1485

Item 1485

OTHER: Rotor Concept - Reverse Velocity Utilization - Reverse Velocity - Blade (alternative A)

Overview:

An attempt to envision what would be optimal for a rotor blade that operates inside and outside of a reverse velocity environment.

A fundamental requirement is that the sum of the L/D improvements during reverse velocity exceeds the sum of the L/D degradations during forward velocity.

Belief: At each elements along the span of the blade the two edges will be different. The shape of each element's so-called leading edge and trailing edge may primarily be based upon the division of [lift * time] between the element's two edges.

Locations on Span:

There are two primary locations of interest:

Location R₀

The very center of the mast is not experiencing any rotational velocity. However, in forward flight it is experiencing a forward velocity on it's advancing side and an equal reverse velocity on its retreating side. Therefore, if the root of a blade were theoretically extended in to the center of the mast, this theoretical blade root would experience no velocity from rotation. However, at 90º azimuth it would experience a forward velocity and at 270º azimuth it would experience exactly the same velocity, but from the opposite edge. This location will be called (R₀), and R₀ = 0.0 R, where R is the radius of the disk.

This means that at this theoretical blade root, which is located at the centerline of the mast, should have identical 'so called' leading and trailing edges.

Location R_RV

If the tip speed ratio (advance ratio) (μ) is less than 1 there will be a location on the span of the retreating blade at 270º azimuth where the airflow over the blade will be zero at cruise speed. This location will be called (R_RV), and R_RV=R * μ.

If the tip speed ratio (advance ratio) (μ) is greater than 1 there will be a location inline with the span but beyond the tip of the retreating blade at 270º azimuth where the airflow over this theoretically extended blade will be zero at cruise speed. This location will also be called (R_RV).and as above R_RV=R * μ.

At the location R_RV the blade, or the theoretical blade, will only experience forward velocity. It will never experience reverse velocity. For this reason, the blade, or the theoretical blade, at this location can have a conventional airfoil.

The objective then is to optimize the locations along the 'actual' blade that is located between R₀ and R_RV. This optimization may consist of a linear interpolation between these 2 locations or it may consist of an exponential interpolation. If μ < 1 then the portion of the blade that is outboard of R_RVwill have a conventional airfoil, since it is subjected to forward velocity only.

Two secondary locations of interest:

Location R_R~ The root of the actual airfoil (R₀ minus Cutout)

Location R_TL ~ The tip of the blade. Any radiusing of the tip will be outboard of this dimension.

The following material is a consideration of the design of the blade that is located between R₀ and R_RV.

1. Blade X-section @ Theoretical Root @ Mast Centerline: (R₀)

The blade profile will have in-plane symmetry. See drawing below.

The pitch axis will be at 50% of chord. This is because this theoretical root will be experiencing forward velocity half the time and reverse velocity half the time. In addition, the airflow velocity is identical for both forward and reverse flow at the center of the mast.

Having the pitch axis at 50% of chord will result in the individual blade not having static stability in pitch. This is one of the reasons why the root flight-control must have power assist.

Note that during forward flight, the forward velocity and the reverse velocity are equal, therefor the degree of negative pitch on the retreating side will be identical to the degree of positive pitch on the advancing side. With three and particularly four blades per rotor the forces at the flight-controller will offset each other.
Note that during hover, the 'theoretical' blades at this location are not experiencing any air velocity.

Raising the pitch axis above the chord line at the root of the blade should reduce some of the static instability; in both forward and reverse velocity. This is because the 'leading' edge is pitched upward in both conditions and this results in the pitch axis being closer to the 'leading' edge, from the perspective of the tip path plane.

In addition, this raising of the pitch axis will place it in the center of the blade's thickness and this will be better for structural strength.

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2. Blade X-section @ Zero Velocity @ 270º Azimuth (270ψ) @ Cruise: (R_RV)

The blade profile will be asymmetrical, in-plane and out-of-plane. See drawing below.
The location of pitch axis will be at approximately 25% of chord because this location is never experiencing reverse flow, See drawing below.
The blade profile will be optimized for the advancing side since the Advancing Blade Concept will result in most of the thrust being generated on this side.
The tip flight-control MIGHT be small enough that only cyclic stick forces are required, in a small craft.

Preliminary Example w/ mu = 1; Using the UniCopter:

Drawing:

The theoretical root airfoil @ mast centerline is shown above in red. It is the mean line between face-to-face VR7 - 24% thick airfoils on a common pitch axis.

Note that the area of reverse velocity will extend further aft, then shown above, between the two rotors. This is because the propeller is increasing the velocity of the air in this region. The reverse flow near the root of the blade may continue until the blade is a 360º.

