3 Blown Wing Performance Relative to Hover . . . 128

B.7.4 Separation of Upper Surface . . . 129

B.7.5 Pitching Moment Behavior . . . 130

B.8 Conclusion . . . 130

B.9 Derivation of jet excess power coefficient . . . 131

B.9.1 Load cell calibration matrix . . . 132

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List of Figures

1-1 Categorization of emerging electric aircraft architectures, based on method of lift generation and use of distributed electric propulsion.

Vehicle categories are described in Appendix A. . . 22

1-2 The NASA X-57 Maxwell will demonstrate the feasibility of distributed electric propulsion and enhanced cruise efficiency. Image from NASA [1] 23 2-1 Methods of lift augmentation based on both propeller-wing interactions (a) and jet-wing interactions (b-d). a) from [2], b)-d) from [3]. . . . 26

2-2 The Breuget 941 used a blown wing to achieve exceptional short-field performance. . . 26

2-3 a) Representative geometry from wind tunnel tests exploring blown wing performance. b) Landing flap configuration for the Breuget 941. a) from [4], b) from [5] . . . 27

2-4 Actual blown airfoil flow (top), and vortex sheet model (bottom).Figure by Mark Drela . . . 29

2-5 Jet sheet of finite thickness h, and vortex sheet model. The turning of the jet’s momentum-excess J0 implies an apparent pressure load on the vortex sheet.Figure by Mark Drela . . . 30

2-6 Multiple propellers spaced along the leading edge generate a jet sheet of uniform height hd . . . 33

2-7 Momentum theory model of jet contraction . . . 33

3-1 Overview of the wind tunnel test setup. . . 40

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3-3 Top view showing the wind tunnel data collection system layout . . . 41 3-4 c`, cx, cm plotted against angle of attack for angle for various flap and

motor power settings. Points represent measured data and the lines represent the best-fit functions, for cJ between 0 and 4.5 in

incre-ments of .5.Figure from [6] . . . 45 3-5 cl-cx polars, where points represent measured data and the lines

rep-resent the best-fit functions, for cJ between 0 and 4.5 in increments

of .5. . . 46 3-6 A comparison between the measured c` values (points) and those

pre-dicted by an inviscid model based on thin airfoil theory (lines) . . . . 47 3-7 A comparison between the measured c` values and inviscid theory, with

the initial jet deflection angle reduced to account for inefficient turning of the flow. . . 48 4-1 Overview of the aircraft takeoff distances . . . 53 4-2 Overview of the aircraft landing distances . . . 55 4-3 Wind tunnel data corrected for 3D effects, assuming blowing across

85% of the wing . . . 56 4-4 In blown lift configurations, there is substantial variation of CL with

airspeed, which complicates takeoff and landing calculations . . . 58 4-5 Plot of the relationship between takeoff ground roll and design max

CL, for the SR22 retrofit with a blown wing. . . 60

4-6 Plot of the relationship between takeoff ground roll and design max CL, for the enhanced STOL aircraft. . . 61

4-7 Plot of the relationship between takeoff ground roll and passenger hor-izontal acceleration, for the enhanced STOL aircraft. . . 62 4-8 Plot of the relationship between takeoff distance over a 50 ft. obstacle

and design max CL, for the retrofit aircraft. . . 63

4-9 Plot of the relationship between takeoff distance over a 50 ft. obstacle and design max CL, for the STOL aircraft. . . 63

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4-10 Variation of steepest achievable descent angle with increasing CL . . . 65

4-11 Variation of steepest achievable climb angle with increasing CL . . . . 66

4-12 Airspeed/flight path angle operational envelopes, for 0 ,20 ,and 40

flap deflections. . . 67 4-13 Landing ground roll variation with flap deflection . . . 68 4-14 Total landing distance over a 50 ft obstacle . . . 69 4-15 Total landing distance, landing ground roll, and obstacle clearance

distance shown for the enhanced STOL configuration at two landing flap settings. . . 70 A-1 Risk matrix showing high-(red), medium-(yellow), and low-(green)

sever-ity risk areas. . . 82 A-2 Categorization of emerging electric aircraft architectures. . . 85 A-3 Key hazards for each electric aircraft configuration group, with a

base-line risk severity assessment for each. . . 90 A-4 Baseline risk severity associated with common mode power system

fail-ure for each vehicle architectfail-ure group. . . 91 A-5 The demonstrated (dark blue) and likely successful (light blue) parachute

deployment envelopes for a Cirrus SR20. . . 95 A-6 Battery thermal runaway presents a significant source of risk for any

all- electric aircraft architecture utilizing lithium-polymer batteries. . 97 A-7 The hazard severity rankings associated with battery energy

uncer-tainty reflect the increased probability that an all-electric vehicle will deplete its batteries before reaching its intended destination . . . 99 A-8 Unmitigated risk associated with fly-by-wire system failure. . . 102 A-9 There is uncertainty around the likelihood of bird strikes on low-altitude,

high-speed UAM vehicles that could increase the severity of this haz-ard. . . 105 B-1 Actual blown airfoil flow, and vortex sheet model. . . 112

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B-2 Jet sheet of finite thickness h, and vortex sheet model. The turning of the jet’s momentum-excess J0 implies an apparent pressure load on

the vortex sheet. . . 113 B-3 Cross-section schematic of experimental set up. . . 116 B-4 Photos of test rig. The left shows a front view of the setup, and the

right shows a closeup of the wake survey rake. . . 116 B-5 CAD rendering of the wing sections displayed in side and rear isometric

views. . . 117 B-6 Two CAD renderings demonstrating the motor mount design. . . 118 B-7 Combined motor and propeller characterization test results. (a) Thrust

and electrical power coefficients, (b) Overall power efficiency curve of motor. Colors show the different angle of attacks of the motor relative to free stream. . . 121 B-8 c`, cx, cm against angle of attack for 20 motor axis angle. Points

rep-resent collected data and the lines reprep-resent the best-fit functions (ex-plained in B.5.5) at constant cJ, plotted at cJ increments of 0.5. . 123

B-9 c`, cx, cm against angle of attack for 10 motor axis angle. Points

rep-resent collected data and the lines reprep-resent the best-fit functions (ex-plained in B.5.5) at constant cJ, plotted at cJ increments of 0.5. . 124

B-10 Illustration depicting the alignment of 2D rake data plots to the phys-ical model . . . 125 B-11 Wake profiles for (a) unpowered, and (b) powered wing at = 4. Both

profiles are at f = 20 and ↵ = 0. The spanwise consistency

demon-strates uniform jet profile. Projected motor locations are indicated with red lines. . . 126 B-12 Vertical wake profile for (a) ↵ = 0 and (b) ↵ = 10 . Both are at f = 20 126

B-13 cl-cx polars for 10 motor axis angle. Points represent collected data,

lines are polynomial fit. . . 127 B-14 cl-cx polars for 20 motor axis angle. Points represent collected data,

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B-15 c` cx fit function polars for m = 10 and m = 20 , for ↵ ranging from

-5 to 23 . The data points have been excluded for ease of visualization.128 B-16 Ratio of excess power in blown-lift to excess power of hovering for

equivalent thrust and disk area, at different flap angles and at ↵ which maximizes c` . . . 129

