Airplanes with flat plate wings

Over in RCGroups, there are a whole raft of depron planes that use
flat-pate wings (as opposed to the traditional rib/spar style of
construction.)
I am looking at doing a design for a pusher and am thinking about going
to a balsa flat plate for the main wing.
Is there anything that I shoulde be consering besides using C-grain to
minimalize twist?
At which point should I be considering strengthening measures such as
fibreglass/strapping tape, basswood inserts or CF tubing to give a spar
equivalence?
For those who have built balsa flat plate wings, just how big did you
go? I'm currently looking at a 32-inch wingspan.
Thanks in advance!
Oh yes, the big question: WHY? 1) this is a quick-and-dirty design to
prove the concept. 2) I'm absolutely lousy at cutting ribs.
Reply to
byrocat
Loading thread data ...
"byrocat" wrote in news:1134597183.508269.311900 @o13g2000cwo.googlegroups.com:
I've done a number (maybe 10) of R/C planes with sheet wings. Most of them were cambered, but a few were not. For all except a few low aspect- ratio planes, wing twist was a very real problem.
So, unless it's going to be very small, low aspect, or thick wood, assume that twist will be an issue. Flat wings will have flexing problems, too.
I generally used 1/16 or 3/32 sheet, but I've gone to 1/8 in some cases.
If it's a monoplane, can you add some struts? Far more effective. If it's a biplane, you can put in some interplane struts that will solve a lot of problems.
Whuf! None of mine have been that big. My biggest was a 28" disk powered by a .25. For more conventional layouts, I've had a few electric biplanes at around 20" span top & bottom, and I'm flying a cute little monoplane profile that's 24". Those were all cambered, though.
I think I've only built 2 flat plates, and I think both were around 20" span.
Be aware that flat-plate airfoils have some unpleasant characteristics. The foamies typically get through it by being ludicrously overpowered and using the wing more like a big horizontal fin.
Reply to
Mark Miller
Hi, care to elaborate on this. I have seen designs for flat wings (just a little bit of shaping.. maybe 1/4 inch balsa). I have thought about making one just for a `knockabout' model. Maybe 30 inch or so wingspan and possibly a .15 glow. I would appreciate comments on adverse aspects before finding out the hard way !
Reg
Reply to
tux_powered
| | | > | > Be aware that flat-plate airfoils have some unpleasant characteristics. | | Hi, care to elaborate on this.
Mostly they're just less efficient than a proper airfoil. (But they do still generate lift -- just less of it. A tear-drop shape airfoil is not essential to flight.)
And if your wing is really flat, then there's no washout, so your plane is goign to be more likely to tip-stall.
And finally, it's trickier to make a flat wing strong, so they tend to twist and flex more, which often causes unpleasant characteristics.
Reply to
Doug McLaren
Not so much less efficient as they stall quicker. Just about anything with a sharp leading edge will have this property. Any wing with a sharp leading edge will have a narrower range of angles of attack over which it will not stall. Within this range they tend to be less draggy, but outside of it embarrassing things can happen.
The airfoils they used in the first airplanes (up to the 20's or so) had thin airfoils with sharp leading edges and significant camber. They'd give good characteristics at their design angle of attack, but they'd stall at either higher or lower angle of attacks -- on the low lift end they'd be draggy, and on the high lift end they'd let go with a bang.
This is probably part of the reason that you notice a tip stall with a flat-plate wing -- they just let go more suddenly, so it's going to be obvious compared to a wing with a big round leading edge.
Reply to
Tim Wescott
Hi Tim
It is a surprise that small ripples on the front edge lowers friction and increases possible wing angles of attack? I assume that it is valid for anything that was smooth and are supposed to go through air (like shark skin through water?):
formatting link
"... For low speed applications, such as method of transport (at a fraction of a Mach) that works well in all directions in the horizontal plane, the front-to-front airfoil shapes works best, with its rounded edges on both ends ... And the tiny ridges on the Frisbee's top surface introduce microscopic turbulence into the layer of air just above the label. Oddly enough, this turbulence helps to keep the upper airstream attached to the Frisbee, thereby allowing it to travel farther ..."
Skin of the Teeth:
formatting link
"...Thus, like a dimpled golf ball, a grooved Great White may glide farther on a given amount of energy than would a smooth one..."
regards,
Glenn
Reply to
Glenn Møller-Holst
Or free-flight model airplane wings, with turbulators? Or the turbulators on jet airliner wings?
