Lifting Bodies Are More Than Just Another Pretty Shape - Opinions on Aircraft Design

Lifting Bodies Are More Than Just Another Pretty  Shape - Opinions on Aircraft Design

There are many ways to look at aircraft design. Most of which are field dependent, why design for supersonic flight if your device will never climb above 500'? It would be cool thought, right? I digress, if you are designing for normal flight regimes you will be operating at an altitude with an engine power curve which will vary by altitude and temperature. Now, if you are designing in other regimes, you need to know where you can get small performance boosts where they are available.

Managing wing thicknesses is and use the concept of "wing tip thrust". By making tip vortices more manageable there is a significant reduction in overall wing drag. This "free" reduction in drag is called "wing tip thrust". Like this, there is another simple idea to take into account. If you can design a fuselage that is not pressurized with an essentially flat belly, you can play some shape games. These shape games can effectively make a Clark-Y airfoil. Now it is more complicated than this, but if you begin your mental experiments from this perspective, you can eek out some under-represented performance.

But how do he do it? It is all in the magic. If lift is generated by circulation of a lift envelope, that is created by the difference in pressure created by fluid moving around a shape. Why not generate lift around your fuselage? It will not get you 25% of your lift... but if your fuselage planform area is 15% of your wing area and you can get 40% efficient lift out of minding your p's and q's you could be looking at 6% more total lift. Yeah, you are right, this is all pie in the sky stuff. However, if you could generate 2-3% more lift for the length of your flight, you could reduce the angle of attack on your wings and trim out your drag. Reducing your drag means that you use less energy in the case of electric or less fuel in the engine.

Less fuel means that you can carry more, or fly farther. Nice. 1-2% may not be a lot if you weigh 4oz. . However, if you are looking at varying wind conditions or being able to react to changing conditions and you can play some games about fuselage profiles. Why not, it is not really so hard to get as much as 5-6% out of playing your profiles against each other. That makes for a good amount more flight time in rc. Not the 7min guys, but as you go for 20min... you get 21min. Yeah, it does not sound like much, but if it makes your fun go for 22min... It will be worth it.

Why do I pick Clark-Y? They have flat bottoms, reasonable thickness and a fast taper to the trailing edge. Construction-wise they are easy to construct, because you can lay them on a table. Their CL/alpha is pretty steep, so 1-2deg can get you something and if you can play with what level is, you can get a fuselage angle of attack to a point where you can make some dividends. Most importantly is that they do not separate their boundary layer fast. Most designs will never get to a critical angle of attack, drag will eat you alive if you fly your fuselage at such a high angle of attack.

We make lots of 60" fuselages these days with a mean 12" beam. That gets us an additional 4-5lbs of lift at take off and 1-2 lbs at cruise. Nothing to write home about, NASA will never give me a Ph.D. for it, but it does get me lots of "clever"s and "I would not have thought of that"s. Pretty high praise in engineering circles.

Fuselage Design Schemes - Vertical Tails do not Make Your Ass End Look Better

Lots of things cross my mind when I start putting pen to paper on a new fuselage. Mostly, it is about needs to go inside, and then how to build it. Over the last few generations of this design, it has become clear that slow-speed, heavy lift (payload/fuselage <0.7) We start to see several key principles begin to precipitate. Today we will focus on the differences in aircraft balance schemes.

Aesthetically, I am not a vertical tail man. They are functional and in many designs they are necessary. My career began in the low-observability sphere. So a large perpendicular plate nailed to the end of your vehicle who is trying to hide invites bigger radar returns. In most of my training and experience, we get away from this with large sweep angle wings and oblique surfaces. Sometimes, these choices do impact performance. If you are working against sines of the angle, you will always have more surface area to get the same net effect.

Balancing the vertical surface weight and the total surface area is always a game. If you look through Jane's for modern high performance, low-observable aircraft, you will see a common theme of split tails. Two tails, let a designer get a net effect and still not have a large single vertical surface. Ok, yeah it weighs more sometimes this is necessary and even suggested.

