# New Aerodynamic Theory: Drag-based Flyers

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#### David liang

##### Active Member
Hi all,

I have been considering how birds and insects fly with flapping wings.
These days I have some new thoughts about the flapping wing flight principle.
My idea is very different from the conventional aerodynamic theory for airplanes.

What do you think about my idea?
Any comments will be much appreciated.

Best Regards,
David Liang

*************************************

New Aerodynamic Theory: Drag-based Flyers

The conventional aerodynamic theory for airplanes cannot explain the force of lift for flapping wings. I put forward a new aerodynamic theory that can explain the flapping wing flight of insects and birds very well.

First, to cite a reference here.

Airflow over any object creates two types of aerodynamic forces: the drag force, in the direction of the airflow, and the lift force, perpendicular to the airflow. According to the conventional aerodynamic theory, a flyer can fly by using the aerodynamic lift force, but the aerodynamic drag force hinders flying.

I put forward a new aerodynamic theory. According to the new theory, a flyer can also fly by using the aerodynamic drag force.

To explain the new theory, the windturbines are good examples to understand how a flyer can use the aerodynamic drag force to fly. It is because that the principle of windturbines is the inverse principle of flyers.

It is well known that windturbines can be classified into two types based on their working principles: the lift-based windturbines and the drag-based windturbines. The blades of lift-based windturbines are rotated by the aerodynamic lift force; the blades of drag-based windturbines are rotated by the aerodynamic drag force.

Fig.1 is a comparison of a helicopter and a conventional lift-based windturbine. The helicopter and the conventional lift-based windturbine both work based on the aerodynamic lift force; their working principle is the same.

Fig.2 shows the working principle of a drag-based windturbine using cup blades. The drag force on the cup moving forward is FF; the drag force on the cup moving backward is FB.

The difference between the FB and the FF creates a net aerodynamic force, rotating the blades. The rotating force Frotating can be written as:
Frotating =FB - FF

For the sake of comparison with the drag-based windturbine using cup blades, we can assume a drag-based flyer using cup wings.

Fig.3 shows a diagram of the drag-based flyer with two cup wings. The cup wing is connected to the body by a horizontal axis. The flyer flaps both the left and right cup wings with an up-and-down motion (reciprocating motion).

Fig.4 shows the working principle of the drag-based flyer with two cup wings. The drag force on the cup moving upward is FU; the drag force on the cup moving downward is FD.

The difference between the FD and the FU creates a net aerodynamic force, pointing upward. This force is the lift force Flift.
Flift =FD - FU

Fig. 5 is a comparison of a drag-based windturbine with two cup blades, and a drag-based flyer with two cup wings. Both of them work based on the aerodynamic drag force; their working principle is the same.

Theoretically, the drag-based flyer using cup wings can fly. To test if it will fly or not, I built a prototype of the drag-based flyer. Fig.6 is a picture of the drag-based prototype flyer.

Fig.7 is a video clip to show the test flight of the drag-based prototype flyer. (This video clip can be seen at: https://youtu.be/quaKRoFILtw).

In the test flight, the prototype flyer can get off the ground vertically. The result of the test flight validates that a flyer can fly by using the aerodynamic drag force.

I also formulate a ‘flapping-wing flight formula’ based on the flapping wing flight theory.

Where, f is the wing flapping frequency of the flyer, WS is the wing load of the flyer, S is the wingspan of the flyer, and k is a constant.

Equation (3) can be called ‘flapping-wing flight formula’, because it describes the relationship between the wing’s static character (wing dimension, i.e. wing span and wing load) and the wing’s dynamic character (wing flapping frequency).

Here uses some realistic data to test the ‘flapping-wing flight formula’.
According to the ‘flapping-wing flight formula’, i.e. Equation (3), it can be predicted that the graph of the f value versus the value will be a straight line with slope k. Fig.8 shows the graph of the f value vs. the value. This graph agrees very well with the prediction. So the result shows that the ‘flapping-wing flight formula’ is correct.

