# Putting a tapered wing on an RV

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#### Fenix

##### Well-Known Member
HBA Supporter
I will keep saying it. Lift unavoidably MUST go to zero at the tips.
I agree. Lift must go to zero at the tips. The rest of your explanation is beyond my understanding but I agree lift must go to zero at the tips, certainly 1 millimeter beyond for sure.....

I just followed the formula in the attached document. It appears that in all iterations of this formula the Cla line will be at 0.5 at the tips, to include the example in the document. I won't attempt to explain what this means or what Cla means or represents. I just "followed the instructions" or at least I think I did.

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#### Fenix

##### Well-Known Member
HBA Supporter
Fenix: Your wing is very close to mine. If you could post the following numbers I will run them through my Schrenk spreadsheet and post the result.

Chord at fuselage side
Spanwise location of above
Tip chord
Span
Twist
The chord at the fuse is 58 inches, same as standard RV4
The fuselage side is angled and intersect the wing at the leading edge at 14" from A/C Centerline and at the Trailing edge 12" from A/C CL
Tip chord is 38"
Span is 25.0 feet
Twist: I think it is 2.75 degrees but I don't have access to that info from my present location.
Note the twist is geometric, not aerodynamic. The airfoil is the same from root to tip (and is the same foil as the standard RV4)

I tried to attach my spreadsheet of data, I hope it attached.

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#### davefried

##### Active Member
The chord at the fuse is 58 inches, same as standard RV4
The fuselage side is angled and intersect the wing at the leading edge at 14" from A/C Centerline and at the Trailing edge 12" from A/C CL
Tip chord is 38"
Span is 25.0 feet
Twist: I think it is 2.75 degrees but I don't have access to that info from my present location.
Note the twist is geometric, not aerodynamic. The airfoil is the same from root to tip (and is the same foil as the standard RV4)

I tried to attach my spreadsheet of data, I hope it attached.
From the numbers you posted, this is the wing planform I came up with...

Cr @centre 59.74 in
Cfus @ y=12 in 58.00 in
Ctip 38.00 in
Cbar 48.87 in
Taper Ratio 0.64
S 101.81 ft^2
Twist 2.75 deg

The plots that follow are for three configurations. Each reaches section cl max at some point on the span (''stall")
at slightly different speeds.

Original Planform Vs = 55.56 kt CLmax = 1.376 Planform Zero Lift wrt Root 0.00 deg.
Tapered Planform Vs = 56.49 kt CLmax = 1.453 Planform Zero Lift wrt Root 0.00 deg.
Tapered and Twisted Planform Vs = 56.95 kt CLmax = 1.430 Planform Zero Lift wrt Root 1.27 deg.

The Schrenk approximation is an average between linear and elliptic distribution of lift. If the model doesn't quite reach zero at the tip it may overpredict the bending moment at the root. This is a conservative assumption and leaves a little extra strength along with some extra weight. There may be better models out there for those who wish to optimize further.

I included the shear and moments but this is not the design case for strength. I can run it again at Va given the desired weight and g limit.

#### davefried

##### Active Member
I will keep saying it. Lift unavoidably MUST go to zero at the tips. Any lift distribution with lift at the tip is exaggerating the shear and bending moment, which you then design for. Any lift distribution with lift at the tip is also exaggerating the Cl curve as you go outward, which you then make (un-needed) changes to correct for it. Relying upon a bogus lift distribution to make fine detail changes is bogus too. Lift distribution based entirely upon planview area is putting you there. Please get beyond it. These math models are all for the dual purposes of estimating loads (for structural design) and estimating Cl distributions along the span (to anticipate and correct stall progression). They need to as accurately as possible reflect reality or you will just be putting in unneeded changes that otherwise hinder utility, speed and efficiency.

Lift distribution usually looks elliptical and is an excellent starting point. Going further, the pressure distribution along the span is what is usually really close to elliptical. If you want to be a philosopher about this, yes, the pressures are distributed over the area, so you can start with spanwise elliptical in one column of your spreadsheet, then in the next column put in the fraction of root chord you have at each station, and multiply the local elliptical by that fraction. This is modifying the lift outboard based upon plan view. This reduces total lift and lowers the curve of shear and moment vs spanwise position. Yes, you will have to adjust your calculated stall speed upwards to carry the weight of the airplane and the downforce from the tail. That will avoid finding out later that your actual stall speed is higher than you thought...

You can go further. If you washout the wing (for whatever reason), either by twist or foil choices at root and tip, you can figure out what the reduction in local Cl would be as you go outward, divide local Cl by base Cl, and multiply your local lift by that ratio. This too reduces the total lift and lowers the shear and moment curves.

