Canard Forum: Show,Discuss, Learn - Page 384 - RC Groups
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Feb 11, 2012, 10:44 PM
who has rabbit ears down
Captain Canardly's Avatar
Take a look at page 312 for some very important infos about all Rocketman!
also, the renolds #'s are an (X +Z) axi only formula!
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Feb 11, 2012, 11:39 PM
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Long EZ

Rocketman Here are airfoil shapes
Feb 12, 2012, 12:22 AM
Registered User
But Al said something like "twist can generate thrust". Surely that can only be through negative lift at the tip. Positive lift always generates drag, yes? Now that all sounds very simple to me, so what have I missed? Vortices?

Hi Nick

I think the thrust is to do with the vertical component of the airflow on the outboard LE tilting the thrust vector forward. When aileron moves down increasing lift with lift vector tilted forward it increases "thrust" more so than the drag produced.

Feb 12, 2012, 03:02 AM

Reynolds number.

Originally Posted by Rocketman1092
Hey guys,

I'm also considering lengthening the main wing and canard chords to add wing area and help avoid low Reynolds numbers.

I'm not an expert in any field, however my understanding of Reynolds numbers suggests that this is an entirely viable way to maximize Reynolds numbers for wings and other flying surfaces (horizontal / vertical stabilizers)

[In the computation of Reynolds number, Re = r V l / m, the characteristic length, l, for a body (fuselage, nacelle) is the overall length, and for the aerodynamic surfaces (wing, tail, pylon) it is usually the exposed mean aerodynamic chord]

Keeping the chord Re# for the wing / canard well above the transition area (~50,000) at stall speeds can help prevent unpredictable stall behavior arising from unstable laminar flow. It is important to note that the Re# for the tip of a tapered wing can be much lower than the Re# for the average chord. For a small, slow flying model, a rectangular wing with a low aspect ratio can make a lot of sense!

Feb 12, 2012, 03:10 AM
What could possibly go wrong?
nickchud's Avatar
Another Starship, hooray!

My preliminary thoughts for the wing and canard layout are a 1.5 degree root incidence for the main wing with a progressive twist to 0 degrees at the tips, and a 3.5-4.5 degree canard incidence. I'm also considering lengthening the main wing and canard chords to add wing area and help avoid low Reynolds numbers.

Of course, what you do with the elevator control quickly overrides the initial canard incidence. The full size Starship has elevons, I believe. None of my models do but I think the next one will.

How big and what materials? Let me know if you'd like any of my files and build photos.

The Starship was also my first canard, though the guys on here persuaded me that a simpler prototype was a worthwhile first step. I did get a lot of help from them. My wife said it looked like an accident waiting to happen, but it worked well, to our surprise!

Hi Dave

I'm scratching my head here! "vertical component of the airflow" - is that the leading edge compressing the air and pushing it up? It still looks to me as if washout is the only way to get a net effect where the drag becomes thrust. If you look again at that photo of the Northrop flying wing I posted, I think you can see that the outboard control panel is split, which suggests no down aileron at all, at least not at the tip.

Modern commercial airliners (and the Starship) all recover some of the energy from the tip vortex using tip fins. The fins have an airfoil shape because high pressure is on the outside. The rudders on the Starship have a differential that favors movement to the outside.

But Al Bowers lecture was suggesting that you don't need tip fins.

We live and learn, if we're lucky. Which golfer was it who said "the harder I practice, the luckier I get?"

Feb 12, 2012, 09:13 AM
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Don Stackhouse's Avatar
Reynolds number is the ratio of inertial forces in the airflow to the viscous forces. It's the speed times some characteristic dimension, divided by the kinematic viscosity (that's the fluid viscosity divided by the fluid density). For airfoils, we use the chord length.

In Sea Level ISA Standard Day air, the formula works out to:

Re = 778 x speed (MPH) x chord (inches)

You have to be a little careful, because the basis for Re (specifically the "characteristic length") varies. For example, for flow in pipes they use the hydraulic diameter. Therefore the Re for certain things like laminar/turbulent transition can vary.

There is also the local Re, such as the Re at some place along the chord. For example, if you had a 5" chord wing, with the high point at 25% aft of the leading edge, flying at 25 MPH, the overall Re would be about 97,300. However, the local Re at the high point would be 24,300, and of course the local Re at the leading edge would be zero.

As far as where transition from laminar to turbulent flow occurs, it depends on a lot of factors. Yes, some references suggest an Re of about 50,000, but that's actually somewhat low for our situation. Full-scale laminar-flow airfoils struggle to keep the flow laminar as long as possible, and in some cases may succeed up to local Re's of maybe several hundred thousand or more.