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List of Tables

3.1 Key geometric parameters of the wind tunnel model . . . 41

3.2 Key wind tunnel test parameters . . . 42

4.1 Key physical parameters for the reference aircraft. . . 50

4.2 Key performance parameters for the reference aircraft. . . 52

4.3 Takeoff Performance Summary . . . 64

4.4 Takeoff and landing performance summary, showing calculated perfor-mance numbers and relative perforperfor-mance to the baseline or published data. All distances given in ft. . . 71

A.1 Hazard consequence is ranked based on the impact to passengers, crew, and aircraft [7]. . . 82

A.2 Quantitative definitions of differing likelihood levels based on the num-ber of passengers and engine numnum-ber and type. [7]. . . 84

A.3 Mitigation strategies for common mode power system failures . . . . 93

A.4 Mitigation strategies for battery thermal runaway . . . 98

A.5 Mitigation strategies for battery energy uncertainty . . . 99

A.6 Mitigation strategies for flight control system failures . . . 102

A.7 Mitigation strategies for bird strike . . . 106

B.1 Controlled Test Parameters . . . 115

B.2 NRMSE of the fits c` generated for different f and m . . . 122

B.3 NRMSE of the cx fits generated for different f and m . . . 122

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B.5 c` fit coefficients . . . 134

B.6 cx fit coefficients . . . 134

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List of Symbols

b span

c chord

cE 2D jet energy coefficient

cJ 2D jet momentum coefficient

cJ 2D jet momentum-excess coefficient

cQ 2D jet mass flow coefficient

c` 2D lift coefficient

cm 2D pitching moment coefficient

cx 2D net streamwise force coefficient

fb fraction of wing with blowing

hJ downstream jet height

hd effective jet height at propeller disk

q = 1 2⇢V

2 dynamic pressure

s Distance

u jet local velocity

w downwash velocity

AR Wing aspect ratio

CE 3D jet energy coefficient

CJ 3D jet momentum coefficient

CJ 3D jet momentum-excess coefficient

CQ 3D jet mass flow coefficient

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CX 3D net streamwise force coefficient

D0 Drag per span

MTOW Maximum takeoff weight

Re Reynolds number

S Wing reference area

T0 Thrust per span

T0 Static thrust

V1 freestream velocity

VJ jet velocity

W weight

X = D T Net streamwise force

↵ angle of attack

↵i induced angle at wing

↵i1 far downstream induced angle

f flap deflection angle

⌘ efficiency

✓ angle of streamline from the x-axis

w wake vortex strength

flight path angle

 streamline curvature

⇢ density

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Chapter 1

Introduction

Within the aviation industry there is currently widespread interest in the develop-ment of electric aircraft for a variety of missions. One significant way electric aircraft may differ from existing vehicles is in having primary propulsion systems comprised of many small propulsors distributed around the airframe, with power supplied elec-trically to each. The benefits of this concept, which is known as distributed electric propulsion or DEP, arise from increased design freedom and opportunities for bene-ficial aero-propulsive interactions [8]. Figure 1-1 shows an overview of the space of emerging electric aircraft architectures, grouped by the method of lift generation as well as whether or not they utilize DEP. Here, DEP defined as having more than four propulsors fed from a centralized energy storage system, which could be a battery, hybrid-electric generator, or some other alternative.

The performance benefits of DEP differ depending on the design mission of the vehicle. One mission of particular interest for electric vehicles is short-range passenger transport within and around major urban areas, using small aircraft operating off a distributed network of small takeoff and landing sites. This concept is commonly referred to as Urban Air Mobility (UAM) [9].

A defining requirement for UAM missions is the need to be able to take off and landing using ground infrastructure much shorter than a traditional runway. The exact size requirements are unclear but for most UAM concepts to be viable the required takeoff and landing area must be small enough that a useful number can

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Rotor Lift Tilting Hybrid Lift Static Hybrid Lift Blown Lift Conventional Wing Few Propulsors

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Helicopter Tilt-lift Static Hybrid

No current examples

Fixed Wing

Many Propulsors (4+)

Multirotor DEP Tilt-lift Stopped Rotor DEP Blown Wing DEP Fixed Wing Image from Jaunt

Image from Elytron

Image from Pipistrell

Image from Aurora Image from Airbus

Image from Volocopter Image from NASA Image from Airbus Image from Airbus

Figure 1-1: Categorization of emerging electric aircraft architectures, based on method of lift generation and use of distributed electric propulsion. Vehicle cate-gories are described in Appendix A.

be placed in and around densely populated urban areas. This precludes the use of vehicles with conventional takeoff and landing (CTOL) capability [10].

It is widely assumed that adding vertical takeoff and landing (VTOL) capability is the only way to develop a vehicle with sufficiently small infrastructure demands, as vertical flight minimizes the ground area required [10][11]. Many VTOL aircraft being proposed for UAM missions use DEP to increase cruise efficiency, reduce mechanical complexity, and reduce noise. These typically fall under the Rotor Lift, Tilting Hybrid Lift, or Static Hybrid Lift columns of Figure 1-1. Because of this reliance on electric power distribution, the term eVTOL is common to describe this class of aircraft [12]. However, there are significant challenges associated with developing this new class of eVTOL aircraft. One is that VTOL capability requires large vertical lift systems, which add weight and reduce vehicle efficiency in other phases of flight [2]. This reduces the mission utility or increases the weight of the vehicle; vehicle weight is highly correlated with vehicle cost [13]. Another is that, as discussed in detail in Appendix A, eVTOL aircraft may face challenges during the FAA airworthiness cer-tification process due to the complexity of the required flight control systems and the potential for catastrophic loss of control in the event of a low-altitude power system failure.

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meet-ing the UAM mission requirements, referred to here as as Super-Short Takeoff and Landing (SSTOL) aircraft. In this configuration, which is similar to the NASA X-57 shown in Figure 1-2, the lifting capabilities of the wing are greatly enhanced by the beneficial interaction between the trailing edge flap and propellers distributed along the leading edge of the wing. The term "blown wing" or "blown lift" will to describe this system. This alternative use of DEP has, as this work will show, the potential to greatly reduce the runway requirements of a fixed wing aircraft, potentially to the point where SSTOL vehicles could be competitive with VTOL configurations.

Figure 1-2: The NASA X-57 Maxwell will demonstrate the feasibility of distributed electric propulsion and enhanced cruise ef-ficiency. Image from NASA [1]

The motivation for investigating the SSTOL concept comes from benefits re-lated to the performance and certifica-tion of these aircraft, compared to eV-TOLs. One of the main findings of the certification analysis in Appendix A is that fixed wing aircraft have lower cer-tification risk associated with them than

eVTOL configurations, primarily because they avoid the control system complexity and loss of power hazard described above. While there are many systemic challenges to be overcome before a UAM system can be implemented, certification of new vehicle types is especially critical because it is a prerequisite for commercial operations at any scale [9]. Historically, this process is time-consuming and expensive, especially for novel vehicle configurations.

SSTOL aircraft are also expected to have improved utility or reduced weight and cost relative to eVTOLs, because of the lower required thrust-to-weight ratios and improved aerodynamic efficiency. The magnitude of these performance benefits are clearly dependent on the relationship between the power input to the blown wing and the resulting takeoff and landing performance of the vehicle. Currently, that relationship is not well understood for this class of aircraft. While power-augmented high-lift systems have been used on other types of aircraft as described in Chapter 2,

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the methods developed to predict the performance of those vehicles do not extend reliably to the DEP blown lift concept.

