1. Principles of Regenerative Electric-powered Flight
J. Philip Barnes April 2014 Update
In his 1926 landmark text, “Aerofoil and Airscrew Theory,” the great British aerodynamicist Hermann Glauert suggested we “consider the case of a windmill on an aeroplane.” Although Glauert offered no specific application thereof, he knew the airborne wind turbine would one day find important applications.
In 1998, American engineer Paul MacCready introduced “with caution” regenerative electric-powered flight, where an aircraft would incorporate energy storage, a propeller, and a wind turbine, or dual-role machine thereof, to propel the aircraft and regenerate stored energy in updrafts.
In this multi-disciplinary study, we shall evaluate component and system performance with the intent of showing that regenerative electric flight is both feasible and useful. Although to some our charts may often appear technical, while to others they may often appear rudimentary, in either case it's ok to fall asleep during the presentation. But remember at least this:
We can fly our electric-powered aircraft for an hour or so and largely deplete the battery ~ good enough. But if our aircraft incorporates the regeneration feature, and if we take advantage of that, our flight can be longer, farther, and safer. And, depending on special geography and weather conditions along the way, we can regenerate before and during descent, landing with a significant state of charge remaining.
Regenerative Electric-powered Flight J. Philip Barnes Apr

2. Presentation Contents
Nature’s “Regen” ~ the Great Frigate Bird
Regen aircraft elements & operating modes
“Windprop” aero design and performance
DC motor-generator, controller, and battery
“Regenosoar” vehicle & system performance
Summary & Recommendations

3. Nature’s Regen Aircraft ~ the Great Frigate Bird
Flight sustained by atmospheric vertical motion
Energy rate sensor ~ air temp, air pressure...?
Permeable plumage ~ no water landing or takeoff
Feed by surface plucking ~ Pterodactyl heritage?
Thermal day and night up to 2800 m
Lowest wing loading of any bird
Self-contained takeoff
Emergency thrust
Sortie radius to 1800 km
Sortie duration up to 4 days
30-year lifespan
The Great Frigate Bird is our role model for a "regen" aircraft. Prevalent in tropical areas such as Baja California and the Galapagos Islands, the Frigate Bird has many capabilities which our regen shall attempt to emulate. These include self-contained takeoff, emergency thrust on demand, and flight sustained often or overall by vertical motion of the atmosphere. We must also follow the example of the Frigate Bird by incorporating an "energy rate sensor" so that we can recognize and capitalize on lift while minimizing exposure to sink. Perhaps the Frigate Bird senses the slight differences in air temperature which mark rising or sinking air. Perhaps it can sense changes in barometric pressure. But whatever its energy-rate-sensing method, the Frigate Bird soars day and night on thermals* at altitudes up to 2.8 km, largely on shoulder-locked wings, traveling great distances in a given sortie which may last several days. Thus, like the Wandering Albatross, the Frigate Bird soars for long periods over water as far as the eye can see. But of the two, only the Frigate Bird can never land on the water, due to its permeable plumage. Thus the Frigate Bird feeds mostly by following waterborne predators and plucking scraps from the surface.
* H. Weimerskirch, et.al., Frigate Birds Ride High on Thermals, Nature, Jan 2003
M. Allen, Autonomous Soaring for Improved Endurance of a Small Uninhabited Air Vehicle, AiAA
Data:
Henri Weimerskirch,
et.al. Nature Jan 2003
Photography:
Phil Barnes
Regenerative Electric-powered Flight J. Philip Barnes Apr

4. Regen Aircraft Elements and Operation
Windprop
Fixed rotation direction
Sign change with mode
Thrust, Torque
Power, Current
Speed
Control
Motor
Gen
Optional solar panel
Energy Storage:
Battery
Ultra capacitor
Flywheel motor-generator
ESU
The powertrain of a regenerative electric aircraft begins with an energy-storage unit, connected with electrical cables to a speed control which bi-directionally conditions the motor-generator power. The system always rotates in the same direction, but when the power mode changes from propeller to turbine, the thrust, torque, power, and current change sign.
For the system operating in cruise or in high-efficiency regeneration, if we assume 84% efficiency for the powertrain (excluding the windprop) and 82% “isolated” windprop efficiency, we obtain 69% “system efficiency.” System efficiency is lower during climb or max-capacity regeneration.
We show above an optional solar panel package to support solar-augmented regenerative-electric flight. This option also may prevent loss of charge on the ground. However, solar power is not included in the performance analysis herein.
Self-contained takeoff
Emergency cruise/climb
Exploit vertical air motion
Regenerative Electric-powered Flight J. Philip Barnes Apr

5. Thermal Updraft Contours
Elevation, zo ~ m
1oC warmer-air column
20-minute lifetime
~ solar power x 10
U ~ m/s 1 2 3
Total Energy
= Kinetic
+ Potential 4
The representative thermal shown above, including contours of local updraft velocity (u,m/s), has a diameter of 200-m at its base and 1-km diameter at its top where the elevation is perhaps 4-km. A thermal is aptly named, since its air temperature is typically 1oC higher than that of the surrounding air.
The peak-updraft core of 5-m/s resides at an elevation of 1000-m. In the core, a regen aircraft with a still-air sink rate of 1 m/s, including the effects of regeneration, would be carried aloft at 4 m/s. At the top of the thermal, updraft velocity falls to zero.
We will study the performance of the regen operating in the thermal. However, “regen time” is also well spent in ridge lift, wave lift, or final descent. But in the thermal, the optimal trajectory yields the maximum total specific energy (zt), representing the total kinetic, potential, and stored energy per unit weight, whereby (zt) has the units of height in meters.
Total Energy
= Kinetic
+ Potential
+ Stored
Regenerative Electric-powered Flight J. Philip Barnes Apr