In our case, the flow tends to be laminar. In fact, if you turbulate it, it may even revert to being laminar. The problem is that laminar flow does not like to stay attached. If you have an area with an "adverse pressure gradient" (the static pressure is rising, such as aft of the high point on the upper surface of an airfoil, where the flow is slowing down), the flow in the boundary layer at the surface has to have enough kinetic energy to overcome the rising static pressure. It's like trying to coast a bicycle up a hill, if you have enough speed, you can make it to the top, but if not, you will come to a stop before then.

By turbulating the boundary layer, we mix fresh kinetic energy into the boundary layer from the free-stream flow above it. This does increase drag, but it gives the boundary layer enough kinetic energy to continue fighting the adverse pressure gradient, allowing it to stay attached for at least a little longer. A turbulent boundary layer has more drag than a laminar one, but FAR less drag than a separated boundary layer!

So, for full scale Re's, the problem is keeping the flow laminar as long as possible. For most of our applications, we are more likely to want it to be turbulent when it still wants to be laminar.

At low Re's like ours, the airfoils need to be thinner (typically less than about 8.5 - 9% max), with the high point fairly far forward, typically around 23% to 25%. The shapes aft of the high point need to be flat, or nearly flat. Camber also needs to be kept fairly modest. The intensity of the adverse pressure gradient depends on the slopes on the rear portion of the airfoil. A lot of slope due to too much thickness, too much camber, too much angle of attack, etc., worsens that slope, and with it the adverse pressure gradient.

On the undersurface, too much undercamber can create similar problems, especially at high speeds and low angles of attack. You get an airfoil that does OK at low speeds, but throws out an anchor when you try to fly faster. For a trainer this can be a plus (the plane won't pick up as much speed in a dive), but if you have to be able to penetrate some wind (such as a sailplane trying to come home from downwind), you have a plane that literally can't get out of its own way.

If you have decent airfoils for your operating Re's, things like chord increases to try to keep the Re's higher should not be necessary, and can create other problems, unless your Re's are really low to begin with.

K-F airfoils tend to have high drag and poor L/D at all speeds. They tend to have fairly good stall characteristics, because in effect they are already stalled all the time. There are other ways to get good stall characteristics (which themselves depend on far more than just the airfoil characteristics) without the drag penalties, and ways to get easy construction while still having good L/D (such as Jedelsky wings).

The full-scale Starship does not have elevons. It uses the same setup as its ancestor, the VariEze, elevators on the canard and ailerons on the wing. It also has flaps on the wing, coupled through a safety-of-flight-critical linkage to the variable sweep feature on the canard. When the wing flaps go down, it creates more nose-down pitching moment from the wing than the canard can handle. Sweeping the canard forward gives the canard more moment arm, and the extra leverage it needs to counteract the effects of the wing flaps.

As far as "the vertical component of the flow", what's really going on here is the flow associated with the tip vortex.

To understand this, first you have to remember that drag is the force parallel to the flow, and lift is perpendicular to the flow. That local flow direction might not be the same as the direction of the flight path of the plane.

In particular, at the wing tip we have the tip vortex. High pressure air under the wing spills around the tip towards the low pressure flow on top, creating a vortex, a long horizontal tornado of cork-screwing air around and flowing aft behind the wing tip. The energy required to create that vortex is what we call "induced drag", the drag that is the by-product of making lift. At L/D max, that induced drag is exactly half the total drag of the plane, and at speeds slower than L/D max, it's more than half the total drag.

The resulting airflow above and behind the tip of the wing is in a part of the vortex that is flowing inwards, towards the fuselage. If you park a lifting surface (such as the Starship's winglets) in this flow, it will make lift inwards, towards the fuselage. However, because the airflow is angled, the lift vector is angled forwards as well. If the angle is enough, and the lift is great enough compared to the winglet's own drag, the forward component of the winglet's lift is greater than the winglet's drag, and that the net force is forwards, so "negative drag", or "thrust". The winglet is actually recovering energy from the tip vortex, in effect reducing the total induced drag.

The problem is that the winglet has both parasite and induced drags of its own, and the lift it makes is directed horizontally, so it does not contribute to helping hold the airplane up. If it recovers more energy from the wing tip vortex than its own total drag, then the net effect is positive. However, as the plane flies faster, the wing's induced drag goes down, while the parasite drag of the winglet goes up. At some point (the "crossover velocity") the total drag of the winglet equals the induced drag it is recovering from the wing, so the net effect is zero. Above that speed, the net effect of the winglet is negative, and you would be better off without it.

