Very low aspect ratio planes?

[Norman]

So, if I understand correctly, instead of summing Y forces and using the resultant force to create a moment around the AC, we keep both Y+ and Y- components, and use that instead, now we always end up with a moment even with zero lift.

I think we're on the same page here. To get c.p. you sum all the pressure on the airfoil and divide that force by the observed moment at 1/4c. To get Cm you separate the pressure force on the top from the bottom and calculate the couple about the 1/4c. So Cm has 2 short real leaver arms and c.p. has one long imaginary arm.

And since both magnitude and chordwise position are moving depending on alpha, the moment at ac stays the same.

Both methods show the same data if that's what you mean by "stays the same". Cm is the product of those 2 short arms. c.p. is the product of taking the measured lift force and the measured moment and calculating the arm that would produce that moment.

Regarding the ac position, I finally found a paper explaining a method to find it in a manner I can understand:

View attachment 103136

My math skills and memory never were very good and have gone down the toilet with age so I put a simple little formula to find the actual AC in a spreadsheet years ago.

Would you say it looks right? If so, how do I know where on the x axis was Cm measurement taken, for instance on the graph below:

It used to be (before 1940) that different labs put their force balance pitch axis at different places but now the 1/4 chord point is standard. Computer programs should all use 1/4c.

View attachment 103137
The Cm value being all over the place means it's not Cm measured at the ac but at some other point, correct?

Cm is only constant in a small range of AoA, and boundary layer conditions can really obscure it. Often when the Cm over alpha graph looks like that it's because of a laminar separation bubble on the lower surface. Forcing transition at 75 or 80% on the lower surface will usually give a flatter curve as in the attached graph. Notice that the Cm at zero lift doesn't change much, if at all.

 

[Riggerrob]

Right, but in narrow-bodied planes it's usually easy to see the ground by looking down on either side of the engine, which you can't do in a facetmobile or verhees delta. Small twin engines does solve two other issues. Those being asymmetrical prop torque and engine cost.

Helicopters and competition aerobatic airplanes routinely have clear plastic windows in cockpit floors and lower side walls. Since the aerobats depend upon welded steel tubing for fuselage structure, windows have little to no effect on crash-worthiness.

... and I agree with Hesham that building a twin that cannot do a go-around on a single engine is "doing it the hard way."

 

[Riggerrob]

Dear nest of dragons,
Congratulations on using your university degree in "thinkology"#.
This proves that you are waaaaaaaay brighter than the diploma'd engineers who designed the failed A-12 navy plane.

The key advantage of your design is the inclusion of a front spar 1 foot or 1.5 feet deep just in front of the rudder pedals. This spar depth helps transfer lateral loads far more efficiently than the A-12.
When listening to Barnaby Wainfain's lecture on "The Seven Deadly Sins of Airplane Design" you will learn that A-12 designers depended upon the rear spar to transfer all span-wise loads. Since this required routing loads from one outboard leading edge, back to the rear spar, across the rear spar, then forwards to the other outboard leading-edge, they ended up with a long and heavy load path. A-12 could not use simple, full-depth, span-wise spars because its belly was riddled with holes for bomb-bays, wheel-wells and landing-gear retraction.

The second advantage of your design is that it depends upon tubes to carry structural loads, so cutting holes for windows makes little difference strength-wise.

 

[Arfang]

I think we're on the same page here. To get c.p. you sum all the pressure on the airfoil and divide that force by the observed moment at 1/4c. To get Cm you separate the pressure force on the top from the bottom and calculate the couple about the 1/4c. So Cm has 2 short real leaver arms and c.p. has one long imaginary arm.



Both methods show the same data if that's what you mean by "stays the same". Cm is the product of those 2 short arms. c.p. is the product of taking the measured lift force and the measured moment and calculating the arm that would produce that moment.





My math skills and memory never were very good and have gone down the toilet with age so I put a simple little formula to find the actual AC in a spreadsheet years ago.


It used to be (before 1940) that different labs put their force balance pitch axis at different places but now the 1/4 chord point is standard. Computer programs should all use 1/4c.



Cm is only constant in a small range of AoA, and boundary layer conditions can really obscure it. Often when the Cm over alpha graph looks like that it's because of a laminar separation bubble on the lower surface. Forcing transition at 75 or 80% on the lower surface will usually give a flatter curve as in the attached graph. Notice that the Cm at zero lift doesn't change much, if at all.
View attachment 103142

Your spreadsheet makes it a lot easier, now I'm going to learn how to analyze airfoils with XFLR5 and hopefully learn a lot more in the process. Thanks again!