6. Dual-role Propeller and Airborne Wind Turbine

7. Propeller Wake, Pitch, and Blade Angles
Horseshoe
Vortices r R
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
Each blade of the windprop sheds a helical wake of vortices. The wake from one blade is shown above. As with a wing, the wake induces a “downwash” normal to the wake leading edge (taken near 25% chord, as in the sketch above). Also as with a wing, we can calculate the wake-induced velocities and aerodynamic loading with a vector integration using the horseshoe vortices arranged along each blade. This method, documented in our SAE technical paper “Math Modeling of Propeller Geometry and Aerodynamics,” was used to compute the fixed-geometry windprop performance described next.
More blades at fixed thrust & diameter:
More wakes (one per blade)
Higher pitch ~ wakes farther aft / rotation
Lower rotational speed, lower tip Mach
Upshot: ~ similar efficiency, 2 to 8 blades
Blade angle (b ) at radius (r)
is measured from rotation
plane to the chord line at (r)
Regenerative Electric-powered Flight J. Philip Barnes Apr

8. Windprop Blade Angle and Operational Mode
Specify symmetrical sections & uniform pitch
Turbine
Efficient turbine: Rotate ~ 87% of “pinwheel RPM,” or fly at 115% of “pinwheel airspeed” v
w r L b w v
w r b w v
w r -L b w
Propeller
Efficient prop: Rotate ~115% of “pinwheel RPM,” or fly at 87% of “pinwheel airspeed”
Pinwheel
Pinwheeling: Zero angle of attack, root-to-tip
- No thrust, no torque, small drag
The "windprop" blade section shown above has its chord line at the angle (b) from the plane of rotation. The blade-relative wind (w) is the vector combination of the airspeed (v) and rotational velocity (w r). For the diagram representing pinwheeling, the blade section has zero angle of attack(a) since the relative wind vector (w) is aligned with the chord. With the specified uniform pitch, this condition applies from root to tip.
If we now increase the rotational speed while holding constant airspeed, the blade will develop lift, thrust, and torque as a propeller. Conversely, reducing rotational speed, the blade will develop negative values thereof, thus acting as a turbine. Alternatively, we can imagine holding fixed rotational speed as flight velocity varies.
We are thus led to define a new term, the “speed ratio” (s), which applies to both propeller and turbine operation, and which also highlights the pinwheeling regime separating the two power-exchange modes. We define (s) as the ratio of flight velocity to the “pinwheeling” flight velocity where, for the stated pitch and rotational speed, windprop thrust in propeller mode falls to zero. Any subsequent increase of airspeed (s>1) yields turbine operation. A speed ratio of zero (s=0) represents ground static propeller-mode operation, where thrust and torque coefficients must include the effects of stalled blades. Although the speed ratio (s) enjoys some similarity to the more familiar “advance ratio” (J), only (s) describes at once the relationship of the three conditions represented by propeller, pinwheel, and turbine operation.
Note that the relative wind vector (w) is shorter for the turbine mode. Local forces vary with (w2), while shaft power varies roughly with the cube of rotational speed (w). Thus, turbine operation is significantly “power limited” in relation to propeller operation.
Define: “Speed ratio,” s  v / vpinwheel = v / [ wr tanb ]
Regenerative Electric-powered Flight J. Philip Barnes Apr

9. Windprop Efficiency and Thrust
Low-RPM Blades, b
tip
= 30 o
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 h
Turbine
t w / (f v)
Blades_btip
2_14o
8_30o c
l_min
l_max
Propeller
f v / (t w)
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
Force Coefficient, F ≡ f/(qpR2)
B=2 2
B=8 8 F
Propeller ~ climb
High-RPM 2 Blades, b
tip
= 14 o
Here we plot windprop efficiency versus the “speed ratio” (s) for two fixed-geometry, uniform-pitch windprop designs with the same diameter, climb thrust, and symmetrical sections. The high-RPM option has two blades with 14-deg blade tip angle, and the low-RPM design has eight blades with 30-deg blade tip angle. In either case, propeller efficiency has the traditional definition with shaft power in the denominator, whereas turbine efficiency follows Glauert’s definition for an airborne turbine, with shaft power in the numerator. Since for turbine operation both torque and force change sign, turbine efficiency remains positive. Note that airborne turbine efficiency is not subject to the “Betz Limit” (59%) of a ground-based wind turbine having a different definition of efficiency.
As noted earlier, the speed ratio (s) is defined as the ratio of flight velocity to “pinwheel flight velocity,” where thrust and torque fall to zero with the windprop operating as a propeller at a stated rotational speed. Windprop efficiency is zero in the pinwheel regime (s1). At speed ratios above unity, the windprop operates as a turbine. For both propeller and turbine operation, the curves terminate at the first appearance, anywhere along the blade, of blade section maximum lift coefficient (cl_max).
Finally, we plot force coefficient (F), versus speed ratio (s). The force (f) is non-dimensionalized as a group (F) including windprop disk area and flight dynamic pressure (q). This characterization, with the formula in the blue box, allows us to relate the installed thrust-to-drag ratio (T/D), aircraft drag coefficient (cD), wing area (s), windprop radius (R), number of windprops (Nwp), and still-air climb rate (dz/dt). Regardless of operational mode, installed thrust (T) includes the normalized change in drag (DD/D) due to windprop system addition.
Propeller ~ cruise
r / R
0.00
0.25
0.50
0.75
1.00
Blade Geometry
0.05
0.10
0.15
0.20
0.30
Thickness
Chord, c/
Sym. Sections r
tan b =
tip
hub
Max efficiency
Regeneration
Max capacity
Regeneration
Pinwheel
F= B=2
F= B=8
Regenerative Electric-powered Flight J. Philip Barnes Apr

