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Regenerative Electric-powered Flight J. Philip Barnes 1
Regenerative Electric FlightSynergy and Integration of Dual-role Machines
J. Philip Barnes 27 Dec 2014
Animated slides: F5 keyAlso: View ~ "Notes Page"
2Regenerative Electric-powered Flight J. Philip Barnes
Great theoreticians and experimentalists (all Ph.D.)
Ludwig Prandtl - Germany
Hermann Glauert - U.K.Royal Aeronautical Society
Albert Betz - Germany
Paul MacCready - USA
3
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
4
Exploit opportunities tostore Vs. expend energy
Energy Storage Unit:• Battery and/or:• Ultra capacitor• Flywheel w/M-G
Regen Aircraft Elements and Operation
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
PowerElectronics
Motor-Gen (M-G)
Windprop• Fixed rotation direction• Sign change with mode
• Thrust, Torque• Power, Current
5
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
6
Blade angle (b ) at radius (r)is measured from rotationplane to the chord line at (r)
Propeller Wake, Pitch, and Blade Angles
Effect of more blades (fixed T, R):• Steep blade angle, much lower RPM• Lower tip Mach, much-reduced noise • High torque → dual & counter rotation• Numerically integrate wake for loading
• Wake induces downwash (normal to local section) • Pitch:
helix length per rotation htip = 2 p R tan btip
• Uniform pitch: r tan b = R tan btip
• Blade tip angle (btip): 14o ~ low pitch 30o ~ high pitch
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
HorseshoeVortices
r
R
8Regenerative Electric-powered Flight J. Philip Barnes
Test data validating Glauert's rationale on induced velocity
Gradual buildup
F.E. Weick, Aircraft Propeller Design, McGraw-Hill, p. 102-103
Immediate swirl, as predicted by Glauert
J. Philip Barnes www.HowFliesTheAlbatross.com
• Propeller or wind turbine• Angle of attack = 0 • No change to flow direction• No change to relative wind• Helical drag wake (unloaded)• wr tanb = Vo (all sections)
• or, r tanb = const.= R tanbtip
Blade section Looking outboard,Blade at 3 o’clock
Cho
rd li
ne
b
Rotor blade velocity diagram - "Pinwheeling" condition
Pinwheeling sets up "Betz Condition"• Propeller or turbine at no load Perturb w or Vo to load rotor• Helical wake (drag and/or vortex)• Sets blade angle distribution b(r):
b = tan-1 [ Vo / (wr) ]• Says nothing about blade planform
Axial wind
Vo
Vo
Rotationalwind, w r
Rel
ativ
ew
ind
W1
b
Vo
W2
Hel
ical
wak
e
w r
J. Philip Barnes www.HowFliesTheAlbatross.com
• Non-rotational (axial) inflow• Axial velocity locally conserved • Final swirl imparted suddenly• Helical wake anchored at c/4• Wake ~ aligned with chordline• Wake-induced velocity (Vi)
• Glauert: 2Viq at "rotor out"• Absolute velocity (V) increased• Relative wind (W) decreased• Immediate static pressure rise
Propeller blade - comprehensive velocity diagram
Glauert: consistent physics & geometryVortex wake ~ aligned with chord lineBetz cond. (wake helix), prop or turbine,with or without rotor loading, provided:r tan b = const. and z=0 (sym. sections)
Relativewind W1
a
Wq w w r - Viq
f
V1
z Ze
ro-li
ft lin
e
Rotational wind
Axial wind
V1 w Vo+Vix
Hel
ical
wak
evo
rtex
shee
t
W2
V1
w r - 2Viq
V2
Blade section Looking outboardBlade at 3 o’clock
Chord line
b
Viq
Vix
Vi
11
Windprop Blade Angle and Operational Mode
v
wr
b
w
Pinwheel
• Pinwheeling: Zero angle of attack, root-to-tip- No thrust, no torque, small drag
v
wr
L b
w
Propeller
• Efficient prop: Rotate ~115% of “pinwheel RPM,” or fly at 87% of “pinwheel airspeed”
v w
r -L
b
w
Turbine
• Efficient turbine: Rotate ~ 87% of “pinwheel RPM,” or fly at 115% of “pinwheel airspeed”
Define: “Speed ratio,” s w v / vpinwheel = v / [ wR tanbtip ]
• Symmetrical sections and r tan b = R tanbtip
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
12