The goal of the NASA X-57, which does have a DEP blown lift system, is to demonstrate the feasibility of DEP, as well as enhanced cruise efficiency by enabling a smaller wing without compromising takeoff and landing performance [1]. Its runway requirements therefore will not be indicative of what may be possible with an aircraft designed for SSTOL performance. At the time of this writing, the X-57 is still under development and only preliminary results of ground tests of the high-lift system have been published [14].

The goal of this thesis is to assess the potential of the SSTOL concept by combin-ing the results of a 2D wind tunnel test of a representative blown wcombin-ing section with established methods for preliminary estimates of takeoff and landing performance. The performance of reference aircraft with wing and power loading representative of typical GA vehicles will be assessed. This will give a first estimate of achievable runway requirements, as well as to highlight key trade-offs in the vehicle design and challenges that will have to be overcome to achieve reliable SSTOL performance. Chapter 2 provides background on the blown lift concept, and introduces theoretical models to predict the performance of a blown wing. Chapter 3 presents and overview and key findings of the blown lift wind tunnel testing, which is described more com-pletely in Appendix B. Chapter 4 uses the results of this testing to estimate the takeoff and landing performance of reference blown lift aircraft.

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Chapter 2

Background

2.1 Blown Lift Overview

Several different systems have previously been developed where power added to a wing-flap system significantly increases the effective lift coefficient. In the existing literature such systems are generically termed "powered-lift" configurations [15], al-though the meaning of that term has evolved; currently it describes any aircraft with VTOL capability that is also capable of wing-borne flight [16].

Lift-enhancing powered-lift systems can be broadly divided into two categories. The first uses interactions between the wing and the propeller slipstream to augment the lift of the wing. These systems are commonly called blown lift, blown wing, or deflected slipstream vehicles and are shown notionally in Figure 2-1(a). The second category uses the interaction of jet turbine exhaust gasses, bypass air, or high pressure bleed air with aerodynamic surfaces to provide the lift enhancement. These systems are often referred to as jet flaps, augmentor wings, or blown flaps. There are many different variants [3]; three main ones are shown in Figure 2-1 (b)-(d).

Propeller-wing interactions have been used to improve high-lift system perfor-mance on several aircraft concepts, perhaps most significantly the Breuget 941 STOL transport shown in Figure 2-2, which had total takeoff and landing distances of less than 850 ft over a 50 ft obstacle, at a gross weight of 40,800 lbs. There is also a substantial existing body of work focused on predicting the high-lift performance of

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Scanned with CamScanner

Scanned with CamScanner Figure from McCormick Figures from DATCOM

a) b) c) d)

Figure 2-1: Methods of lift augmentation based on both propeller-wing interactions (a) and jet-wing interactions (b-d). a) from [2], b)-d) from [3].

these systems, largely based on empirical wind tunnel test results [4]. [17] offers a good summary of different methods of modeling wing-propeller interactions.

Figure 2-2: The Breuget 941 used a blown wing to achieve exceptional short-field per-formance.

For the best performance from a blown lift vehicle, it is desirable to have blowing over as much of the span as

possible. Because of the mechanical

complexity associated with having many small engines in non-electric configura-tions, previous blown lift aircraft have been restricted to the case where there are one or two large propellers per semi-span, and wind tunnel testing to date has

focused on these configurations. Figure 2-3 (a) shows a representative test setup from [4], which shows a typical test propeller size relative to the wing span and chord.

This testing identified the ratio of rotor diameter to flap chord as critical for the performance of a blown wing. When the rotor diameter is small relative to the flap chord, the slipstream is more effectively turned by the flap and the lifting performance is enhanced. This trades directly with the need to for the slipstream to cover the entire wing, which in the case of one or two propellers per semi-span can only be done with relatively large propellers.

To generate sufficient high lift and high drag on landing with these large propellers, large and complex flaps deflected to very high angles are required. Figure 2-3 (b) shows the double-slotted inboard flaps of the Breguet 941 in the landing configuration;

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Figure 2-3: a) Representative geometry from wind tunnel tests exploring blown wing performance. b) Landing flap configuration for the Breuget 941. a) from [4], b) from [5]

the slots enhance the maximum deflection angle of the slipstream [4]. The need to descend at high power settings presents a particular challenge for blown lift aircraft, as high lift coefficients that are only achievable with large net thrust are not usable on landing.

Jet flaps, such as those shown in Figure 2-1 (b)-(d), offer an advantage over propeller-based systems in that the height of the jet can be quite small relative to the chord of the flap. This enables very efficient turning of the jet flow, or even direction control over the deflection angle in the case of the internally ducted jet flap, shown in Figure 2-1 b). This corresponds to higher lift for lower power settings, and as a consequence less excess thrust on landing. However, these systems are typically restricted to use on military aircraft because of weight, cost, and complexity, especially in the case where internal ducting of engine bleed air is required[18].

The DEP blown wing configuration proposed for SSTOL applications does not fit neatly into either category. It is not clear that existing blown wing test results, based on one or two propellers per semi-span, are applicable to the case where there are many small propellers arranged along the leading edge. In the limit where the propeller diameter is small compared to the flap chord, the performance of this system is expected closely approximate the performance of a jet flap [2]. Therefore, the main advantage of DEP blown wing is that it provides equivalent or superior performance to jet flap or deflected slipstream vehicles, without the complexity of internal ducting

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or the requirement of large flap systems.

However, it is also unclear how well an array of small electric motors approximates jet flap performance. This uncertainty motivates the wind tunnel testing described in Chapter 3. The results of this test are compared to theoretical models that describe the idealized performance of the jet flap. While they are not able to capture all the relevant physical interactions that effect the performance of a blown lift system, they do offer useful insight into the key relationships between the various components of the system.

In the remainder of this chapter, Section 2.1.1 describes the physical mechanisms by which blowing enhancing lift. Sections 2.2 and 2.3 develop a theoretical model for the 2D section performance of a jet flap or DEP blown wing, and define key parameters that affect the system performance. Section 2.4 describes corrections to 2D data used to predict the performance of a finite-winged vehicle.

2.1.1 Mechanisms of Blown Lift

There are several physical mechanisms by which blowing augments the lift of the wing. The key similarity between all jet flap and blown wing configurations is the deflection of a high-momentum stream of air - the jet or propeller slipstream - downward from the trailing edge of the airfoil. After leaving the airfoil, this jet is turned from some initial jet deflection angle back towards the freestream. This turning coincides with a pressure difference between the upper and lower surfaces of the jet, which in turn further deflects the freestream flow. Because the jet can sustain this pressure load, the pressure differences between the upper and lower surface of the airfoil do not have to vanish at the trailing edge. Therefore, the lift of the airfoil is substantially increased [2].

Another significant mechanism which contributes to increased lift of blown wings or externally blown flaps is the delayed bursting of the main-element wake and the delayed separation of the flap boundary layer [19]. This effect is mainly achieved through the injection of the blowing jet’s high total pressure flow through the flap gap. If there is sufficient flow over the airfoil upper surface, leading-edge separation is

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also suppressed, allowing blown wings to achieve higher angles of attack and/or flap deflections.

In finite-wing vehicles, the jet does not ultimately align itself with the freestream but rather with the downwash far behind the wing. This flow turning produces a vertical force that also contributes to lift [2].

There are well-developed inviscid models for the performance of a jet flap, which account for the change in lift as a function of wing angle of attack, flap deflection, and jet momentum. While at high angles of attack or flap deflection angles the performance of a jet flap is dominated by viscous phenomena (separation) that this model can’t capture, it is useful for developing a sense of the key physical relationships and defining parameters.

