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The ELIPPSE Propeller

By Paul Lipps
elippse@sbcglobal.net

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Paul Lipps 
Paul Lipps

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propeller
Paul’s propeller is like none other, seemingly breaking all the rules, yet the performance is unparalleled.

Propeller twist
This end view of Paul’s propeller shows the high angle of incidence at the root and the extremely thin, low-drag tip.

Inlets
Many aircraft manufacturers design their cowls with the inlets as far outboard as possible. This is due to the normally stagnant or even negative airflow near the spinner. Paul’s propeller is designed to produce thrust at the root, allowing the cooling inlets to be inboard.

Rear view
From behind, the unusual shape can be clearly seen, especially the thinness of the tip.

Golden West Fly-In
Editor Pat Panzera first met Paul at the 2003 Golden West Fly-In in Marysville,California. He was looking for interesting aircraft to showcase in CONTACT! Magazine and found Paul in line with a several other pilots awaiting the end of the air show so that they could take off.

Departure
Just in case you think we are pulling your leg with this propeller design, here’s photographic proof that it actually works! The camera’s shutter didn’t completely stop the prop, but you can still make out the planform of Paul’s three-blade prop as he departs California’s HanfordMunicipalAirport (HJO).

The Program
Several years ago I loaded Peter Talbot’s “Prop Performance” BASIC program on my computer. I obtained this program from a listing in Modern Propeller and Duct Design by Hollman and Bettosini. After playing around with the program for a while, I used it as the basis for developing a program of my own. I read about propeller, wing, and airfoil theory in several books and tried to incorporate what I had read into my program. These were things that were not contained in the original program - things such as the effects on lift and drag coefficients from Reynolds number and high Mach compressibility, as well as lift distribution, design lift coefficient, and planform.

The Propeller is a Wing
All books on wing theory state that the most efficient wing makes use of an elliptical planform/elliptical lift distribution. Since a propeller is basically a wing in rotary motion, creating its lift and thrust from the combination of rotary and forward motion, I reasoned that an elliptical lift would be my “E” ticket choice.

Lift on a wing is a function of the flow of air generating a force that is resolved into lift and drag. That force is proportional to the square of the velocity. Double the speed and the available lift goes up by a factor of four. Cut the speed in half and the available lift is only one-fourth as much.

All parts of the wing of an airplane basically go through the air at the same airspeed, except in a tight turn at low airspeed. But now consider that on a propeller, the rotational velocity at any point on it is mainly based on the radius at that point. Except for propeller-induced inflow, the static flow of a 72-inch rotating propeller will be six times as fast at the 36-inch tip as it is at the 6-inch hub/spinner radius. This means that the available force at 36 inches will be 36 times as great as at 6 inches! A propeller having a constant chord, with correct helical twist, would be similar to having a wing on a plane that had a tip chord 36 times wider than at the root! This would be exactly the opposite of an elliptically loaded wing. Think of the incredible bending force that would result from a wing like that.

To obtain a propeller with an elliptical lift distribution, it is first necessary to start off with a planform that has a constant lift distribution and then modify this by the coordinates of an ellipse. Without considering forward speed, a constant lift planform would result from tapering the prop inversely proportional to the radius squared, making it extremely wide at the root and very narrow at the tip. See the propellers on the CarterCopter and AeroVironment’s 14-motor solar-powered flying wing.

A wing has to operate over a wide range of speeds, in some cases as much as 5:1, and 3:1 is not at all unusual. That means the available lift force will vary over a 9:1 to 25:1 ratio. At the lower end, near stall, the wing will operate near the peak lift coefficient (CL). For a wing with flaps, that would be about 2.0. At high speed, the CL would only be one-ninth as much, or 0.22. A propeller, on the other hand, does not have nearly as much velocity variation along its span, except in the root area, since its major velocity is due to rotation, so it does not need as much CL range. This is a real advantage, as it is possible to make use of the higher lift/drag (L/D) ratio of a more highly loaded airfoil. Some of the laminar-flow airfoils in the 63-65 series have L/D ratios in excess of 100 at high CL.

