Why do moderate tapered wings stall first at mid-wing section and high tapered wings stall at tip first? The effective AoA should be always higher close to the root? (considering no geometric or aerodynamic washout)
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2$\begingroup$ Please take a look at this answer here and see if it clears your question: aviation.stackexchange.com/a/75333/41375. With taper, the local Cl is actually lower at the root at higher AOA. $\endgroup$– JZYLJan 10 at 16:28
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$\begingroup$ Related: Twist optimization for a low speed aircraft $\endgroup$– ymb1May 10 at 12:30
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$\begingroup$ This is a great question. Kermode (The Mechanics of Flight pp.86-7) notes that the stalling angle is essentially constant regardless of airfoil section or airspeed. Clancy (Aerodynamics p.99) notes the phenomenon of tip stall on a tapered wing but does not attempt to explain it. Many pretty diagrams can be found of what happens, but none that I have seen explain why. $\endgroup$– Guy InchbaldMay 11 at 9:39
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I will try to make it simple without going into mathematical details.
Here, λ = ctip/croot
The important factors controlling the lift in the Tapered wing.
The ctip being too small affects the Reynolds Number (as the distance travelled is very small). Assuming the constant speed, density and viscosity, Reynolds number only varies with the distance travelled (x) directly. As the tip distance is too small, Reynolds number is not much increased for the boundary layer and therefore transition from laminar flow to turbulent can not happen. Also due to skin friction, the flow gets slow and becomes separated. The separation causes loss of Lift and thus Wing Tips stall first.
The sweepback effect makes the boundary layer tends to flow spanwise toward the tips and becomes separated near the leading edges of tip.
- Increasing Span Efficiency Factor,e as it is higher for tapered wings, it produces more Cl.
There may be other factors too, that I might have missed. But these are the most prominent. You can refer to below image. The Red Line shows seperated flows.
Yes, wingroot has a higher effective AoA. It is easier to understand this way. For a given AoA, the wingtips suffer from downwash and vortices which decreases AoAeff and increases Induced AoA (AoAi). As the wingroots do not suffer from the vortices, their AoAeff is higher.
Figure 2 & 3: FAA Pilot's Handbook of Aeronautical Knowledge
Figure 4: Introduction to Flight, Anderson
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$\begingroup$ You might consider replacing the second diagram with one of a trapezoidal wing. Otherwise, the point you make about the "sweep effect" is lost on the inattentive reader. $\endgroup$– AbdullahMay 10 at 15:35
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$\begingroup$ How does Reynolds number affect it? As pointed out in the original question, at first sight, the downwash over a tapered wing reduces its AoA which should reduce its tendency to stall. Why do you claim it makes matters worse? $\endgroup$ May 10 at 17:36
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$\begingroup$ @GuyInchbald Low Reynolds number (Laminar flow) are easily separated from the boundary layer, causing stall. aviation.stackexchange.com/q/78923/44391 A downwash decreases AoA"effective". The AoA measured from relative airflow is higher, which increases CL, and is directly proportional to Cd,induced. $\endgroup$ May 10 at 20:56
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$\begingroup$ @NoorulQuamar The discussion you link to does not mention Reynolds number. Nor is it clear how an "effective" decrease in AoA causes the effects of an increase. The lack of clarity in reply suggests to me a lack of clarity in understanding, and therefore no guarantee of being correct. $\endgroup$ May 11 at 9:22
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$\begingroup$ @GuyInchbald The link was for separation vs turbulent,(I am sorry, I did not mention it). Reynolds Number is proportional to distance travelled (x). Due to Ctip being smaller, Reynolds Number is not much for the flow to transit into turbulent, and it is slowed to such speed that separation becomes easier. The separation causes loss of lift and thus stall. $\endgroup$ May 11 at 10:57
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The main reason is the Reynolds number and the way it affects the airflow.
The stalling angle is more or less constant for all airfoils over a range of speeds. The shape and airspeed of the airfoil in themselves make very little difference to the stall angle. The stalling speed of a plane is dictated mainly by the angle of attack required to provide adequate lift at that speed.
Spanwise flow is also not a primary issue, as its direction varies markedly between types with a more sharply swept leading edge vs. types with a more forward-swept trailing edge. Yet both have the same problem with tip stall.
For a straight, constant-chord wing the lifting pressure causes an upflow in front of the leading edge near the root. This increases the effective AoA, so it reaches the critical angle and stalls first. The sideways spillage around the tip reduces the lift and hence also the AoA effect.