Based on the new aerodynamic theory, it can be concluded that a flyer can fly by using either the aerodynamic lifts force or the aerodynamic drag force.

The relationship among aerodynamic forces, windturbines and flyers can be described as follows:

1. There are two types of aerodynamic forces: the lift force and the drag force.
2. Windturbines have two types: the lift-based windturbines and the drag-based windturbines.
3. Flyers have two types: the lift-based flyers and the drag-based flyers.

Fig.9 shows the relationship among aerodynamic forces, windturbines and flyers.

http://linaircraft.blogspot.com/.

‘New Aerodynamic Theory: Drag-based Flyers’:
http://linaircraft.blogspot.jp/2016/12/newaerodynamic-theory-drag-based-flyers.html

‘Flapping Wing Flight Principle’:
http://linaircraft.blogspot.jp/2016/11/ornithopter-principles-and-designs_22.html

‘How to design ornithopters’:
http://linaircraft.blogspot.jp/2016/11/ornithopter-principles-and-designs-2.html

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#### BJC

##### Well-Known Member
HBA Supporter
To understand how an airplane wing or helicopter rotor or a wind turbine rotor or a bird wing generates a force from airflow, you should read Understanding Aerodynamics by Doug McLean.

BJC

#### StarJar

##### Well-Known Member
I think there is a confusion about the terms "lift" and "drag". Anything desirable falls under 'lift' even if it's created by air impacting the wing or blade from the underside (along with other phenomena).
Sorry to make it short, but that's my first impression.

#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
What you propose works like an umbrella helicopter (0:55 in the video below).

#### BBerson

##### Light Plane Philosopher
HBA Supporter
Insects use many tricks to make "negative pressure above the wings"*.
For example dragonflies slap the wings together at the top to make a negative pressure.

*call it lift or drag, it's just a force from changing pressures.

#### Swampyankee

##### Well-Known Member
Lift is force perpendicular to the relative wind; drag is force parallel, and thrust is anti-parallel. Insects and birds take advantage of unsteady aerodynamics; this is well known. Check out the work of Ilan Kroo's group at Stanford.

Spiders' ballooning uses drag-based aerodynamics. Check it out!

#### BBerson

##### Light Plane Philosopher
HBA Supporter
Helicopter books often call the vertical force from the rotor thrust.

#### jedi

##### Well-Known Member
Your theory is correct and you have done some nice work. You may find an application where it will be useful.

However, for conventional human flight the power requirements will be very large and efficiency very poor. The concept of the wing is similar to that of an inclined plane. That is lifting a large load (lift force) with a small thrust (equal to the drag force). If the equivalent airplane has a 10 to one glide ratio (L/D) your flyer would require ten times or greater power. Greater because there is also considerable drag on the upstroke. Furthermore, the airplane can glide to a power off landing while your proposal would fall out of the sky like a heavy parachute.

It would work in water where the fluid forces are much greater and flotation can assist or in very small insects where scale effects make floating in air much easier as with a speck of dust.

#### Swampyankee

##### Well-Known Member
Helicopter books often call the vertical force from the rotor thrust.
Outside of hover?

#### BBerson

##### Light Plane Philosopher
HBA Supporter
Outside of hover?
Yes. From my Prouty book: "Just as in hover, the thrust in forward flight can be computed from the integration of the lift on each blade element along the blade and around the azimuth".

The blades each have lift but the whole rotor can tilt forward to provide forward thrust. I saw a helicopter tow a barge with the cable at a 60° angle. It was using excess thrust to do that. Rotors provide lift and thrust and control.
A rotating wing (rotor or prop) can produce full thrust in any direction, even straight down, so calling it lift would seem odd.
The capability and terminology for flapping wings would be different from fixed wings, I think.

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#### Armchair Flying Ace

##### Active Member
Okay... I'm not an aerodynamics expert, but nothing in here appears to not make sense - on the other hand, nothing's particularly revolutionary.