Apparently by inducing an intense, small turbulence right at the surface of the wing the point where the flow separates into a big, billowy turbulence that creates the stall.
Reply to
Tim Wescott
Not true at all. Within the acceptable angles of attack a flat wing is a very efficient airfoil and provides lift in essentually the same amount as a more normal airfoil shape Regardless of the shape of the airfoil most of the lift results from all the air UNDER the horizontal line ahead of the leading edge (I am assuming we are talking level flight) that is deflected up and accelerated over the top of the foil. A flat airfoil deflects air from under the leading edge and accelerates it over the top very nicely.
Not true at all. A flat foil has a narrower acceptable angle of attack then a more conventionally shaped airfoil. Exceed that angle of attack and the airstream detaches abruptly over the whole foil with loss of lift. The detachment of air on a flat foil is more abrupt over the whole surface then for a more standard shape. I have never once built in any washout in any plane I have built with standard airfoils and tip stalls are exactly zero problem. After all, I have no reason to want to make a wing that will stall worse inverted then it does upright. Build in outwash and that is what you are doing. The exception would be if you are specifically designing a plane for flat spins of course.
Mostly true and the actual reason most model foils are not flat. The weakness of a flat foil is mainly in the twisting moment. When you get a flat foil too long the tips will start to twist up and down. Just like flutter on any other surface. This twisting can cause alternatively the top and bottom of the foil to stall suddenly which drives the twisting even further with the result of loss of control or actual breakage of the foil. This stall induced flutter does happen first at the tip because that is where the twist is the very worst. If that is what you are calling a tip stall I guess I will say they do tip stall worse then a normal foil. But that is distinctly different then what the aviation industry calls a tip stall. The faster you go the worse this gets in far more then linear relation to speed. Also the faster you go the narrower the acceptable range of angle of attack. So you could have a nice flying plane at 3/4 throttle that would destroy itself at full throttle. Just like aileron flutter on a goldberg tiger in a dive. Rips the control surface right off the plane no matter what hinges you use if you follow the construction methods that goldberg suggets. It would be fairly hard to design a model where flex was the main problem and still have a plane you could get off the ground. You would need to have a pretty extreme span to chord ratio to ever get real flex problems.
An excellent compromise between the ease of flat and the building pain of a standard foil is something like a diamond shape. In the case of a flat bottom wing it would be a triangle shape. Just a flat bottom and two flat top surfaces. The front flat top surface would angle up to the point of max thickness on a more normal foil shape. The rear flat top surface would angle down from that point to the trailing edge. For peak lift the max thickness should be about 11% of the chord the same as a normal foil shape. This gives all straight cuts on the ribs and all sheeting is flat. Easy to build and almost as strong as a normal foil shape and way stronger then you need in any case. This will also widen out the acceptable angle of attack compared to a flat foil to very nearly the same as a normal foil shape. It will obviously give the wing the resistance to twist to get rid of that problem.
If you do this get ready for every expert at the field to have a fun day picking on you for being such an ignorant fool. Just recognize they are the same people who put pusher props on backwards and can not figure out why the thing blows air like crazy but will not even taxi down the runway at full throttle.
Reply to
bm459
| Doug McLaren wrote:
| > Mostly they're just less efficient than a proper airfoil. (But they | > do still generate lift -- just less of it. A tear-drop shape airfoil | > is not essential to flight.) | | Not true at all
`Not true at all' = it's all untrue?
| Within the acceptable angles of attack a flat wing is | a very efficient airfoil and provides lift in essentually the same | amount as a more normal airfoil shape.
I should have been more precise -- it's not so much that lift is reduced, it's that the L/D ratio (lift to drag) ratio is lower.
| Regardless of the shape of the airfoil most of the lift results from | all the air UNDER the horizontal line ahead of the leading edge
Actually, both the upper and lower surfaces of a wing contribute to the turning of the flow of a gas (which is what creates lift.)
formatting link
says this --
There is also an incorrect theory which uses Newton's third law applied to the bottom surface of a wing. This theory equates aerodynamic lift to a stone skipping across the water. It neglects the physical reality that both the lower and upper surface of a wing contribute to the turning of a flow of gas.
formatting link
also talks about how both the top and the bottom of an airfoil are involved in creating lift.
| (I am assuming we are talking level flight)
`Level flight' doesn't really mean much when you're looking at aerodynamics. It's all about airspeed and angle of attack. The airfoil doesn't care if your plane is going up or down -- all it cares about is airspeed and angle of attack.
| that is deflected up and accelerated over the top of the foil. | A flat airfoil deflects air from under the leading edge and accelerates | it over the top very nicely.