Speed Ratio, s ≡ v / ( w R tan btip) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Force Coefficient, F ≡ f/(qpR2)
B=2
2
B=8
8
F
Low-RPM 8 Blades, btip = 30o
High-RPM 2 Blades, btip = 14o
Speed Ratio, s ≡ v / ( w R tan btip) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Efficiency
0.0
0.2
0.4
0.6
0.8
1.0
h Turbine t w / (f v)
Blades_btip
2_14o
8_30o
c l_minc l_max
Propellerf v / ( t w)
Pinwheel
F= -0.011 @ B=2
F= -0.008 @ B=8
Propeller ~ climb
Max efficiencyRegeneration Max capacity
Regeneration
Propeller ~ cruise
Windprop Efficiency and Thrust
r / R 0.00 0.25 0.50 0.75 1.00
Blade Geometry
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Thickness
Chord, c/ R
Sym. Sectionsr tan b = R tan b tip
hub
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
• Comparable efficiency by mode• Eight blades quieter than two• Climb power ~ 7x cruise power
sc
NF
DT
DD
sc
NF
vLDn
z
D
T
D
wp
D
wp
n
22
/
/1
)/(1
RR
13
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
14
e
t
w
E
N turns
Generating
i
vi vq
Fp
Fq
B
iChange to generator mode:Same direction, rotation, wSame sign for EMF, e Sign change of torque, t Sign change of current, i
Electromotive force, e= potential energy / charge= work / charge, (Fp / q) L= 2 N w (D/2) B L e = NDBL w ≡ k w
Torque, t = 2N (D/2) B (dx/dt) dq = 2N (D/2) B (dq/dt) dxt = NDBiL = NDBL i = k i
(+) Charge (q) with velocity, V in magnetic field of strength, B:Force vector, F = q V x B
e
t
w
E
N turns
Motoring
B
i
vi vq
Fp
Fq
B
i
L
Motor-generator Principles
= t w e iBoth
modes
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
k = "EMF constant"
15
System Motoring and Regeneration Efficiencies
"Ideal system efficiency" ignoring controller and all losseshsystem motor ≈ t w/(eb i) ≈ em i / (eb i) = em / eb = k w /
eb hsystem regen ≈ eb i / (tw) ≈ eb i / (emi) = eb / em = eb / (k
w)
Torque
em=kwt
w
Rt
eb
System total resistance
(*) AiAA 2010-483, Lundstrom, p.8
i MotorRegen
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
Typical controller pulse-widthmodulation (PWM) of duty cycle( ) d and efficiency h ≈ d 0.25 (*)
16
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Speed Ratio, kw/eb = EMF Ratio, emg/eb
Non-dimensional Characterization of Permanent-magnet DC Motor-generator-battery System Performance ~ Theory and Test Data
eb
Rtem
Motor-generator & Battery ~ Performance Envelope and Data
REGENERATIONLMC "generator curve"48V / 3,600 RPMk = 0.16 N-m/ARt = 0.041 OhmLMCLTD.net
MOTORINGEEMCO 427D10024V / 15,000 RPMk = 0.015 N-m/ARt = 0.075 Ohm
CURRENT GROUP, i Rt / e
b
TORQUE GROUP, t Rt / (k e
b )
Phil
Barn
es A
pr-0
8-20
11
i
t
100% Duty Cycle
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
THEO. EFFICIENCY, kw/e b e
b /(kw)
Trends match theory
Windprop synergy
17
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
Regenerative Electric-powered Flight J. Philip Barnes 18
Brushless "DC" Motor-generator ~ "Y" configuration
Brushed Vs. BrushlessVirtues, features, & limits
Brushed:Theory foundation =tw ei ; =e kw ; =t ki
2-wire interfaceSimplified controlBrush maintenance~120V limit (arcing)Low-speed cogging
N
SBrushless:Inverter required3-wire interface>1000V capableMinimal coggingSame as brushed:
=tw ei ; =e kw ; =t ki
19
Equivalent DC machine
Brushless motor-gen. & inverter: Equivalent DC machine
Brushless machine with inverter/rectifier as a system follows brushed DC machine principles: tw = emi ; em = kw ; t = k iBoth systems have 2-wire interface with the power circuit
M-Geb
i
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
= t w em imotor or gen
Inverter-Rectifier
t
w
21
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
Regenerative Electric-powered Flight J. Philip Barnes 22
0
20
40
60
80
100
120
8 10 12 14 16 18
Collector current,
Amps
Base Voltage
Linearized transfer characteristic
Gate voltage, VGE