However, if you can make the winglet do "double duty", such as acting as vertical fins that would have to be there anyway, then that can "pay for" the drag of the winglets, and the winglet's parasite drag drops out of the equation. There is still a crossover velocity, but it's due to the winglet's induced drag alone, so it is much higher.

As far as the bell-shaped lift distribution, the lift at the tips is zero, not negative, at least at the design point, and the lift just inboard of the tip is positive, but very low. You can see this in the upper graph in Al Bowers' presentation. The lower graph shows the local induced drag along the span, and you can see that the induced drag near the tip is indeed negative, i.e.: induced THRUST. However, the tip acts something like a winglet extending horizontally out into the tip vortex, and can therefore make forward thrust just like a vertical winglet. The key difference is that whatever lift the tip does make is contributing to the support of the plane's weight, so there is no crossover velocity.

Prandtl's original analysis that established the familiar elliptical lift distribution as having the lowest induced drag was based on assuming a constant span. However, he continued studying the problem, wondering if "constant span" was the best parameter to achieve the lowest induced drag for a given amount of airplane. He eventually found that by using a bell-shaped lift distribution, allowing span to vary, and instead using constant wing weight (which equates to a constant bending moment at the root, and the weight of the spar), the span ended up being 22% longer, the wing weight ended up the same, but the total induced drag ended up being 11% lower than an equivalent elliptical lift distribution.

By achieving Prandtl's bell-shaped lift distribution ("BSLD") mainly through twist (as opposed to planform), the Horten brothers also found they eliminated adverse yaw, and therefore the need for vertical surfaces, as well as bringing some other performance and handling benefits. One key is that the ailerons needed to be limited to the tip, within or nearly within the region of induced thrust. If the ailerons went too far inboard, into the area of positive induced drag, the adverse yaw gradually returned.

In the '50's, NASA's R.T.Jones independently came up with essentially the same analysis, although some differences in the initial assumptions resulted in a 15% span increase in his analysis, instead of the 22% called for by Prandtl.

For a lot more on this subject, visit
"Nurflugel" is German for "only wing", or flying wing.

Note, the basic analyses by both Prandtl and Jones were simply looking for minimum induced drag, and only looked for a distribution of lift along the span. That could be achieved a number of ways, on wings that were straight or swept, tapered by various schedules, twisted or not twisted. All that mattered was how the lift was distributed along the span. The Hortens used a combination of sweep, straight taper (and quite extreme in many cases) along with twist distribution, not just to achieve minimum induced drag, but also to eliminate adverse yaw and the need for vertical fins, provide pitch stability without a horizontal tail, and to improve handling qualities. The down side of their approach is that twist can be optimized fairly easily for one operating point, but getting near-optimum performance at off-design operating conditions can be a serious issue. In other words, if you only have to fly at one speed and power setting, it's great, but if you want to do well at a variety of airspeeds and power settings, you have a very difficult design problem to solve. Not impossible, but very difficult.

Of course you can implement the BSLD through planform alone, just as with an elliptical lift distribution, but then you miss out on the stability and handling benefits.

The other problem with that in models is the Re effects. Theoretically, if you build a perfectly elliptical wing, with a constant airfoil along the span and with no twist ("washout"), the lift coefficient along the span will be constant, and the lift distribution will be perfectly elliptical. However, this ignores the fact that the chord (and therefore the Re) at the tip is a small fraction of the chord and Re at the root. The airfoil characteristics along the span will therefore not be constant. For full-scale wings this effect is not terribly significant, but for models it's a killer. A model with an un-twisted, constant airfoil, perfectly elliptical wing will most certainly NOT have an elliptical lift distribution, will not have minimum induced drag for that span, and furthermore is very likely to be a tip-stalling monster! The elliptical shape needs to have the outer portions widened a bit from the perfect ellipse shape, enough to counteract the Re effects.

More later. Right now I have some non-elliptical wings to repair.
Last edited by Don Stackhouse; Feb 12, 2012 at 09:51 AM.
Feb 12, 2012, 11:08 AM
Purdue Engineering
Rocketman1092's Avatar
Wow, thanks for all the help guys!

nickchud: My model will be around 50" span, CNC milled from pink foam and then either covered or glassed. I do have a couple questions about your build, if you don't mind. Firstly, would you change the incidence angles or thrustline if you had the chance, or did they all work out? Secondly, I see that you used seperate ailerons and elevator control surfaces. Would you forsee any problems using elevons coupled with the canard, as the full-scale Starship did? Finally, how useful is the rudder control? I'm thinking about leaving it out to save weight and complexity.

