OK, on to the fuselage, which is unfortunately something that needs to be fitted to the pilot. Me, I'm rather tall, so you may benefit from a lower-slung wing and a slightly lower tail. These modifications are measured in inches, but I can easily imagine the difference between a large and a small version to be as much as a foot. I plan to build the fuselage pilot cage and modify it until it fits my leg length and torso height, then build the tail feathers and mount the engine, and only then position the wings.
They say the center of lift of the wing is at about the 25% point back from the wing leading edge, and we need the center of mass to be below this and perhaps a bit forward. IMPORTANT: The elevator will be a down-flying design, the airflow pushing the tail down, lifting the heavier nose up. This gives us pitch stability. At slow airspeed the elevator will not be as efficient, the nose will drop, the aircraft will decrease altitude and gain airspeed; as the speed increases the elevator will push down, lifting the nose to level flight. We certainly don't want it the other way around. Notice geese have a long neck that gives greater weight to the front of the flying structure; in flight they stick their necks out forward to gain this balanced condition.
This makes the balance of the aircraft complicated, especially when our undefined engine could range from the 10HP DL-100 with a pull start at a mass of about 3kg to the 28HP F-33 with electric start but weighing about 22Kg. We won't be able to swap from one engine to the other without changing the wing position, or mounting the lighter engine much further forward.
The best place I can think of for the fuel is directly behind the pilot seat, and not for safety reasons... As the fuel depletes the aircraft weight will lower, but the center of gravity will move forward. Keeping the gas as close to the center of mass is important, but I can't imagine it being in the pilot's lap. Wing tanks seem too complicated, and we need to be able to easily prove the 5 gallon max fuel capacity to an FAA official.
The fuselage, from what I can tell, brings the airplane together. We have wings that provide the only lift, so while we're in flight the entire weight of the airplane and pilot (minus the wing weight) must be supported by the connections between the wings and the fuselage. In this design there are four connection points for each wing, two from the leading edge spar and two from the trailing edge spar. The leading edge will carry the larger share of the load. These load points for each wing are: leading edge root, trailing edge root, leading edge strut and trailing edge strut. The two struts are terminated at essentially the same point, to the bottom rear of the pilot cage, on each side of the airplane. The wing root connections are to the upper edge of the pilot cage, one in front the other in back.
The frame can be divided into three sections: Engine mount and covering, pilot cage and tail section. In the Flying Machine, the pilot cage is built around the pilot's dimensions, with a seat that leans against the back of the pilot cage and a rudder pedal area that extends toward the engine, to which is added a crappy firewall and engine mounts out front, and a tail section that is tacked onto the rear. The most serious stresses are between the wing and the cage, the tail and the cage, the engine and the cage, and maybe the worst: the landing gear and the cage.
When the aircraft lands the impact can be significant, yet we don't want the airplane to be damaged. The landing gear should have brakes connected to toe brake pedals on the rudder pedals, which is a somewhat complicated configuration but very nice feature when landing. A few sources would be Air-Tech or Grove Aircraft Company. The biggest problem I'm encountering is the suspension system. Grove Aircraft offers landing gear that is heavy and expensive, but can take a real pounding. See this video. Both aluminum and steel have to be very strong to take such a flexure, and the resulting assemblies are heavy. The Grove gear is made from bent 7075-T6 aluminum, which must be bent in the fully annealed condition and then re-hardened to obtain the required strength. Still, the aluminum is massive, probably as much as 12 pounds for this application, and expensive, probably on the order of $1000. I've considered actually finding a way to build a set on a reduced scale, but the material cost, the bending and the hardening processes are clear complications.
Alternatively, I like the scheme illustrated on the previous page, which I'll copy here:
The wheel axle mounting is welded to a Chromalloy tube that pivots at the same general point where the wing struts terminate, at the bottom rear of the pilot cage, holding the aircraft to the ground through compliant tires. Another Chromalloy tube comes forward from the gear axle to a pivot point at the front of the cage. Finally, a gas spring connects the gear to the upper rear of the pilot cage through tubing that is pivoted at both ends. This structure gives good support to the gear in the aircraft's axial and lateral directions, while allowing about 10" of vertical gear compliance through the gas spring.
Gas springs are ubiquitous, but getting details on them is frustratingly difficult. A gas spring is simply a piston connected to a rod, inserted into a piece of thin-walled tubing that is filled with pressurized nitrogen. The piston seal is assisted by the addition of a small quantity of oil, and if the spring is kept rod end down, the gas will supposedly stay put for years. Springs that can take a reasonable load, say 250 pounds, are not light when made from steel or even aluminum, but a 1" piston pushing against 320 PSI of gas does the job well. If this can be fitted to our airplane, we will have a really light and efficient suspension system.