For a sharply tapered wing the Reynolds number becomes relevant. It is, for the present purpose, a function of the size of the airfoil and the speed and viscosity of the air. Since we are not discussing altitude we can take the viscosity as constant. Large size and high speed mean a large Reynolds number.
For a high Reynolds number, inertial effects of the air mass dominate and flow tends to be laminar for a long way back.
For a low Reynolds number, the viscosity of the air comes to dominate and it is this which tends to create turbulence as the pressure falls above the wing.
The angle of attack at which flow separation occurs thus depends critically on the Reynolds number.
A sharply tapered wing has a high Reynolds number at the root, so smooth flow is maintained to a relatively high AoA. But it has a low Reynolds number at the tip, so the air viscosity leads to flow separation and stall.
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$\begingroup$ This is much better, as it discusses the underside of the wing root, but... focusing on the top of the wing, spanwise flow is an issue as it weakens the downwash behind the wing, allowing the low pressure bubble to shorten (onset buffeting). Laminar flow separation (oh, the other stall) is the Reynolds effect on the shorter chord. Slower, shorter chords try to "trip" the flow, creating an energized layer less prone to separation. But I would submit it is inertial mass of air that resists bending, and viscosity that enables air stream molecules not to fly apart when "bent". $\endgroup$ May 11 at 12:52
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$\begingroup$ So, we must do this in a wind tunnel, first with air, then helium, then (why not!), CO2. A little Ingenuity, I guess. $\endgroup$ May 11 at 12:53
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$\begingroup$ @RobertDiGiovanni Viscosity does not work that way round. Superfluid helium has no viscosity and no turbulence. Warm it up above the critical temperature and as the viscosity appears so that it is no longer superfluid, so does the turbulence. $\endgroup$ May 11 at 13:01
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$\begingroup$ There are really 2 ends to it. Viscosity more important at low Re (insects) and laminar to turbulent at high Re. Forming a stable low pressure "bubble". Beyond that its all bottom lift. It seems the modeling is with "inviscid flow" for that reason. $\endgroup$ May 11 at 16:01
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Spanwise flow seems to have a lot to do with it, and the wingtip vortices can affect both the local effective Angle of Attack and the airflow of the upper wing. (Credit to @Noorul Quamar)
Let's start with the rectangular wing. It stalls at the root first. Maximum pressure differential between upper and lower wing, and interference of the fuselage (and prop) with the airflow, cause flow separation here first as AOA increases. The wing tip vortices also help create a "weak spot" in the upper rear center of the wing by drawing airflow towards the wing tips.
Lower Reynolds number, from shorter chord, will also cause a wing section to stall at a lower AOA. With a moderately tapered wing, both effects tend to cancel each other out, and the onset of stall averages between the wing tip and fuselage.
With a highly tapered wing (without washout), the progressively shorter chord becomes the overriding factor. In spite of their excellent aerodynamic efficiency (as seen on sea gulls and DC 3s), these wings stall at the tips first, and are notoriously dangerous in "low and slow" turning flight.
Washout, and/or leading edge slats, makes these wings much safer. Bending a tapered tip up to form a "winglet" is also currently in vouge. Reverse sweep has also been studied.
Further information is available at airfoil tools
answered May 10 at 10:50
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$\begingroup$ Per the JZYL's linked answer fuselage isn't needed; rectangular wing stalls root-first even by itself, the reduction of efficiency towards the tips is all it takes. $\endgroup$ May 10 at 10:57
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$\begingroup$ For a circular bracing wire, airflow is smoother at low Reynolds numbers. Why should an airfoil be different? $\endgroup$ May 10 at 11:34
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$\begingroup$ @Guy Inchbald Because bracing wires are not tasked to generate lift. Here the velocity factor of the Reynolds may be more significant. With a wing, for a given situation, velocity is constant, leaving chord as the variable (for a given AOA). Thanks Jan. $\endgroup$ May 10 at 11:35
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2$\begingroup$ Found this neat explanation by Peter: The tapered wing will produce induced loads on the outer wing due to the amount of suction of the deep inner wing. $\endgroup$– ymb1May 10 at 12:24
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1$\begingroup$ While smaller Reynolds numbers are indeed part of the explanation, the stronger effect is the higher lift coefficient at the outer section of the tapered wing. Circulation (equivalent to local lift coefficient times local chord) always tends to be elliptical over span and the local lift coefficient has to make up for the missing chord. $\endgroup$ May 10 at 18:01