2.2 Thin Airfoil Theory Model of a Blown Wing

( ) V α w γ ( )x x γ ( )x θ Actual Flow

Vortex Sheet Model

V streamline ( ) wx total velocity vortex−sheet velocity vortex sheet x freestream velocity V α camber ( )x Z δj jet angle at TE δf flap angle −θTE J J

jet momentum flow

h

jet height

Figure 2-4: Actual blown airfoil flow (top), and vortex sheet model (bottom).Figure by Mark Drela

Following the formulation of Thwaites [20] and Spence [21], an airfoil with jet blowing can be modeled using a vortex sheet both over the airfoil and in the wake, as shown in Figure B-1. The vorticity in the wake arises from the curvature the jet, which has an initial trailing deflection angle ✓T E = f and far downstream is aligned

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which is associated with an external velocity increase across the wake. This can be modeled as an idealized velocity jump across a vortex sheet, as shown in Figure B-2. The strength of the wake vorticity is determined by the jet curvature  = d✓

ds, which, γw V 1 V2 r n Model J m. E V 1 u 1 u 2 V 2 ρ ρ r n Actual Flow h ρ= j

Figure 2-5: Jet sheet of finite thickness h, and vortex sheet model. The turning of the jet’s momentum-excess J0 implies an apparent pressure load on the vortex

sheet.Figure by Mark Drela

combined with the free-vortex velocity distribution u ⇠ 1/r within the jet, is related to the velocity change within the jet u.

u = u1 u2 = uah (2.1)

ua = 12(u1+ u2) is the average jet velocity. The external velocity jump V can

be similarly defined.

V = V1 V2 (2.2)

The average external velocity Va= 12(V1+ V2)⇡ V1.

Because the pressure is continuous across the jet boundaries, the pressure dif-ference in the external flow must be the same as the pressure difference across the jet.

(p2 p1)outer = (p2 p1)inner (2.3)

The velocity jumps can therefore be related using Bernoulli’s equations, applied in both the inner flow and in the jet.

1 2⇢(V 2 1 V22) = 1 2⇢J(u 2 1 u22) (2.4)

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This equation can also be expressed in terms of velocity jumps and average velocity.

⇢Va V = ⇢Jua u = ⇢Ju2ah (2.5)

The wake vortex strength is related to the velocity jump by

w = V Vah =

⇢Ju2a ⇢Va2

⇢Va

h (2.6)

where the Vah term represents the extrapolation of the effects of a vortex sheet at

the wake centerline to its boundaries at a distance h/2.

Approximating Va ⇡ V1, renaming ua as the jet velocity Vj, and defining the jet

momentum per span J0 as

J0 = Z h/2

h/2

⇢u2dn⇡ ⇢JVJ2h (2.7)

the expression for the vortex strength can be rewritten as

w V1 = J0 ⇢V2 1h ⇢V2 1 = J0 ⇢1V2 1 (2.8) where the term J compactly expresses the jet momentum-excess per span. This can be represented in terms of the dimensionless momentum-excess coefficient cJ

cJ ⌘

J0

1V2 1c

(2.9) which allows Equation 2.8 to be approximated as

w V1 ⇡ cJ 2 c d✓ dx (2.10)

This identifies the parameter cJ as the critical parameter for determining the

strength of the wake vorticity, and thus the effect of blowing on the lift and moments generated.

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The streamline angle can be determined from the vortex strengths by ✓(x) ⌘ ↵ +w(x) V1 = ↵ + 1 2⇡ Z c 0 (x0) V1 dx0 x0 x + cJ 2 1 2⇡ Z 1 c cd✓ dx0 dx0 x0 x (2.11)

which is an integro-differential equation that in practice must be solved numerically using a discretized wake and airfoil geometry to determine the airfoil vortex sheet strength and the wake curvature ✓. Once these values are known, c` and cm can be

determined by integration of the pressure difference across the wing.

Spence [21] presents an numerical solution to this equation for the case of a thin wing at small angles of attack. This is used to develop a linear approximation of c`

based on a given angle of attack ↵, jet deflection angle f, and momentum coefficient

cJ, which shows close agreement with the numerically computed values.

cJ ⌘

J0

⇢1V12c

(2.12) cJ is closely related to cJ = cJ 2hc; in the limit where VJ >> V1 they are

approximately equivalent. Spence’s model is presented in Eqn. 2.13- 2.15. c` = @c` @↵↵ + @c` @ F F (2.13) @c` @↵ = 2⇡(1 + 0.151 p cJ + 0.219cJ) (2.14) @c` @ F = 2p⇡cJ(1 + 0.151pcJ + 0.139cJ) 1 2 (2.15)

2.3 Key Flow Parameters

This section defines additional dimensionless parameters useful for assessing the per-formance of a blown wing. In this model, the propellers are assumed to be spaced closely enough that they create a uniform jet over the entire blown portion of the wing. This is shown graphically in Figure 2-6, where the dashed line represents the effective jet height and the solid lines represent the propellers. The frontal area of

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the jet is assumed to be the same as the area of the propellers, and so the effective height of the jet at the propeller disk hd is given by Equation 2.16.

b rprop

hd

rhub

Figure 2-6: Multiple propellers spaced along the leading edge gen-erate a jet sheet of uniform height hd

It is important to note that the downstream jet height hJ will differ from the jet height at

the propeller disk hd because of contraction of

the propeller wake, shown notionally in Figure 2-7. This effect can be estimated from classical propeller momentum theory, which assumes a in-stantaneous pressure jump across the propeller disk [2].

V

1

; ρ

1

V

D

V

J

; ρ

J

h

d

h

J Actuator Disk

Figure 2-7: Momentum theory model of jet contraction hd=

⇡(r2

prop r2hub)Nprop

b (2.16)

Mass flow conservation along the jet

hd⇢dVD = hJ⇢JVJ (2.17)

can be combined with the classical momentum theory result VD =

VJ + V1

2 (2.18)

and the assumption of constant density throughout, which is valid for the low-speed cases being considered here, to give the relationship between jet height at the propeller

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and far downstream. hJ = 1 2 V1 VJ + 1 hd (2.19)

Similar to the jet momentum and momentum-excess coefficients defined in Equa-tions 2.12 and 2.9, the jet mass and energy flow coefficients can be defined.

cQ ⌘ ˙ m0 ⇢1V1c = Rh/2 h/2⇢ u dn ⇢1V1c ⇡ hJ c VJ V1 = 1 2 hd c VJ V1 + 1 (2.20) cE ⌘ E0 1 2⇢1V13c = Rh/2 h/2 1 2⇢ u 3 dn 1 2⇢1V13c ⇡ hJ c V3 J V3 1 = cQ V2 J V2 1 (2.21) It is also convenient to express cJ and cJ in terms of the effective jet or disk

height and velocity ratios, assuming constant density. cJ = 2 hJ c V2 J V2 1 = hd c ✓ V2 J V2 1 ◆ ✓ V1 VJ + 1 ◆ (2.22) cJ = 2 hJ c ✓ V2 J V2 1 1 ◆ = hd c ✓ V2 J V2 1 1 ◆ ✓ V1 VJ + 1 ◆ (2.23) cJ is similar to the propeller thrust coefficient cT, which is given by

Equa-tion 2.24. cT = T0 1/2⇢V2 1c = ⇢hJVJ(VJ V1) 1/2⇢1V2 1c = 2hJ c V2 J V2 1 VJ V1 (2.24)

Combining Equations 2.23 and 2.24 gives the ratio of cJ to cT as

cJ

cT

= V1 VJ

+ 1 (2.25)

which shows that the two are approximately equivalent in the limit where the jet velocity is much larger than the freestream VJ >> V1.