10. How Flow the Electrons Motor-generator principles Synergy: motor-gen & windprop DC Voltage conversion

11. Motor-generator Principles
Electromotive force, e
= potential energy / charge
= work / charge, (Fp / q) L
= 2 N w (D/2) B L
e = NDBL w ≡ k w
(+) 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 L
tw=ei
Both
modes
Torque, t
= 2N (D/2) B (dx/dt) dq
= 2N (D/2) B (dq/dt) dx
t = NDBiL = NDBL i = k i e t w E
N turns
Generating i vi vq Fp Fq B
Let's now characterize the performance of electrical machines with fixed magnetic-field strength (B). We show a "classical" brushed machine which, if fitted with several armature loops at different clock angles, will largely exhibit the performance of the one loop shown at the moment of peak torque development. The moving charge has two velocity components, one for machine rotation and the other for current parallel to the machine axis. These velocities crossing the magnetic field give rise to forces on the charge, one along the path and the other normal to the path. Along the current path, work on the charge increases its potential energy, giving rise to "electromotive force, or EMF" designated (e) with units of Voltage (representing energy per charge, N-m per Coulomb). For the classical machine shown, (e) is proportional to (B), as well as to the number (N) of armature-loop turns, armature length (L), diameter (D), and rotational speed (w). Furthermore, we find that the torque (t) is proportional to current (i), with the proportionality constant given by (k = e/w = t/i). Both torque and current change sign with generator operation, but (e) retains the same sign.
For motor operation, the EMF (e) is less than the terminal voltage (E). For generator operation (e>E). If we imagine the terminal connected to a battery of EMF (eb), we can define an "EMF ratio," equivalent to a "speed ratio," which we shall designate (k), defined by k  e/eb = kw/eb. Unity speed ratio (k=1) then marks the boundary between motor and generator operation.
Change to generator mode:
Same direction, rotation, w
Same sign for EMF, e
Sign change of torque, t
Sign change of current, i
Regenerative Electric-powered Flight J. Philip Barnes Apr

12. System Motoring and Regeneration Efficiencies
Pulse-width modulation (PWM)
d ≡ “Duty cycle” ; h ≈ 0.99 d 0.25
(Refs 1,2) Rb eb Vb Rm
Torque loss
brushes,
iron loss,
windage... em
t+Dt w Vm
Inverter
(for brushless MG)
h ≈ (Ref.3)
Quote regen power here i
Motor
Regen
The electrical circuit above begins with the battery of EMF (eb), internal resistance (Rb), and terminal voltage (VB). Also shown are the electronic speed control, typically implementing pulse-width-modulation (PWM), and an optional inverter if a brushless machine is used. Completing the circuit are the motor-generator electrical "machine" (subscript m) with internal resistance (Rm) and torque loss increment (Dt<0). When PWM is progressively "throttled down," the controller continues to sustain switching losses, but motor-generator power vanishes, whereby controller efficiency approaches zero, approximately and empirically according to the one-fourth power of its duty cycle (d) representing the fraction of "on" time. Although a brushless machine can rotate much faster and operate at perhaps 10 times the voltage of a brushed machine, it must be electronically commutated by the controller. In addition, whereas the high speed of a brushless machine is perhaps most efficient with a high-speed, 2-blade windprop, a brushed DC machine would be compatible with a much slower-turning (and quieter) 8-blade windprop. If the multi-blade windprop is preferred either way, additional losses with inversion and a speed reduction mechanism may be incurred if a brushless DC machine is selected. But copper weight is of course higher with brushed DC.
Putting aside for now the issues of motor and controller selection, let us apply a "first-principle" model of the system to more readily grasp the fundamentals of system efficiency for each mode. Ignoring all losses, we obtain the system efficiencies shown above for motoring and regeneration modes. First, motoring system efficiency is found linearly proportional to rotational speed (w), reaching unity when the motor-gen EMF matches the battery EMF (i.e., em = kw = eb), but where current falls to zero. Second, regen system efficiency is found inversely proportional to rotational speed, with unity efficiency when the generator EMF matches battery voltage, but again with no current. Clearly, useful operation of the battery and motor-generator requires rotational speed "away from" the theoretical-unity-efficiency condition, and this is reflected in the next slide which compares our first principle model to test data.
"Ideal system efficiency" ignoring controller & torque losses
system motor ≈ t w/(eb i) ≈ e i / (eb i) = e / eb = k w / eb
system regen ≈ eb i / (tw) ≈ eb i / (ei) = eb / e = eb / (k w)
Refs: (1) AiAA , Lundstrom, p.8 ; (2) NASA CP 2282, Echolds, p.89 ; (3) Technical Soaring, Vol. xxi, No. 2, Rehmet, p. 39
Regenerative Electric-powered Flight J. Philip Barnes Apr