These principles are not necessarily limited to high-performance  aircraft. Just trying to keep the sail-area down on the aircraft is important. Otherwise it is blown all over the sky like a potato chip in a hurricane. If you are trying to make a vehicle that can stay on station it is easy to fly a slow  constant angular speed turn with a bit of roll angle, rather than balancing a lot of rudder input and trying to fight the wind the whole time and flying search patterns. Sweep angle also lets designers move the center of pressure around for the wing alowing for different internal position management of work payloads.

Many designs on which I have worked use low angle wing tips instead of a vertical tail. Highy-swept low speed wings get most of their roll control from the wing sweep and large ailerons or spoilerons are goos at helping with pitch contro. One interesting solution is coined a "duckeron". I cannot vouch for the scientific nature of the name. A "duckeron" or even a "quackeron" is a surface that consists of a pair of  tip-mounted surfaces at the far end of each aieron. These surfaces open and increase the drag on the wing tip. This is a bit counter intuitive, unike spoilers which run along the span of the wing these are actuay on the trailing edge of the wing and allow for effective yaw control. Sweep helps increase the distance between the wing tip and the aircraft center of gravity. This is the moment arm distance used to calculate the force applied to yaw the aircraft.

It is a pretty clever idea and allows for reduced cross-section yaw control. On rc models and small UAVs the duckeron is a simple single-servo-per-side solution. Rather than only connecting a single surface to the servo arm, you use a pair of rods. As the arm swings pushing the rods away from the hing line opening the surfaces equally. However if there is a clearance issue, the ratio of the opening rates can be changed via a cam or simply varying the lengths of the rods. A shorter rod needs more arm sweep to move the surface through a given range. The air disruption over the wing would make the use of a spoiler less effective. There could be several reasons to use spoilers and ducks at the same time for different flight control cases.

You do have to take into account that the drag at the tip may be an unplanned load on your wing spar. One other kind of side-benefit of using ducks is that they act as airbrakes during landing, even as a counter-balancing yaw force during approach. As a counter-balance on approach you would pay a much steeper drag penalty than a rudder, but they woud be able to apply a much larger yaw force.

Wing Loading, Bah! Land It Like A Man! Full-Throttle and Nose Up!

Recently, we have heard lots of talk about our normally well loaded wings. The balsa versions of our planes work great, and have normal stall speeds around 15-20mph. That is great for normal flying. They are hybrid flying wings and should fly like a Dutch Roll resistant frisbee.

I have been building the carbon fiber and Aluminum versions. They are a bit heavier than we expected, but that is due to real materials. We certainly will take out some of the fat in future revisions, but I think that the issue here is approach speed. You bunch of sissy girls. These planes are UAS, unmanned means the computer should be doing the work to bring the plane in on glide path. I hope our spars are strong enough for the cut the power approach.

What the heck am I talking about? Nope, never been asked that in polite company either. Wing loading is a relative measure that comes out of the basic low-speed aerodynamics of any fixed-aircraft. In some ways, it is a measure of the relative performance of a device with respect to constant thrust. It is most easily expressed as the mass of the aircraft divided by the wing area.

This essentially describes how strong the pressure difference must be between the surfaces to keep the plane in the air. Considering that the higher the wing loading, the larger the drag due to lift turn will be. This will change the trim characteristics of the plane in cruise and require more thrust to keep the plane above stall. Any F-4 or F-15 driver will tell you that more thrust is the answer to everything.

"The critical limit for bird flight is about 5 lb/ft² (25 kg/m²)^[3]. An analysis of bird flight which looked at 138 species ranging in mass from 1x10^-2 to 10 kg, from small passerines to swans and cranes found wing loadings from about 1 to 20 kg/m^2[4]. The wing loadings of some of the lightest aircraft fall comfortably within this range. One typical hang-glider (see table) has a maximum wing loading of 6.3 kg/m², and an ultralight rigid glider^[5] 8.3 kg/m²." - wikipedia

The wing loading also changes the stall speed. If you have to use forward speed to generate enough lift for a given flight regime, you have to go faster to balance the weight of the aircraft with the lift generated. In a flying wing, you cannot just pick the nose up, roll control has to be gentle. The old adage "Little planes add flap, big planes add power" is our friend. If you were interested the effect of wing loading on stall speed is expressed as the following.

v^2 is the stall speed

g is the acceleration due to gravity

Ws is the wing loading, mass/wing area

rho is the density of air

CL is the coefficient of lift of the net wing

Another interesting equation, is the rate of climb. This is just a force balance between the net acceleration, lift generated and the weight of the device.

ac is the climbing acceleration

Ws is still the mass wing loading

vc is the new airspeed

rho is the density of the free stream air

CL is the coefficient of lift of the net wing

g is the acceleration due to gravity

The wing loading term is in the denominator, so if you want to climb faster you need to lower the wing loading, or increase speed. Increasing the speed is way more fun than having gossamer wings. More Power!