Feb 12, 2012, 11:10 AM
Registered User
Keeping the chord Re# for the wing / canard well above the transition area (~50,000) at stall speeds can help prevent unpredictable stall behavior arising from unstable laminar flow. It is important to note that the Re# for the tip of a tapered wing can be much lower than the Re# for the average chord. For a small, slow flying model, a rectangular wing with a low aspect ratio can make a lot of sense!
That sounds reasonable, Mitch. A 5" tip chord is considered minimum. I believe that wing loading should become increasingly lower as model size decreases.

If you look again at that photo of the Northrop flying wing I posted, I think you can see that the outboard control panel is split, which suggests no down aileron at all, at least not at the tip.
Nick, As I see it, the UP reflex at the wing tips will reduce lift on the tips which will prolong the stall at high AOA and behave as washout.

Rocketman, There are excellent build threads on Scale Electric Planes. One is by Nickchud which we are fortunate to have here. IMHO, the wing twist could be avoided on a model. The fuselage center line should coincide with the thrust line and the chord line. Four degrees of canard incidence seems correct. The large center section of the wing should not allowed to lift the model before the canard does.With 1.5 degrees of center chord angle, the motors at zero thrust angle would provide down thrust which seems counter productive.

Last edited by canard addict; Feb 12, 2012 at 09:15 PM.
Feb 12, 2012, 11:41 AM
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Don Stackhouse's Avatar
Well, um, NO.

Incidence is something that will vary from one plane to another. The numbers batted around here in this latest discussion fall within the range of what's typical, but trying to specify incidences without first studying the details of the plane is like asking what size shoes to buy without first measuring your feet.

Wing/fuselage incidence depends on what incidence will make the fuselage level when the wing in flight is at the angle of attack it needs to have to support the plane. Wing/canard incidence ("decalage") and the resulting canard/fuselage incidence depends on what angle of attack the canard needs in flight to make the lift required from it to keep the forces from the rest of the plane in balance. The angle of the thrust line depends on what will make the thrust line pass through the C/G location (in both the horizontal and vertical sense), to minimize the effects of thrust on pitch trim.

5" is by no means a "lower limit" on tip chord. Keeping the taper ratio moderate (0.6 or more) does make the whole tip stalling issue less critical, but much steeper taper ratios (0.3 or worse) are quite reasonable, especially with a suitable dose of washout. I've had models with tip chords less than 1.5" that had perfectly decent performance and handling, including stall characteristics. If you use airfoils and twist that properly take into account the size and shape of the plane and the way it is to be flown, all sorts of things are possible.

Don't let these "rules of thumb" paint you into an unnecessary corner. Figure out what you're trying to do, and what you need to do it. If you're unsure, try building some small balsa free flight gliders of your concept before committing to the more expensive R/C design.

And, as I said before, the full-scale Starship did not use elevons on the canard nor the wings. It had elevators on the canard, and ailerons on the wings. Trying to get the canard to stall before the wing in all flight conditions, but not too much before, is a demanding enough requirement that trying to make it also do the aileron function (something it would not be good at anyway, because of its shorter span) is not a wise move. Likewise, using elevons on the wing just takes that whole issue of keeping the wing flying until after the canard has stalled and turns that into a "moving target". Again, not a wise move.

Charles gets away with it on his planes because his canards are too small to do the full job of providing pitch stability and control by themselves. His planes are actually more of a tailless model, with a little help in pitch from what amounts to a large trim tab on the nose. As I recall from the last time we discussed it in this thread, he's running horizontal tail volume coefficients ("Vht") down around 0.2 or 0.3, where a properly sized tail has a Vht around 0.45 to 0.55, so his canards are about half the size they should be according to the typical range of volume coefficients.
Last edited by Don Stackhouse; Feb 12, 2012 at 11:54 AM.
Feb 12, 2012, 12:20 PM
Purdue Engineering
Rocketman1092's Avatar
Originally Posted by Don Stackhouse
And, as I said before, the full-scale Starship did not use elevons on the canard nor the wings. It had elevators on the canard, and ailerons on the wings. Trying to get the canard to stall before the wing in all flight conditions, but not too much before, is a demanding enough requirement that trying to make it also do the aileron function (something it would not be good at anyway, because of its shorter span) is not a wise move. Likewise, using elevons on the wing just takes that whole issue of keeping the wing flying until after the canard has stalled and turns that into a "moving target". Again, not a wise move.

I'm fairly certain that the Starship had elevons working in conjunction with the canard - they appear in the cutaway drawing here: and also several times in the Starship's maintence manual. In fact, the word "aileron" doesn't appear even once in the 1000+ pages of the manual, just "elevon".