13. Motor-generator & Battery ~ Performance Envelope and Data
100% Duty Cycle
eb /(kw)
CURRENT GROUP, i Rt / eb
THEORETICAL EFFICIENCY, kw/eb
TORQUE GROUP, t Rt / (k eb)
MOTORING
EEMCO 427D100
24V / 15,000 RPM
k = N-m/A
Rt = Ohm
REGENERATION
LMC "generator curve"
48V / 3,600 RPM
k = 0.16 N-m/A
Rt = Ohm
LMCLTD.net i
The chart above applies and illustrates the "first principle" model, first by showing the upper limits of system motoring and regen efficiencies (dashed blue curves), together with component efficiency test data (solid red curves), and second by characterizing the torque and current as dimensionless groups (see solid straight lines). Two DC machines, with some similarities but also with many differences, were used for the above plot (data for a given machine, both motoring and generating, is scarce). However, a wide range of DC machines (with permanent magnets or otherwise fixed magnetic field strength) will exhibit similar trends.
At a speed ratio below unity, we have motoring operation. Above unity speed ratio we have regeneration. Near unity speed ratio, the first-principle model fails because there, for a real machine, the torque loss remains as motoring torque or generated current vanish. Thus for a real machine, the efficiency follows the trends of the test data shown. For the most efficient machines, efficiency peaks will push (red arrows) more deeply into the "corners" of the theoretical limits. But with PWM and brushless DC, the system efficiency peaks will move away from the corners at low throttle. At any rate, for both motoring and regeneration at 100% duty cycle, the test data approaches asymptotically the trends predicted by the first-principle model.
Notice the extraordinary synergy of the motor-generator efficiency shown above, when compared to the windprop efficiency shown on slide 9 herein. Both machines (motor-generator and windprop) exhibit a "neutral point" (at unity speed ratio) and both exhibit optimal efficiencies (around 80%) at rotational speeds 10-15% above or below the neutral point, depending on the desired operating mode. t
Phil Barnes Apr
Regenerative Electric-powered Flight J. Philip Barnes Apr

14. “Low-tech” Regen DC Electric Propulsion With Battery Shuffler1 5
Positive
terminal
of battery
number: D C B A E 2 3 4 4 5 3 2 1
Negative
terminal
of battery
number: E D C B F
BATTERY
SHUFFLE
SWITCH
Phil Barnes 07 Apr 2011 F E D C B A
Battery Series “Totem Pole” Voltage Node
Takeoff / climb
Motor
Gen
Cruise
Voltage
Node
~Pinwheel
Best regen
Max regen
Rotate 80o
Clockwise,
then counter
clockwise
Battery effective
shuffled position
Electrical Ground
The "low-tech" approach shown above is intended more to explain the problem of regeneration than to offer a solution thereof. The fundamental problem is to ensure that the generator EMF exceeds battery voltage, and by a controllable extent, during regeneration. When the windprop is regenerating, its rotational speed, and generated EMF, will be relatively low. With the "low-tech" solution above, the motor-generator would connect to one of several voltage nodes in a battery "totem-pole" series, depending on operating regime. For example, takeoff and climb would use voltage node (A), whereas max regen might use node (E). Node (E) might also be used for ground windmilling where windprop rotational speed is quite low. In flight, nodes in the middle (B, C, D) would accommodate efficient motoring or regeneration.
An additional feature of our notional "low-tech" architecture is a unique "battery shuffler" which ensures that each battery of a series spends equal time at each "totem pole" position (without changing the physical position of the battery in the aircraft). The envisioned rotary switch for the battery shuffler would be periodically rotated manually or automatically, back and forth to share the workload on each battery in the circuit. This arrangement has the advantage that regenerative electrical power enters only the active batteries, thus reducing the battery resistance loss during regeneration.
The system above is perhaps impractical. Thus, we next turn to a "high-tech" solution, enabled by an extraordinary device - the "DC boost converter."
Periodic (about once per minute) battery shuffle via rotary switch
ensures equal time for all batteries at each “totem pole” position
Applicable: Brushed or Brushless, but no pulse-width modulation
Regeneration enjoys reduced active battery resistance
Regenerative Electric-powered Flight J. Philip Barnes Apr