One would assume that the force on the piston would increase as the gas is compressed, providing an ever-increasing force as the piston closes down on the limited gas volume, but manufacturers seem to tout just how much their springs are 'constant force', which seem ridiculous, in that there doesn't seem to be enough volume within the spring structure to contain a sufficient excess volume of gas. -This I will have to research upon my return to civilization. Perhaps I can obtain a source for standard gas shocks, say, McMaster-Carr, take one apart and figure out how to add pressure as I like until the strength is what I need. Then again, if you wake up one morning with the urge to go flying and find the Flying Machine limp on one side, it will take a cylinder of N2 to get it back up... I'll bet your shop air compressor won't go to 300PSI.
The construction of the tail appendage could be done with wood, but I see no way around using Chromalloy tube for the pilot cage. Dimensions, weights and costs of 4130 tubing can be found here. Welding is an issue of cost, not talent. I have a cheap TIG welder that cost about $1200, and in a few hours I was welding up all kinds of things. Not that precision welding is easy, but doing things like the airframe should not be difficult. I like to lay in rather large puddles, making sure the metal is well melted into the joint. Chromalloy should be a bit tricky, but only with the very thin walled stuff that we will be using. Practice, practice, practice.
Notes On Mechanical Engineering:
In industry today you can spend a lot of time with very expensive software entering your mechanical design, then 'testing' it by pushing on it here and there, finding out where and how it bends and ultimately, how it breaks. This is very useful, but what you learn from it depends on how you 'test' it. How do you evaluate the pressure of wind against your wing? What unexpected forces could be brought to bear on your craft that would destroy it? Although you can engineer something with the best of skill and intent, it only matters when the design hits the real world. At some point you have to build it and fly it. Without these expensive and time consuming tools we can still design an aircraft, and if we are careful modifying the design as we proceed, learning along the way, we will possibly have a better product.
When it comes to constructions of tubing, we can say a few things that are very important to design. First of all, the tubing is very strong in tension and compression but fairly weak in bending. This is why tubing constructions are often made of triangles:
In A, the applied side force is transferred to the left leg as a compression force, and to the right leg as a tension force. In B, the vertical legs bend, which will cause severe stress at the corner joints and leave the structure much more 'flimsy'. In C, we have added a diagonal brace, turning the square shape into two triangles, one of which couples the forces much the same as in A.
Tubing in tension is very strong. The tensile strength of 4130 is nearly 100,000 psi, so calculating the cross sectional area of the tubing will give the breaking point, but the tubing will permanently deform at a lower tension, somewhere around 75,000 PSI. 4130 is tough, in that it will deform significantly before it breaks, absorbing impact energy in the process. Perhaps you should design around half these stress values, assuming applied forces that are beyond your expectations. In compression however, especially as the tubing becomes long, the safely applied values are much lower than what you may expect, because if the tube is bent, even ever-so-slightly, it will bend further under compression and collapse. See here for details. Tubes in compression must be larger in diameter to remain stiff against bending, and such sections should be as short as possible. In tension, a thin walled, large diameter tube may be equivalent to a small diameter, thick walled tube, but in compression, the larger diameter with a thin wall is preferred.
4130 can be welded with low carbon filler material; don't go looking for 4130 filler, you probably won't find it. It has been suggested that welded joints be 'stress relieved', which simply means heating the entire joint uniformly with your torch to orange-yellow after finishing the joint, and allowing to cool slowly.
Update on landing gear:
Thinking about tubing in compression and our landing gear with gas springs, I really have to drop back to a firmer, simpler and possibly lighter solution. We could mount slightly larger tires, maybe 18" diameter, on axles that are connected to each other and the pilot cage through a piece of tubing.
Although the main gear crossbar will be subject to bending, this is exactly what we want for "springiness", and the larger diameter tires (18") give us some 'gas spring' action too. This scheme sets us 4" closer to the ground, which will make crawling into the Flying Machine yet more difficult...
