Hi Serge
We may well be saying much the same thing, difficult to explain just with words.
>Ken-
>
>You have kind of lost me on some of this. From what you said
>in your earlier post, you seem to have a lot of experience
>in this, but some of the things below go contrary to what
>I've read or think I've seen. Also, you may have
>misunderstood the main point above, which was to be able to
>change the aspect ratio with slightly less compromise to
>stability in gusts.
Only private study and RC comp glider design.
I think I do understand your main point.
While induced drag (Cdi) is proportional to AR, so is induced incidence. It is induced incidence that is responsable for pitch sensativity. So by playing with planform to effectively reduce vortex effects, you will reduce induced drag but also increase pitch sensativity just like a model of higher AR.
>>I admitt I have not looked too closely at your maths but I
>>doubt the concept because any formulae concerning tip vortex
>>effects take wing plan form into account. That means that
>>tapering will have the exact same downwash effects as a wing
>>of equivilant apparant AR.
>
>I think that's really my intent - to change these effects
>with a greater aspect ratio. However, I'm not clear on the
>meaning of "same downwash effects". My understanding was
>that the closer a wing comes to elliptical lift
>distribution, the more uniform the downwash is across the
>span. Is this what you mean here? My purpose was to get
>effects of a higher A/R with less compromise - i.e. reduce
>vortex losses while maintaining the position of the lift
>center.
OK By downwash effect, I an trying to refere to induced incidence in more lay terms. I think you need to distinguish between geometric AR and apparent AR. Aparent AR is a term I coined to so as not to get into an involved explanation of the plan form correction factor used in induced drag and induced incidence calculations.
Basically, taper can make a wing act like a slightly higher AR wing. That is what I mean by apparant AR. You reduce in induced drag but also reduce the induces incidence so the pitch sensativity to turbulance will be the same as for the higher aparant AR wing.
>
>>The main reason for taper is to
>>ensure a more even spanwise lift distribution. From what I
>>have seen, spanwise disrtibution of lift force tends to
>>follow an eliptical curve regardless of taper.
>
>My understanding was/is that taper can be employed to more
>or less closely approximate elliptical lift distribution or
>even go past it. Even more taper of higher aspect ratio
>wings can produce a wing with the maximum lift for a given
>root bending moment, another kind of efficiency. Past that,
>it's just reduction of vortex losses.
I was talking of lift force there, not lift coefficient
We have to be clear on the difference here or will completey
misunderstand and seem very wrong.
>Basically, the texts I've read espouse the idea that the
>longer the chord at a given inboard station, the greater the
>local lift. In other words, the further from the tip you
>get, the more two-dimensional the flow. They then shape the
>spanwise lift distribution somewhat according to the shape
>of the wing. That is at least consonant with the idea of
>placing the MAC where you want it.
>
>
Yep I think you have the right idea.
Take a constant chord wing. The tip vortex produces a downwash effect ahead of the wing due to viscosity. This extends the entire length of the wing but is more pronounced near the tip. I am calling this effect induced incidence. This is in effect an aerodynamic twist or wash out despite the wing being geometrically straight. So the aerodynamic angle of attack (AAOA) is higher at the root than near the tip. Therefore Cl at the root is above wing mean Cl and reduces to 0 at the tip. The spanwise distribution of Cl is shown to be eliptical in texts and as the chord is constant, spanwise lift force distribution is also eliptical.
Now if we take an eliptical wing planform, texts show that the spanwise distribution of CL is constant almost the the tip. That means, there is almost no erodynamic twist along the span, the whole wing is working at the same Cl. It also means that spanwise lift force distribution is again eliptical due to the local chord in our eliptical plan form.
So in both cases the spanwise lift force distribution is eliptical.
Wing taper has not changed this but has improved induced drag due to the whole wing operating at the same AAOA and CL. So I agree that local chord does not effect local lift force and therfore will not influence moment loading about the root.
We can see than that an eliptical plan form is the ideal. A tapered wing may be employed as a practical approximation though excessive taper can result in tip stalling and should be avoided.
Not at all sure what you mean by bending moment. Do you mean that since the tips of a tapered wing are loaded better, any rolling forces will be greater?
By MAC, do you mean wing aerodynamic centre?
Wings are often designed of convenience with all the chords AC in a straight line but you don't have to do that. You can gain the wing AC by chord weighted means of the staggered sections. Just the same as summing moment forces.
Does this seem a better, more accurate explanation?
>>For this reason an eliptical plan form allows most of the
>>wing to work at the same AAOA and therefore lift
>>coefficient.
>
>I'll have to think about this.
See above.
>
>>The Spitfire, wing planform was designed
>>around a straight line aerodynamic centre (AC, 25% of chord)
>>this results in a swept forward TE that encourages the tip
>>vortices to centre more inboard as in a lower AR wing. The
>>best solution therefore is a half eliptical LE and a
>>straight TE.
>
>I did read something in the NACA literature indicating that
>spanwise straight trailing edges gave greatest efficiencies.
>However, won't spanwise flow from more than mildly swept
>leading edges cause boundary layer difficulties, especially
>at the tips? This is what I have read is a problem in
>back-swept flying wings and their pitch/roll controls near
>the tips. Several historical designs have developed peculiar
>habits due to this shape, when too severe. Not that I doubt
>your description, but I am having trouble visualizing tip
>vortices centering "more inboard"; I'm trying to visualize
>that. Do you mean that they can swirl more inboard without
>obstruction BEHIND the trailing edge?
>
The exact centre of the vortex is usually slightly inboard of the tip on most wings, special tip shapes being mostely ineffective.
