Dang, Thong (5110 Waterford Wood Way, Fayetteville NY, 13066, US)
Kummer, Joseph (105 Churchill Lane, Fayetteville, New York, 13066, US)
Dang, Thong (5110 Waterford Wood Way, Fayetteville NY, 13066, US)
CROSS-FLOW FAN PROPULSION SYSTEM
 This application claims priority to U.S. Provisional Patent Application Ser. No.
60/673,541, filed March 21, 2005, U.S. Provisional Patent Application Ser. No. 60/673,624, filed March 21, 2005 and U.S. Provisional Patent Application Ser. No. 60/673,552, filed March 21, 2005.
Background of the Invention
1. Field of the Invention
 The present invention relates to aircraft propulsion systems and, more specifically, a cross-flow fan propulsion system.
2. Description of the Prior Art
 The cross-flow fan (CFF), developed in 1893 by Mortier, is used extensively in the HVAC industry. The fan is usually long in relation to the diameter, so the flow approximately remains 2-dimensional (2D). The CFF uses an impeller with forward curved blades, placed in a housing consisting of a rear wall and vortex wall. Unlike radial machines, the main flow moves transversely across the impeller, passing the blading twice. Figure 1 shows a typical heating, ventilation, and air conditioning (HVAC) configuration. For an aircraft installation, the propulsor must ingest and expel the flow in a linear manner to produce forward thrust. The conventional HVAC -type CFF housing, characterized by approximately a 90 degree turn from inlet to outlet, is not well suited for this application
 Inherent in all designs is a vortex region near the fan discharge, called an eccentric vortex, and a paddling region directly opposite. These regions are dissipative, and as a result, only a portion of the impeller imparts useable work on the flow. The cross-flow fan, or
transverse Mi1'; u 1S"i:iOTs"a ^stagrpiarttai admission machine. The popularity of the cross-flow fan comes from its ability to handle flow distortion and provide high pressure coefficient. Effectively a rectangular fan, the diameter readily scales to fit the available space, and the length is adjustable to meet flow rate requirements for the particular application. Since the flow both enters and exits the impeller radially, the cross-flow fan is well suited for aircraft applications. Due to the 2D nature of the flow, the fan readily integrates into a wing for use in both thrust production and boundary layer control.
 In addition to increased propulsive efficiency, embedded propulsion provides reduced noise and increased safety, since the propulsor is now buried within the structure of the aircraft (e.g. no exposed propellers). Also, based on the methods in Ref. 4, by eliminating the engine pylon/nacelle support structure, the aircraft parasite drag can be reduced by up to 18 to 20%, thus improving cruise efficiency and range.
 Attempts to provide a cross-flow fan in aircraft wings haven been unsuccessful.
For example, some designs uses cross-flow fans embedded within the middle of a conventional airplane wing. Other designs distribute fully embedded cross-flow fans near the trailing edge of a conventional transport aircraft, with shafts and couplings connecting them to wing-tip and root-mounted gas turbines. Air is ducted into the fan from both wing surfaces, and expelled out at the trailing edge. These designs, however, limits the fan size and ducting. Also, the CFF may not be a viable option for high-speed applications due to compressibility effects (i.e. choking). These configurations fall short of expectations due to poor fan placement and poor housing design. These deficiencies result in low fan performance, reduced circulation control, and low thrust production.
Summary of the Invention
 It is therefore a principal object and advantage of the present invention to provide a distributed cross-flow fan wing design that provides high propulsive efficiency.
«[00081 "" 1 H-IIs 11 I further W| etf'ahd advantage of the present invention to provide a distributed cross-flow fan wing design that provides low parasite drag.  It is an additional object and advantage of the present invention to provide a distributed cross-flow fan wing design that provides reduced flow separation at high angle of attack.
 In accordance with the foregoing objects and advantages, in one application, the present invention provides a cross-flow propulsion mechanism for use in providing propulsion to an aircraft, that includes a housing defining an inlet, a rotor compartment, and an outlet, with the inlet adapted to receive an inflow of air along a first longitudinal axis; a rotor mounted within the rotor compartment and adapted to receive the airflow introduced into said housing through the inlet and rotate about a second longitudinal axis that is substantially perpendicular to the first longitudinal axis; and an outlet adapted to receive the airflow processed through the rotor and exhaust air along a third longitudinal axis that is substantially parallel to the first longitudinal axis.