We will need a good start on selecting the main gear spring tubing so let's look at bending properties. There's a program on the internet called BeamBoy that can be helpful, download it from this page. I tried a 4" wide by 0.5" thick aluminum beam (emod=10,000,000PSI), 40 inches long, supported at one end and in the center, with a 200 pound load on the far end. This is to simulate the bar being held to the lower edge of the pilot cage in two places, with the free end able to take the load (one tire). The plot showed the peak stress on the bar was about 24,000 PSI (which is 1/3rd the yield point of 7075-T6), and the deflection at the tire connection was 2.5" Also, that the peak stress was at the center mounting point, and decreases linearly out to the ends of the bar. This indicates to me that a single bar of 7075-T6, perhaps 6" wide could be used, with tapering to distribute the stress more evenly across the entire bar; this way the flexure occurs over a wider area rather than just at the support points. This is good, because I should be able to assemble the spring out of a single bar of 7075, shaped something like this:
This one is 64" long, flat, out of 6" x 0.5" 7075-T6 material. It has holes in the ends to engage plates to which the axles are fitted. The fat areas toward the center are intended to be clamped to the airplane undercarriage and are wider at the semicircular attachment points. There will not be bolt holes for attachment, because this is where the stress is the greatest; I'm hoping these radiused cutouts will do. Also, where the tips enter the wider areas for connection to the axle plates, a generous radius is applied, to minimize any concentration of stress. Online metals offers a 6' chunk for $148, but this is only 4" wide. Here, I found a 6" wide piece in 6061 for only $57, heat treated to T6. This I can grind away on with my power hack saw and smooth out with a sander. That, and we don't need to anneal, bend and re-harden (hopefully)! In fact, we may have enough spring to this that we can go back to the smaller 12" wheels, because our gear is now supported by axle blocks. The axle blocks by the way, may need to be slightly tapered, so that the aircraft (with pilot) has its wheels squarely against the tarmac. Unfortunately, I calculate a weight of about 14 pounds at 0.1 lb/cu in for aluminum. Still, this does give us our springs, protecting the aircraft from damaging accelerations during landing and ground maneuvers, and its a bit of work, but cheap.
Finally, we can pull in the wheels to a 5 foot center spacing and get away with a lighter aluminum bar. Here we can order a chunk of half inch 7075 for about $100, and hack it into shape. This may be the best solution, getting the weight down below 10 lbs.
Actually, working with BeamBoy, it doesn't seem to matter whether you use steel, aluminum or a wood 2x6, the weight for a given deflection and load (appropriate for the material) all come out to approximately the same weight, 10 to 15 pounds!
Don't quite know where to go next, still uncomfortable with such heavy landing gear. We have the frame, the tail, the controls, and then the details which need to be left until after building is complete. We can't do the controls until we have the tail, and we need to know what the tail is so we can allow for it in the frame. So, on to the dreaded tail feathers:
I'm not comfortable here, because the wing seems so essential in an obvious sense, but the tail, despite it's lower weight and size, is just as important to flying. Also, I think we will want large movable surfaces so that we have as much slow-flight control as possible, and hinging large surfaces makes me uncomfortable. A bad mistake made here, and the tail could break off in flight! We need a down flying elevator with a large control surface, and a vertical stabilizer with a large rudder surface.
Judging from other aircraft, the tail may be made smaller by extending the frame so that the tail is on a longer lever arm, but I like the Flying Machine as a small thing, and excessive length is as ugly to me as a 30 foot wingspan. This means the tail surfaces will need to be large. I've drawn the elevator as 6 feet by 2 1/2 feet, with half of this as the controllable surface. The stabilizer can be sloped at the front and stand 2.5 feet off the elevator.
I am worried about airflow over the tail at high angles of attack, which will hopefully be the aircraft attitude during take off climb-out. If the wake of the wing is a turbulent mess, as opposed to a nice clean airflow, then the tail will have less affect on the aircraft attitude. Notice the tail is set high; when the craft is on the ground the elevator is at about the same level as the wing. In normal flight the downwash from the wing trailing edge should avoid the tail, but at high angles of attack and the upper surface of the wing beginning to stall, we may have a problem. Also, the tail is set high so that we can come in for landing at an extreme angle, getting as much lift as possible from our complicated wing, landing on the main gear without banging the tail on the runway.
My concerns have caused me to enlarge the elevator to 6' x 3', and I'm considering a full rudder as a vertical stabilizer. The advantage of the full rudder is that it has extreme control over the aircraft's yaw, but must be supported by bearings at the frame only. If I build a strong vertical stabilizer, fixed to the frame, maybe reinforced with tubing, then I have a stable surface along which to hinge the rudder. Perhaps a trade off can be made, a small vertical stabilizer, reinforced with tubing, from which is mounted the rather large rudder.
My first impulse is to make these surfaces detachable, built as independent elements. This allows for example, the adjustment of the angle of attack of the elevator later, during preliminary flight tests.
After considerable wrangling with dimensions, I now feel like I'm about to climb into an airplane that will stall on take off and go nose first into the dirt. The elevator has everything to do with overcoming pitch imbalance, and I don't know how to model the wing's center of lift! If the CG of the craft is way off from the CL, then the only way the airplane can sustain flight is with lots of power and a really effective elevator, which I might not have here... Either we do some scaled down experiments or make the elevator over-sized to get us into the air with confidence.