Airfoils
A laminar-flow airfoil will have a minimum drag coefficient, CD, of about .004. On a symmetrical section, that minimum occurs at CL = 0. Dividing the CL by CD gives a zero lift/drag ratio. Not something to write home about. But taking that same section and giving it sufficient camber so that this CD minimum occurs at a CL of 0.55 would yield an L/D of 110 to 138!

A symmetrical airfoil must operate at a high angle of attack (AOA) in order to generate lift, so it also has a high induced drag, which results from the rearward tilt of the airfoil. A cambered section can generate a moderate CL at zero AOA, so it has minimum induced drag. Did you ever look at where the bugs are smashed on the leading edge of your wing? Notice that they are usually just above the leading edge. That’s because you usually pick them up when landing over a field that’s next to a runway. With the flaps down, the airfoil is very highly cambered and generates lift at a negative AOA; the bugs hit on the top of the airfoil, not the bottom!

Most wood propellers generally have a flat-bottom airfoil that is somewhat similar to a Clark or RAF section. These are referred to as turbulent flow sections. Two of the big-name prop makers I’m aware of use a section that has a completely flat bottom with a sharp leading edge! A sharp leading edge will only perform reasonably well when it intercepts the incoming flow on a line that bisects the edge angle (i.e., where the point is pointed into the relative wind). At small flow angles off this line the flow will get tripped right at the leading edge, creating much drag. How many subsonic jets have you seen with a flat-bottom airfoil? None, right? Those airfoils have drag coefficients almost 50 percent greater than the laminar-flow airfoils. For that matter, when have you seen a high-performance sailplane with a flat-bottom airfoil? Does this give you a clue as to proper airfoil selection and use? Granted, laminar-flow sections are harder to carve but are well worth the extra time it takes to make them. Why use high-drag airfoils on the high velocity of a prop? As long as the Reynolds number is greater than about 400,000, the laminar-flow section will outperform the turbulent-flow sections.

Blade Angle
Now it is necessary to determine the blade angle versus the radius, the helical path each portion of the blade follows as it passes through the air. Without consideration of the AOA, the tangent of the helical path at any radius is obtained by dividing the design forward speed by the rotational velocity at that radius. For a plane with a design speed of 200 mph, we multiply by 22/15 to get the speed in feet/second. To get the rotational velocity at a given radius, we multiply the radius, in inches, by 2 x π x rpm/60 x radius/12. With the engine operated at its rated 2800 rpm, we would obtain 63.4 degrees at 6-inch radius, 36.9 degrees at 15-inch, and 21.8 degrees at 30-inch.

Some would look at that high angle at 6-inch radius and have a tizzy! The inner portion of a prop generates no thrust, right? Wrong! The portion right up to the spinner can generate very high thrust-to-horsepower ratios.

But you’ll say, “Look how steep the prop is here. It’s working against the engine.” Trigonometry to the rescue. We can resolve the lift force at any radius of the blade into a forward thrust force and a rotary force acting against the engine’s rotation. Using the root and tip angles we just obtained, one unit of lift at 6-inch would give 0.45 units of thrust and 0.89 units of rotary force. One unit of lift at 30-inch would give 0.93 units of thrust and 0.37 units of rotary force. But—now we have to multiply the rotary force by the radius, in feet, to get the torque force acting against the engine. That means that the thrust/torque ratio at 6-inch is 0.45/(6-inch/12-inchx 0.89) = 1.00, and at 30-inch is 0.93/(30-inch/12-inchx 0.37) = 1.00.

The root section can do one of three things: generate thrust as well as drag, generate no thrust as well as drag, and generate reverse thrust as well as drag. The drag is always there; only thrust can be designed in!

Cowling and Inlets
If the prop has too little angle in the root region, it develops reverse thrust, slowing down the air needed for cooling. That’s why so many cowlings have cooling inlets mounted so far outboard where the prop’s angles are more conducive to producing thrust. The inlets on my Lancair are mounted with their inner wall in line with the spinner. So too is my induction inlet. In this way I pick up the accelerated flow displaced by the spinner. My O-235, with 123 horsepower, gets its cooling air from 1.5—inch-by-4-inch inlets—6 square inches per side! Compare that to others! And guess what? My engine runs too cool; I can’t always get the CHT up to the correct temperature of 385 F/195 C.