In this highly-coupled system, it is ambiguous to separate thrust and drag as is done for conventional vehicles. Therefore, it is convenient to define the net streamwise for coefficient cx, which can be measured directly, and avoids the ambiguities between

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drag and thrust inherent in blown wing systems. cx ⌘ cT cd= T0 qc D0 qc (2.26) .

2.4 3D Corrections

The models presented so far describe the performance of an ideal 2D wing section, with infinite span. To predict the performance of a finite wing, additional corrections are required. Two main effects are induced drag and additional jet lift, both of which are caused by the downwash due to shed vorticity in the wake, especially near the wingtips. Additionally, uniform blowing across the entire wing will be difficult to achieve in practice, especially at the fuselage attachment point. This will also reduce the performance of the system relative to the ideal 2D case.

A simple approach to these corrections, following the method of [22] and [23], is presented here. This approach assumes a span efficiency e of the wing, a constant average downstream induced angle ai1, and uniform blowing across a constant

frac-tion of the wing fb. The wing chord and twist are also assumed to be constant across

the span.

The lift of the airfoil is the sum of the lift from wing and jet sheet circulation LC,

as well as the lift from thrust LT. This is the vertical component of the jet momentum

at some far downstream deflection angle ↵i1.

L = LC+ LT (2.27) LC = 1 2⇢V 2 1 Z b/2 b/2 c`c dy (2.28) LT = Z b/2 b/2 d ˙mJVJsin↵i1 ⇡ b fb⇢ hJV 2 J sin↵i1 (2.29)

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sources of drag.

X = DC + DP T + DT (2.30)

DC is the usual circulation-induced drag, DT is the increased drag or thrust

re-duction associated with the downstream deflection of the jet and associated rere-duction in streamwise jet momentum. DP is the profile drag, associated with losses due to

skin friction and separation.

DC = 1 2⇢V 2 1 Z b/2 b/2 c c`↵idy (2.31) DT = Z b/2 b/2 d ˙mjVj(1 cos↵i1) (2.32)

Since this method will be applied to experimental data, it is useful to reformulate Equation 2.30 terms of a measured streamwise force Xmeas = DP T, which accounts

for the thrust and profile drag of the wing, as well as any interference drag, propeller effects, regions of separation, and losses associated with the jet deflection.

Xmeas= 1 2⇢V 2 1 Z b/2 b/2 cxc dy (2.33) X = DC + Xmeas+ DT (2.34)

In this case, X only describes the blown wing system. Additional drag terms to account for the rest of the airframe, as well as any additional non-interacting thrust sources, must be added to determine the total vehicle streamwise force. The section values of c` and cx are assumed to be known, either from theoretical predictions or

experiment.

For convenience the 3D dimensionless jet performance coefficients are defined only over the fraction of the wing that has blowing over it, making them numerically equivalent to the section values for the blown sections.

CQ ⌘ 1 Sfb Z fbb/2 fbb/2 cQcdy = VJ V1 hJ c (2.35)

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CJ ⌘ 1 Sfb Z fbb/2 fbb/2 cJcdy = 2 V2 J V2 1 hJ c (2.36) CE ⌘ 1 Sfb Z fbb/2 fbb/2 cEcdy = V3 J V3 1 hJ c (2.37)

The required shaft power Pshaft to develop a given VJ over the blown sections is

therefore Pshaft⌘p = 1 2⇢V 3 1 Z fbb/2 fbb/2 (cE cQ)c = 1 2⇢V 3 1fbSref(CE CQ) (2.38)

The lift coefficient CLCdue to circulation can be calculated from the 2D c` mea-sured in the wind tunnel experiments, or predicted by theory. The lift due to thrust deflection CLT is an additional lift source that is not present in the wind tunnel experiments. The circulation-related lift and drag force coefficients are

CLC ⌘ LC qS = 1 S Z c`c dy (2.39) CDC ⌘ DC qS ⇡ CLC↵i (2.40)

If the wing chord and twist are constant along the span, CLC can be expressed in terms of the blowing fraction.

CLC = (c`fb + c`,0 (1 fb)) cos

2

i (2.41)

c`(↵, f, CJ)is the 2D lift coefficient at the specified flight condition. c`0(↵, f, 0) is the lift of the wing section with zero blowing. The cos2

i term represents the

reduction in the apparent freestream at the wing due to large downwash angles ↵i.

For typical wings these angles are small and so the change in apparent freestream is usually neglected.

The induced angle at the wing ↵i is given by

↵i =

CLC

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and is related to the induced angle far downstream ↵i1 by

↵i1 = 2↵i (2.43)

. The thrust-related lift and drag coefficients are CLT ⌘ LT qS = CJsin ↵i1fb ⇡ 2 CJ↵ifb (2.44) CDT ⌘ DT qS = CJfb(1 cos ↵i1)⇡ 2 CJfb↵ 2 i (2.45)

CXmeas can also be represented based on fb

CXmeas = cxfb+ cx,0(1 fb) (2.46)

where cx(↵, f, CJ) and cx0(↵, f, 0) are known from the section data. Defining CDi = CDT + CDC, Equation 2.34 becomes

CX = CXmeas+ CDi. (2.47)

and the total CL is given by

CL= CLC + CLT (2.48)

These equations allow CLand CX to be determined as a function of wing ↵, f,and

cJ. In practice, because CLdepends on ↵i and vice versa, some iteration is required

to determine CL and CX for a specified flight condition.

These corrections are limited in their application as they do not consider the effect of varying spanwise induced angle, blowing, flap deflection, or chord/twist distribu-tions. All of those will be significant in an actual vehicle design. However, they are useful to obtain a preliminary estimate of the performance of a blown wing aircraft, especially at high power settings where blowing effects will dominate.

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Chapter 3

2D Wind Tunnel Testing

This chapter describes results from wind tunnel testing to determine the performance of a blown wing with multiple propellers distributed along the span. The performance of the test article approximates the 2D section performance of a blown wing with a single-slotted trailing edge flap over a range of angles of attack, flap deflections, and blowing power settings. The results of the experiment described in this section were published in the paper Wind Tunnel Testing of a Blown Flap Wing [6], which provides a more complete description of the experimental setup and results and is included as Appendix B. A brief overview of the experiment and the results that are relevant to the subsequent analysis is provided here.

3.1 Experimental Overview

The goal of the wind tunnel testing was to measure how the wing lift, streamwise force, and pitching moment coefficients c`, cx, and cm change with flap deflection, motor

power, angle of attack, and other key parameters. In order to do this, a representative section of a blown wing was mounted in the MIT Wright Brothers Wing Tunnel, with endplates on either side to eliminate tip effects and approximate an ideal 2D flow. Figure 3-1 shows an overview of the experimental setup.

A cross section of the wing is shown in Figure 3-2. The wing is printed in PLA in four sections and rigidly mounted on a 3/4" steel rod passing through the airfoil

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Figure 3-1: Overview of the wind tunnel test setup.

c/4 point. The motor mounts were printed from ABS to prevent melting; the flap is also printed from PLA. The flap is not hinged but mounted using removable steel brackets. Changing the brackets allows different flap angles and gap geometries to be tested.