Regardless, would you suggest that using the main wing's control surfaces as ailerons only would be the way to go?
Feb 12, 2012, 12:23 PM
Registered User
Galand's Avatar

Signflyer's GNOT-EZ

Built and flew that design.
Differential thrust works well.
Flies very stable even underpowered but only one flight due to poor landing.
The problems I had all relate to my building and flying, not the design. See:
No idea whether the KF profile does anything. It certainly makes it easier to rum the wires through the wing.
Feb 12, 2012, 12:35 PM
What could possibly go wrong?
nickchud's Avatar


Brilliant! Many thanks for all the work you have put into that Don.

At the first reading, I have to say "My brain hurts". But I did understand enough to make me believe that reading it again will pay dividends.

I don't like using elevons, or any fancy linked control surfaces on my canards, being a believer in the KISS principal. I didn't think they had them on the Starship till I found this diagram on Bob Scherer's website. I hungrily accept that the diagram is wrong. Having said that about the KISS principal I did use elevons on the delta duck I built. I think it helped shorten the take-off run, perhaps by reducing the pressure under the TE resulting from ground effect. Another trick I tried with one of my twin water planes was differential thrust, linked to the rudders. That was useful on the water and very interesting in the air.

Rocketman, have you seen this little Starship, which is just getting near to its maiden flight?

Presently, I'm home alone and making progress on my monster Starship, I'll post some pictures in a moment. I have a cunning plan for the rudders, borrowed from something I saw on this thread before. By the way, I didn't put rudders on my 46" Starship. On the larger model, I find that when I use them I have to add some up elevator. Makes nice flat turns though.

The plan for the rudders I refer to is to use servos attached only by strings to pull a lever in front of the hinge line. (I have to have 2 as the wings are detachable). So the rudders only function on the inside of the turns. They will be kept from flapping by a piece of flat acetate cut from some packaging or other and placed on the opposite side of the hinge so that they gently oppose the lever. If you see what I mean.

I'm delighted to see all this extra activity here!

Feb 12, 2012, 02:09 PM
Registered User

Re vertical component.

On swept wings the span wise flow about the LE behaves like the wingtip, in a sense it is somewhat a wingtip. The more outboard you go is the stronger the outflow from high to low press which is moving up from underside to upper side of wing, ie, vertical component to local airflow.

At high alpha the outboard LE stalls, tipstall, because the aoa becomes too great at that section of the wing and that causes the infamous high alpha pitch up of many swept wing jets as the cp moves forward because the inboard wing area is still producing lift ahead of cg.

Twisting the wing so that the aoa remains almost constant spanwise not only delays stall at the outboard LE but increases the lift as the outboard wing section continues to produce lift at high alpha. With correct twist ideal span loading could be maintained while at the same time producing 'thrust' and reducing adverse yaw. In fact the wing could probably be engineered to flex so that it maintains ideal twist for all wing loads.(prob spar at wingtip closer to LE than at root so that loading causes it to pivot about the spar reducing incidence)

In addition to that if winglets are added as they are aft of cg they are ideally located to act as rudders eliminating the need for a long fuse to support a tail while reducing vortices and increasing lift and thrust.

Stabs could be added in 'C' wing fashion, but we would probably prefer our canards.

The other nice swept wing benefit is the outboard TEs are ideal for elevons as they r aft of cg and the inboard TEs if on cg r ideal to mount flaps as they may not affect pitch.

Feb 12, 2012, 03:10 PM
What could possibly go wrong?
nickchud's Avatar

Starship wings

If your wife asks you what we do while she's away, show her these pictures. To build this plane has taken a lot of space, only available when you're home alone

I've used 6mm x 0.8mm cf strips. One piece in each wing is upright all the way to the tip. In other places as cap strips top and bottom of the depron spars. For the inboard section, there is more wood and there will be more when I can get some 6mm balsa to use in the spars in place of the depron in the outer parts of the wings. To fix the outer wings there are 8mm cf tube with 6mm tube sliding in and out as they are removed. This tube also helps to stiffen the structure.

I'm learning to use white Gorilla Glue and I like it a lot in this context. Lightweight, very strong, not brittle, gives me time to slide things into place. It's very important to use plenty of weights or tape to stop the foam running amok.

Still on target for a very low wing loading, I think.

Feb 12, 2012, 03:26 PM
Registered User
Nick, Don, Charles,

how do the low sweep deltas like the delta duck compare to the more swept deltas like the Polaris?

I also read that close coupled canards increase effective 'sweep'. Any thoughts on the aerodynamics involved?