Transistor and flyback diode
Collector
Emitter
GateFlybackDiode
ICVCE
VGE
iGBTMOSFET
104
0
20
40
60
80
100
120
0.1 1 10 100 1000
Collector current, IC ~Amps
Collector-to-emitter Voltage drop, VCE
iGBT conduction characteristic"iGBT Basics," IXYS Corporation, IXAN0063
17
15
13
11
09
Gate voltage, VGE
• "High-tech, high-power light switch"• Inverter commutation & DCBC boost adjust• Lo-freq. (20-100 Hz) for commutation• Hi-freq. (>10 kHz) pulse-width-mod (PWM)• VGE (say 12 V) sets the collector current IC
• Collector voltage VCE (say 600 V) sets power• Flyback diode for switch energy dissipation• iGBT & diode unidirectional (via arrows)• Transistor ~ 2V loss ; Diode ~ 0.7V loss
Gate voltage (VGE) "opens the valve"
Regenerative Electric-powered Flight J. Philip Barnes 23
Inverter-rectifier ("inverter" for motoring mode)
• Each phase, per cycle: - Connect to battery voltage 120o
- Connect to ground 120o
- "Float" twice for 60o each float• Inverter converts 2-wire DC to 3-wire "AC"• Commutation toggles each phase 0-to-VB
• Switch pairs: one "upper" & one "lower“• Switch applies +15/-7V for iGBT on/off• Avoid short circuit: Always "diagonalize"
VB
VB
12
3
1
2
3-7V 15V S
N
Regenerative Electric-powered Flight J. Philip Barnes 24
DC-to-AC conversion ~ "inverter" commutation waveforms
AC basis
Inverter
"Dead time" avoids short
circuit
Regenerative Electric-powered Flight J. Philip Barnes 25
Inverter-rectifier ("inverter" for motoring mode) ~ Snapshots
VB
VB1
23
1
2
3
VB
VB1
23
1
2
3
VB
VB1
23
1
2
3
VB
VB1
23
1
2
3
"Upper" switch pairs diagonally with a lower switchTwo phases are operating; one phase is "floating"
Regenerative Electric-powered Flight J. Philip Barnes 26
Inverter-rectifier ("rectifier" for generating mode) - iGBT
EB
12
3
• Rectifier converts 3-wire AC to 2-wire DC• Battery is recharged via flyback diodes• Diodes enable only two phases at once• Commutation "ignored" (unidirect. iGBT)
SnapshotE1 - E3 > EB
1
2
3
Current to battery!
Diodes provide"free" regen!
Regenerative Electric-powered Flight J. Philip Barnes 27
Inverter-rectifier ("rectifier" for generating mode) - MOSFET
EB
12
3
• Rectifier converts 3-wire AC to 2-wire DC• Charge battery via MOSFETs & flyback diodes• Bi-directional: Comm. MOSFET assists diode
1
2
3
E1 - E3 > EB
Current to battery
Regenerative Electric-powered Flight J. Philip Barnes 28
Pulse-width modulation: Energy loss due to "chopping"
• At a given voltage, cruise current ≈ 15% of climb or accel current• Superimposed on commutation: PWM "chopping" at cruise• Typical switching frequency (f) for chopping ≈ 20 kHz (inaudible)• Reduce the duty cycle (d) to reduce average current (iav = d ion)• Energy is lost (iGBT & diode) with each on/off switching cycle• Per-iGBT switching energy loss (Sp) ≈ 20 mJ per switching cycle • Reduce chop losses: use PWM only on “upper” phase of 6-pack• Cruise chopping loss = f Sp = 0.4 kW = 20% @ 2 kW/phase
Remove PWM from commutation; Incorporate DC boost converter
• Commutation voltage cycle
• Comm. + PWM superimposed
ion
iav| |
dt| t |
29
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
Regenerative Electric-powered Flight J. Philip Barnes 30
• DCBC: Key enabler, efficient bi-directional power management– Only the motoring mode is shown in the introductory graphic above
• “Boosts” DC voltage ~ 0-500 % with minor input/output ripple• Power conservation: doubling the voltage halves the current • Enables reduced battery totem pole length, i.e. Toyota Prius* • DC voltage gain or “boost” is controlled by PWM “duty cycle”• PWM used for DCBC gate current, not motor-gen main current
DC boost converter enables efficient motoring & regen
Boost battery voltage to efficiently drive the M-G as a motorBoost motor-generator EMF to efficiently recharge the battery
M-Gbrushed
or brushless
with inv.