Another Myth
Many propeller articles state that there is increased drag from having the prop accelerate the air over the cowl. In other words, if the prop is producing thrust there, the cowl will have more drag. So by having the prop not produce thrust at its inboard region, there will be no additional drag. Following this line of reasoning, it would seem to be better to have a lot of reverse thrust in front of the cowl and so reduce its drag! Wow! That really makes sense! Why not just use a pusher prop on a tractor airplane so that there will be no air flowing to the rear over the fuselage and thus no drag? The air being sucked in by the prop from rear to front flowing over the fuselage will propel the plane forward?

The Truth
My prop in cruise at 200 mph gives a delta-v to the air behind the prop of less than 10 feet/second, even less in the inner 6 inches. Two hundred miles per hour is 293 feet/second; (293 + 10)/293 = 3.4 percent increase in the airspeed over the cowl. Not too much cowling drag created here.

A school of propeller theory says that the cowling behind the propeller causes a large bubble of air to be pushed ahead, which causes a slowing of the flow into the prop. With this supposed slower flow field, it would be necessary to take this into account when calculating the helix angle, which would result in reduced angles. I think much of this theory is from the 1930s, when planes had radial engines with large surface areas normal to the airflow.

I’ve even seen illustrations showing the view looking downward on the front of the cowl/prop, which shows the cheeks of the cowl sticking out each side apparently blocking the airflow. But when the cowling is viewed from the side, it can be seen that the line from the spinner usually blends in smoothly to the top and bottom of the cowling. Only that portion of the cowling around the inlets is normal to the flow, and if the inlet apertures are properly sized, there is little reverse flow. But consider: If the prop angles are reduced in this area, when they pass through the top and bottom region unblocked by the cowling, they will be at too low an angle of attack, producing either no or reverse thrust there. Only in the small region where the flow velocity is somewhat reduced will the prop be producing thrust. With the correct helix angles, the prop will be at the correct AOA through most of its revolution (especially the 180-degree arc over the top of the cowl, as viewed from the front), and at a higher AOA in the blocked area, but still producing thrust!

The Tip
This brings up another issue. It is easy to see that a drag force acting near the tip can generate large values of torque due to the long lever arm. A Cessna 182 flying at 7,500 feet, 2700 rpm, 156 mph, on a standard day, with a 72-inch prop, will have a tip Mach of 0.81. Its drag coefficient will be at least three times as much as in the root area—that is, if the tip is in good, smooth condition without a lot of pitting from stones and rain. But on a propeller, as on a wing, there is no lift at the tip. The lift pressure differential on a wing or prop goes to zero at the tip—therefore, no lift. But there is drag, and lots of it, due to the high Mach. And since area is a product of span and chord, the wider the tip chord, the greater the area and the greater the drag. This is one of the main reasons why props with wide, rounded tips are so inefficient. A high-efficiency prop will have a pointed tip, zero chord. The high-Mach, wide, rounded-tip props are also the ones that generate so much noise. That noise is engine power being thrown away. And any prop that further complicates a wide tip with a wide, turned-under or turned-up tip really throws away engine power. Those may look very techie, but they aren’t very efficient!

Another Propeller
The following will illustrate how important to efficiency it is to have the root section of the prop produce thrust and to minimize tip drag. We had a prop with turned-under tips, absolutely flat bottom, sharp leading edge, and a root angle about 15 degrees less than the correct helix angle. This prop gave 214 mph TAS at 8,000 feet density altitude (D.Alt.) and 2950 rpm. Removing the turned-under portion of the tips and creating a “slashed” tip, along with adding fiberglass layers from the spinner out 12-inch to increase chord 1-inch and increase its angle, gave a prop that gave 218 mph TAS at 8,000 feet D.Alt. and 2720 rpm. By a method to be shown later, the efficiency of the prop was increased by 15 percent! More speed at less power!
A slashed tip on a square-tip prop is created by first drawing a line across the blade on the bottom surface about 15 percent of the tip chord in from the tip. Shape the tip from this line straight radially outward up to the top surface of the tip, forming a very sharp edge. This sharp edge trips the vortex at the very outer edge, giving the most efficient tip. It will increase full-throttle rpm by 20 to 50 and give a 1- to 5-mph speed increase.