Then you can do the downward deflected aileron and its adjusted Cl over the portion of the wing that is aileron influenced. The wing should remain intact when the aileron is deflected at Vne, so this is a load case you need to check for structure. How? Same way, figure out the ratio of Cldeflected divided by Clbase and multiply by that value. This increases shear and bending moment curves. You might be concerned about stall here too.

All of this drives one to say, but don't these reduce total lift? Hmm. Where your foil is clean (no control deflections) local Cl can not exceed stall Cl. And where your high lift devices are deflected, the local Cl can not exceed the stall Cl of that deflection. So when any part your local Cl exceeds Cl at stall, you need to scale back Cl everywhere. Reduce AOA everywhere. Easy way is to find the biggest delta between computed Cl (which we know is not actually available to the wing) and max CL, then divide that by your wing's lift slope (include correction for AR). That is the number of degrees you need to lower the AOA. Or if you are working only in Cl, just lower the entire Cl curve by that difference between computed and known max Cl...

I just added three columns to your spreadsheet to correct elliptical for taper, for twist, and then for aileron deflection. All make your math model more closely resemble what is actually happening, and none exaggerate the actual wing mechanical loads or tendency to tip stall.

Billski
What does your lift distribution look like and how does taper change it? Do you have a reference for your model?

#### Fenix

##### Well-Known Member
HBA Supporter
From the numbers you posted, this is the wing planform I came up with...

Cr @centre 59.74 in
Cfus @ y=12 in 58.00 in
Ctip 38.00 in
Cbar 48.87 in
Taper Ratio 0.64
S 101.81 ft^2
Twist 2.75 deg

The plots that follow are for three configurations. Each reaches section cl max at some point on the span (''stall")
at slightly different speeds.

Original Planform Vs = 55.56 kt CLmax = 1.376 Planform Zero Lift wrt Root 0.00 deg.
Tapered Planform Vs = 56.49 kt CLmax = 1.453 Planform Zero Lift wrt Root 0.00 deg.
Tapered and Twisted Planform Vs = 56.95 kt CLmax = 1.430 Planform Zero Lift wrt Root 1.27 deg.

View attachment 108709View attachment 108710

The Schrenk approximation is an average between linear and elliptic distribution of lift. If the model doesn't quite reach zero at the tip it may overpredict the bending moment at the root. This is a conservative assumption and leaves a little extra strength along with some extra weight. There may be better models out there for those who wish to optimize further.

I included the shear and moments but this is not the design case for strength. I can run it again at Va given the desired weight and g limit.
Dave, Thanks for the charts.

From my limited understanding of these matters is does appear to me that perhaps the washout will have some value in "returning" the stall characteristics closer to the original wing. But if IIRC you have no washout in yours and find the stall characteristics to be good.

#### davefried

##### Active Member
Dave, Thanks for the charts.

From my limited understanding of these matters is does appear to me that perhaps the washout will have some value in "returning" the stall characteristics closer to the original wing. But if IIRC you have no washout in yours and find the stall characteristics to be good.
I have had no problems with the way it handles. The taper is moderate and the resulting spanwise location of Clmax is at 40% span... it behaves.

Perhaps there are corners to the flight envelope yet unexplored that might might reveal something interesting. The basic design has good bones, lots of room in that envelope.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
What does your lift distribution look like and how does taper change it? Do you have a reference for your model?
Elliptical. Reference is TOWS, chapter 1, page 10. I did not make any of this up. It has been around for over 90 years. A real authority on these topics once told me "lift always ends up looking elliptically distributed". After that, it is just mechanics of solids to get to structure requirements- straightforward modeling, something I have a lot of experience in.

So, you can do it with span loading distributed elliptically. With Excel, you can easily break the wing into spanwise elements and compute shear, bending, torsion, etc at stations. If you feel a need for more fidelity in your calculations because you think it will make a difference, knock yourself out. Expansion to apply elliptical pressure distribution (instead of elliptical spanwise lift distribution), correct for local wing loading for tapered planform, washout, foil differences, deflected control surfaces, and so on is straightforward.

Depending upon how closely you are willing to tailor your sparset, you can keep going with finer definition of loads. My experience designing composite wings indicates most of us will end up with increasing FOS as we go out towards the tips. Most of us use a "gunfighter's rule" or three plus minimum gages in our structures. I do not like to taper whatever I am laminating with more than one ply per inch, and carry each ply at least a inch beyond where I know I need it. The upshot is I end up with Scaled Composite's famous "throw another ply in for Grandma". I have not worried over any of my Grandma's for 35 years, but I have met Mom Rutan... Anyway, we frequently end up with moment tapering faster than we taper the laminate, and then we get to our minumum of two plies, and stop tapering the thickness. We can taper the width of caps too, but there are also minimum overlaps between cap and web that we like to honor too. So the outer half of the wing ends up over strength and over stiffness - not a bad thing really.