CL
VM
VB PWM
+15/-7ViGBT
Regenerative Electric-powered Flight J. Philip Barnes 31
|-- --|dt t
d ≡ duty cycle ; t ≡ periodiGBT gate PWM
DC boost converter – Equivalent circuits
L diB /dt
C dVM/dtVB
iB
iM
VM
iGBT off
C dVM/dt
L diB /dt
iB
VB
iM
VM
iGBT on
M-Gbrushed
or brushless
with inv.
CL
VM
VB
PWMiGBT
Regenerative Electric-powered Flight J. Philip Barnes 32
DC boost converter – Voltage gain & conversion efficiency
L DiB2 /[(1-d)t]
C DVM2 /[(1-d)t]VB
iB
iM
VM
Segment 2: iGBT off for Dt = (1-d)t
C DVM1/(dt)L DiB1 /(dt)
iB
VB
iM
VM
Time segment 1: iGBT on for Dt = dt
[a] Voltage loop: VB - L DiB1 /(dt) = 0[c] Output current: iM - C DVM1 /(dt) = 0
[b] VB - L DiB2 /[(1-d)t] = VM
[d] iB - C DVM2 /[(1-d)t] = iM
[e] PWM cycle: DiB1 + DiB2 = 0 [f] DVM1 + DVM2 = 0
• Voltage gain is set by duty cycle (d) • Efficiency = 1 (resistance neglected)
[g] Combine [a,b,e]: VM/VB = 1/(1-d) [h] via [c,d,f]: iM/iB = 1-d
Combine [g,h]: h ≡ iMVM /(iBVB) = 1
dt |-- --|t
d ≡ duty cycle ; t ≡ periodiGBT gate PWM
Regenerative Electric-powered Flight J. Philip Barnes 33
DC boost converter - efficiency and regen application
"Evaluation of 2004 Toyota Prius,"Oakridge National Lab, U.S. Dept. of Energy
233 Vdc in
5 10 15 20 kW
Regen
M-G
Motor
PWMiGBT
CL VB
• DC boost converter integrates windprop and motor-generator• Adjust PWM duty cycle to hold voltage gain as RPM decreases• Efficient bi-directional power over a wide operating range
Climb Regen
Cruise
Regenerative Electric-powered Flight J. Philip Barnes 34
Circuit models, motor-generator efficiency, and current
ib /Gb
tw
Gb
Rh kw
eb
Rh
ib
a
Motoring
Gm ib
tw
Gm
Rh kw
eb
Rh
ib
a
Regenib = [eb Gb
2- Gb kw] / [Rh (1+Gb2)] motoring
ib = [kwGm - eb] / [Rh (1+Gm2)] regeneration
G ≡ DCBC voltage gain
Regenerative Electric-powered Flight J. Philip Barnes 35
0 10 20 30 40 50 60 70 80 90 1000
100
200
300
400
500
600
Voltage Map - Motoring and Regen with DC boost converter
Voltage
%RPM
Motor-gen EMF
M-G, gain 2.0
M-G
, gain
3.0
Battery, no boost
Batt, voltage gain 2.0
Batt, voltage gain 3.0
• Boost the battery for motoring• Boost the M-G to regenerate
Climb220 AmpsBatt: 540VM-G: 285V
Capacity Regen-8 Amps Optimal Regen
-11 Amps
Cruise35 Amps
36
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
37
Architectures compared
"Chopper" architecturePWM main current chopCruise: high chopping lossRegen: none or inefficient
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
M-Geb
i
t w
PWM superimposed on commutation
Inverter-Rectifier
"Boost" architecturePWM sets DCBC boostEfficient motor & regen
M-Geb
i
DC BoostConverter
2-way boost t w
PWM
12V
Inverter-Rectifier
Commutation
38
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
Regenerative Electric-powered Flight J. Philip Barnes 39
Regenosoar - Features and Design Rationale
Counter rotorsSymmetric flowZero net torque
8-blade rotorsLow RPM, quiet, Low vibrationLow tip Mach
Ground handlingNo assistance req'dWinglet tip wheels
Pusher Config.Symmetry upstreamMax. laminar flow
Compact power trainBattery, motor-genand powertrain
Pod-air-cooled MG & PE
Regen parked in the windWith safety perimeter
40
Drag Coefficient, cD or cd
0.00 0.01 0.02 0.03 0.04 0.05