Practical Application
The first prop I designed (with my prop design program) was for use on a Lancair 235 with an O-320. It was to be used for mild racing and was intended to be capable of turning 10 percent over redline rpm. It was carbon fiber over a laminated wood core. The wood core was carved on a CNC (computer numerical control) machine specially made for propeller carving. When I gave the chord and angle data to my friend who makes props, he wanted to know if I really wanted him to make it for me, as its chord and angle distribution was like nothing else he had ever seen. He and others felt that it would not work well, if at all.

I can tell you I had a lot of trepidation at this point, not only because of the feedback from those I respected, but also because the prop really did have an extremely unusual planform and helix angle distribution. One of my programs predicted the Lancair’s speed at 1,000 feet, 5,500 feet, and 10,000 feet density altitudes at 100 rpm increments from 2400 rpm to 3100 rpm. Since this was my first go at prop design, I would have been happy if it had performed within 5 percent to 10 percent of my predictions. The prop met or slightly exceeded the speeds at all test points. We were able to get 2,000 feet/minute rate of climb at 110 mph IAS, 2,700 rpm and 240 mph at 5,500 feet D.Alt. at 3150 rpm.

The program predicted the peak cruise efficiency at 90 percent. Some other props that we tested on the Lancair were from 12 percent to 27 percent less efficient than this prop. The 27 percent figure was relative to that flat-bottom, turned-under tip prop that I later modified! That’s like throwing away 19 hp to 43 hp on a 160-hp engine.

My latest prop is a 63-inch-diameter three-blade for my Lancair 235 with an O-235-L2C. It is fiberglass over a laminated wood core and was made by Craig Catto of Catto Props. It uses a 13 percent thick, 63series laminar-flow airfoil. The blades have a lot of flex near the tip and can be bent forward about 1 inch without too much effort. It should be remembered, though, that there is little lift/thrust near the tip, and combining that with the centrifugal stiffening, this flex usually occurs only in static conditions and not in cruise.

I designed it to give 200 mph TAS at 10,000 feet density altitude at 2800 rpm. I am actually getting about 202 to 203 mph. With me and 20 gallons of fuel for 1,350 pounds gross, I get a 1,550 feet/minute rate of climb at 2370 rpm, 110 mph IAS, at sea-level density. That computes to about 82 percent to 84 percent efficiency in a climb! That’s better than most fixed-pitch props get in cruise! On a recent trip with a friend, the plane had 211 mph TAS at 8,330 feet density altitude at 2840 rpm, 6.8-7.0 gph! Several people I have spoken with who own Lancairs with an O-235 tell me they get more like 180 to 200 mph.

Efficiency Can Mean Economy
To see what fuel economy I could get by slowing the plane down, I got a fuel flow of 2.8-3.3 gph at 130 knots true airspeed (KTAS), 150 mph on May 17, 2004. That’s 45-54 mpg! As a point of comparison, I had a Great American 62-inch-diameter prop that I tried. At 8,042 feet density altitude, I got 202 mph TAS at 2950 rpm, 7.9 gph.

To get a full-throttle efficiency comparison between two propellers operated on the same plane at about the same density altitude, multiply Prop2 rpm times Prop1 TAS3 and then divide by Prop1 rpm times Prop2 TAS3. So 2950 rpm x (211 TAS)3 / 2840 rpm x (202 TAS)3 = 1.18—that is, 18 percent more efficient.

Single-Blade Myth
One of the myths that has been propagated in the aviation community, to the point that it’s almost become gospel, is that the most efficient prop is a single-blade and that all props with higher numbers of blades fall further and further short of this paragon. Did you ever consider that a single-blade prop, developing thrust on only one side of the plane as it revolves, would cause the engine to cone violently in its mounts as it is twisted by the prop?

Airbus Military’s latest turboprop transport, the A400M, has eight-blade props! The Boeing MD-900 helicopter has a five-blade rotor. A popular regional turboprop airliner has a five-blade prop. Hasn’t anybody filled these aircraft manufacturers in on the errors of their ways? In a past issue of a popular aviation magazine, the author of an article on props uttered the same fallacy. He maintained that multiple blades interfere with each other.