15. * Wikipedia, “DC boost converter”
DC boost converter enables efficient motoring & regen C L VB
M-G
iGBT
PWM
DCBC: Key enabler, efficient bi-directional power management
Only the motoring mode is shown in the introductory graphic above
“Boosts” DC voltage ~ % with minor input/output ripple
Enables low-voltage battery to drive high-voltage LED lamp*
Enables reduced battery totem pole length, i.e. Toyota Prius*
DC voltage “boost” is controlled by PWM “duty cycle”
Power in ~ Power out: DC output current is thus reduced
Options: brushed-DC/low voltage or brushless/high voltage
Adjusts effective battery voltage to efficiently drive the M-G
Boosts motor-gen effective EMF for efficient battery recharge
* Wikipedia, “DC boost converter”
Regenerative Electric-powered Flight J. Philip Barnes Apr 2014

16. DC boost converter – Equivalent circuitsVB
Mot-gen
iGBT
PWM VM
C dVM/dt
L diB /dt iB VB iM VM
iGBT on
L diB /dt
C dVM/dt VB iB iM VM
iGBT off
To model the performance of the DC boost converter, we implement the equivalent circuits shown above, one for the insulated-gate-bipolar transistor (iGBT) switch on, and the other for the switch off. Such switching happens at very high frequency with a "duty cycle" seen at the bottom. For either equivalent circuit (switch condition), the inductor is replaced by its counter EMF voltage which is proportional to both the inductance (L) and rate of change (di/dt) of inductor input current which, for the circuit above, equates to battery current (iB). When the iGBT switch is turned off, the rate of change of current is negative, whereby the inductor counter-EMF voltage in effect supplements the battery voltage (VB). Whether the switch is on or off, the capacitor buffers changes to circuit-output conditions.
Also for both equivalent circuits, the capacitor is replaced by a current source, with such current proportional to both the capacitance (C) and rate of change (dV/dt) of capacitor voltage drop which, in the circuit above, equates to motor-generator "electrical machine" input voltage (VM).
With switching at high frequency, circuit phenomena for each sector of the switching period will be essentially linear with time. We next compute voltage and current gain and "ripple" for the above circuits.
dt |--t--|
d ≡ duty cycle ; t ≡ period
iGBT gate PWM
Regenerative Electric-powered Flight J. Philip Barnes Apr 2014

17. DC boost converter – Voltage gain & conversion efficiency
C DVM1/(dt)
L DiB1 /(dt) iB VB iM VM
Time segment 1: iGBT on for Dt = dt
L DiB2 /[(1-d)t]
C DVM2 /[(1-d)t] VB iB iM VM
Segment 2: iGBT off for Dt = (1-d)t
[a] Voltage loop: VB - L DiB1 /(dt) = 0
[b] VB - L DiB2 /[(1-d)t] = VM
[c] Output current: iM - C DVM1 /(dt) = 0
[d] iB - C DVM2 /[(1-d)t] = iM
[e] PWM cycle: DiB1 + DiB2 = 0
[f] DVM1 + DVM2 = 0
[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
As noted in the chart above, any changes in current or voltage with the switch on must be matched by equal and opposite changes for the period with the switch off. Such changes represent input and output ripple which will be quite small in relation to the basic DC current and voltage. Neglecting circuit resistances, we obtain the well-documented result that the voltage gain is set by the duty cycle per the formula shown. But perhaps not well documented in the literature is our companion result that the current gain is similarly set by the duty cycle with an inverse relationship, such that the theoretical efficiency of the DCBC is unity. Thus, if output voltage is doubled, output current is halved. Such "gains" are readily adjusted by changing the pulse-width-modulation (PWM) duty cycle, and these gains are largely unaffected by the chosen PWM frequency, provided such frequency is "high" for the chosen inductance and capacitance.
We may have expected the duty cycle to affect the efficiency, but in fact the circuit (neglecting resistance) is fundamentally characterized by an inductor and capacitor cyclically storing and releasing energy. Whereas a low-power DCBC circuit may exhibit efficiencies around 85%, the Toyota Prius system, perhaps in the power regime of our regen aircraft, delivers the very high DCBC efficiencies shown on the next chart where, with a "selection switch," we implement a single DCBC for our regen application operating in either the motoring or regeneration mode.
Voltage & current gains set by duty cycle (d) alone [high-frequency assumed]
Efficiency is unity (resistance neglected) and is thus unaffected by L, C, d, t
“Deltas” (D) represent ripple applied to input current (iB) & outputs (iM, VM)
Regenerative Electric-powered Flight J. Philip Barnes Apr 2014

18. DC boost converter - efficiency and regen application
"Evaluation of 2004 Toyota Prius,"
Oakridge National Lab, U.S. Dept. of Energy
233 Vdc in kW
Regen
Motor VB L C
M-G
iGBT
PWM
90o rotary mode selector switch for motoring or regeneration
Low-voltage option: Batteries in parallel, brushed-DC motor-gen
Hi-voltage option: Batteries in series, inverter & brushless DCMG
Regenerative Electric-powered Flight J. Philip Barnes Apr 2014