Lift Coefficient, c L or cl
0.00
0.25
0.50
0.75
1.00
1.25
1.50
Section and Vehicle Drag Polars
Max L/D
Min. Sink
"Clean configuration" ~ Windprop System Removed
Section
WindpropSystemRemoved
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
"Clean" aircr
aft
41
Load Factor and Turn Radius
Airspeed, v_km/h0 20 40 60 80 100 120 140
Turn Radius, m
0
50
100
150
200
250
300
350
400
nn
1.1
1.4
1.2
1.05
Thermaling1.6
r = v2 (cosg) / (g tanf)
Load Factor and Bank Angle
Load Factor, nn
1.0 1.1 1.2 1.3 1.4 1.5 1.6
Bank Anglefo
0
10
20
30
40
50
= f cos-1 [(cos )g /nn)]
Steady-state load factor (nn) ~ “g-load” and turn radius
nn w L / w = cos g / cos *f
Glide: nn w 1
Turn: nn w 1 / cosf
v L= nn w
w
g f
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
* SAE 2004-01-3088 EQN 5.2, dg/dt = 0
42
Airspeed, v ~ km/h
50 60 70 80 90 100 110 120 130 140 150
dz/dt ~m/s
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
g-Load, nn
1.0
1.2
Sea level25 kg / m 2
A = 16
1.4
1.6
Min SinkMax L/D
Load Factor and “Clean” Sink Rate
“Clean” REGENWindprop removed
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
cL = nn w / (qs)
43
Steady-state climb or descent ~ New Formulation, New Insight
L= nn w
T-Df
w
g
Glider, soaring bird, or "clean" regen• T/D=0 (no thrust)• Sink rate (-dz/dt) = nn(D/L)v
With or without propulsion system• Sink increases with g-load (nn)• D/L also increases with (nn)• Sink increases with airspeed (v)
Regen operating mode T/D• climb w 6.3 • cruise = 1.0 • pinwheel glide w -0.1• efficient regen (thermal) w -0.4 • capacity regen (descent) w -1.0
v
g
1][(T/D)v(D/L)ndz/dt
Therefore,
γvsindz/dtrate,climb)3
(T/D)(D/w)/w)2
D/Ln(L/W)(D/L)/W)1
vsinγ(D/W)]v[(T/W)
/Wndefinev/W;bymultiply
state}{steadysinγT
n
n
n
T
D
L
WD
Derive steady-climb Equation
Note: nn= cos g /cos *f cL = nn w / (qs)
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
* SAE 2004-01-3088 EQN 5.2, dg/dt = 0
“Total Sink”
e ≡ “Exchange Ratio,” as applicable:• turbine system efficiency ~71% • 1 / propeller system efficiency• 0 for pinwheeling (no exchange)
“TotalClimb”
WindpropEffect
“Clean” sink rateUpdraft
D
TV
L
Dnuz nt 11
Regen must have • Updraft - or final descent• High L/D, Low sink• High sys. efficiency
Regenerative Electric Flight Equation and Implications
45
0
0
0
0
1
0
0
0
000
2
00
0
0
0
3
4
Radius from Centerline, m0 100 200 300 400 5000100200300400500
Elevation, zo ~ m
0
500
1000
1500
2000
2500
3000
3500
4000
u, m/s
Thermal Updraft Contours
Total Energy = Kinetic + Potential
Total Energy = Kinetic + Potential + Stored
• 1oC warmer-air column• 20-minute lifetime• ~ solar power x 10
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
U ~ m/s
Elevation, zo ~ m
12
34
46
Ground-relative Climb Rate, m/sMax-capacity Regeneration in the Thermal
Normal Load Factor, Nn
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Elevation, m
0
500
1000
1500
2000
2500
3000
0.0
1.0
1.51.6
0.5
Ground-relative Climb Rate, m/sMax-efficiency Regeneration in the Thermal
Normal Load Factor, Nn1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Elevation, m
0
500
1000
1500
2000
2500
3000
3500
2.2
0.0
1.01.5
2.0
0.5