IIRC there are two main reasons why insect flight appears to follow different physical laws. First, insects operate at far lower Reynolds Numbers than an airplane or even most birds, so the behavior of air is a bit different. Second, insects move their wings in a more complex pattern.

Anyway: while a drag-based aircraft may be possible, I doubt it would be practical in anything but a very small scale. The first reason is that just because it works doesn't mean it's efficient. According to Wikipedia, typical lift-based wind turbines can deliver about 75-80% of the theoretical maximum efficiency of 59%, so they're up to around 45% efficient. On the other hand, the most common "drag-based" turbine is a Savonius Turbine, which typically has about a 15% efficiency. I would expect a "drag-based propeller" to similarly be far less efficient than a conventional one. And cutting efficiency by a factor of three is HUGE.

The second reason is that there are major mechanical design challenges inherent to ornithopters. Basically instead of having your wing either be fixed or rotating at an approximately constant speed and maybe cyclically changing its angle of attack, an ornithopter throws the entire mass up and down large distances at high frequencies. This is absolutely brutal on your structure. Not only can the vibrations themselves rip an aircraft apart, but you're adding a whole bunch of "forward/reverse" or "up/down" load cycles, which makes fatigue worse.

#### Armchair Flying Ace

##### Active Member
So, OP, I'm looking through your blog, and I think a couple other things there deserve comment.

http://linaircraft.blogspot.com/2016/07/heli-drone-new-concept-manned-drone.html

In the idea of people, helicopters must be driven by professionally trained pilots because helicopters have the reputation of being extremely difficult to drive. If there was the helicopter that anyone can easily drive it like driving a car, our lifestyle could change dramatically. People would commute by helicopters; soldiers would drive helicopters into battle.
So, to start with, no we wouldn't. Reason 1 is because your "easy to control" helicopter would still be much more expensive and less fuel-efficient than a ground vehicle carrying the same payload. We use aircraft when things like speed and ability to reach areas ground vehicles can't easily get to are more important than those factors - i.e. not your typical commute. Militaries use helicopters for transport all the time, though. Also, no aircraft can operate in as wide a range of weather conditions as a car, especially with a low-skill pilot. I can drive a car in snow, 50 MPH winds, or fog by being very cautious and operating slowly. Show me an aircraft where an average person can do that.

Finally, no matter how easy the basic control of an aircraft is, it will still always be harder than driving a car because, quite simply, an aircraft has far more ways of killing you.

A stable object must have more than three supporting points. For example, a unicycle vehicle is very hard to keep the balance (Fig.2); a bicycle vehicle is also very hard to keep the balance at very low speed; a quadcycle vehicle is inherently stable (Fig.2).
Okay, this is a huge and dangerous oversimplification of the physics involved. It sort of applies on the ground, but is completely useless in the air.

You need to look at the actual mathematics of stability. A unicycle is unstable because if you disturb it slightly in pitch or roll, the center of mass is horizontally displaced so that the normal force from the ground creates a moment about the CoM, and the larger the disturbance, the larger the moment which is acting to make the disturbance bigger. A properly-designed airplane in level flight is stable because, if disturbed slightly in any of the three rotational axes, the forces will change in a way that produces a restoring moment, i.e. one that pushes it back toward its original orientation.

The one-rotor helicopter has one supporting point; it is very hard to keep the balance.
Number of rotors doesn't matter, forces do. A helicopter with a single rotor would be similar to a unicycle - uncontrollable except by shifting its weight - except for one very important thing. A helicopter's pitch and roll motion are controlled with cyclic, which changes the distribution of lift around the circumference of the rotor. Really you could think of it as an infinite number of "supporting points" each generating an infinitesimal amount of force. This means that a helicopter CAN be controlled.

However, a helicopter, unlike an airplane, is approximately neutrally stable in all three rotational axes when hovering (erm... does the blades deflecting upwards and creating a dihedral add stability). If you push a helicopter's nose upward, it will tilt backwards, and if the pilot doesn't do anything there's nothing creating a restoring moment, so it will fly away backwards (well, actually the gyroscopic effect might make it go roll and fly away sideways instead).