So, how much fidelity you need to model with is in there too. If you are designing a cantilever wing, it can matter. If you are designing a fabric covered wing with two spars and two struts per side, tailoring the spars matter way less...

Billski

#### rv7charlie

##### Well-Known Member
And all the aero efficiency difference in taper vs Hershey Bar will be lost in build quality noise....

oops; forgot the obligatory ;-)

#### davefried

##### Active Member
And all the aero efficiency difference in taper vs Hershey Bar will be lost in build quality noise....

oops; forgot the obligatory ;-)
Where has the passion gone? Lost in a sea of sameness.

#### rv7charlie

##### Well-Known Member
No lack of passion here; I'm putting a rotary in my RV7. Because I want to do it; I don't really want a cookie cutter RV. But I'm enough of a pragmatist that I recognize the fact that I almost certainly won't be *improving* the plane, and I'll absolutely destroy the value of the plane.

The art aficionado in me says tapered wing RVs will certainly look cooler, but the Pragmatist in me says that they almost certainly won't fly any better, except perhaps up in the O2 altitudes, where I don't go. and there's the RV9 & RV14 for that. As analogy, there have been a couple of RV4s with retracts. They look cool in flight, but all the reports I've seen say they aren't any faster than fixed gear versions. (And it's a pretty safe bet that their useful load is greatly reduced, too.)

Again, I wasn't saying 'don't do it'; but I'd expect aesthetics to be the primary benefit.

Charlie

#### Fenix

##### Well-Known Member
HBA Supporter
And all the aero efficiency difference in taper vs Hershey Bar will be lost in build quality noise....

oops; forgot the obligatory ;-)
I'm not sure I understand "build quality noise". You mean scratch built won't have the build quality of assembled kit?
If that is what you mean I'd say that would be true if you compared a group of one to a group of the other. I mean walking the flight line at KOSH you can find some pretty awful stuff while the RV field has a relative degree of consistency. But it is not necessarily true in individual examples, take the Polen Special and many others. Or maybe you meant something else by build quality noise.

Again, I wasn't saying 'don't do it'; but I'd expect aesthetics to be the primary benefit.
Yes I think you are correct, but aesthetics, to some degree, drives almost every decision we make - for better of for worse - obligatory ; - )

No lack of passion here; I'm putting a rotary in my RV7. Because I want to do it; I don't really want a cookie cutter RV. But I'm enough of a pragmatist that I recognize the fact that I almost certainly won't be *improving* the plane, and I'll absolutely destroy the value of the plane.

The art aficionado in me says tapered wing RVs will certainly look cooler, but the Pragmatist in me says that they almost certainly won't fly any better, except perhaps up in the O2 altitudes, where I don't go. and there's the RV9 & RV14 for that. As analogy, there have been a couple of RV4s with retracts. They look cool in flight, but all the reports I've seen say they aren't any faster than fixed gear versions. (And it's a pretty safe bet that their useful load is greatly reduced, too.)

Again, I wasn't saying 'don't do it'; but I'd expect aesthetics to be the primary benefit.

Charlie
'm putting a rotary in my RV7.
I'm thinking something like a "wankel/mazda" not something like a Gnome. What stage is that conversion in? I'd like to see a pic of the engine cowl if it is built.

#### Marc W

##### Well-Known Member
Gnome would be cooler! Just sayin!

#### davefried

##### Active Member
No lack of passion here; I'm putting a rotary in my RV7. Because I want to do it; I don't really want a cookie cutter RV. But I'm enough of a pragmatist that I recognize the fact that I almost certainly won't be *improving* the plane, and I'll absolutely destroy the value of the plane.

The art aficionado in me says tapered wing RVs will certainly look cooler, but the Pragmatist in me says that they almost certainly won't fly any better, except perhaps up in the O2 altitudes, where I don't go. and there's the RV9 & RV14 for that. As analogy, there have been a couple of RV4s with retracts. They look cool in flight, but all the reports I've seen say they aren't any faster than fixed gear versions. (And it's a pretty safe bet that their useful load is greatly reduced, too.)

Again, I wasn't saying 'don't do it'; but I'd expect aesthetics to be the primary benefit.

Charlie
I didn't think I was the only one who thought that way. Sometimes you just want to do something different. Best of luck with your project.