In a second application of the invention, it provides an aircraft including an aircraft body shaped in the form of an airfoil having leading and trailing edges; and a cross-flow propulsion mechanism for use in providing propulsion to an aircraft, that includes a housing defining an inlet, a rotor compartment, and an outlet, with the inlet adapted to receive an inflow of air along a first longitudinal axis; a rotor mounted within the rotor compartment and adapted to receive the airflow introduced into said housing through the inlet and rotate about a second longitudinal axis that is substantially perpendicular to the first longitudinal axis; and an outlet adapted to receive the airflow processed through the rotor and exhaust air along a third longitudinal axis that is substantially parallel to the first longitudinal axis.
 In a third application of the present invention, it provides a vehicle convertible between land travel and air travel, that includes a vehicle body shaped in the form of an airfoil having leading and trailing edges; and a cross-flow propulsion mechanism for use in providing
li pr6pul l si'6ri 1 tb"a!ii i 'd!itd l rift',» i! tli ' a!iMuais a housing defining an inlet, a rotor compartment, and an outlet, with the inlet adapted to receive an inflow of air along a first longitudinal axis; a rotor mounted within the rotor compartment and adapted to receive the airflow introduced into said housing through the inlet and rotate about a second longitudinal axis that is substantially perpendicular to the first longitudinal axis; and an outlet adapted to receive the airflow processed through the rotor and exhaust air along a third longitudinal axis that is substantially parallel to the first longitudinal axis.
Brief Description of the Drawings
 The present invention will be more folly understood and appreciated by reading the following Detailed Description in conjunction with the accompanying drawings, in which:
 Fig. 1 is a diagram of a prior art cross-flow fan.
 Fig. 2 is a diagram of a baseline inline housing according to the present invention.
 Fig. 3 is a diagram of a cross-flow fan airfoil geometry according to the present invention.
 Fig. 4 is a diagram of the grid according to the present invention near the fan blades.
 Fig. 5 is a chart of computed inline housing performance according to the present invention.
 Fig. 6 is a diagram of time-averaged streamlines at 10 degrees angle of attack according to the present invention.
 Fig. 7 is a diagram of total pressure ratios at 10 degrees angle of attack according to the present invention.
 Fig. 8 is a chart of total pressure wake profiles according to the present invention.
" ' [002Il Ψi&!"9 is aMMgrM of time-averaged streamlines at 40 degrees angle of attack according to the present invention.
 Fig. 10 is a diagram of system analysis with wake ingestion according to the present invention.
 Fig. 11 is a diagram of a modified airfoil according to the present invention.
 Fig. 12 is a chart of cross-flow fan performance according to the present invention.
 Fig. 13 is a chart of the effect of boundary layer ingestion according to the present invention.
 Fig. 14 is a chart of the effect of boundary layer ingestion according to the present invention.
 Fig. 15 is a chart of airfoil performance according to the present invention.
 Fig. 16 is a series of charts comparing system analysis according to the present invention.
 Fig. 17 is a perspective view of an aircraft according to the present invention.
 Fig. 18 is another perspective view of an aircraft according to the present invention.
 Fig. 19 is a perspective view of a further embodiment of an aircraft according to the present invention.
 Fig. 20 is a perspective view of an additional embodiment of an aircraft according to the present invention.
 Fig. 21 is a perspective view of another embodiment of an aircraft according to the present invention.
 Fig. 22 is a perspective view of a convertible automobile/aircraft in the automobile configuration according to the present invention.
» •■ [01)35] " 'Fi|:"23 is-'a 1 p'efspe'ctiv 1 e view of a convertible automobile/aircraft in the aircraft configuration according to the present invention.