I am not sure if the vortex centre starts at the tip then drifts inboard on if it is centred inboard from the start. Just something I read in a text without detailed explanation.
Swept foward TE encourages the vortex to centre more inboard than usuall. So a straight TE has a higher apparent AR (more efficient). I don't know the basis of your boundary layer concerns unless it is based on crossflows changing the pressure gradient from the designed profile. Surely that is not a huge concern on a model plane and on such a wing, only gets serious near the tip where the vortex will cause similar effects anyway. It seems to me that sweep imposes an inboard or outboard cross flow upon the usuall vortex cross flows.
So a foward sweep pulls the vortex inboard, reducing aparant AR while a back sweep pushes the vortex outboard increasing the aparant AR.
It's not like the whole wing is extremely swept so I would not expect
to have a large cumulative crossflow problem.
I think the main problem with this plan form for CL is that the AC and therefore CG are so far behing the root LE, it becomes difficult the get the engine back for enough for good ballance without having to add tail weight.
>>I am not convinced that yaw and roll are aerodynamic issues
>>for CL.
>
>They seem to be a trim issue for the top flyers (a SSW
>search will probably find some relevant analysis; try
>'hingeing' - sp? - for instance), and I have had some
>interesting roll and yaw adventures with my "SkyRay" on
>windy and turbulent days. They are of course related, when
>one wing is faster than the other or when dihedral effects
>from sweep enter in. In fact, this coupling seems to be the
>chief stumbling block for Bill Netzeband in his efforts to
>refine his swept-leading-edge "Fierce Arrow" design.
Yes but I am not sure it is necessarily an aerodynamic problem.
I am suggesting it may be mostely an enertia, ballance, engine run and leadout position problem. For CL, I think these are way more important for pitch and roll than any aerodynamic forces. As far as diferential speed across the span goes, given the radius of the circle, just how significant is that? In say a 2.5cc class on 15.9m lines, thats only +- 3% in velocity and +- 6% in aerpdynamic forces at the extreme tips and less at other stations along the span so the combined effect is even smaller. That is why I think it a mistake to extend the inboard wing or add much tip weight. I think the real problem lies in the tradition of overcompensating.
If the pilot can see the top or bottom of the wing in a loop, I think it's overcompensated. It would be interesting to do the math on it.
>>In my limited experience, roll is more related to engine run
>>and torque reaction variations than to turbulance.
>
>Certainly that too, although any asymmetrical aerodynamic
>effect is liable to upset stability about more than one
>axis, and unless care is taken, any action about one axis is
>liable to influence motion about the others. IMO.
True but not equal effects.
>Overall, the control and stability of models constrained to
>flight in a hemisphere (or for me, slightly more than the
>hemisphere
) is deceptively complex. To get it right is a
>real challenge, since, unlike other modes, the plane flies
>in constantly changing relative wind (all three directions)
>and other externally applied forces. The mathematics is
>complicated - not just for the dynamics, but for the paths
>and manuevers.
Yes but I think You only need be concerned with the major issues and so can simplify the math. After all engineering is just to get you in the ball park, after that, it's down to experimintation and refinement. The trick is to identify the major issues and factors in physics so you can ignore the trivial. I guess I just go for the first 1 or 2 significant figures.
>>I think a lot of CL use way too much tip weight.
>
>May be true, since this is an inertial as well as
>gravitational influence. No doubt it can induce yaw AND
>roll, whenever a manuever is begun. Any yaw will induce a
>roll tendency, and vice versa, since lift varies as the
>square of the speed for parts of the wing.
Yaw only has a significant roll effect where there is wing dihedral. In that case, the yaw causes a diferential incidence effect on dihedral wings. Flat wings = no differential incidence = no roll, except a slight wind shadow along the fuselage wing junction but that is so small and inboard, the roll is very slow indeed by compasison. That is why all rudder controlled RC models have loads of dihedral while aleron ones have very little.
> One model
>>had a tendancy to come in on slack lines during the
>>transition of an fig 8.
>Complex moment, when accelerations are reversed.
Yes the model was rolled in the loop because the CG was too far outboard. Then it could not roll back the othe way quickly enough.
the solution was to remove most of the tip weight to prevent rolling either way.
> The numbers showed correct lead out
>>postition, rudder size and offset more than adequate.
>
>The rudder offset affects the model differently at different
>speeds. This also yaws and thus rolls the plane as speed
>changes, subject to control line tension influences,
>including their varied application point as line tension
>alternates.
Interestingly aerodynamic formula reveal forces are proportional to velocity squared as are centrapetal forces. So you would expect all the physics to be in ballance regardless of velocity. However what does change is the Reynolds number (Re) which explains reduced aerodynamic efficiency at low speed and why the lines go slack when the engine runs out.
>>The problem was the inclined angle of the wing in a loop.
>>Reversing elevator made the model loop inside the circle and
>>loose line tension. Now I just make sure the tip weight is
>>just a little more than required to counterballance the
>>lines and I don't extent the inboard wing any more for the
>>same reason.
>
>These are valid concerns.
>
>I'll have to admit that, as I try to analyze the "simple"
>controlliner, I continue to be awestruck at its complexity.
>There's a whole world of physics right here.
>
>SK
>
Indead aircraft are the ultimate example of physics.
>P.S. I know there are better ways of saying yhese things and
>that I'll probably regret not having edited more, but I've
>GOT to get some sleep and get up and build some tomorrow. I
>may revisit this one sometime later.
>
Me too so much to say, so little time.
This is getting too big for the net.
Mabe just pull out a few main points for reply.