#### bifft

##### Well-Known Member
I have had no problems with the way it handles. The taper is moderate and the resulting spanwise location of Clmax is at 40% span... it behaves.
Have you ever spun it? I would expect that at least to be a little different.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
I agree. Lift must go to zero at the tips. The rest of your explanation is beyond my understanding but I agree lift must go to zero at the tips, certainly 1 millimeter beyond for sure.....

I just followed the formula in the attached document. It appears that in all iterations of this formula the Cla line will be at 0.5 at the tips, to include the example in the document. I won't attempt to explain what this means or what Cla means or represents. I just "followed the instructions" or at least I think I did.
Funny thing though is that the article tries to tell us the Shrenk Approximation goes to zero at the tip. Well, not the way the included program does it.

I think you did what the enclosed page said to do. Shrenk's Approximation is nominally splitting the difference between elliptical and planform based spanwise loading, so it gives a finite lift at the tip, which I have been telling everyone who will listen, over estimates shear and bending over much of the wing and drives you to put in more weight than you have any need to do. To do it, you are doing the elliptical distribution anyway. So why so something that is NOT what nature does when we pass a foil through a fluid?

Billski

#### davefried

##### Active Member
Funny thing though is that the article tries to tell us the Shrenk Approximation goes to zero at the tip. Well, not the way the included program does it.

I think you did what the enclosed page said to do. Shrenk's Approximation is nominally splitting the difference between elliptical and planform based spanwise loading, so it gives a finite lift at the tip, which I have been telling everyone who will listen, over estimates shear and bending over much of the wing and drives you to put in more weight than you have any need to do. To do it, you are doing the elliptical distribution anyway. So why so something that is NOT what nature does when we pass a foil through a fluid?

Billski
You certainly have given this some thought. How does Schrenk compare quantitatively with the method you referenced in TOWS?

Just saying... If the planform analysed with Schrenk happened to have rounded tips, the resulting lift distribution would go to zero at the tips. A wing with an elliptical planform will have an elliptical lift distribution.

#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
If the planform analysed with Schrenk happened to have rounded tips, the resulting lift distribution would go to zero at the tips. A wing with an elliptical planform will have an elliptical lift distribution.
Of course, Billski is quite correct that Schrenk doesn't result in zero lift at the tip, but Schrenk himself says it's satisfactory for many purposes. After all, it's conservative if it marginally overestimates lift at the very tip. I'm using Schrenk until I need to squeeze out a few more ounces. YMMV.

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#### Fenix

##### Well-Known Member
HBA Supporter
Shrenk's Approximation is nominally splitting the difference between elliptical and planform based spanwise loading, so it gives a finite lift at the tip, which I have been telling everyone who will listen, over estimates shear and bending over much of the wing and drives you to put in more weight than you have any need to do. To do it, you are doing the elliptical distribution anyway. So why so something that is NOT what nature does when we pass a foil through a fluid?
Yes it is exactly that, an average of planform and elliptical. And while it would call for additional weight to the spars it would also give a conservative value to the load on lift struts of a strut based wing would it not? But this would then cause a reduced calculated load on the root fitting and/or cabane struts.
Perhaps using the Shrenk values to engineer the lift struts and the elliptical value to engineer the cabanes would give each a conservative value, and still be much less "overbuilt" than using planform or a rectangular distribution to calculate the lift struts and a linear (triangular?" lift distribution to calculate the cabane struts. - But I guess this is the RV thread with no struts....

#### Fenix

##### Well-Known Member
HBA Supporter
Just saying... If the planform analysed with Schrenk happened to have rounded tips, the resulting lift distribution would go to zero at the tips. A wing with an elliptical planform will have an elliptical lift distribution.

That seems correct. Since the "Schrenk line" is an average of elliptical lift and planform lift, if the planform were elliptical both the planform line and elliptical line would be, well, elliptical. Therefore the average of the two identical lines would be the same identical line. The only way the schrenk line will go to zero at the tip is if the planform goes to zero at the tip, such as the elliptical planform or the unlikely case of a wing that tapered to a point at the tip.

#### mcrae0104

##### Well-Known Member
HBA Supporter
Log Member
Yes it is exactly that, an average of planform and elliptical.
The heart of practical engineering judgment is discerning between zero and near zero (to three or four decimal places). Since your margin of safety in aircraft design will be 50% or greater, you can decide whether those thousandths will matter.

(Please note this is not an endorsement of sloppy engineering, only a perspective on the usefulness of the precision of our calculations. Run your wing bending loads with purely trapezoidal lift distribution, then by Shrenk, then by lifting line theory, and see how much practical differenece it makes in your spar moment of inertia requirement, and decide for yourself.)