A — area
CD = airfoil drag coefficient, DI(0.5pUjc)
CL = airfoil lift coefficient, LI(0.5pU ∞ 2 c)
CP = power coefficient, Powerl(pU ∞ Df)
CT = thrust coefficient, T/(0.5pU ∞ 2 D f )
CS control surface
D drag per unit span
DBL = drag due to boundary layer build-up
Df = cross-flow fan diameter
F x x-component of force
H arbitrarily large distance hi = propulsor inlet height h j = propulsor outlet height h w ingested wake height h non-dimensionalized ingested wake height
L lift per unit span m = mass flow rate
^P = propulsive power
PT total pressure p τ, = total pressure at propulsor inlet mass-weighted total pressure at propulsor inlet
Q flow rate per unit span r = radial distance propulsor thrust
Uf = fan tip speed non-dimensionalized jet velocity, U j / U ∞ u w = propulsor inlet velocity with wake ingestion
U n = velocity in freestream
X = x-coordinate y y-coordinate
Δ change in value
Φ flow coefficient, Q I (DfUj)
% propulsive efficiency
It total efficiency, (QΔP T ) I (Ωτ) μ advance ratio, U ∞ / Uf μ v absolute viscosity
P density ψ/ = total pressure coefficient, ΔPγ/ (0.5 p U/)
τ = lan torque
Ω = fan speed, rad/s
Subscripts and Superscripts in = into control volume j = in jet
1 = non-wake ingestion
 Referring now to the drawings, wherein like reference numerals refer to like parts throughout, there is seen in Figures 2 and 3, a cross-flow fan (CFF) propulsion system designated generally by reference numeral 10 generally comprises a housing 11 that defines an inlet 12 into which air flows along a first longitudinal axis A-A, a rotor compartment 14 in which a rotor 16 is mounted for rotational movement about a second longitudinal axis B-B that is substantially perpendicular to axis A-A, and an outlet 18 from which air is exhausted along a third longitudinal axis C-C that is substantially parallel to and vertically spaced below axis A-A. A movable deflector 20 may be attached to the housing 11 to alter the flow direction of the inlet 12 and outlet 18.
 With reference to Figures 17-21, a personal aircraft 100 that incorporates CFF 10 therein is illustrated. Aircraft 100 includes a body 102 that shaped in the form of an airfoil and that extends along a longitudinal axis D-D. CFF 10 is mounted transversely across body 102 (i.e., the trailing edge of the airfoil), such that axis B-B is transverse to axis D-D. Preferably, CFF 10 is mounted above body 102 such that the airflow passing over body 102 is effectively captured by inlet 12, while not being impacted by other vortices created by body 102, as explained in greater detail hereinafter. CFF 10 is preferably of a width that approximates the width of the body 102. Deflector 20 may be used, preferably via computer control as is in known to those skilled in the art, to change the direction of the exhausted airflow to enhance lift or drag as desired for take-off or landing. Streamed exit ducting allows for easily controlled vectored thrust. The middle section of aircraft 100 contains ample space for passenger seating or cargo.  With reference to Figures 22-23, a vehicle 200 that is convertible between a land based vehicle (i.e., car) and aircraft and that incorporates CFF 10 is illustrated. Vehicle 200
the trailing edge of which CFF 10 is mounted. Wings 204 and 206 may be detachably mounted to opposing sides of body 202 to enhance lift characteristics of the vehicle, as can stability elements 208, such as canards, elevators, and the like. As with the other applications, CFF is preferably of a width that approximates the width of the body.
 Vehicle 200 may dimensioned to meet the maximum width allowed over conventional roads and highways. Vehicle 200 includes an airfoil shaped exterior preferably with a 34 percent thickness-to-chord ration. In addition, vehicle 200 has removable or retractable access to CFF 10. Vehicle may be converted with the addition or removal of stability element 208, such as rotating canards, on either side of a body 202, and detachable wings 204, 206 having conventional circulation control airfoil shapes for both lift enhancement (increasing wing aspect ratio) and flight control (e.g., ailerons, elevators, tail). Flight control may also be enhanced with vectored thrust from deflector 20 of CFF 10. The detachable wings may be taken off and stored when not in use.
 Despite relatively low fan efficiency, the present invention is competitive with conventional propulsion technologies. The raised inlet eliminates the fan size restriction caused by fully embedding the fan within the airfoil. Also, cross-flow fan performance is quite insensitive to even large amounts of wake ingestion, making it ideal for this type of configuration. In fact, the fan of the present invention is capable of drawing in the boundary layer, regardless of its thickness.
 Referring to the 34 percent thick airfoil seen in Fig. 3, even at low angle of attack, the wake can be quite large, producing large pressure drag. This renders very thick wing sections impractical for most aircraft applications as the drag penalty outweighs any benefits gained in lift or interior volume. Without the suction effect of a rear-mounted CFF, the flow separates given only a small angle of attack. The embedded cross-flow fans near the trailing edge eliminate flow separation by drawing the flow back toward the surface and into the fan
"dutfin^; yMdmg'V'ef y ' higliiiffcoefffcients. This is turn results in short takeoff and landing
(STOL) capability and low in-flight aircraft stall speed without the use of additional high lift devices, such as slotted flaps and leading edge slats. The combination of circulation control and differential thrust, accomplished through fan speed and inlet height regulation, may eliminate the need for control surfaces. By vectoring the thrust via a jet flap, additional lifting force and control are also possible. Additionally, the low fan efficiency will be off-set by lower drag (e.g. engine nacelle, pylon, and interference drag not present).