19. "RegenoSoar" Air Vehicle and System Performance

20. RegenoSoar Design Rationale
Configuration Rationale
Maximum laminar airflow aero & counter-rotation props
Pusher avoids windprop helix downstream aero upset
One-person handling/steering (remote or in the cockpit)
Winglets include tip wheels (wings flex up under load)
Our rationale for the design of “RegenoSoar” begins with our intent to minimize in-flight aerodynamic interference between the windprops and other aerodynamic surfaces, while also providing self-contained and robust ground handling by the pilot alone. Thus, the counter-rotating windprops, which allow steering on the ground, are kept aerodynamically clear of the wing and empennage via twin pod installations.
The windprops are arranged in a pusher configuration, whereby the sudden rotational flow imparted by the blades (the upstream flow has no rotation) cannot impinge on the leading edges of downstream lifting surfaces which otherwise would suffer interference and induced drag penalties. If necessary, pod-boom trailing-edge blowing may mitigate any adverse affects of the pod-boom wake on windprop operation.
Windprop noise is dramatically reduced via low rotational speed afforded by multiple blades operating at high pitch. The windprop has the smallest diameter meeting requirements for climb thrust and cruise/regen efficiency. The speed control and motor-generator units, housed and air-cooled in the pods, are relatively close to the fuselage-enclosed energy storage unit, mitigating line losses and effects on c.g. position.
The system enjoys the simplicity of fixed geometry for the windprops and their installation. Retraction or folding mechanisms are not required, and as illustrated later herein, the windprops simply “pinwheel,” with minimal drag penalty, when neither the propeller nor turbine mode is used. A study of a “constant-speed” windprop (actuated blades) yielded 40% greater max-capacity regen power, but did not offer gains in efficiency for either operational mode. Uniform fixed pitch was therefore retained for our study herein.
Finally, the wing design incorporates downward-pointing winglets with integrated tip wheels, the latter required regardless of wingtip configuration. The winglets, which develop aerodynamic thrust in flight, are somewhat elevated above the ground via wingtip dihedral. Such clearance is enhanced as the wing flexes upward under steady lift load. Above a threshold ground-roll speed during takeoff and landing, the empennage and tail wheels will lift off from the ground.
Regenerative Electric-powered Flight J. Philip Barnes Apr

21. RegenoSoar ~ In Flight Applications and Operations
Fleet broadcast energy rate
High-altitude earthwatch
Jet-stream rider
Storm rider
The 3D geometry of “RegenoSoar,” rendered above with NASA's free software "Vehicle Sketch Pad," is fully characterized with equations. The fuselage, wings, empennage, and windprop blades are modeled as “distorted cylinders.” Canopy-body, wing-body, and windprop blade-spinner intersections are iteratively determined. We show here a wireframe model consisting of a fuselage “prime meridian and equator,” together with section cuts of the fuselage, wing, empennage, and windprop blades, as well as “perimeters” for the wing, empennage, and blades.
An earlier paper by the author introduces methods of mathematically characterizing streamlined shapes. Such characterization reduces drag, promotes sharing of consistent geometry for inter-disciplinary analysis, and takes advantage of today’s precision manufacturing technologies. Interested readers may consult the paper “Math Modeling of Airfoil Geometry,” available at SAE.org. An analysis of winglet aerodynamic thrust can be found in the author’s paper , “Semi-empirical Vortex Step Method for the Lift and Induced Drag of 2D and 3D Wings.”
Regenerative Electric-powered Flight J. Philip Barnes Apr

22. Section and Vehicle Drag Polars
"Clean configuration" ~ Windprop System Removed
1.50
Lift Coefficient, c
or c
Min
Sink
here L l
cLmax
1.25
Section
1.00
Windprop
System
Removed
0.75
Max L/D here
0.50
Above we plot the drag polars of both the wing airfoil and total vehicle. Our “thrust-drag accounting” for the regen defines drag to represent the “clean” configuration (windprop system removed), but holding total system weight. All windprop forces, including drag increments associated with windprop system addition, are treated as thrust, with installation penalty modeled as a non-dimensional drag increment (DD/D). We assume cruising at max-L/D airspeed and also assume thermaling, with or without regeneration, at min-sink airspeed.
cDo
0.25
Drag Coefficient, c
or c D d
0.00
0.00
0.01
0.02
0.03
0.04
0.05
Regenerative Electric-powered Flight J. Philip Barnes Apr

23. Load Factor (nn) ~ “g-load” and Turn Radiusv
L= nn w w g f
nn  L / w = cosg / cosf
Glide: nn  1
Turn: nn  1 / cosf
Load Factor and Bank Angle
Load Factor, nn
1.0
1.1
1.2
1.3
1.4
1.5
1.6
Bank Angle, f o 10 20 30 40 50 ) n /
(cos
cos g = - 1
Load Factor and Turn Radius
Airspeed, v_km/h 20 40 60 80
100
120
140
Turn Radius, m 50
150
200
250
300
350
400 n
1.1
1.4
1.2
1.05
Thermaling
1.6 )
tan g /(
cos v r f = 2
In a wings-level glide, the load factor (again, nn is defined as lift/weight) is essentially unity (actually “cos g”). With turning, the load factor will be greater than unity, and it has a unique bank angle, for example 40-deg at nn=1.3 (or “1.3-g”). Together with airspeed, the load factor determines the turn radius (r), for example 250-m at 100 km/h and 1.05-g. All of these results apply to any aircraft with flight conditions with cosg near unity (most subsonic aircraft).
The red line at lower right indicates the locus of minimum-sink, an essential performance characteristic for any sailplane or regen. Let’s next determine how to show where that line resides.
Regenerative Electric-powered Flight J. Philip Barnes Apr