 

[Arfang]

I’m no theorist, I build, fly and observe. My method is fraught with problems, there a many variables which effect the results, small differences in rigging and shape have a greater effect on a model, scale effect, surface roughness etc.. To really get very accurate results requires an accurate shape in a wind tunnel. Never the less I do get some pretty interesting results and a lot of entertainment.
As Norman has said the 2D predictions of airfoil performance pretty much apply to all wings irrespective of shape But as Zimmerman showed this does not apply universally at high alpha where certain shapes at very low aspect ratios continue to produce lift long after higher aspect planforms have stalled, there is a drag penalty to produce the lift, but if the craft is landing, drag is an acceptable trade off for a very low landing speed, stall and spin resistance

Thanks for your input. Any more advice you would like to share before I start experimenting with scale models?

 

[erkki67]

Just my idea about pilot position and overal view in very low aspect ratio.
Why not place a thicker root chord and get as much as possible the pilot inside the wing? Just put his eyeline over the wing-surface so he can see above the wing. Due to the pilot being mostly inside the wing, you only need to make the front transparent. Not really the underside.
About the spar. I came up with this (probably crazy) idea to create a struss spar in which a pilot can be seated in between. With a reinforcement between front and rear of rear besides the pilot, torsion might be no problem. Remember ... i am not a engineer. I am just guessing.
Here a draft (from the past) of a glider i drew in 3D using that idea.
View attachment 103139
View attachment 103140

And the engine in-front of the feet! I like it somehow!

 

[Sockmonkey]

Helicopters and competition aerobatic airplanes routinely have clear plastic windows in cockpit floors and lower side walls. Since the aerobats depend upon welded steel tubing for fuselage structure, windows have little to no effect on crash-worthiness.

... and I agree with Hesham that building a twin that cannot do a go-around on a single engine is "doing it the hard way."

A 20-30 hp ebgine is enough for a light airplane to maintain altitude, so a pair of them lets you throttle them back a little for cruise, which is what you want if you're using cheaper engines not originally intended for aircraft use.

 

[Norman]

Your spreadsheet makes it a lot easier, now I'm going to learn how to analyze airfoils with XFLR5 and hopefully learn a lot more in the process. Thanks again!

Welcome to the dark side, Arfang. Just keep in mind that the airfoil design and analysis part of XFLR5 is XFoil and XFoil is a 2D panel method with a crude correction for viscosity. Panel methods are basically inviscid solvers that do not have the math to truly model the boundary layer because the viscosity calculations take a long time. They replace the viscosity model with some empirical formulae that estimate what the boundary layer might look like. This isn't a problem until you get near CLmax or have a lot of turbulence. These extremely low AR wings being discussed in this thread have a lot of turbulence so 2D panel code results won't be valid except for very low CL (like around 0.2). The 3D air-frame analysis part of FXLR5 does handle some planform effects but it gives results pretty fast so I don't think it does a deep calculation of viscosity either. Here's a picture of the worst example of the CLmax error and 2D stall error that I know of. Note that the error I'm referring to is just the part in the box that I've labeled "fiction", the difference in the slope of the lines is mostly (perhaps all) because a planform correction has to be applied to the 2D data to get 3D results (less than infinite span results in a shallower slope of the cl over alpha curve) . The 3D airplane analysis part of XFLR5 should do that for you. There are also planform correction factor tables in some books.

 

[Sockmonkey]

Just my idea about pilot position and overal view in very low aspect ratio.
Why not place a thicker root chord and get as much as possible the pilot inside the wing? Just put his eyeline over the wing-surface so he can see above the wing. Due to the pilot being mostly inside the wing, you only need to make the front transparent. Not really the underside.
About the spar. I came up with this (probably crazy) idea to create a struss spar in which a pilot can be seated in between. With a reinforcement between front and rear of rear besides the pilot, torsion might be no problem. Remember ... i am not a engineer. I am just guessing.

A Warren truss type arrangement could work. Similar stiffness to what you envision, but made from several sets of identical tubes so it's easier to make.

 

[Arfang]

Welcome to the dark side, Arfang. Just keep in mind that the airfoil design and analysis part of XFLR5 is XFoil and XFoil is a 2D panel method with a crude correction for viscosity. Panel methods are basically inviscid solvers that do not have the math to truly model the boundary layer because the viscosity calculations take a long time. They replace the viscosity model with some empirical formulae that estimate what the boundary layer might look like. This isn't a problem until you get near CLmax or have a lot of turbulence. These extremely low AR wings being discussed in this thread have a lot of turbulence so 2D panel code results won't be valid except for very low CL (like around 0.2). The 3D air-frame analysis part of FXLR5 does handle some planform effects but it gives results pretty fast so I don't think it does a deep calculation of viscosity either. Here's a picture of the worst example of the CLmax error and 2D stall error that I know of. Note that the error I'm referring to is just the part in the box that I've labeled "fiction", the difference in the slope of the lines is mostly (perhaps all) because a planform correction has to be applied to the 2D data to get 3D results (less than infinite span results in a shallower slope of the cl over alpha curve) . The 3D airplane analysis part of XFLR5 should do that for you. There are also planform correction factor tables in some books.
View attachment 103176

Is the 'fiction' you showed due to 3D analysis? If I remember correctly the Cl/alpha slope gets more shallow with lower AR. Or is it 2D data that would later be corrected to match the real curve?