 CFD simulations of the cross-flow fan airfoil were performed using a 2D double- precision segregated solver. Second-order discretization of the convective terms was used throughout all calculations, and the SIMPLE algorithm provided pressure-velocity coupling. The standard Ic-D turbulence model was used with the enhanced wall treatment option, which combines a two-layer model with enhanced wall functions for greater robustness in near-wall grid generation (i.e. relaxed requirements on wall y values). In order to simulate the fan rotating, the area surrounding the blades was designated as a sliding mesh region.  Unsteady simulations require proper setting of both the time step size and the convergence criteria within each time step. For cross-flow fan simulations, a time step size equal to l/20 th the blade passing period (e.g. 720 time steps per revolution for a 36-bladed fan) captured the unsteady flow quite well. Within each time step, iterations were performed until the solution no longer changed. It was found necessary to reduce all residuals (continuity, momentum, and turbulence quantities) to at least 10 "5 , although for most cases, the residuals were reduced several orders of magnitude less (usually 10 "7 to 10 "10 ). All results are time- averaged data over one fan revolution. Dual-CPU Pentium 4 PCs, as well as multiple nodes of a 30-node Beowulf cluster, were used, with the computational time ranging from two days for the housing alone up to about two weeks for the full cross-flow fan airfoil.  Baseline Inline Housing
[O(M]" " ' ' u ' -TM b'&S'elife'iMiy ffitising shown in Fig. 2 is divided into three regions: the flow through the duct, the fan bladed region, and the fan interior. The fan bladed region rotated at a specified rpm, while the other two regions remained stationary. A close-up of the grid surrounding the blades is shown in Fig. 4. Quadrilateral mesh was used near the blade surfaces and along the casing walls, and triangular mesh filled in the remainder of the domain. The combination gave a smooth transition from the blade and wall surfaces to the sliding interfaces. Since no experimental data exists for the current configuration, validation of the CFD model was performed using published results for other housings, and will be presented in a future paper.  For the simulation, a 0.3 m diameter 36-blade fan was selected. The blades consisted of simple circular arcs with rounded leading and trailing edges. T he inlet and outlet heights were 0.3 m and 0.176 m, respectively. The density and viscosity were set to standard sea level conditions: D = 1.225 kg/m 3 and D v = 1.7894 x 10 '5 kg/(m-s). At the inlet, uniform ambient total pressure was specified with a turbulence intensity of 1% and hydraulic diameter of 0.3 m. A uniform static pressure boundary condition was specified at the outlet. Changes in mass flow rate, and hence flow coefficient, were achieved by adjusting the back-pressure. The data presented corresponds to a fixed fan speed of 2,000 rpm and a time step size of 4.17 x 10 "5 s.
 A grid dependency study was performed, with the final mesh consisting of
81,000 cells. The calculated fan performance for this case is shown in Fig. 5. The figure also shows the results for a coarser grid with only 43,000 cells. The graph shows that using half the grid cells produces only a small change in the results. A common feature of cross-flow fans, it is interesting to note that the operating point corresponding to maximum total pressure coefficient does not coincide with that for maximum total efficiency. For the fine mesh, the maximum total pressure coefficient is 4.03 at D = 1.1; the total efficiency reaches a maximum value of 67% at D = 0.5.  Cross-Flow Fan Airfoil
[ ' 00 ' 5O] " ' " " " Simulation ' bϊ ' th ' e cross-flow fan airfoil takes considerably more time than for the housing alone. The time to reach steady-state is based on the flow time from inlet to outlet. As the domain is small, for the baseline housing this occurs after only a few thousand time steps. In contrast, for the CFF-Airfoil simulations, the steady-state is not reached for many times that number, since the computational domain measures 20c x 20c, where c is the airfoil chord length. As an example, with the airfoil at zero degree angle of attack and the fan speed set to 1 ,000 rpm, the unsteady calculations took about 24,000 time steps, or about 2 seconds of flow time, to reach the steady-state. The drastic increase in computation time stems from the fact that in the latter case enough time must elapsed for the error in the initial solution to convect downstream and out of the domain. The same is true for the housing alone; however, the domain is significantly smaller, allowing the error to propagate out much faster.