24. Load Factor and “Clean” Sink Rate
cL = nn w / (qs)
“Clean” REGEN
Windprop removed
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 level
25 kg / m 2
A = 16
1.4
1.6
Min Sink
Max L/D
To relate the normal load factor (nn) to sink rate and airspeed, we first recognize that the lift coefficient (cL) includes the load factor as shown in the formula at the upper right. The drag polar then provides the drag coefficient, and the ratio of drag-to-lift (D/L) is then equal to the ratio of drag-to-lift coefficients (cD/cL).
Now we can calculate the still-air clean sink rate, [nn(D/L)v], the latter including the load factor. For example, the aircraft in max L/D glide (1.0-g) sinks at 0.75 m/s at 85 km/h airspeed. However, the aircraft turning at 1.4-g sinks at 1.25-m/s at 100 km/r airspeed. The left-hand tip of each curve represents operation at max lift coefficient, and the maximum of each curve represents minimum-sink operation.
Finally, we note that the graph above shows the “clean sink rate.” When the windprop system is added, operating in the turbine mode, the regen aircraft will fall more quickly. We will calculate the still-air sink rate with regeneration later herein.
Regenerative Electric-powered Flight J. Philip Barnes Apr

25. Vehicle Performance ~ New Formulation, New Insight
Derive steady-climb Equation
L= nn w v
T-D g f g w
Note: nn= cosg /cosf
cL = nn w / (qs)
Regen T/D
climb:  6.3
cruise: = 1.0
solar-augmented glide:  0.5
pinwheel glide:  -0.1
efficient regen (thermal):  -0.4
capacity regen (descent):  -1.0
Frigate Bird
T/D=0 (no thrust)
sink rate (-dz/dt) = nn(D/L)v
Frigate Bird and Regen
sink increases with g-load (nn)
sink increases with airspeed (v)
To evaluate regen performance, we must know the climb rate (or sink rate) of the maneuvering aircraft, taken relative to the local airmass. In particular, we are interested in the effects of g-load, or normal load factor (nn), lift-to-drag ratio (L/D), and thrust-to-drag ratio (T/D). Our diagram and analysis together describe the effects of the forces acting on the aircraft climbing at a flight path angle (g) and banked at the angle (f). The lift vector (L), normal to the airspeed vector (v), has the value (nnw), where (w) designates weight. Note that flight path angle (g), taken relative to the local airmass, will be negative if the aircraft is sinking in relation to the surrounding airmass.
After “normalizing” the various forces in terms of dimensionless ratios, we find that the steady-state climb rate (dz/dt), whether in still air or as seen by a balloon-based observer rising with the thermal, is given by the product of an “aerodynamic group” [nn(D/L)v] and a “propulsive group” [(T/D)-1]. Indeed, the aerodynamic group is the sink rate in still air with the propulsion system “aerodynamically removed.” For a sailplane or frigate bird (T/D=0), still-air climb rate is of course negative.
For either the sailplane or “clean” regen, sink or climb performance is degraded as load factor (nn) is increased, with (L/D) evaluated at the lift coefficient under load. Thus, turning “twice increases” the drag penalty, and this calls for high aspect ratio (learning from the albatross and frigate bird!) to mitigate this effect.
For the regen, climb rate depends on the “clean sink rate” for the chosen airspeed, and the propulsive group. The latter will be positive for climb, zero for cruise (dz/dt=0), and negative during regen. As expected, the regen sinks faster when the windprop operates as a turbine. In the glide between thermals, the windprop pinwheels with a small drag penalty (T/D<0).
Regenerative Electric-powered Flight J. Philip Barnes Apr

26. Regenerative Flight Equation
“Total Climb”
Rate of change of
total specific energy
Updraft
“Total Sink”
Still-air “clean” sink rate
Effect of
windprop
“Exchange Ratio,” as applicable:
turbine system efficiency ~71%
1 / propeller system efficiency
0 for pinwheeling (no exchange)
A key product of our study is a fundamental “Regenerative Flight Equation” (RFE) relating the total climb rate to the updraft and total sink rate. Interested readers can consult the SAE technical paper “Flight Without Fuel,” for its derivation. Whereas the updraft provides the specific power into the system, "total sink" represents the specific power lost to aerodynamic drag and windprop operation.
The RFE is generally applicable to either a soaring frigate bird (where T/D=0) or a regen in any operating mode. The “exchange ratio” (e), determined by operating mode and not applicable to a glider, is set to zero if the regen is pinwheeling, whereby the system “exchanges” no shaft power, and whereby the term (T/D, about -0.10) represents pinwheeling thrust (negative) as a fraction of aircraft drag. Otherwise, the exchange ratio is set to turbine system efficiency or the inverse of propeller system efficiency, whichever is applicable. Recall that thrust is negative in the turbine mode.
Regenerative Electric-powered Flight J. Philip Barnes Apr