The way I see it, XFLR5 would be used to get 2D airfoil data below alpha where vortex mode starts. Check stability and control on a scale model using dynamic scale modelling factors. When I get good results, build a model large enough so that same Re number range can be achieved with 'acceptable' speeds and hopefully help me understand 3D-related behavior (how does planform affect vortex formation, stability and what conditions will blanket the control surfaces).
Combination of 2D analysis and scale modelling would lead to good enough data, if not, I would still learn something in the process.

First step for me, before even using XFLR5, is to re-read the theory and sort out what's usefull among the pile of textbooks, I realized that most of them simply state 'ac is at the quarter chord' and nothing more for instance, which makes me suspicious about the content quality. It's good to have people with first-hand experience like yourself. And thanks for the link you provided.

 

[Norman]

Is the 'fiction' you showed due to 3D analysis? If I remember correctly the Cl/alpha slope gets more shallow with lower AR. Or is it 2D data that would later be corrected to match the real curve?

First let me apologize for the low quality of that attachment. The original is small but legible. This site seems to automatically compress images more than it used to.

The red data curve is 2D from XFLR5 and the green curve is from the Langley variable density wind tunnel of an AR=6 model, both at Re~3.8 million. I keep telling people that you can't trust panel method data after the curve starts to round over and finally got around to making a graphic. They (panel codes) all do this with all airfoils ( they just can't handle large separated areas.). The CLmax round-over will look different depending on the stall and boundary layer transition models but none of them get it quite right. JavaFoil has 9 transition models and 2 stall models. It's interesting to look at all of them but not one shows this so I just ignore that data after the cl/alpha curve starts to round over. The straight part of the data curve and the zero lift angle are OK though. Fortunately planform effects and washout dominate the stall of an actual airplane wing.

The way I see it, XFLR5 would be used to get 2D airfoil data below alpha where vortex mode starts. Check stability and control on a scale model using dynamic scale modelling factors. When I get good results, build a model large enough so that same Re number range can be achieved with 'acceptable' speeds and hopefully help me understand 3D-related behavior (how does planform affect vortex formation, stability and what conditions will blanket the control surfaces).
Combination of 2D analysis and scale modelling would lead to good enough data, if not, I would still learn something in the process.

That's more than Lippisch had. Well he had access to wind tunnels later but all of his early work was pencil & paper and small free flight models. That (scale effect) was actually one of the problems he had with the DM-1. Small models have small enough leading edge radius to generate the leading edge vortex but the full size glider would have just stalled because the LE rad was too large. Good thing he had access to a fine full scale wind tunnel after the war.

First step for me, before even using XFLR5, is to re-read the theory and sort out what's useful among the pile of textbooks, I realized that most of them simply state 'ac is at the quarter chord' and nothing more for instance, which makes me suspicious about the content quality.

.25c is close enough for planes with long tails so why spend too much time on a <2% difference between thin airfoil theory and actual thick airfoils?

It's good to have people with first-hand experience like yourself.

"first-hand experience"? You must be new here. I'm just a liberal arts school dropout with an interest in aviation and a good collection of books. The majors that I didn't finish were in architecture, commercial art and mass communication. Changed majors too many times and ran out of money. I did work on an airplane for a few years though.

 

[Hot Wings]

I did work on an airplane for a few years though.

What is that thing!?!
Looks kind of like a shotgun wedding of a U-2 and a CH 701.
Is that the end product of the U-2 you were helping rebuild?

 

[Norman]

What is that thing!?!
Looks kind of like a shotgun wedding of a U-2 and a CH 701.
Is that the end product of the U-2 you were helping rebuild?

Yep. Those leading edge cuffs weren't my idea. Hope he doesn't kill himself.

 

[Arfang]

First let me apologize for the low quality of that attachment. The original is small but legible. This site seems to automatically compress images more than it used to.

The red data curve is 2D from XFLR5 and the green curve is from the Langley variable density wind tunnel of an AR=6 model, both at Re~3.8 million. I keep telling people that you can't trust panel method data after the curve starts to round over and finally got around to making a graphic. They (panel codes) all do this with all airfoils ( they just can't handel large separated areas.). The CLmax round-over will look different depending on the stall and boundary layer transition models but none of them get it quite right. JavaFoil has 9 transition models and 2 stall models. It's interesting to look at all of them but not one shows this so I just ignore that data after the cl/alpha curve starts to round over. The straight part of the data curve and the zero lift angle are OK though. Fortunately planform effects and washout dominate the stall of an actual airplane wing.