 The airfoil geometry is seen in Fig. 3. An airfoil chord length of 15 ft was selected, and the corresponding cross-flow fan diameter was 2.1 ft. At the inlet, uniform velocity was specified in the positive x-direction with a turbulence intensity of 1% and turbulence viscosity ratio of 5%. At the outlet, a uniform static pressure boundary condition was used. Symmetry boundaries were specified for the top and bottom of the domain.  Mesh generation was similar to the inline housing case. Quadrilateral mesh covered the blade surfaces and exterior airfoil geometry, and triangular mesh filled in between. Two interfaces were again used: one just outside of the fan blades, and one just inside. To demonstrate solution dependency to mesh changes, the present invention was simulated at zero degree angle of attack at an altitude of 8,000 ft: D= 0.001868 slug/ft 3 and D v = 3.5753 x 10 "7 Ibf-s/ft 2 . T he freestream velocity was set to 206 ft/s, and the fan speed to 1,000 rpm. The corresponding time step size used was 8.33 x 10 "5 s. The starting solution for the unsteady case was obtained by first performing a steady calculation with the fan modeled as a moving reference frame zone. In doing this, the fan region does not rotate; however, the no-slip boundary condition on the fan blades is still enforced in the relative frame (i.e. the local blade
veldbify Is" eφM'Ϋό tlf)'- "MiS p ' πMuces a total pressure rise through the fan with magnitude comparable to the unsteady calculation, and consequently provides a good initial solution for the external aerodynamics.
 The grid dependency study presented consists of three grids of increasing resolution: 64,000 cells, 88,000 cells, and 131,000 cells. The average fan blade y + values for the coarse, medium, and fine grids were 63, 46, and 22, respectively. Table 1 gives the final computed results for each grid, along with the percent difference between the fine and the two coarser grids. In the current configuration, the jet leaves the fan with a large amount of swirl, causing the flow to deflect upwards, and resulting in a net downward force on the airfoil (i.e. negative lift coefficient). The results show only a small difference between the medium and fine grids, justifying use of the fine grid for the remainder of the CFF -Airfoil simulations.
Table 1 Grid comparison at 1,000 rpm
Coarse Grid Medium Grid Fine Grid
Paramet % Difference % Difference er Value from Fine Grid Value from Fine Grid Value
Φ 0.933 1.7 0.909 -1.0 0.918
Ψt 4.260 5.8 4.032 0.1 4.026 ηt 0.547 -1.6 0.555 0.0 0.555
CL -10.7 -3.9 -0.628
 The present invention was next simulated at 10 degrees angle of attack at 200 ft/s and standard sea level conditions. The fan speed was again set at 1,000 rpm; the time step size remained at 8.33 x 10 "5 s. The grid was generated by rotating the airfoil clockwise and reconstructing the grid as done previously. The jet deflector was aligned horizontally to force the flow to leave the CFF ducting in the freestream direction.
 Figure 6 illustrates the streamlines for this test. With the fan off, the flow effectively bypasses the fan ducting, producing a large wake behind the airfoil. With the fan on, however, the wake size reduces dramatically. Total pressure contours with the fan on are seen in
Fi|r7 > "and'^eS'dffl '& 1 cilea.'l! |i p i -i5ftM of "Where energy is gained and lost. The values in Fig. 7 are presented as total pressure ratio, defined as the local total pressure divided by the freestream value. The large values for total pressure ratio in the exhaust correspond to the thrust producing high momentum jet flow, whereas values less than 1.0 represent energy loss. In Fig, 7, the boundary layer growth over the suction surface is apparent. An important feature of the cross- flow fan is its ability to operate well even when the inlet profile is non-uniform due to ingestion of low momentum boundary layer flow. Also visible in Fig. 7 is the eccentric vortex, the region of very low total pressure located within the fan.