Mounting Spar

Motor Mount

Flap Bracket Flap

Figure 3-2: Cross section of the wing test article

Figure 3-3 shows the layout of the data collection system, which uses load cells to measure the lift, streamwise force, and moment generated by the blown lift system. The spar is mounted directly to the drag and lift load cells via a U-joint just outboard of the endplates. A shaft collar connects one end of the moment arm to the spar. Force

mea-sured at the other end of the arm, by the moment load cell, is used to determine the wing pitching moment. Adjustment to the shaft collar changes the wing angle of attack. Key parameters of the motors, propellers, and model are shown in Ta-ble 3.1. The span of the test article is 23.9in, and the chord with flap retracted is a uniform 9 in. The motors used in the test were small motors designed for RC aircraft (T-Motor F40 Pro II), each of which has a maximum power of 750W. In practice, motor maximum power was not usable for testing because of excessive motor heating.

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X-Force Load Cell

Moment Load Cell Lift Load Cell

Shaft Collar

Pillow Block Pillow Block

Top View

Flap Main Spar

Wing U-Joint

End Plate Not to scale

Figure 3-3: Top view showing the wind tunnel data collection system layout This limited the testable power range of the experiment to a maximum cJ ⇡ 4.5.

Four-bladed COTS propellers were used (APC 5x4E-4), and 40A YEP ESCs were used for motor control. Table 3.1 describes the geometry of the test article. hd

c is the

average jet height at the propeller disk as defined in Section 2.3.

Wing span 23.9 in cflap/c .38

Wing chord 9 in dprop/c .56

Flap chord 3.4 in hd/c .35

Prop. diameter 5 in Sref 215 in2

cflap/dprop .68 hd/cflap .93

Table 3.1: Key geometric parameters of the wind tunnel model

3.1.1 Experimental Procedures

The procedures for taking and reducing the data are summarized here; see Appendix B for a full description. Dimensional force and moment data was calculated from mea-suring load cell voltages, corrected using wind-off tare values and a calibration matrix generated based on known weights. Motor RPM was controlled via commanded PWM signal to the ESC, and measured via a stroboscope. Tunnel speed was calculated from measured dynamic pressure. Motor jet velocity was calculated curves of propeller thrust coefficient vs. advance ratio J = V1

⌦R at the measured RPM. These curves

were determined experimentally, using measured thrust of the same motor-propeller combination. Thrust and jet velocity are assumed to be related by the actuator disk relationship given in Equation 3.1. Angle of attack was measured directly from the

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Variable Symbol Tested Range

Angle of attack ↵ ⇠ 10 to ⇠ 20

Flap deflection flap 0,20,40,55,90

Jet momentum-excess cJ 0 to 4.5

Freestream velocity V1 17.4 kts

Table 3.2: Key wind tunnel test parameters

model using an inclinometer. Due to play in the mounting joints when the shaft collar was tightened there was ⇠ 2.5 of movement possible in the angle of attack. Both the high and low value of angle of attack were measured. The actual angle of attack was taken to be either the high or the low end of the measured range, depending on the sign of the pitching moment (positive pitching moment was associated with higher angle of attack).The tested range of key independent variables is shown in Table 3.2.

T = Adisk⇢VJ(VJ V1) (3.1)

The motor control signal was set manually, based on a reading of the motor current. In practice, this meant that motor RPM varied between each test run, and hence the effective cJ values varied between runs. Since motor RPM was measured directly

this did not introduce a new source of error into the experiment, but it complicated visualization of the data. For clarity, the results of this experiment were fit using a polynomial function described in Appendix B. Functions were fit to c`, cx, amd

cm based on ↵, cJ and f. In the following sections, experimental data is shown as

points. The lines show the results of the polynomial fit for uniformly spaced cJ

values, across the same range of angle of attack and flap deflections. No corrections were performed on the data for blockage or other wind tunnel effects. For a 2D test these effects are small, especially compared to the large c` and cx values being

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3.2 Key Results

The main results of this study are shown in Figure B-9, which displays variations in c`,cxand cmacross varying angles of attack, motor power settings, and flap deflections.

The measured data points are shown as the points in the various subfigures and the lines represent a polynomial fit to the data as described above.

Significant lift enhancement is shown to be possible with a DEP blown wing system, with maximum 2D lift coefficients up to 9 measured. There is a flap deflection which provides maximum lift enhancement; 40 deg in this case, above and below which the system is not as effective. It also shows that, at high angles of attack, there is an apparent increase in cx for constant motor power settings, i.e. an increase in drag.

This is likely due to separation on the upper surface of the airfoil and flap, as well as other losses associated with the jet turning.

The increase of stall angle of attack with increased blowing is also observable, most clearly in the 0 polar. In the unblown case the stall angle appears to be around 10 . As blowing power increases, the stall angle of the wing also increases. This is in agreement with predictions in literature [15]. It is unclear from this data set if the wing is stalled at the highest blowing power, or if continued increase in angle of attack would increase lift further. This effect is also observable in the 20 and 40 data.

There is also an interesting trend observable in the pitching moment data on the bottom row. It can be seen that when the flap is retracted, increasing motor power adds a positive (nose-up) pitching moment, due to the fact that the motors are located below the wing and that the flap is not significantly affecting the motor wake.

At higher flap deflections and angles of attack, this trend is reversed and increas-ing motor power increases the nose-down pitchincreas-ing moment, as it moves the airfoil center of pressure rearward through interactions with the flap. At very high angles of attack, the pitching moment rapidly changes towards a nose-up moment, likely to due separation of the the flow over the flap, which moves the center of pressure forward. This wide range of pitching moments and pitching moment sign reversal near

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stall will present one challenge in the design of a SSTOL vehicle. The horizontal stabilizer must be large enough to trim out a wide range of large pitching moments. Additionally, significant trim changes or elevator inputs will be required near stall due to the moment sign reversal, which may adversely effect the handling qualities of a SSTOL aircraft. It is also expected that high blowing levels will have an effect on the horizontal tail effectiveness; this is an area for further research that is not captured in this study.

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0 5 10 2 0 -2 -4 -6 -20 -10 0 10 20 -0.8 -0.4 0 0.4 o 0 0 0 Δ cJ = 4.5 Δ cJ = 4.5 Δ cJ = 4.5 -10 0 10 20 o 0 0 0 Δ cJ = 4.5 Δ cJ = 4.5 Δ cJ = 4.5 -10 0 10 20 Δ cJ 0 4.5 o 0 0 0 Δ cJ = 4.5 Δc J = 4.5 Δ cJ = 4.5 -10 0 10 20 o 0 0 0 Δ cJ = 4.5 Δ cJ = 4.5 Δ cJ = 4.5 -10 0 10 20 o 0 0 0 Δ cJ = 4.5 Δ cJ = 4.5 Δ cJ = 4.5 Fig ure 3-4: c` ,cx ,cm plo tted ag ainst ang le of atta ck fo r ang le fo r va rio us fla p and mo to r po w er setting s. P oin ts represen t mea sured da ta and the lines represen t the best-fit functio ns, fo r cJ be tw ee n 0 an d 4. 5 in in cr em en ts of .5 .Figur e fr om [6]

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Figure B-13 shows another useful way to visualize this data, as a c` vs cx polar.