Yes it does. It just creates more drag as it does so, especially as the angle of attack increases.
| > And if your wing is really flat, then there's no washout, so your | > plane is goign to be more likely to tip-stall. | | Not true at all.
You keep saying that. I don't think it means what you think it means ... unless you really are saying that a perfectly flat wing does have washout, or that a plane without a tear-drop shaped airfoil can't fly?
| A flat foil has a narrower acceptable angle of attack then a more | conventionally shaped airfoil.
That much is true, and it's why planes meant to be aerobatic have very thick airfoils.
| Exceed that angle of attack and the airstream detaches abruptly over | the whole foil with loss of lift.
Yes, we've heard of stalls before.
| I have never once built in any washout in any plane I have built | with standard airfoils and tip stalls are exactly zero problem. | After all, I have no reason to want to make a wing that will stall | worse inverted then it does upright.
Yes, you do not generally want washout in a plane that is supposed to fly inverted. But most planes are built to fly right side up, and if your plane is not meant to ever fly inverted, then a little washout is probably a good thing.
| > And finally, it's trickier to make a flat wing strong, so they tend to | > twist and flex more, which often causes unpleasant characteristics. | | Mostly true and the actual reason most model foils are not flat.
Well, that and 1) the flat wing being less efficient and 2) it will permit a smaller angle of attack before stalling. In the case of glow powered models, the strength issue may be the biggest issue, but in the case of gliders, efficiency is far more important than it is in the overpowered glow planes.
formatting link
also mentions that flat wings create lift as well, but mentions that they create more turbulence, and creating turbulence is just another way of creating drag.
formatting link
it well too.
| An excellent compromise between the ease of flat and the building pain | of a standard foil is something like a diamond shape.
Probably true. The SPAD people do this often, since it's easy to make a SPAD wing like that.
| If you do this get ready for every expert at the field to have a fun | day picking on you for being such an ignorant fool.
Are you talking to me or the original poster?
Who cares what the `experts' say? They can all talk about why his plane won't fly, and while they're doing that, he can actually fly it.
Reply to
Doug McLaren
snipped-for-privacy@scn.org wrote in news: snipped-for-privacy@z14g2000cwz.googlegroups.com:
I really should stay out of this, and I'm going to be away from my computer for the next couple weeks so I'll have to miss the rest of the lively debate - but I don't think it's fair to say a flat plate generates "essentially the same amount" of lift or that it's "very efficient." If we use the Soartech data, for example, CLmax for the flat plate is around 0.7, and by that point the CD is up to 0.056. A Clark Y, which is about as normal as an airfoil gets, has a ClMax around 1.2, and its CD is only 0.03 at that point. So, the flat plate has only 60% as much lift and nearly twice the profile drag at its peak lift. At low Cl, say, 0.2, the flat plate has less drag than the Clark Y, but by 0.3 it's worse.
Depends on what you're flying, and how. If you're flying a racer that's normally flying at several times stall speed, then your CLs really will be that low and the flat plate probably looks good (although a NACA 0009 looks better). If you're flying something slower, then the flat plate won't be as attractive.
With badly overpowered models, the airfoil isn't as critical. Flat plates tend to have a vicious stall, though, because the leading edge is relatively sharp.
I snipped the remainder, but I will say that I'm not a big fan of diamond airfoils for subsonic aircraft. And I'm not a huge fan of them for supersonic aircraft, either, but I like the fact that they're so much easier to analyze.
Reply to
Mark Miller
Are turbulators and vortex generator not the same?
formatting link
formatting link
Glenn
Reply to
Glenn Møller-Holst
I always thought that turbulators were used along the upper leading edge portion of the wing to create additional life at low speeds and to forestall the stall.
I've heard of trying to prevent vortex formation, or minimize same, at the wing tips. It reduces drag. Is there another application that I am not aware of (it could happen).