Notes:

Air speed = 250 knots = 288 mph = 422 fps

Rotor diameter = 9'-6" = 114"

Rotor speed @ cruise = 425 RRPM. Tip speed = 422 fps

Tip air velocity at 90º azimuth is 844 fps and at 270º azimuth it is 0 fps.

The blade has a relatively large taper therefore the blade will have much greater strength and resistance to deformation at the root end.

Assuming mu = 1, the mean twist will probably be near 0.75R. If mu < 1 then the mean twist will be located closer to the root. If mu > 1 then the mean twist will be located closer to the tip or it will be a theoretical one beyond the tip. The fact that the 'rootward' end will have a greater x-section than the 'tipward' end means that it may be impossible to consider ideal twist.

The pitch axis will be a straight line from the tip to the root irrespective of where R_RV is located.

There may well be a short portion of reverse taper at the root end of the blade, Particularly if the blade is to be used in an intermeshing configuration, due to the requirement to get sufficient airflow to the propeller's upper quadrant. In other words, when moving toward the root, the chord may decrease but the thickness will continue to increase.

Some of these Centers, Radii and Moments should be looked into in the future.

Data from Drawing:

The following table uses velocity that are different from the above but this is OK since these are only used for comparative values within the table.

The following is an incomplete (so far) attempt to see if .5R should have characteristics that are exactly half way between those of 1R and 0.0R (i.e. linear interpolation) or if .5R should be closer to the characteristics of 1R or closer to 0R. (i.e. curved line)

For an airplane wing: L_W = (ρ / 2) * V² * S * C_L . Where S is the area of the wing.

The following is an attempt to determine to optimum blade profile at different locations on the radius of the disk. It is based on the premise that a location that always operated in forward airflow would have an 'airfoil' profile and a location that operated 50% in forward airflow and 50% in reverse airflow would have an 'ellipse'profile.

Definitions:

'airfoil' designates the optimum airfoil profile for the smallest radius of the disk that never experiences reverse airflow (reverse velocity).

'ellipse' designates the optimum profile for that radius for R = 0. This radius is experiencing equal amounts of forward airflow (forward velocity) and reverse airflow (reverse velocity). This so-called 'ellipse' will have a profile that is symmetrical in-plane but not symmetrical out-of-plane.

'resultant' designates the optimum profile for that radius of the disk. It's profile is based on its proximity to the 'airfoil' and the 'ellipse',

Forward airflow: Air flowing from the so-called leading edge to the so-called trailing edge. The conventional airfoil profile will be fatter at the leading edge and sharp at the trailing edge.

Reverse airflow: Air flowing from the above-called trailing edge' to the above-called leading edge. An optimal airfoil profile will be fatter at the so-called trailing edge and sharp at the so-called leading edge.

Balanced airflow: The profile will be an 'ellipse' since the total amount of forward airflow is equal to the amount of reverse airflow.

The first value in the following ratios relates to the 'airfoil' profile and the second value relates to the 'ellipse' profile. The resultant profile is based on these two values, with the size of the value designating the closeness of the 'resultant' profile to the profile that that number represents. Ie. 240:120 means that the resultant profile is twice as close to the 'airfoil' profile as it is to the 'ellipse' profile.

Time in Forward Airflow vs. Reverse Airflow:

Radius:	1.00R	0.75R	0.50R	0.25R	^{(2) 0.125R}	0.00R
A/ Rotational travel in forward airflow	360º	277º	240º	209º	194º	180º
B/ Rotational travel in reverse airflow	0º	83º	120º	151º	166º	180º
C/ = 2 * B Doubling of time in reverse airflow to get equal rotational travel in both airflows. ⁽³⁾	0º	166º	240º	302º	332º	360º
D/ = A - B (same as 360º - C) Rotational travel in forward airflow minus equal rotational travel in both airflows	360º	194º	120º	58º	28º	0º
E/ = D : C Ratio of rotational travel in forward airflow to rotational travel in both airflows.	360:0	194:166	120:240	58:302	28:332	0:360
F/ = E in percent [Time] ⁽⁴⁾	100%:0%	54%:46%	33%:67%	16%:84%	8%:92%	100%:0%
Profile:	All 'airfoil'	Closer to 'airfoil'	Closer to 'ellipse'	Much closer to 'ellipse'	Much closer to 'ellipse'	All 'ellipse'
*Was (temporarily) using.*	100%		66.7%	58.1%		50%

(3) This is done because the 'ellipse' profile is intended for equal airflow in both directions.

(4) This is a ratio of time in both airflows. A better ratio will be that of the actual airflow volume ratio. In other words faster velocities have greater airflow.

Airflow in Forward Airflow vs. Reverse Airflow: The following must be redone. Would the square of the velocity result in a better answer?