Had some time tonight during a barbeque to speak with a PhD in mechanical engineering who helped me better understand metallurgy. I also took advantage of a rather large fan to imagine wind tunnel tests. This was very disturbing; the exit of a common fan is really turbulent. If we need a wind tunnel to gain confidence in the basic design, we'll need to build one. So I research wind tunnels.
The Wright brothers were not just bicycle hacks that happened to build an airplane, they were researchers. There are many references to this, a good start is here. Apparently they were able to test hundreds of airfoils, evaluating them for lift and drag, and even with their crude instrumentation the results were quite accurate. One important aspect of a wind tunnel is a zone of fins that take the turbulent air from a fan and straighten it out to a nice smooth flow. The Wright brothers used a gasoline engine in their setup, despite the photo of an electric motor, they had no electricity in their shop. Wilbur claimed that they took the engine off of a lathe. I consider a wind tunnel, but I realize this will put me back 2 weeks and maybe a few hundred bucks. On the other hand, maybe I can calculate these things... After all, we're not in the pre-flight era now, we have plenty of airfoils that are known to work, and ours is strikingly familiar.
So I take a closer look at my design, assigning weights to the various components, like the pilot, the engine, the fuel, etc., and positions for center of mass for each. Whoops! -The combined center of mass is about 15" aft of the center of lift, which is assumed to be at the 25% of chord location on the wing. My initial worry was that the tail wouldn't have sufficient control over attitude, but now I'm much more concerned about just getting static stability! After the exercise though, I think the tail is OK in terms of its ability to provide torque in pitch, but we do need to do a more detailed balance evaluation, and certainly move the mass forward which means moving the wing back. Moving the wing back means moving the tail back too. How do we keep this thing compact?
Further, we need to keep the tail really light, because with the wing moved rearwards, the machine is dangerously on the edge of being able to tilt backwards on its main gear, coming to rest on it's tail. With a pilot in place this will not be the case, but I would really like the Flying Machine to always sit upright and proud when empty.
Having other thoughts about the whole design... Simple paper airplanes I've made did benefit from a down-flying tail with the CG definitely forward of the wing center of lift, but there's a certain inefficiency with this design; as a model airplane, this would allow the craft to 'find' a level flight attitude at a certain constant speed. Chris Heintz made the CH-701 with a down flying tail, and I immediately understood this from my experience, but then again, what if the tail provided lift? Wouldn't an aircraft, already deficient in wing area, benefit from a flying tail that helps support the tail and allow the CG to be aft of the main wing's center of lift?
I like this from a design perspective too, having the elevator 'right side up'. If the tail can support itself aerodynamically, then the flying CG is right about where it needs to be, with the wing in a comfortable position.
Bingo! the Flying Machine now has an up-flying tail, the main wing brought aft by 6", and a 24" space between the main wing flap trailing edge and the elevator leading edge. I like these simple numbers, but will it fly?
After much thinking over dinner, I'm now interested in a high T tail, to get the elevator out of the wing wash. Rudder not so important, as I expect the design to be symmetrical in yaw, but pitch is a potential problem. -Have no idea as to how this thing will be structured. I noticed over dinner that the table was exactly 6'x3', and it seemed really big. Leave it to tomorrow.
The high elevator, 'T' tail will require some pretty strong reinforcement to be solid, but I'm guessing the tubing is mighty stiff, and if we make the vertical stabilizer wide, maybe even 9" at the root, we can get the stiffness we need. New side view:
The tail does look pretty large...Way more 'wing' than we need for just lifting the tail section in flight, but that's our strategy, no? Also, the elevator doesn't have a slot, so how will it perform at the high angle of attack that we expect from the main wing? We could add a slot to the elevator, and ultimately make the whole structure smaller. As it stands here, the top of the elevator is 6.5' off the ground, and I'd like it to be 6' even... Then I can inspect the elevator hinges during preflight at eye level.
Yes! I like it.
Before I go much further, I suppose I need to talk with my life insurance agent. -The kids will want to know if the insurance will be in force when I perish in an ultralight accident; I'd like to think that they would miss their dad, but I know they would miss the money. Along those lines, I think about a word I've heard in conjunction with 'airplane', that is, 'spin'.