 Figure 8 depicts the wake profiles for the 1,000 rpm case, for the fan turned off, and for the original airfoil at 10 degrees angle of attack. The data are shown along a line 20% chord behind the airfoil. With the fan turned off, the wake profile is very similar to that for the original airfoil alone, only shifted in the vertical direction due to the change in the tailing edge geometry. The large total pressure deficit indicates a substantial wake immediately behind the airfoil. With the fan turned on, the total pressure profile outside the jet matches the freestream almost exactly. The jet produces a total pressure increase in the wake region, and entrains the flow near the airfoil tailing edge, virtually eliminating boundary layer separation. Additionally, the jet provides excess thrust, which is necessary in practice, since 3 -dimensional effects will be present, while at the same time, complete span- wise distribution of the cross-flow fan system will probably not be possible.
 As explained above, the cross-flow fan airfoil is ideal for high-lift STOL applications. To demonstrate this, the airfoil was next placed at 40 degrees angle of attack, with a freestream velocity of 50 ft/s at standard sea level conditions. Additionally, to demonstrate the mechanism for vectored thrust, the exit ducting was deflected 30 degrees downward.  Figure 9(a) shows the streamlines with the fan off. As expected, a large area of separated flow results. The airfoil here is fully stalled, with a calculated lift coefficient of 1.054. This is in stark contact to the case with the fan turned on. The time-averaged streamlines at
T ' ,25'0 rpm 'kfø 1 ψTθ'tfeQ"in"Fig:"9tbJ, Md show that the flow remains fully attached. With the fan on there is a strong suction effect, which draws the flow into the fan housing, prohibiting separation. The computed lift coefficient is 6.408 for this test of the present invention. Assuming the engine has enough power, the rpm can always be increased to provide a stronger suction effect, effectively creating a stall-free airfoil. The effect will only be limited by the mass-flow rate (i.e. fan choking). It is unlikely, however, that choking will be a problem, since the high-lift configuration would only be used at takeoff and landing, where the freestream Mach number is low, and for low-speed maneuvers.
 Table 2 provides a summary of the numerical results for the simulations of the present invention at 10 and 40 degrees angle of attack. The negative values for drag coefficient indicate a net thrust. Horsepower was computed using the time-averaged torque on the cross- flow fan blades.
Table 2 Summary of numerical results
Anj a;le of Attack, degrees C L CD Φ Ψt ηt HP per foot of span
10, Fan off 0.423 0.035 10, Fan on - 1,000 rpm 0.543 -0.056 0 .943 4 .544 0 .550 46.964
40, Fan off 1.054 0.225 40, Fan on - ■ 1,250 rpm 6.408 -0.987 0 .506 2 .337 0 .601 23.167
 To adequately implement the present invention, several important features must be included. As already demonstrated by the preceding CFD results, the propulsion system ingests a large amount of boundary layer, or wake, flow from the airfoil suction surface. Inlet momentum deficit does not strongly affect CFF performance; however, it does play a major role at the system level. In the current design, the flow exits the propulsor at the trailing edge as a jet, and fills up the wake behind the airfoil. As mentioned previously, this too has a positive effect, and hence must be included in the model. Finally, and probably most importantly, the cross-flow fan itself must be modeled.
TOOβl] 1 ' is based on the model given in Fig. 10. The inlet velocity profile is given by U W) and the inlet height by /z,-. The flow accelerates through the propulsor, and leaves with velocity U j . Ambient static pressure is assumed at both the inlet and outlet. For low- speed applications, this is usually a good approximation at the outlet, but will not be correct at the inlet, since the pressure is inherently different due to airfoil curvature (i.e. potential field effects), In the design process, one needs to consider this when sizing the inlet. Likewise, when making comparisons with experimental or CFD results, the inlet velocity must be converted to an equivalent profile corresponding to the same total pressure, but at ambient static pressure.  Using conservation of mass and conservation of momentum in the x-direction, given in Eqs. (1) and (2), respectively, propulsor thrust and inlet momentum deficit, termed here boundary layer drag, are deteπnined. 
 For the present model, a constant jet velocity was assumed (Uj = Constant). At the inlet, a power-law relation was used, since when compared to the CFD results, this was found to give a good approximation to the mass-flow rate with wake ingestion. The inlet profile is given in Eq. (3), where p is yet to be determined.