When I pointed out to him that at 200 mph and 2800 rpm the blades on my three-blade prop follow three distinct helical paths through the air, and each blade is 25 inches ahead of the previous blade at the same point of rotation, he rather lamely explained that in static conditions interference occurs. Static? Who uses static thrust? Airplanes are meant to fly, not pull tree stumps!

Static And Aerodynamic Balance
Another thing to consider about props is balance. Whenever people speak of balancing a prop, they are always referring to mass balance. But just as with the case of the single-blade prop, if any one blade or a combination of more than one pulls harder than the others, there will be a thrust imbalance that will cause the engine to cone in its mounts. This effect is exactly the same as the effect from a mass imbalance. In a mass imbalance, the mass center of the blades is not coincident with the crankshaft rotational center; this causes the engine-propeller system to rotate about its common mass center, generating a whirling or coning on its mounts. With an aerodynamic imbalance, due to blade-to-blade differences in chord or angle distribution, the thrust center does not coincide with the rotational center. The result? Engine whirl! This can also result from the plane of the prop hub face not being equidistant from all of the blade angles. To illustrate, consider what would happen if you placed a shim between the hub and crankshaft flange on the side of a two-blade prop hub 90 degrees from a line between the two blades. That would cause one blade to be at an overall lower angle and one to be at a higher angle.

I had a prop that I balanced over and over, and it still shook the plane. When I took a piece of paper and drew an outline around each blade and compared them, it immediately became apparent that one blade had about 1/4 inch more chord than the other over a short span. After correcting this, the prop was very smooth. I have found that a prop could actually have a slight imbalance, and you would never detect it over a four-cylinder engine’s own roughness.

Pitch - The “P” Word
You’ll notice I never once used the word “pitch” in reference to my propeller. In my opinion, that word should be reserved for use with screws and worm gears that travel a definite linear distance per revolution. In order to discuss a propeller using “pitch,” it’s necessary to introduce another word: slippage! Here again, I feel that slippage should only be used to describe a condition in which a device, such as a v-belt or clutch, is supposed to have a 1:1 relation between input and output does not. Since a propeller is nothing more than a wing in rotation, if pitch and slippage are appropriate for a propeller, then they should also be appropriate for a wing, which they’re not! Nowhere have I seen these terms applied to the main and tail rotors of a helicopter or the rotor of an autogyro. Why? Aren’t they also propellers? In a hover, the helicopter’s main and tail rotors must have 100 percent slip, since they go nowhere. See what I mean?

It is really an inappropriate, nontechnical term for use with props and introduces the idea that all propellers of a certain diameter and pitch are alike. It’s as if chord and planform have no bearing on a propeller’s characteristics; but nothing could be further from the truth! Go buy the same diameter and pitch prop from three different prop makers and you’ll get three different performances. That is the source of much frustration for someone shopping for a prop for his plane. To properly characterize a prop, the prop maker should tell you the engine horsepower required to turn the prop at a given rpm, density altitude, and speed, as well as the efficiency under those conditions. I’d like to see you get that information from any of them!

I would like to design propellers for various aircraft, but in order for me to design a prop for a plane, I have to be able to form a drag model of the plane for my equations. The best way to do this is to have one of my props installed on a plane and then measure the plane’s performance with it. I can form a less accurate model by measuring the chord and angle of someone’s prop every inch from the spinner to the tip and using those data along with the full-throttle performance of the plane with that prop to obtain the drag model. This requires the use of a very accurate electronic tach and flying the plane around a wide circle while measuring GPS-derived groundspeed and holding a constant altitude to minimize speed variations. It’s also helpful to have a fuel-flow meter in order to determine the actual installed engine horsepower, not the exaggerations of some of the engine makers! This makes use of the fact that a moderate-compression-ratio four-cycle engine (8:1-9:1), leaned for best power, will burn about 0.5 pounds/hp-hour. Using this and 5.9 pounds/gallon, you can estimate the installed horsepower to within about 5 percent.