Actually, the early pioneers first attempted the four-rotor helicopter because of the inherent stability (Fig.3), but these attempts failed.
Citation that this was for stability reasons? I would guess it was probably for structural reasons: making four small rotors that don't fall apart when you spin them up may be lighter than one big rotor, the same way that making two short wings that will survive the forces placed on them is lighter than one long wing. In the olden days, aircraft materials weren't as good as they are now, and engines were much less powerful so structures had to be made extremely light. This is a large part of why biplanes and triplanes were so common; two or more short wings braced to each other with wires is much stronger for the same weight than a single long wing braced to the fuselage.

Although the four-rotor helicopter has good inherent stability, the pilot must control four rotors respectively. However, at a time when computers did not yet exist, it was in fact impossible for a human to respectively control four rotors at the same time.
A four-rotor helicopter doesn't have good inherent stability unless you cant the rotors inward. In fact, without this dihedral, a quadcopter is WORSE than a helicopter. It's still neutrally stable, but now because the rotors spin in opposite directions the gyroscopic effect, which would otherwise at least slow down its pitch and roll response, cancels out. And actually a human would have no problem controlling four rotors. How? Just connect them all to a single engine using drive shafts, and use the exact same control scheme as a helicopter, but with a different mechanical linkage. Collective changes the pitch of all four rotors the same way, counter-torque pedals increase the pitch on opposite rotors and decrease it on the other two, forward cyclic increases pitch on the rear rotor and decreases it on the front one, etc.

Oh, and I think the reason for two-rotor helicopters is usually either because your vehicle is so heavy that a single rotor would be impractically large (either for structural concerns or for practical reasons like folding the blades up to put it in a hangar), or because two rotors allows a more favorable fuselage design for your application. One big rotor is more efficient at moving air than 2+ smaller rotors, so designers use a single rotor whenever there isn't a compelling reason not to.

Radio-controlled one-rotor helicopters had been introduced in the market as early as the 1970's, but only a few people could fly them (Fig.4).
However, when RC four-rotor helicopters (quadrotor drones) have been introduced in the market, they become rapidly famous (Fig.4). This is because the quadrotor drones are very easy to fly.
Okay. Multirotors seem easy to fly precisely BECAUSE they're actually harder to fly. What? That sounds crazy! But basically, multirotors are so darned twitchy that they are, for all practical purposes, IMPOSSIBLE for a human being to fly without a computer. IIRC there are three main control modes for a multirotor. The usual "beginner" mode is auto-level, where when you move the stick the drone changes to a certain pitch/roll angle or yaw rate and stays there, then automatically levels itself or stops the yaw rotation when you let go of the stick. The "advanced" mode lets you control the pitch and roll rotation rate with the sticks, but still automatically stops its rotation when you let go. Many drones also have a mode where they'll just hold a position, and stop their movement when you let go of the stick, or even outright just fly a flight path you tell them to. You are NEVER given direct control of rotor speed. RC helicopters usually do give you something much closer to full control, although they often have gyros adjusting your control inputs because otherwise at small scales they get very "twitchy" too. An RC helicopter with the same level of computing as a typical multirotor would be just as easy to fly.

Why do we use multi-rotors? Because they are MECHANICALLY SIMPLE. Putting a fixed-pitch propeller on a motor and then adding a whole bunch of identical units is much simpler than the complex swashplate and driveshaft a helicopter needs, and is much easier and cheaper to manufacture at small scales.

(i) The range and endurance of the full size four-rotor helicopter is too short.
The rotors of RC quadrotor drones use electric motors and batteries. However, the energy density of batteries is very low; the range and endurance of the full size four-rotor helicopter using electric power will be too short.
Sort of true; but there's nothing stopping you from building a Collective-Pitch Quadcopter using driveshafts or belts and a single ICE, and then using servos to adjust blade pitch.