 Inserting Eq. (3) into Eqs. (1) and (2) and performing the integration
 ^ + 1 AP + 1 J (4)
" ' '" Dividing EqT " (4) " b ' y Eq. (5) gives the ratio of ingested boundary layer drag to thrust. This quantity ranges from zero, corresponding to no wake ingestion (or infinitely large thrust), to one (exhaust velocity equal to freestream velocity), and is a convenient means for comparing different designs. In Eq. (6) Λ is the ratio of the ingested wake height to the inlet
height, and also ranges from zero to one. It is important to note that a small value for ll may correspond to either minimal wake ingestion (for a fixed inlet height) or a large inlet height (for a fixed wake ingestion).
 p + 1 2p + l (6)
 Where h = h »l h ι (J)
 The cross-flow fan is modeled by bringing in the fan performance map. This is accomplished by using either CFD or experimental data for a particular design, or by using a "nominal" performance map, corresponding to configurations very similar to the present application. This is possible, since it was found that alterations in the baseline inline housing geometry for installation purposes produce only minor changes in the fan performance.  In order to bridge the gap between the exterior analysis and the fan performance curves, it is necessary to match the total pressure rise through the propulsor. Here, the mass- weighted total pressure is used at the inlet
 Of particular interest are the quantities relating propulsor thrust to the kinetic energy input to the flow and the power input to the fan. The first is called propulsive efficiency, and is defined in Eq. (9).
 Where P ,' ^ 2 p ' t J ) 'V ' 4 - y -? 2 p ' t J> vl "4 ' y (I 0 )  Substituting Eqs. (5) and (10) into Eq. (9)
 Non-dimensionalizing thrust and power, the second relation, given by Eq. (12), represents the amount of thrust produced per unit power. By maximizing this quantity, for a given thrust, the necessary power input will be minimized.
 Where D is the advance ratio, and is related to the flow coefficient through the relation
 The system analysis formulation thus involves evaluating the effect of the 3
independent parameters D, h , and hi Df, on the overall measures of system performance: D B L/T,
 In order to proceed further, it ist necessary to determine the value of the exponent
'p' in the preceding analysis. In addition, comparison runs were needed. CFD simulations of the baseline inline housing and the present invention were used for these tasks. For the present invention, two different geometries were run. The first corresponded to Fig. 3, where the chord length was 15 ft and the cross-flow fan diameter 2.1 ft. Calculations were performed for seven
aififerdhf rpWseMrfg^at^ercT flSgre&'tngle of attack with fan speeds ranging from 500 rpm to
1,250 rpm. The second set of runs corresponded to approximately the same exterior airfoil shape, but with a 1.0 ft diameter fan included. This modified geometry is shown in Fig. 11.  A compilation of the fan performance data for all three cases is depicted in Fig.
12. It is important to note that the non-dimensional quantities D / and D ( are not strong functions of inlet/outlet ducting geometry. This is fortunate from the standpoint of system analysis comparisons, since it allows a single curve to represent the fan performance for all cases. The solid and dashed lines plotted in Fig. 12 are polynomial curve-fits for total pressure coefficient and total efficiency, and are given by eqs. (14) and (15), respectively. From the CFF-Airfoil simulations, it was found that p = 0.28 gave the best match for mass flow rate across all cases, with an average error of less than 0.3%.
[00891 Ψ, = -5.3731^ 4 +11.166φ 3 - S.3403φ 2 + 6.5663^ + 0.4212 „ „
[00901 ?7, = 0.2898^i 3 - 1.3829^ 2 + 1.3682^ + 0.2479 „ «
 The present invention includes boundary layer ingestion into the fan, whereas in the conventional propulsion model, the propulsor ingests only uniform freestream flow. From Ref. 2, the thrust, propulsive power, and propulsive efficiency for the latter case are
 p 2 Λ j ∞ J (17)
^ - 2
" U' + 1  J (18)
 For comparison, two propulsors with equal thrust and mass flow rate will be used: one with and one without boundary layer ingestion. Dividing Eq. (10) by Eq. (17) yields the propulsive power ratio, which represents the energy savings relative to the conventional non- wake ingestion case.
'./ - + — -1
 Where P + 1 Ii (20)
 Propulsive power ratio and propulsive efficiency are plotted in Figs. 13 and 14 versus D B L/T 'for 0.5, In the figures, small values of D BL /T correspond to large thrust production, whereas DBL/T = 1 coiτesponds to a perfect fϊlling-in of the wake behind the airfoil
(i.e. the ideal cruising condition). As D B L/T and h increase, propulsive power ratio decreases.