Total Specific Energy-gain Rate, m/sMax-efficiency Regeneration in the Thermal
Normal Load Factor, Nn
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Elevation, m
0
500
1000
1500
2000
2500
3000
3500
2.5
0.0
1.01.5
0.5
2.0
Climb and Regeneration in the Thermal (minimum-sink airspeed)
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
Climb rate Contours Energy rate Contours
Equilibrium Regeneration
Optimum
Total Specific Energy-gain Rate, m/sMax-capacity Regeneration in the Thermal
Normal Load Factor, Nn
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80
500
1000
1500
2000
2500
3000
0.0
1.01.5
2.0
0.5
2.1
Elevation, m Elevation, m
Elevation, m
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Item / mode ---> Climb max L/D Cruise max L/DPinwheel max L/D
Regen max efficiency, minimum sink,
zo=1480-m
Regen max capacity, minimum sink,
zo=1480-m
Airspeed, v ~ km/hr 85.0 85.0 85.0 77.2 77.2
Updraft, u ~ m/s 0.00 0.00 0.00 3.72 3.72
Turn radius, r ~ m n/a n/a n/a 56.5 56.5
Load factor, n ~ g 1.00 1.00 1.00 1.30 1.30
Lift coefficient, cL 0.64 0.64 0.64 1.12 1.12
Drag coefficient, cD (clean) 0.022 0.022 0.022 0.040 0.040
Installed thrust/drag ratio, T/D 6.33 1.00 -0.10 -0.40 -1.01
Installation penalty, D/D= -T/D 0.17 0.09 0.10 -0.03 -0.03
Clean sink rate, still air, n (D/L)v ~ m/s 0.75 0.75 0.75 1.03 1.03
Climb rate in still-air, dz/dt ~ m/s 4.00 0.00 -0.83 -1.43 -2.06
Total energy rate, dz t /dt ~ m/s -5.40 -1.05 -0.83 2.58 2.18
Ground-observed climb, dz o /dt ~ m/s 4.00 0.00 -0.83 2.29 1.66
Windprop speed ratio, s 0.57 0.85 1.00 1.15 1.75
Windprop speed ~ RPM 1096 735 625 494 324
Windprop Force group, F 0.92 0.14 -0.0070 -0.10 -0.26
Windprop efficiency, ht or hp 0.63 0.84 n/a 0.85 0.64
Powertrain efficiency (non-windprop) 0.80 0.85 n/a 0.85 0.8
System efficiency hst or hsp 0.50 0.71 n/a 0.72 0.51
Exch. ratio, 1/hsp : hst : 0 applic.) 1.98 1.40 0.0 0.72 0.51
Total Shaft power, tw ~ kW 29.5 3.50 0.00 -1.36 -2.58
Energy storage rate ~ kW -36.9 -4.12 0.00 1.16 2.07
0.82
0.88
Regenerative Electric Flight Equation Applied for RegenoSoar
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
48
Presentation Contents
• Regen. elec. flight: Origin & Introduction
• Dual-role machines:– Propeller and wind turbine– DC motor-generator– Brushless motor-generator
• Integration: – Inverter-rectifier– DC boost converter– "Chop" Vs. "Boost" architecture
• “Regenosoar” aircraft concept
• Summary & Look Ahead
49
Regenerative Electric-powered Flight• Windprop: 8 blades spin slow, quiet, & efficient
• DC & BLDC machines: EMF proportional to RPM
• M-G & battery verify theoretical efficiency trends
• Synergy of windprop & MG: Efficiency Vs. RPM - Optimum “speed ratios” ~ 85% & 115% by mode
• Popular "chopper" control: inefficient at cruise
• DC boost converter: efficient climb, cruise, regen
• Regen applications:– Thermal, ridge, wave, final descent, ....– UAV fleet, storm rider, earth observer, ....
• Give up 2% prop efficiency w/symmetric sections to gain perhaps 5-15% range and/or flying time
Regenerative Electric-powered Flight J. Philip Barnes www.HowFliesTheAlbatross.com
M-GiGBT
VM
A "regen" is coming soon to an airport near you!