For a great set of videos, go here. Yes, airplanes can get into spin modes of flight, especially when one wing is stalled, the other is not, and the airplane is heading toward the ground at high speed. How's this? The plane is rotating like a maple seed, essentially around one wing. The outer wing has air flowing across it and lifts up, while the inside wing is stalled, more or less the center point of rotation, and falls from its weight. The procedure to get out of the stall depends on the aircraft, and if you don't know the procedure, you're dead. Normally the solution is to center the controls and apply strong rudder in the opposite direction to the spin. Sometimes abrupt forward stick (down elevator) is suggested, but are our tail feathers up to this degree of control? Scary. Somehow I feel the low aspect ratio of the wings and the short lever to the tail, all of those things that make the plane 'cute' also make it unsafe. ...
Today we travel back to the US and face the jetlag. Also, much to do before we leave.
It seems as though the spin recovery technique has everything to do with the tail section. Power to idle, elevator down to increase overall airspeed, hopefully taking the dropped wing out of stall, and reverse rudder to catch air at the tail, slowing the spin, ailerons neutral. Once the airspeed comes up and the rotating rate decreases we're in a deep dive that corrects itself due to both wings operating, whereupon we center the rudder and pull back slowly on the stick to get to cruise airspeed without tearing the wings off, trading altitude for airspeed. -The tail is what makes this spin recovery possible. I'll figure the tail area times it's moment arm to the CG is a value that we don't want to go below. Also, that we need a rudder that actually has an effect in this aircraft orientation, not just a little one that corrects for yaw in stable flight.
I've put the elevator high to get it out of the wing wash, but this is only while the craft is at a high angle of attack where the wing wash would possibly confuse the air over the tail. This is the attitude that would inspire a spin, approaching stall. With a high elevator, we need a strong support, which is the vertical tail that can't support the elevator if its all movable! -If the elevator was low, we could build a vertical stabilizer that rotates in its entirety, providing a more effective control surface.
I've noticed that the Piper PA-28 rolls toward the left at the peak of a stall, which makes sense; the prop is turning clockwise (from the pilot's view, a traditional direction) and the engine causes a counter-clockwise torque to the airframe. When the nose arcs over down, the gyroscopic action of the prop arcs us to the left in yaw, and we're into a left turning, nose down spin.
The prop torque that rolls us to the left does not cause the problem; since we have a straight wing, both wings are, at this point, equally efficient. It seems that the gyroscopic action of the prop that turns us in yaw to the left (as the nose falls) is what kills the airspeed on the inside wing and puts us in a spin... Too bad we can't reverse the engine direction and the prop pitch in flight, because that should solve the problem immediately. In fact, the instruction to lower engine speed to idle is a good one, because in large part, it is the prop (as a gyroscope) that keeps us in the spin. -I'll bet a right spin is easier to recover from in a traditional single engine airplane...
Our engine, a 2 stroke, has a rather narrow speed range, so in comparison to a 4 stroke with a lower idle speed, we're in a tougher position. Also, the ailerons won't have much effect; the stalled wing doesn't have the airflow to make it's aileron work, and the air over the wing that has some lift is spilling air out over its wingtip, not directly over its aileron. -Tough position; we probably shouldn't kill the engine, and short of putting airbrakes on the wings, we need a large tail on a long moment arm.
My guess is that large tail sections or little ones on long arms have more to do with spin recovery than flight control. So, how do we install a sufficiently large tail and keep the design 'cute'?
I think cuteness has to do with compactness, and its the long tail we want to avoid, not a large one. In fact, the tail can be scrunched even closer to the wing (I know, an even shorter lever arm), to retain cuteness. Also, the tail may be a bit lower, allowing a 20 degree angle of attack on landing rather than the current 30 degrees, giving more space for rudder area.
NASA produced a paper on spin, found here. This is for a low wing aircraft, but shows the complexity of the problem. This gives me a lot more confidence. The research indicates that a large broadside area of the fuselage is a good thing to resist spin, but the high tail is the best, in that a low elevator would shield the rudder in a spin condition. Unfortunately this was all done with a low wing design that has a pretty large wing aspect ratio (24' to 4'), whereas our design is 'chubby' in that respect. Also, their model wings didn't have slots, and slots have been indicated elsewhere to also be a good thing to resist spin. I'll bet that we can make the rudder larger, put the tail on top to 'catch' air coming up from below, and expect that a large broadside area to the whole plane will help. New, improved drawing:
Wow, the tail is huge, but because its stuck right up toward the the cabin, it's still kinda' cute. Well, I think so... Its not that the tail is stuck out on a long boom; certainly that would help. The objective here is to offer a lot of 'barn door' to the craft when winds blow from the side. Crosswind landings I can figure out, even land across the runway if needed, but to get caught in a stall-spin that you can't steer out of... Well, that's a more critical problem!
Maybe the forward tail supports could terminate even closer to the rear of the pilot box. I'll have to noodle this.
Next: Tail details