By the way, the name ELIPPSE is a faux spelling of the word “ellipse,” using my last name, Lipps. I chose it because it refers to the elliptical lift distribution of my propeller design. My prop’s logo consists of a 3:1 ellipse surrounding the LIPPS name, with the Greek letter epsilon in front of my name and behind it in reverse. Epsilon looks like a squashed, somewhat triangular “C” with a horizontal line in the middle to form a rounded “E.” Epsilon in mathematics is used to denote the long/short axis ratio of an ellipse—its eccentricity.

There are people writing articles about props who say that the elliptical lift distribution does not work for props and mention the work of theorists such as Theodorsen, Goldstein, and Betz. But, as they used to say, the proof of the pudding is in the eating! If someone can design a prop for a particular aircraft and predict beforehand its efficiency and its performance to within 1 percent, well, I’ll tell you, that’s where you want to put your money!

Some Final Thoughts
It’s important for makers of UAVs and UCAVs to understand how improved propeller efficiency can add much to the performance of their product. A 1 percent efficiency increase will add 1 percent to the range or loiter time of the vehicle, and a 3 peecent increase will increase the speed 1 percent, plus additional efficiency will increase rate-of-climb. For a plane with 80 hp weighing 1,000 pounds that requires 20 thrust hp at best L/D, an 80 percent efficient prop will give 1,452 fpm and an 81 percent efficient prop will give 1,478.4 fpm for a 1.8 percent increase! And an efficiency increase from 80 percent to 85 percent is not a 5 percent increase but an 85/80 increase or 6.25 percent!

Testing of the fixed-pitch, three-blade ELIPPSE prop on my Lancair shows that it is performing at 82 percent efficiency in a climb at 105 mph IAS and at least 90 percent efficiency in cruise at 200 mph TAS. Also, multi-blade, fixed-pitch propellers with correct aerodynamic shape where the blades enter the spinner have as good a cruise efficiency as a two-blade propeller, but will have better static thrust and climb performance. And because a multi-blade propeller can be made smaller in diameter than a two-blade and still pump as much mass flow, it will be quieter because of the reduced tip speed at a given rpm. Tom Aberle’s “Phantom” Reno biplane qualified at 221 mph with its 64-inch two-blade prop in 2003, 241 mph with its 59-inch diameter three-blade propeller in 2004 at 250 rpm less than in 2003, and 251 mph with its 59-inch diameter four-blade propeller in 2007 at the 2003 rpm. Many commented on how quiet his propeller was as he flew by on the home course, where his noise was mainly from the engine exhaust. This in contrast to the T-6-like scream of the other racers!

Paul Lipps spent many years in the aerospace industry, 28 of which were with General Electric (GE), where he worked on the Atlas Space Launch Vehicle radar/computer guidance system at Vandenberg Air Force Base. While with GE, Paul developed high-accuracy refraction-correction equations and a tropospheric radar noise model for use in the Kalman filter guidance equations. He also designed a computer-driven radar simulator, with phase- and amplitude-modulated X-band signals that were injected into the radar’s antennas to produce a high-fidelity, interactive radar simulation of an ATLAS flight. This allowed radar checkout, training of radar and computer operators, and simulation of radar and computer problems and gave accurate ATLAS flight simulation for checkout of the computer guidance program under non-nominal trajectory, booster performance, and high tropospheric noise conditions.

Prior to these accomplishments, Paul worked for Bell Telephone of Pennsylvania for six years and then spent five years working for Burroughs Corp., on the guidance computer for the ATLAS D ICBM at Vandenberg Air Force Base.

Since his retirement, Paul has developed equations and the computer program for the design of high-efficiency propellers. In addition, Paul has worked with Klaus Savier of Light Speed Engineering in the design of the Plasma series of electronic ignitions and is now working on an electronic fuel injection system.

At 17, Paul’s flying passion came to life while he worked at a seaplane base in his native Pittsburgh. Although at the time he logged 14 hours on floats, his flying had to take a back seat to life. He spent some time with a J-3 flying club and in 1989 earned his private pilot certificate in a Cessna 172. He has since logged more than 780 hours single-engine land, with 577 of that being in his (and another’s) Lancair 235. - Pat

 
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