SB
Reply to
Seezerblue
I believe they do the same thing, at least -- I used 'turbulator' for jet wings because I couldn't remember 'vortex generator'.
Reply to
Tim Wescott
The wikipedia entries look good; they resemble what I've seen elsewhere.
The intentional vortecies generated by turbulators and their like are small and stuck to the wing surface, and are meant to keep the flow along the wing. The vortecies generated by wingtips are big, unattached to anything, and draggy -- to the point where they can be the major contributor to drag at high angles of attack.
Reply to
Tim Wescott
Elaborate they did ! Thanks for all the information guys. There are a number of web sites quoted that I will go read for myself. I have read a couple of articles where the author was a fan of flat plate wings, well maybe 1/4 to 3/8 inch balsa, slightly shaped. These were used on electric models and would probably have been used at reasonably fast flying speeds. The attraction, at first glance, is the simplicity of producing a wing like that. I thought about using the idea for a simple, cheap and quick to make knockabout model with a small glow. Guess I will probably take the time to make a wing with a proper airfoil. Trouble is I am busy with a couple of big wings with Clark Y and SD7036 airfoils so was tempted to sidetrack into a small, quick project. The triangular shape may well be worth further thought...
Reg
Reply to
tux_powered
The PushyCat that was printed in QEFI 01/2005 (design by Ron Laden) has a 36-inch wingspan, flat plate wing composed of three sheets -- LE, TE and interior. The kicker is that both the LE and TE have a sinded profile on the top surface. Nothing fancy but the wing is a flat rhomboid shape when viewed from the side.
There is a design/build thread on RCGroups for the original plus umpteen-other personal builds. Design goes like grass through a goose, so there must be more than enough torsional strength.
Guess that I'll base the SAAB J-21 on the PushyCat for basic construction.
Lessee.... original was the Bob Violette BobCat, then the EDF e-Bobcat, the the PushyCat.... should this be called the Saab-cat? (GD&R)
Reply to
byrocat
I love it. Your answers are wonderfully correct. But just like the wonderfully correct answers you get when you call a computer help desk they are close to worthless. First of all you do not disclose either the reynolds number at which these Cl max were determined nor the aspect ratio of the foil tested. Very often the test conditions are such as to give results for an infinite aspect ratio. This is nice as time honored fudge factors can be easily applied to calculate the Cl for any given finite aspect ratio. But in the case of your numbers who knows? By going from a reynolds number you see with a rc model to one you see in full scale the Cl max can easily swing by .4 or .5. Actually your Clark Y number for Cl max is so miserably low I suspect it was for a model.
But why not try to raise the level of the conversation in this group from heresay to fact? In an attempt, which will likely be futile, I am going to quote from a college level text book. This text was written originally in german by Richard Von Mises. At the end of WWII he was one of the Germans the US imported to teach us what they had learned about aeronautics and give us a chance to catch up on the theory side. We installed him at Harvard University as a professor. His book was translated to english and used as the beginning text in teaching Aero E at Harvard as well as many other US universitys for many years. This book is also kind of the Aero E bible that all subsequent books on the topic use as the starting point before the author puts the information into his own style. The book is "Theory of Flight."
"For moderate values of the angle of incidence the lift coefficient is proportional to the angle of incidence alpha.
Cl = K x alpha
the factor of proportionality K depending mainly on the aspect ratio but being independant of the shape of the profile."
He then goes on for 40 pages expanding on this topic. I will summerize as briefly as I can.
First lets make sure everyone understands angle of incidence. This is not the same as angle of attack. Angle of incidence is defined as zero angle equals that angle at which the Cl is zero. One degree postive from that point is one degree of angle of incidence. In the case of a symmetrical foil like a flat plate the angle of incidence equals the angle of attack. In an unsymmetrical foil like a Clark Y the angle of incidence equals angle of attack plus five degrees.
Next Mises states that his rule is for small angles. His many illustrations show that small angles are angles from zero to roughly 7 or 8 degrees. These kinds of angles of incidence are the attitudes at which our planes fly probably 99% or more of the time. The highest angle you ever experience unless you are purposely doing stalls is during takeoff. I measure on some of my planes and I have a max rotation of only 7 or 8 degrees before the tail end of the fuse is on the ground. As I do not scrape the covering off the tail of the fuse nor grass stain it during takeoffs I do not think it is on the ground. So my actual rotations are less then that. Solidly in the range in which Von Mises states lift is independant of airfoil shape. A Clark Y is about 10 degrees of rotation short of stalling on such planes. So talking about Cl max is useless. You can not get there during takeoff.