The greatest power savings is thus achieved when DBL/T = 1 and h =1 (i.e. boundary layer ingestion is large). Propulsive efficiency also increases with increasing DB L /T, and is always greater with boundary layer ingestion. Propulsive efficiency can actually exceed 100% as D BL /T
approaches unity 2 . It is interesting to note, however, that as /; increases, D p actually decreases. For small values of DB L /T, the effect becomes quite significant, and implies that for a specified boundary layer ingestion and propulsor thrust, from a propulsive efficiency standpoint, it is desirable to have a large inlet opening. The implication of these results is that, although small propulsors benefit greatly from boundary layer ingestion, larger ones may still results in better performance. Thus a design tradeoff exists where using a larger fan results in higher propulsive efficiency, but with an added weight penalty and greater drag due to an increase in surface area.
 The question is now if Λ is fixed, for example at 0.5, is it beneficial to operate at a high or low value of UiI Dβ This situation is plotted in Fig. 15, which shows that the answer
depends on the particular design and operating point. For a fixed value of h , a lower UjIDf always gives a higher possible value for CT/ Cp. The analysis shows that for a fixed inlet height (i.e. fixed Ui), the best choice for fan diameter depends on the value of D BL /T; for a given DBL/T, the fan and housing should be chosen such that operation lies on the maximum C T / Cp line. For
1 B " grveh walcelϊeϊglϊt; 1 miSlfansTateslnto a direct relation between the necessary thrust and fan diameter for minimum power. Also note, as can be seen in the equations, propulsive efficiency is not a function of /;,-/ 'Df.
 In order to validate the system analysis formulation, comparisons were made with the CFF-Airfoil CFD results. The graphs of CT/ Cp and U p versus DBL/T for both the small and large fan cases are shown in Fig. 16. Excellent agreement is seen between the system analysis predictions and CFD data for propulsive efficiency. For CT/ Cp the system analysis also performs well, especially for the larger fan. It is important to note that the comparison depends
heavily on an accurate approximation of the wake height h , This should come as no surprise, since it was already seen that large amounts of propulsor wake ingestion create notable differences in overall system performance.
 As noted previously, it is necessary to compare the analysis with CFD results where the inlet velocity profile is converted to an equivalent one, but at ambient static pressure. In doing this, one also must assume an isentropic contraction or expansion of the flow, depending on whether the pressure is above or below the ambient value. Thus not only is an equivalent velocity profile determined, but also an equivalent inlet height. What is remarkable is the level of agreement between the analytical and the CFD results, given that the system analysis curves correspond to the actual ratio of inlet height to fan diameter (i.e. the physical value of hilDf). If the exact profile for pressure is known at the outset, then even better correlation can be expected. The implication here is that for preliminary design, where the process is reversed, the system analysis will provide a good approximation of the expected performance for a large range of designs, given only a small number of input parameters.
 The present invention thus comprises a successful application of wing-embedded, distributed cross-flow fan propulsion. The inline housing design of the present invention smoothly integrates within the airfoil to produce a high total pressure rise and thrust. Additionally, the embedded propulsion system of the present invention reduces the wake size for
BbI 1 IfI(M aM ϊϊ.g'h" a'ή'gle"0'f 'ήiktl, boundary layer reduction and vectored thrust capability provide for very high lift coefficients. By creating an integrated fan/airfoil system according to the present invention, the interference effects caused by external propulsors and their support structures may be eliminated, increasing overall performance. The high propulsive efficiency and low drag in cruise of the present invention provides for increased range over conventional designs. The present invention also readily allows for the mounting of multiple fans along the span of the aircraft. This redundancy improves safety dramatically in the case of fan failure. In addition, the entire housing can be made to lift directly out of the wing for easy maintenance and replacement.
 The distribution in the present invention of cross-flow fan airfoil sections along the entire span lends itself directly to flying wing or blended-wing-body (BWB) type aircraft. Additionally, by coupling the cross-flow fans with individual fuel cell powered electric motors, the need for shafts connecting the fans is eliminated. Such an aircraft provides a platform for a future BWB-CFF aircraft: low emission, low noise, redundant power source, highly efficient in cruise, highly maneuverable, and with excellent STOL capabilities. In the center region of the aircraft, the cross-flow fans produce the thrust, with the thick airfoil sections providing ample room for passengers (e.g. a 34% thick airfoil with a 15 ft chord length has a maximum thickness of over 5 feet). Outboard airfoil sections will most likely be thinner, but could still contain cross-flow fans for added thrust, wake reduction, and control via differential thrust (for yaw control) and differential lift through circulation control and vectored thrust (for pitch control).