Radius:	1.00R	0.75R	0.50R	0.25R	^{(2) 0.125R}	0.00R
Air velocity at 270ºψ	0 fps	- 125 fps	- 250 fps	- 375 fps	- 437.5 fps	- 500 fps
Air velocity at 90ºψ	1000 fps	825 fps	750 fps	625 fps	562.5 fps	500 fps
Air velocity ratio - 270ºψ /90ºψ velocity	infinity:0	6.6:1	3:1	1.67:1	1.28:1	1:1
Square of air velocity ratio ⁽¹⁾	infinity:0	43.6:1	9.0:1	2.8:1	1.6:1	1:1
Air velocity percentage - 270ºψ /90ºψ velocity	100/0	82.5/12.5	75/25	62.5/37.5	56.3/43.7	50/50
Square of ratio Air velocity percentage	10000/0	6806/156	5625/625	3906/1406	3170/1910	2500/2500
	100-0=100		75-25=50			50-50=0
*Am (temporarily) using.*	100²= 10000		50²= 2500			0²= 0

Chord: ⁽³⁾

Square of Air velocity ratio * Rotational ratio * Chord ⁽³⁾	infinity	145.6	18.0	3.9	1.9	1.0
Percentage of ( Air velocity ratio * Rotational ratio * Chord ⁽³⁾)	1000000 / 0	523381 /3604	375187	226939	170863	125000 / 125000

Lift involves the square of the velocity.

This is probably reasonably close to the actual root of the blade.

The blade will have taper but the chord is not currently included.

The square root of the velocity plots very closely to the rotational ratio plot, therefor this curved line should probably be the basis for the change of blade characteristics along the span of the blade. The reference for the changes is the 'straight' pitch axis. These characteristics are;

The ratio of thickness above and below the pitch axis. This ratio will change between R_RV and R₀.

The ratio of chord in front and behind the pitch axis. This will result in a curved leading and trailing edge between R_RV and R₀.

The locations of the centers of lift, during forward velocity and reverse velocity, in respect to the pitch axis. Note that there are 2 locations.

The center of mass in respect to the pitch axis; the in-plane & out-of-plane location.

Initial Algorithm Consideration for Blade Profile:

Preliminary basic assumption: Blade characteristics that are optimized for lift/drag in reverse velocity flow will be detrimental in forward velocity flow; and visa-versa. This implies that each segment of the blade along it's span should be individually optimized for the aerodynamic and dynamic conditions in which it will operate. Note that any improvement of l/d in reverse velocity airflow must not result in a greater degeneration of the l/d ratio in forward velocity airflow.

Segment optimization will entail the consideration of;

The optimal profile, at each blade segment, for forward velocity airflow during cruise.
The optimal profile, at each blade segment, for forward velocity airflow during hover.
The optimal profile, at each blade segment, for 50/50 forward &reverse velocity airflow during cruise (i.e. in-plane symmetry).

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Each blade segment's 'forward velocity arc' / 'mean velocity arc' ratio during cruise. [Time]

Each blade segment's 'forward velocity average velocity' / 'reverse velocity average velocity' ratio during cruise. [√(FV²/RV²)]

Each blade segment's reverse velocity drag contribution to the rotation of the rotor during cruise, using the optimal forward velocity airfoil profile for that blade segment. [D] Perhaps this values is the percentage increase in drag over that of the conventional profile. In other words, there is an advantage to having high drag???

The greater lift on the advancing side (all forward velocity) compared to that on the retreating side (partial reverse velocity) will shift the blade profile toward the 'airfoil' and away from the 'ellipse'. Advancing Blade Concept [ABC]

The craft's 'hover time' / 'cruise time' ratio. [HC]. If the craft only hovered then the optimal x-section would be 100% airfoil. If the craft spent 50% of the time hovering then the optimal profile would be half way between the optimal profile for cruse and 100% pure airfoil.

Develop an initial theoretical algorithm. Something like an expanded version of VA * √(FV²/RV²)* D * ABC * HC. The following is a preliminary attempt and it does suggest the trend.

R	Time	√(FV²/RV²)	D	ABC	Airfoil/Ellipse Ratio Considering Cruise Only	HC	Airfoil/Ellipse Ratio Considering Cruise & Hover
1.00	100%:0%	√(10000/0) = Infinity	1.1:1⁽³⁾	3:1	100% / 0.0%	10% / 90%	100% / 0.0%
0.75	54%:46%		1.1:1⁽³⁾	3:1		10% / 90%	%
0.50	33%:67%	√(5625/625) = 3:1⁽²⁾2:1	1.1:1⁽³⁾	3:1	326.7:67 = 83.0% / 17.0%	10% / 90%	83.0% + 10% * 17 = 84.7 / 15.3%
0.25	16%:84%	√(3906/1406) =1.67:1	1.1:1⁽³⁾	3:1	88.2:84.0 = 51% / 49%	10% / 90%	51.0% + 10% * 49 = 55.9 / 44.1%
0.125	8%:92%	√(3170/1910) = 1.3:1	1.1:1⁽³⁾	3:1	34.3:92 = 27% / 73%		27% + 10% * 73 = 34.3 / 65.7%
0.00	100%:0%	√(2500/2500) =1:1	1.1:1⁽³⁾	3:1	0.0% / 100%	10% / 90%	0.0% / 100%

The first number is the percentage of deviation from the optimal forward velocity airfoil profile for that blade segment. The second number is the percentage of deviation from the optimal chordwise symmetrical profile for that blade segment.