We are not so bad, we are in the 23-35 kg/m^2 range for our wing loading depending on the equipment load out. Less than a some gliders. We however, cannot skimp on pimping the power plant. As if we would do that.

Aircraft                Wing Loading (kg/sq m)
swan           10
Buzz Labs Schoolgirl UAV         23
Nieuport 17         38
Cessna 152         51
B-17                    190
F-104                  514
A380                  who cares, it is an airbus
B747                   740

We already know you can do your approach at a reasonable speed, but why? Sensible approaches are for people who do not think that 10 ft/s  sink rates are for roller coasters. Land It Like a Man, Full Throttle and Both Hands on the Stick. Or, just let the autopilot do it, it can tell how far it is from the ground and cut the power at stall two inches off the ground.

If the women don't find you handsome, they ought to find you handy!

Basic Quantities and Some Trigonometry

So You Want to Build a DIY Autopilot

Accelerations

One of the most important quantities for you to measure are accelerations. If your two or more-axis accelerometer is mounted along the traditional axes of the aircraft it will be the easiest to code for. The three traditional axes are:

• From the nose through the center of gravity on the line of symmetry, the Y-axis, roll
• From the center of gravity out of the fuselage toward the tip of the right wing, the X-axis, pitch
• From the center of gravity away from the earth, the Z-axis, yaw
  
     

Figure of Rigid Aircraft Axes

So, now for some basic Trigonometry, everyone remembers SOH CAH TOA.

In general, the following picture is true for a vehicle moving through space.

Figure of the Direction of the Force of Gravitation on a Body

As you can see from the image, the angle of pitch relative to the surface of the earth is the same angle offset of the weight vector relative to the z-axis in the body frame of reference. If we put our accelerometer so that one of its axes is parallel to the body's z-axis at its center of gravity we are measuring this offset vector. Which is really neat, because it means that we can express the angle of the body in level, non-accelerating motion as ratios of the accelerations

Pitch: 

The angle theta between the actual gravity vector and the measured gravity is related to the pitch of the aircraft (pitch = theta + 90°). If we know theta, we know our pitch! Since we know the magnitude of the earth’s gravity, simple calculus gives us our pitch angle:

accelerometer = cos (theta) * gravity

theta = acos (accelerometer / gravity)

And since pitch = theta + 90°

pitch = asin (accelerometer / gravity)

Woot, we calculated the pitch orientation of our airplane using an accelerometer. Pretty easy, huh?

The real formula that we need to use for the software looks like this:

pitch = atan2(accelerometer / gravity, z / gravity)

Common piezo-electric accelerometers return in units of, g, 32.17 ft/s^2 or 9.81 m/s^2. We also know some more things about the flight that let us calculate the angles relative to the ground. More on this later, it is a bit more than basic trigonometry to describe. These equations assume non-accelerating flight. You can use a magnetometer to get the relative plane in space with less math, but magnetometers generally take more interface programming in my experience.

Roll:

Roll needs a second accelerometer with an axis perpendicular to the first so that we can figure out the resultant vector between them and then the angle. Essentially the vector between the accelerometers becomes the "gravitational" acceleration and the relative readings lets us calculate the angle with an atan2 function. The second accelerometer will have some other things to manage such as the effects of the distance between them on the accelerations measured. Physics fun and none of the boring class.

Yaw:

Yaw is the hardest of the angles to measure. The only answer is to use a magnetometer or a compass. In many ways, yaw can be solved by dead reckoning. Dead reckoning is all that is important for most of the projects in the DIY garage. They will be covered later.

Next we will discuss gyroscopes and the beauty of rates and integral calculus