This shows that with the flap deflected, there are significant sources of drag associated with the blown wing. At 40 flap deflections, it is possible to generate high lift coefficients at high power settings with positive net drag, if the angle of attack is increased sufficiently. This is an important finding, as it suggests that blown lift is useful for both takeoff and landing, with moderate flap deflections.

-6 -4 -2 0 2 0 5 10 -6 -4 -2 0 2 -6 -4 -2 0 2 Δc J 0 4.5 o o o 0 Δc J = 4.5 0 0 Δc J = 4.5 Δc J = 4.5 -6 -4 -2 0 2 -6 -4 -2 0 2 o o 0 0 Δc J = 4.5 Δc J = 4.5 0 5 10

Figure 3-5: cl-cxpolars, where points represent measured data and the lines represent

the best-fit functions, for cJ between 0 and 4.5 in increments of .5.

3.3 Comparison With Theory

It is interesting to compare this data with the theoretical predictions described in Section 2.2, which describes the idealized performance of a jet flap. This comparison is shown in Figure 3-6, for 0 , 20 , and 40 degree flap deflections. In this case, the solid lines represent the theoretical prediction for the given flap, angle of attack, and

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CJ, while the points are still the measured values. -10 0 10 20 0 5 10 -10 0 10 20 -10 0 10 20 -10 0 10 20 0 5 10 -10 0 10 20 -10 0 10 20

Figure 3-6: A comparison between the measured c`values (points) and those predicted

by an inviscid model based on thin airfoil theory (lines)

It can be seen that the measured lift agrees fairly well with theory for the case where there is no flap deflection, up to the stall angle of attack. At high power, where the stall is suppressed by the blowing, there is good agreement to the limit of the test data.

At higher flap deflection angles, the experiment agrees less well with the predicted results; the theory substantially over-predicts the lift increment due to increased blowing, even at small angles of attack. One possible explanation for this is that, in the derivation of the theory, it is assumed that the jet is thin relative the the flap radius of curvature, and consequently that the jet deflection angle at the flap trailing edge matches the flap deflection angle. In practice, this ideal turning of the relatively thick jet is unlikely, and so the effective jet deflection angle is likely to be reduced. Figure 3-7 shows that if lower effective jet deflection angles are used, the theory again matches the experimental results quite well. The effective jet deflection angles were chosen to provide good agreement with the data, which in both cases is ⇠70% the actual flap deflection.

This result suggests that improved lifting performance may be gained by increasing the effective jet deflection angle to something closer to the theoretical limit. Previous wind tunnel tests of blown wings indicates one way this might be accomplished is to decrease the effective jet height relative to the flap chord [4]. As Table 3.1 shows, in

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-10 0 10 20 0

5 10

-10 0 10 20 -10 0 10 20

Figure 3-7: A comparison between the measured c` values and inviscid theory, with

the initial jet deflection angle reduced to account for inefficient turning of the flow. this experiment they are close to the same size. Changing the geometry and size of the flap slot may also have an effect; further study is required before more definitive conclusions can be drawn.

This result also suggests that, even with the reduced jet deflection effectiveness, further increases in blowing power may give additional increases in lift. Because of the relatively limited amount of power available for these tests, substantially higher cJ values may be achievable with practical engine sizes. The extent to which lift can

be increased by additional power, and any associated limiting phenomena, is another area requiring further research.

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Chapter 4

Performance of STOL Aircraft

Based on the results of the wing tunnel test described in Section 3.2 and using the corrections described in Section 2.4, this chapter explores the predicted performance of notional full-size SSTOL aircraft. Established methods for the preliminary assessment of the takeoff and landing performance of aircraft are applied to a representative set of blown lift vehicles, in order to develop a reasonable preliminary assessment of what a full-scale vehicles might achieve, and to highlight interesting trades and design considerations in SSTOL aircraft.

4.1 Approach

This analysis focuses only on the takeoff and landing segments of the mission, where the greatest effect from blown lift is expected. The actual takeoff and landing per-formance of an aircraft is dependant on many factors beyond just high-lift system performance. These including wing size, available power, and vehicle weight, which is strongly dictated by design mission.

Since the design requirements for a UAM mission (in terms of range, speed, pay-load, and runway size) are currently unclear, rather than sizing a vehicle to an arbi-trary design mission this work will compare the performance of an existing aircraft two similar blown lift vehicles. Since the motivational use case for this study was passenger transport using small aircraft, a modern GA aircraft is used as the basis of

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comparison. The three vehicles analyzed in this study are described below.

SR22 Baseline This vehicle is a conventional propeller-powered GA aircraft with no blown lift system, representative of the Cirrus SR22 G5. The takeoff and landing performance of this vehicle is used to establish a baseline against which the perfor-mance of a blown lift vehicle can be compared, as well as to assess the accuracy of the calculation method used through comparison with published performance figures. SR22 Retrofit The second vehicle is indicative of an SR22 retrofit with a blown lift system, but otherwise unchanged in terms of its power and wing loading. The takeoff weight of the vehicle is also considered constant. In reality, adding such a system to an existing aircraft would add component weight, corresponding to some reduction in useful load of the vehicle. This effect is not quantified here, but would have to be traded against the improved takeoff performance.

Enhanced STOL The third vehicle considered has increased power and wing area to relative to the SR22, as well as a blown lift system. This is a first approximation of a vehicle designed to enhance STOL performance, while staying within the existing bounds of typical wing and power loading. The weight is assumed to be unchanged, so there would be a further reduction in useful load or mission performance to be traded against increased STOL capability.

The key parameters describing the geometry and weight of these three vehicles are shown in Table 4.1. W/S is the wing loading, W/P is the power loading, and T0/W is the static thrust to weight ratio. The effective static thrust increase of the

SR22 Baseline SR22 Retrofit Enhanced STOL

W/S (lbs/ft2) 24.1 24.1 16.0

W/P (lbs/hp) 51.9 51.9 34.6

T0/W .36 .42 .70

AR 9.9 9.9 9.9

MTOW (lbs) 3600 3600 3600

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retrofit vehicle relative to the baseline is due to the increased disk area associated with switching from a single propeller to the distributed propulsion configuration. The power loadings are equivalent, which for this type of aircraft implies similarly sized engines or batteries and motors. The parameters that define the geometry of the blown lift system (hd/c, cflap/c) are assumed to be the same as the wind tunnel

test.

While electric power distribution is an integral part of the blown lift concept examined here, power storage and generation could be via one of several methods, such as batteries, hybrid-electric systems with either a turbine or reciprocating engine, fuel cells, or some other power source. While these choices will have significant implications on the vehicle weight fractions and/or mission performance, for constant vehicle weight the takeoff and landing performance will be affected only by the total amount of power available, and not how it is generated.

Additional performance parameters used in this analysis are shown in Table 4.2. In this case there are slight differences between the parameters used for the SR22 baseline and for the two blown wing variants, most notably in the profile drag calculation CD0. For the baseline vehicle, CD0 represents the profile drag of the entire aircraft. This is estimated for the SR22 by [25] to be 256 counts for the vehicle in the clean configuration, with additional drag increments for the takeoff (20 counts) and landing (50 counts) flap increments.

For the SR22 retrofit and enhanced STOL configurations, the profile drag of the wing and the drag increment from flap deflection will be included in the measured wing tunnel cx. Therefore, CD0 for these vehicles represents only additional non-wing sources of drag. The estimated wing contribution of 122 counts, again from [25], is subtracted from the clean SR22 value to give the value shown in Table 4.2.