This value is too high because it only considers the velocities at 270ºψ and 90ºψ. Therefore I am temporarily going with the value of 2:1. RECALCULATE USING THE VELOCITIES AT 30-DEGREE INCREMENTS AROUND THE DISK.

A guess.

This suggests that the profile at 0.5R should be 16.1 time closer to the 'airfoil profile' than the 'ellipse profile'

Relocated Pitch Axis:

The pitch mechanism must handle large moments when the blade is subjected to reverse velocity. These moments will be greatest at the root since the root will be spending more time in reverse airflow and at larger velocities in reverse airflow then will the tip. The blade root will require power assist. Therefore it will make sense to move the pitch axis away from the 25% of chord to a more optimal location.

Reference the drawing below;

Assume that the average angle of attack is +8º in forward airflow and -8º in reverse airflow. Locate the pitch axis at the intersection of lines that pass through the conventional pitch axis locations. This means that during flight the positive and negative moments will be about equal. In addition, the extreme moments, which would be experienced if the pitch axis was in the normal position, will be eliminated.

If the top forward speed was mu = 1, then the above sketch would only apply to the root of the blade. The tip profile would be conventional since the tip would never experience reverse velocity.

Blade Profile: Note that the profile in the above drawing favors forward velocity over reverse velocity. This is because this profile does not represent the blade at the mast's centerline. It represents a theoretical root of the actual blade.

A Gut Feeling:

An adjacent twin rotor configuration combined with the above considerations appear to suggest that the optimal blade profile (including x-section of mass axis etc.), for most segments, may be quite close to that of a conventional airfoil; particularly if the craft's mu is close to 1. Of course, a 'stopped rotor' (mu = infinity) would be a very different consideration.

Additional Information:

Riblets:

http://home1.gte.net/pjbemail/RibletFlow.html#222 See section on riblets.

Reverse Flow Drag Effect:

Discussion and calculation related to the airflow passing from trailing edge to leading edge.

Technical Documents on ABC, Forward Flight Performance of a Coaxial Rigid Rotor, page 6, ~ V. M. Paglino, May 1971

This is an extract from a removed web page:

for reverse flow is taken to be 1.2 times its value for forward flow, ...

Blade Stall:

A sharp leading edge will cause the blade segment to experience a sudden stall. In other words, the stall will quickly move from the upper trailing edge to the upper leading edge. Look into further. Will this represent a meaningful problem at the root?

Citations:

Title: Model Wind Tunnel Tests of a Reverse Velocity Rotor System

Title: Reverse Velocity Rotor System for Rotorcraft

Time Spent in Various Modes of Flight:

The work on this page relates to Cruise. It would seem that the amount of time spent in various modes for the specific craft should be taken into consideration; particularly the ratio of Hover to Cruise.

Profile Drag:

During cruise the profile drag in the reverse velocity area on the retreating blade is contributing toward the rotation of the rotor. Therefore, it would appear that reverse velocity drag isn't all that detrimental.

Morph:

Is there any way to morph the leading and trailing edges at a rate of once per revolution so that the two edges will be more appropriate for the two alternating directions of the airflow.

Sharp Leading (and Trailing) Edge:

The Advancing Blade Concept combined with Active Blade Control should eliminate high angles of attack. Therefore a sharper leading edge at the root of the blade may be acceptable. [Source ~ PHA p.274]

Thin Airfoil Stall:

The root end of a slow speed wide chord blade will have a large Reynolds number. Therefore a relatively 'thin airfoil' should not be a problem. [Source ~ PHA p.275]

Related Pages at this Web Site:

For information on reverse velocity see; OTHER: Rotor Concept - Reverse Velocity Utilization

For information on blade construction see; UniCopter ~ Rotor - Blade - NACA 00xx - IRAT - Torque Tube Method

For information on blade flight-control see; UniCopter ~ Control - Flight - Independent Root & Tip (IRAT)

Related Outside Information:

The 'Detailed Description' section in Carter's patent application 20020005458 on an airfoil for forward and reverse velocity is of interest. Have hard copy in Reverse Velocity binder.

Figure 46 in Stepniewski's ABC Synchropter shows some theoretical airfoil profiles for use in forward and reverse velocity.

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Initially displayed: December 2, 2005 ~ Last Revised: November 9, 2007

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