The mechanics of the full size four-rotor helicopter is too complex.
To solve the range and endurance problem, a market-competitive full size four-rotor helicopter must use the IC-engine.
If the full size four-rotor helicopter uses the IC-engine to drive its rotors, the mechanical complexity will tremendously increase. If it uses a single IC-engine to drive four rotors via belts or shafts, the transmit mechanism will be too complex and too heavy. If it uses four IC-engines to drive four rotors respectively, it will also be too complex, too heavy and too expensive.
It wouldn't be that terrible compared to a helicopter. Note that driving four rotors off independent ICEs is a terrible idea, though. A quadcopter has four motors, but not only can it not maintain level flight if a single motor fails, but it will tumble violently from the sky if this happens. They can get away with this because electric motors are a lot more reliable than ICEs, but even then larger and manned multirotors tend to use eight or more rotors to give them engine-out capability... which makes a multirotor's efficiency problems even worse. But an ICE on each rotor would be a death trap.

As mentioned above, the new helicopter ‘Heli-Drone’ I designed is very easy to drive. The primary reason is that Heli-Drone has inherent stability.
Heli-Drone is a manned VTOL aircraft combining with an IC-engine powered one-rotor helicopter and an electric powered multirotor. Fig.5 shows the structure and inherent stability of Heli-Drone.
Okay, I'll make this simple: this is a bad idea.

You missed one very important reason why we're not making full-scale fixed-pitch electric multirotors. A fixed-pitch multirotor is controlled by changing the speed of each propeller. This is okay at small sizes, with light plastic props and extremely powerful brushless motors, but on a full-scale vehicle the control response would be extremely sluggish, which is a recipe for horrific pilot-induced oscillations and a crash. Not what I'd call easy to fly. Your scale model might have been okay, but a full-sized vehicle probably won't.

Other potential problems include interference between the main rotor and the little ones, having to fold all those rotor arms up to put the thing in a compact hangar or trailer, and the fact that you have FOUR prop arcs for people to walk into, and you have to thread your way between them to get to the darn door. At least put shrouds on the things.

The control system might be okay, but one major problem I see is that it could be very difficult for people who DO know how to fly regular helicopters to transition. I don't like the "car-type." You're supposed to have both hands on the steering wheel most of the time anyway. I think using the foot pedals for collective is an interesting idea, but I'd use the left foot to descend. There's nothing wrong with autothrottle: it's not that different from a car having automatic transmission.

My major concern is with the hand controls. The swing grip seems like it would be very easy to overcontrol or undercontrol depending on its sensitivity: I'd prefer to put the yaw control on a separate side-stick - so essentially you'd be switching the collective and yaw controls to make it more intuitive for a car driver, and adding fly by wire. Plus with that scheme it would be relatively easy to offer a version that flies like a regular helicopter for regular helicopter pilots.

Anyway: my two cents on a cyclic-free VTOL vehicle with a single main rotor. With the rotor head assembly being simplified, I think that could make it easier to build a coaxial rotor configuration: this would have the advantage of improving top speed by eliminating retreating blade stall, and would allow for yaw control by using differential collective on the two rotors. Now all you need are pitch and roll. A single vertical-axis tail rotor can handle pitch, but for roll, I think the best solution would probably to put two tail rotors on a "T" shaped tail boom, and control roll by changing the pitch of the left and right tail rotors in opposite directions. It would have significantly less roll authority than pitch authority, but it might still work reasonably well.

#### henryk

##### Well-Known Member
-only NONSTATIONARY, NONLINEAR aerodynamic can solve this problem!

#### David liang

##### Active Member
To understand how an airplane wing or helicopter rotor or a wind turbine rotor or a bird wing generates a force from airflow, you should read Understanding Aerodynamics by Doug McLean.

BJC
I think the orthodox aerodynamic theory has been unable to account for the flapping wings of birds and insects. So I thought a different principle.