Implicite in Von Mises discussion of this topic is the idea that his statement above applies to thin airfoils. A thin airfoil is one which is not more then say 13% max thickness relative to the chord. This covers flat plates, normal airfoils such as Clark Y or Eppler 168. It also covers some of the really weird looking extreme undercambers the Germans developed where max thickness is moved clear back to 50% of chord vs the more normal 30% of chord. It also covers an inverted Clark Y. It covers the diamond or triangle shaped foils. Like it or not Von Mises says all these foils produce the same lift if aspect ratio is held constant and angles of incidence are equal. And he is correct as shown by mountains of experimental evidence.
Also clearly stated in multiple place thru his book Von Mises makes it clear that he is confining his consideration to subsonic speeds. Corrections due to compression effects are nil below speeds of at least 400 miles per hour. I know of no RC planes that go this fast. It is possible on occasion that a prop tip can be driven this fast on a model. But I never suggested use of a flat plate for a prop.
Until you understand why this is so do not even think about what it is that actually causes lift.
My original statement that a flat plate was an efficient lift producer is fully supported by the above. It is just as good as a Clark Y in the envelope in which we fly the vast majority of the time.
I think the above addresses this incorrect thought.
Look I never said a flat plate was a great wing to chose did I? I simply said it was an efficient lift producer. Different foil shapes provide different shapes to the plot of Cl vs angle of attack at high angles, particularly past the stall angle. In some cases as you go past critical angle of attack the plot does not do much more the flatten and in other cases the Cl drops a bit and then declines at a slower rate. But just looking at Cl vs attack angle is misleading. Fully as important is the pitch moment at stall. If the pitch moment is in forward rotation the stall will be mean no matter what Cl does. Or if you put some reflex on the trailing edge the Cl can drop badly but the induced backward pitch moment compenstates nicely and can give a nice soft stall. Limiting your thinking to Cl behavior is limiting your understanding of the whole design process. By the way, it is perfectly easy to make a sharp leading edge and still keep the stall soft. Do not concentrate on only one factor when many impact the result.
Reply to
bm459
Not true at all = a zero test score if I being generous or a negative score for not only incorrect but also misleading information if I am being realistic.
I am not going to waste my time looking at your links. The internet is full of nonsense. Even NASA had pure nonsense about lift on their web site. You have in the past made it very clear you believe that lift is explained by downwash. You have also made it very clear you are not going to consider any other explanation as you are so smart that there simply is no way you could possibly be wrong. Well it is a free country. We have not passed any laws making it illegal to be stupid.
But that does not mean when you post drivel I am going to give you a free pass.
Of course the bottom surface of a wing is imporatant in redirecting air flow. If it were not there it would not be able to force all the air needed for lift over the top surface. Ever hear of viscosity?
Go learn about frames of reference.
Off topic drivel.
Irrelevant drivel by someone who has no technical understanding but thinks he does.
Totally incorrect drivel. Very thick airfoils say thickness equal to 20% of chord reduce lift and increase drag.
Points 1 and 2 are respectively incorrect and 2 irrelevant drivel by someone who thinks he understands a topic and in fact has just about zero actual knowledge.
If the shoe fits wear it.
Reply to
bm459
| > | Not true at all | > | > `Not true at all' = it's all untrue? | | Not true at all = a zero test score if I being generous or a negative | score for not only incorrect but also misleading information if I am | being realistic.
Fortunately, you're not in a position to grade any of my work.
| >
formatting link
| >
formatting link
| I am not going to waste my time looking at your links. The internet is | full of nonsense.
Of course. For example, your post is now available on the Internet.
It's also exceedingly arrogant to assume that everything on the Internet is nonsense. And yet you attempt to (later in the post) lecture me about being absolutely sure of myself?
| You have in the past made it very clear you believe that lift is | explained by downwash.
To be more precise, I don't belive that aerodynamic lift can exist without downwash.