Ok, now I get it, 2D panel method can only be trusted for the linear portion, well before stall. And the method will become less accurate the more sweep and less AR you input, correct? Just to be sure, ''red'' is the ''fiction'' one, right?

One last thing: you mentioned a static margin between 2 and 5 percent for tailless airplanes, do you have a report/paper/book explaining that in more details?

I did work on an airplane for a few years though.

Which is more than I did.

 

[Norman]

Ok, now I get it, 2D panel method can only be trusted for the linear portion, well before stall.

Yes. Most airfoils have an aft stall where the flow start to separate at the trailing edge and the separation point moves forward. This separated flow causes you to lose some of the lift increase per alpha. That's why the _delta cl)/(delta alpha) curve rounds over and drops off after a peak. Some airfoils, like the NACA 23015 used in this example (and others with the high point of the mean line too far forward), have front stalls where there's an abrupt loss of around 20% of the lift. The simplified stall models that panel methods use can predict when this separation starts but aren't very good at predicting the effects of it on lift and drag or how fast it progresses and they don't predict front stall at all.

And the method will become less accurate the more sweep and less AR you input, correct? Just to be sure, ''red'' is the ''fiction'' one, right?

You can't have an aspect ratio if you don't have span. The red data curve is XFLR5 2D output, no AR or sweep here. I wouldn't call the whole red line "fiction" just data requiring another processing step. That step is the planform corrections. The part of the curve in the pink rectangle is the only part I'd call fiction. The pitching moment at zero lift and lift & drag up to cl~0.2 is what you are looking for.

One last thing: you mentioned a static margin between 2 and 5 percent for tailless airplanes, do you have a report/paper/book explaining that in more details?

2 to 5% for planks. Swept wings are another kettle of fish (several kettles actually, depending on the washout pattern). I haven't seen an actual tech report on this. It's just the result of pilot experience. I remember a letter from Bill Daniels (the guy who helped Jim Marske back in the '60s) saying 2 to 5% static margin, more than 5 makes the plane uncumfortable. And Jim Marske said 23% MAC was the max aft safe CG location. Modelers are constantly rediscovering that Their planks fly smoothly in that range but bob up and down, sometimes violently, if the CG is farther forward. I think it's the result of too much static stability and not enough dynamic stability possibly with a laminar separation bubble on the lower surface. so you either need to grow a horizontal stabilizer or decrease the static stability.

 

[Topaz]

... The 3D air-frame analysis part of FXLR5 does handle some planform effects but it gives results pretty fast so I don't think it does a deep calculation of viscosity either. ... The 3D airplane analysis part of XFLR5 should do that for you. There are also planform correction factor tables in some books.

My understanding is that the 3D portion of XFLR5 is a vortex-lattice modeler. As-such, it's pretty good for determining the characteristics of wings of reasonably large aspect ratio, before the stall. It's not going to provide accurate results for a partially-stalled wing, or one that is undergoing vortex lift. For that, you're going to need much more sophisticated modelers that can reasonably calculate turbulent and vortex flow.

 

[nestofdragons]

And the engine in-front of the feet! I like it somehow!

Erkki67, my words might seem too obvious. Most engines are in that place. What i tried to say was that the engine might beconnected straight to the spar at the front. So ... no longer need to a long extra fuselage structure to hold the engine.
What might be lesser visible in my draft might be the (brown) tubes that connect upper and lower tube of the airfoils. It creates a really stiff structure together with the double V-shaped spar.

The remark about trying to keep all tubes similar. Yes, but ... hey ... we live in the modern world. Let all the tubes be cut by waterjet-cutter. Using hunderd different tubes is no longer a trouble. Just get them labelled.

A mistake i might have made is that i used double tubes to fill the squares of the spar. Might be easier to just use a single tube. Lesser tubes and probably still strong.

 

[berridos]

In my design the front spar is at the same time the firewall. Wonder if that is a security no go in case of engine fire or similar?

 

[delta]

Say hello to my hi-low aspect ratio design. It's 15' x 20' and can't say for sure if it'd work as good as some of my true LAR ones that I've modeled extensively. I guess I'd call it a high aspect ratio airplane in a low aspect ratio package.

 

[Riggerrob]

In my design the front spar is at the same time the firewall. Wonder if that is a security no go in case of engine fire or similar?

You only need a firewall (stainless steel, galvanized steel or titanium) plus an inch or so of ceramic insulation. The goal is to prevent fire from burning through your main spar - or toes - just long enough for a quick forced landing.