27. Climb and Regeneration in the Thermal (minimum-sink airspeed)
Elevation, m
Elevation, m
Climb rate Contours
Energy rate Contours
Optimum
Elevation, m
Equilibrium Regeneration
The left-hand contour plots above represent ground-observed climb rate, versus load factor and elevation, for the regen in the thermal operating with either max-efficiency (upper) or max-capacity (lower plot) regeneration. The aircraft can thermal over a wide range of normal load factors, with associated bank angles and turn radii (also as described earlier), but a specific "load-factor-altitude trajectory" yields the fastest climb, should rapid climb with regeneration be of interest. For both left-hand plots, the white contour represents equilibrium regeneration, whereby the regen falls through the air at the same rate as the air rises. Such equilibrium can be sustained either "very low" or "very high" in the thermal. In the region between the upper and lower limits of equilibrium regeneration, the aircraft climbs in the thermal, even with maximum regeneration. One scenario for rapid-regen climb might be to make the most of a thermal which will soon vanish.
Perhaps a more likely objective would be maximum total energy gain in the thermal. This is shown in the right-hand contour plots, again for maximum-efficiency regen or maximum-capacity regen. The optimum energy trajectories is indicated by the dashed curve, showing tight turns (~ 1.45-g) near the base of the thermal and wide turns (~ 1.15-g) near the top. Whatever trajectory is chosen for energy gain (right-hand plots) will have a corresponding trajectory for ground-relative climb rate (left-hand plots). Working "left-to-right," we notice that equilibrium regeneration (per the white contours) does not yield attractive rates of change of total energy. Thus the best strategy for regeneration when thermaling is to climb in the thermal. Nevertheless, equilibrium regeneration proves useful in wave or ridge lift.
Regenerative Electric-powered Flight J. Philip Barnes Apr

28. Regenerative Flight Equation Applied for RegenoSoar
0.82
0.87
0.88
Finally, we apply the Regenerative Flight Equation (and related formulas) to compute the performance of the regen at key flight conditions. The table shows the various rates (dz_/dt) with applicable sign conventions. Table entries at lower left show how the propeller climb mode exercises the system capacity.
Notice that thrust/drag ratio (T/D) is 6.33 in climb, but for max-capacity regen as the aircraft turns at 1.3-g with the windprop spinning at only 324 RPM. For this example, the max-capacity regen condition can be interpreted as having the drag doubled by windprop operation.
After takeoff, the aircraft climbs in still air at (dz/dt = 4.00 m/s) as total specific energy (kinetic, potential, & stored) decreases (dzt/dt = m/s). Once the regen is well into the thermal and regenerating, say at max capacity, a balloon-based observer rising with the updraft at 3.72 m/s sees the aircraft falling (dz/dt = m/s). At the same time, a ground-based observer sees the aircraft climbing (dzo/dt = 1.66 m/s).
Although we include max-capacity regen here for study, only max-efficiency regen has competitive flight performance. In particular, while battery energy storage rate (last row) is highest with max-capacity regeneration, the total energy rate (dzt/dt) increases most rapidly with max-efficiency regen. Nevertheless, max-capacity regeneration proves useful in many scenarios, including strong wave lift, slope lift, and final descent. Indeed, if the last encountered updraft is near the airport, landing with significant reserve could become routine. An optional solar panel, and/or ground windmilling (with a safety perimeter) on windy days, could overcome the loss of charge between flights.
Regenerative Electric-powered Flight J. Philip Barnes Apr

29. Summary and Recommendations Regenerative Electric-powered Flight

30. Regenerative Electric-powered Flight
The Great Frigate Bird ~ nature’s “regen”
Self-contained takeoff & emergency thrust on demand
Energy extracted from vertical atmospheric motion
Energy rate sensor, flight sustained day-and-night
“Energy Synergy” of the Windprop & Motor-Gen
Optimum “speed ratios” about 87% & 115% by mode
Windprop: 8 blades spin slow, quiet, & efficient
Pinwheeling ~ imposes only minor performance penalty
DC boost converter - efficient bi-directional power
Climb/sink rates, any mode, g-load, orientation
Climb in the thermal, even with maximum regen
Regen in ridge and wave lift to extend flight
Regenerative Flight Equation ~ total energy rate
We’re good to go ~ Let’s emulate the Frigate Bird
The chart above summarizes the new ideas, methods, and formulas which we developed to support our multi-disciplinary study of regenerative electric-powered flight. We hope to have shown that adding the regeneration feature to an electric-powered aircraft is feasible and attractive, making our flight longer, farther, safer, and greener. Therefore, let’s do our best to emulate the regen optimized over the last fifty million years ~ the Frigate Bird.
Regenerative Electric-powered Flight J. Philip Barnes Apr

31. About the Author
Phil Barnes has a Master’s Degree in Aerospace Engineering from Cal Poly Pomona and a Bachelor’s Degree in Mechanical Engineering from the University of Arizona. He has 30-years of experience in the performance analysis and computer modeling of aerospace vehicles and subsystems at Northrop Grumman. Phil has authored technical papers on aerodynamics, gears, and flight mechanics. Drawing from his SAE technical paper of similar title, this presentation brings together Phil’s knowledge of aerodynamics, flight mechanics, geometry math modeling, and computer graphics with a passion for all types of soaring flight.
Regenerative Electric-powered Flight J. Philip Barnes Apr