If you can somehow create aerodynamic lift without creating downwash, and don't do this by applying creative definitions of the terms, then you have an _extremely_ bright future in front of you in fields like aerodynamics (of course), spacecraft propulsion and probably applications like perpetual motion machines. I am aware that Netwon's Third Law (and indeed any other scientific `law') is really just a theory and could be disproven at any time, but to do it on a macroscopic sacle at sub-relativisitic speeds would be quite extraordinary, and so I would require some extraordinary proof before I believed it to be disproven.
| You have also made it very clear you are not going to consider any | other explanation as you are so smart that there simply is no way | you could possibly be wrong.
You must have me confused with somebody else. I'm far more open to being convinced that I've been wrong on a certain issue than most people you'll find on Usenet, apparantly including yourself. However, it takes more than saying `you're wrong!' over and over.
| Of course the bottom surface of a wing is imporatant in redirecting air | flow. If it were not there it would not be able to force all the air | needed for lift over the top surface. Ever hear of viscosity?
Yes, I've heard of viscosity. Ever hear of brevity? It would have been much more concise for you to just say `yes, you're right'. If you wanted to be condescending about it, you could have added a `Everybody knows that.' or `Thank you, Captain Obvious!'
| > | (I am assuming we are talking level flight) | > | > `Level flight' doesn't really mean much when you're looking at | > aerodynamics. It's all about airspeed and angle of attack. The | > airfoil doesn't care if your plane is going up or down -- all it cares | > about is airspeed and angle of attack. | | Go learn about frames of reference.
Again, `you're right' would have worked just as well. I'm fully aware of what frames of reference are.
| > Yes it does. It just creates more drag as it does so, especially as | > the angle of attack increases. | | Off topic drivel.
?
| > | Not true at all. | > | > You keep saying that. I don't think it means what you think it means | > ... unless you really are saying that a perfectly flat wing does have | > washout, or that a plane without a tear-drop shaped airfoil can't fly? | | Irrelevant drivel by someone who has no technical understanding but | thinks he does.
Really, that point was more about language than technical details. You seem to have problems with both.
| > | A flat foil has a narrower acceptable angle of attack then a more | > | conventionally shaped airfoil. | > | > That much is true, and it's why planes meant to be aerobatic have very | > thick airfoils. | | Totally incorrect drivel. Very thick airfoils say thickness equal to | 20% of chord reduce lift and increase drag.
`Very thick' is relative, but if somebody is going to assign a qualitative figure to my quantitative assertion, it'll be me, not you.
You'll notice that a pylon racer or high performance glider typically has a much thinner wing than a 3D or fun-fly plane, and the reasons are not merely due to structural strength needs.
(Though a pylon racer doesn't really want an airfoil that is _too_ thin, because they do need to make tight turns too, and that's what thicker airfoils help with. As with many things, it's a series of tradeoffs.)
If I recall correctly, Martin Simon's Model Airplane Aerodynamics explains this in some detail if you want to read more. (Though it's really only relevant to this discussion in that a flat (and thin) wing is the most extreme example of a thin airfoil.)
| > Well, that and 1) the flat wing being less efficient and 2) it will | > permit a smaller angle of attack before stalling. In the case of glow | > powered models, the strength issue may be the biggest issue, but in the | > case of gliders, efficiency is far more important than it is in the | > overpowered glow planes. | | Points 1 and 2 are respectively incorrect and 2 irrelevant drivel by | someone who thinks he understands a topic and in fact has just about | zero actual knowledge.
Proof by repetition Otherwise known as the Bellman's proof: ``What I say three times is true.''
Other similar proof techniques can be found at
formatting link
| > | If you do this get ready for every expert at the field to have a fun | > | day picking on you for being such an ignorant fool. | > | > Are you talking to me or the original poster? | | If the shoe fits wear it.
I've got my own shoes, thanks. If you want to convince me that your shoes are superior to mine, you'll need to be a little more convincing than saying `drivel!' over and over or that `there's nonsense on the intraweb!'
Reply to
Doug McLaren
We're talking about experience with flat-plate wings and at what poin
should I consider going to imbedded spars and/or CF rod.
Why don't you two take this spitting-contest off-line since it's no descended to a level I don't want to waste my time reading.
Last warning, or I'll get this thread closed
-- byroca ----------------------------------------------------------------------- byrocat's Profile:
formatting link
this thread:
formatting link
Reply to
byrocat

PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.