CLmax for the baseline vehicle is estimated using the published liftoff speed of 76 kts [26], and assuming the VLO = 1.1Vstall. The coefficients of friction µ are typical

values for the rolling and braking cases from [27]. ⌘p is the efficiency of a typical

propeller operating at low speeds [25]. Section 4.2 describes how these values are used to calculate the takeoff and landing performance, and results are shown in the

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SR22 Baseline SR22 Retrofit & Enhanced STOL fb 0 .85 µroll .03 .03 µbrake .5 .5 CD0,T O .0276 .0134 CD0,LN D .0306 .0134 CLmax 1.5 Varies ⌘p .7 .7

Table 4.2: Key performance parameters for the reference aircraft. subsequent sections.

4.2 Takeoff and Landing Modeling

The method used here for predicting the takeoff and landing performance of a blown lift vehicle follow closely the approach presented in Anderson [27], which is standard for preliminary estimation of vehicle performance.

4.2.1 Takeoff Equations

. Figure 4-1 shows an overview of the notional takeoff procedure of an aircraft, starting from rest and ending with the clearance of a specified obstacle. The total takeoff distance is the sum of the takeoff ground roll, the distance required to accelerate along the runway from rest to the liftoff speed VLO, and the obstacle clearance distance,

which is the distance required in flight to climb above the obstacle. The sum of these two distances is taken to be the total distance. The distance required for rotation is assumed to be included in the ground roll distance. The equation of motion for an aircraft accelerating down a runway, expressed in terms of the net streamwise force X = D T, is given by

W g

dV

dt = X µ(W L) (4.1)

where µ is the coefficient of friction between the wheels and the ground. Instead of time, it is convenient to express the equation in terms of ground roll distance s, which

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h

obs

n

R

obs

θ

obs

s

gr

s

obs

V

LO

V

obs

s

TO

Figure 4-1: Overview of the aircraft takeoff distances can be done by making the convenient substitution dV

dt = ds dt dV ds, yielding Equation 4.2. dV ds = g W V ( X µ(W L)) (4.2)

For a conventional airplane this equation can typically be simplified further. However, in a blown lift vehicle, as speed changes along the ground roll with a fixed engine power, CJ and hence CL and CX vary continuously. Additionally, the ground roll

CL may be quite large. Therefore, both takeoff and landing ground roll will be

calculated via numerical integration of Equation 4.2.

Vehicle weight and dimensional shaft power are assumed to be constant through-out the ground roll. L and X are calculated via a look-up to a corrected polar of wind tunnel data, with the corrections described in Section 2.4. For the blown wing, L = q SrefCL is calculated using CL as given by Equation 2.48.

At the static condition where CX is ill-defined, the flaps are assumed to have a

negligible impact on the total thrust. Therefore, the static thrust is given by the actuator disk relationship

Xstatic = 2(Pshaft⌘)2⇢

hd

c Sreffb

1/3

(4.3) where ⌘ is a figure of merit assumed to be 70%, and fb is the fraction of the wing

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Over the course of the ground roll, X is interpolated linearly between the static thrust condition and the value at the liftoff speed XLO. XLO = qLOSref(CXw + CD0), where CXw is the wing CX given in Equation 2.47 calculated at the liftoff flight con-dition, and CD0 represents the additional drag of the vehicle. This avoids numerical issues at low airspeeds. It is approximately equivalent to an assumption of linear thrust variation with airspeed, which is common [27]. The liftoff speed is defined using the standard definition 1.1Vstall. No correction is made for the difference in

Reynolds number between the full-scale vehicle and the wind tunnel data. There is currently insufficient test data to determine the effects of changing Reynolds number, and standard correction methods for changing skin friction coefficient are not neatly applicable to the blown wing case.

The obstacle clearance distance is calculated assuming the vehicle follows a curved flight path with radius

Robs =

V2 1

g(n 1) (4.4)

where n is the average load factor on the vehicle, as shown in Figure 4-1. Following the method described in [27], a load factor of 1.19 is assumed, representing flight at 90% of CLmax. The speed during rotation is 1.15Vstall, which approximates acceleration between VLO and the obstacle clearance speed Vobs = 1.2Vstall. The obstacle clearance

angle ✓obs and distance sobs follow from the geometry.

✓obs = cos 1 1

hobs

Robs (4.5)

sobs = Robssin ✓obs (4.6)

4.2.2 Landing Equations

Figure 4-2 shows the landing procedure used for calculation. It is assumed that there is no flare distance for the vehicle, and the vehicle touches down onto the runway at approach speed Vapp = 1.3Vstall. Previous flight tests of powered-lift STOL aircraft [5]

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h

obs

s

gr

s

obs

V

app

s

LND

V

app

Figure 4-2: Overview of the aircraft landing distances procedure for a DEP SSTOL aircraft is an area requiring future research.

The obstacle clearance distance is given by the flight path angle at approach speed. = sin 1 CX CL (4.7) sobs = hobs tan (4.8)

is assumed to be small, so CL is given by the level flight constraint

CL =

2W ⇢V2

appSref (4.9)

The angle of attack and power setting required to achieve the target CL are

de-termined from the corrected polars shown in the Section 4.3. To achieve the best approach performance, it is assumed to the maximum angle of attack is maintained (up to the limits of the wind tunnel test range), and that the minimum amount of power required is added to achieve the required CL. If no power is required, angle

of attack is adjusted as in a conventional aircraft. CX is then determined from the

polar at the same angle of attack and power setting.

4.3 3D Polars

The vehicle CL-CX polars are based on the measured wind tunnel data shown in

Section 3.2 corrected using the method laid out in Section 2.4. The results of these corrections are shown in Figure 4-3 for the range of flap deflections tested in the wind

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tunnel.

The application of the corrections to the higher flap deflections (55 and 90 ), where large separated flow regions likely exist, may not be valid. The basis of the correction is that a significant amount of the lift being developed is due to circulation at the wing and in the wake; that assumption may not be valid. The following section will analyze the range of flap deflections from 0 to 40 , which are seen to give the best high-lift performance.

-4 -2 0 2 0 2 4 6 8 10 F=90 -4 -2 0 2 0 2 4 6 8 10 F=55 -4 -2 0 2 0 2 4 6 8 10 F=40 -4 -2 0 2 0 2 4 6 8 10 F=20 -4 -2 0 2 0 2 4 6 8 10 F=0 C J = 0 CJ = 1 CJ = 2 CJ = 3 CJ = 4

Figure 4-3: Wind tunnel data corrected for 3D effects, assuming blowing across 85% of the wing

As expected, the primary effect of the finite wing correction is a large increase in drag compared to the wind tunnel results, due to induced drag from the wing downwash. The changes in the lift coefficient, on the other hand, are relatively minor. These polars will form the basis of the takeoff and landing distance calculations

Figure

Figure 1-1: Categorization of emerging electric aircraft architectures, based on method of lift generation and use of distributed electric propulsion
Figure 2-3: a) Representative geometry from wind tunnel tests exploring blown wing performance
Figure 3-3: Top view showing the wind tunnel data collection system layout This limited the testable power range of the experiment to a maximum c J ⇡ 4.5
Figure B-13 shows another useful way to visualize this data, as a c ` vs c x polar.
+7

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