#### David liang

##### Active Member
I think there is a confusion about the terms "lift" and "drag". Anything desirable falls under 'lift' even if it's created by air impacting the wing or blade from the underside (along with other phenomena).
Sorry to make it short, but that's my first impression.
I agree with the confusion about the terms "lift" and "drag".
However still I haven't found more suitable terms.
These terms come from windturbines such as “lift-based windturbines” and “drag-based windturbines”

#### David liang

##### Active Member
What you propose works like an umbrella helicopter (0:55 in the video below).

It is a rare film! Thank you very much.

The umbrella helicopter and the other aircrafts in the film can fly theoretically, I think.
They didn’t fly because their wings and mechanics were too heavy.

#### David liang

##### Active Member
Insects use many tricks to make "negative pressure above the wings"*.
For example dragonflies slap the wings together at the top to make a negative pressure.

*call it lift or drag, it's just a force from changing pressures.

NASA presents that the lift force generated by "negative pressure" is incorrect.
NASA: https://www.grc.nasa.gov/www/k-12/airplane/wrong1.html

I agree with NASA. I think the theory of “clap and fling” is incorrect.
“Clap and fling” theory: http://homes.cs.washington.edu/~diorio/MURI2003/Publications/sane_review.pdf

#### David liang

##### Active Member
Lift is force perpendicular to the relative wind; drag is force parallel, and thrust is anti-parallel. Insects and birds take advantage of unsteady aerodynamics; this is well known. Check out the work of Ilan Kroo's group at Stanford.

Spiders' ballooning uses drag-based aerodynamics. Check it out!

I have read Ilan Kroo's works. Their insect-scale flying robots are excellent.
But they don’t do much on the flapping wing flight principle

#### David liang

##### Active Member
Helicopter books often call the vertical force from the rotor thrust.

I think the rotor thrust of helicopters is the same as the propeller thrust of airplanes.

A fixed wing can amplify the lift force as a level.
A small force can move a heaver object by using a lever.

A small engine can fly an large aircraft by using a large wing.
The man-powered aircraft must use a very large wing to amplify the lift force.

But an aircraft with too large wings isn’t efficient.

#### David liang

##### Active Member
Your theory is correct and you have done some nice work. You may find an application where it will be useful.

However, for conventional human flight the power requirements will be very large and efficiency very poor. The concept of the wing is similar to that of an inclined plane. That is lifting a large load (lift force) with a small thrust (equal to the drag force). If the equivalent airplane has a 10 to one glide ratio (L/D) your flyer would require ten times or greater power. Greater because there is also considerable drag on the upstroke. Furthermore, the airplane can glide to a power off landing while your proposal would fall out of the sky like a heavy parachute.

It would work in water where the fluid forces are much greater and flotation can assist or in very small insects where scale effects make floating in air much easier as with a speck of dust.
Hi, jedi,
Thank you very much. I’m so glad you agree with me.

I have design a quiet radio-controlled ornithopter based on the drag-wings. This ornithopter will fly like a bird with very low noise.

Quadrotors are very noise. For some specific purposes, such as military purposes, the low noise is important. The quiet radio-controlled ornithopter will have military uses.

I think the fixed wing is like a level; it can amplify the lift force, but cannot amplify the efficiency.

An aircraft with a large wing can use a small engine, but an aircraft with a small wing must use a large engine. The man-powered aircraft uses a very large wing to amplify the lift force, but its efficiency is very poor.

I think the flapping wing will be more efficient. Birds don’t eat too much, but some birds can fly several thousand miles nonstop on their migrations.

Some research shows that the flapping wing can save up to 27% of the aerodynamic power required by the fixed wing.
http://ijetch.org/papers/686-W10020.pdf
http://dragonfly.tam.cornell.edu/publications/2009_09_11_PRL_Pesevento_Wang.pdf

Your suggestion “It works in water”. This is a very nice idea.
I’ll consider it. Thank you very much.