# Some good stuff coming from an online aviation safety posting.

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Overbanking Tendency

When we bank an airplane and allow it to turn—as opposed to performing a slip—one wing creates more lift than the other. That’s the wing outside the turn. If we’re turning left, as depicted in the diagram at right, the right wing generates more lift. Why? Because it’s moving faster through the air than the inside, left wing. Both wings are bolted to the fuselage—how is that possible? Precisely because both wings are bolted to the fuselage, the outside wing has to move faster than the inside one.

Look again at the diagram at right. The dashed red lines detail the paths each wing takes in the turn. The outside/right wing—in this example—has greater distance to travel in the same amount of time, so it has to move through the air faster, however slightly.

Since the outside wing is moving faster, it generates more lift than the inside one. A result of generating more lift is that the outside wing wants to rise, increasing the bank angle. The effect is more pronounced the greater the difference in the wings’ speed—bank angle, in other words. When performing steep turns, the overbanking tendency is at its greatest.

Wishing everyone a fantastic 2022.....

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The bank angle effect is not correct. At 90 degrees both wings travel the same distance. 90 degrees is not possible to obtain but proves the principle. The centre of lift produced spanwise,  would be at a point less than 1/2 each individual wingspan from the fuselage sides.  Do the diagram to anywhere near correct scale and you'd see the difference in distance is a small % . The lower the bank angle the greater the distance difference. From a flat turn (looks like a flat washer) to a medium turn (looks like a truncated cone) to a vertical bank(looks like a cylinder) you can see how it happens.. The inner wing travels  about 50 feet less than the outer one each 360 turn. A reasonably tight turn will achieve about  a 700 ft radius equals 2200 ft distance travelled. 50/2200 isn't much.  and that's about the best you could get.  Look up climbing and descending turns where other factors get involved but when you demonstrate them it's hard to get a convincing result BECAUSE of the same consideration. The effect is not large and just keeping the ball centred is of more use. Nev

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The article was discussing why, in a flat turn, the outer wing rises.  This effect is commonly referred to as the secondary effect of yaw in an aircraft.

The ‘distance’ the inner and outer wing travel in a turn is irrelevant with regards to the outer wing creating more lift.

It is the ‘difference in airspeed’ between the inner and outer wing causing the outer faster travelling wing to create more lift.

Consider the following:

·         A Jabiru UL flying at a 100mph

·         A rate one turn (180deg in one minute)

·         Wingspan 10mtrs.

With these figures the difference in airspeed between the inner and outer wing is around 1%.  The lift difference between the inner and outer wing is around 2% .

Things become a lot more interesting if we now carry out a steeper turn say a 90 deg turn in 6 seconds at a lower airspeed of 60mph.

If you do the math the difference in airspeed between the inner and outer wing is now around 4%.

Since lift is a quadratic function of airspeed the difference in lift between the inner and out wing would be near to 9%.

This is one of the main reasons why, in a long span aircraft such as a glider, there is considerable amount of bank ‘hold off’ when turning steeply either way in a thermal.

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The effect is very noticeable in thermalling gliders, where you are often applying opposite controls to keep the glider from steepening its turn.

And, as usual, Nev is correct. The effect of bank is to  make the speed of each wing more equal.

Once I watched in awe as two 21m span nimbus 3 gliders were thermalling very tightly and approaching that impossible 90 degrees of bank.  Actually the dihedral and flexing meant that the tip of the  outer wing was close to  90 degrees, but the inner wing was less. And yes they were climbing in a tight thermal core and going up fast. I dunno how hard it would have been for them to shift their circle, but it was a great example of how open class gliders really are better.

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Correction....  I looked up the span of the nimbus 3. It can be 22.9 m to 25.5m, depending on the wing extensions in use.

Wow, says me, my jabiru is nearer 8m.

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6 hours ago, lee-wave said:

.... It is the ‘difference in airspeed’ between the inner and outer wing causing the outer faster travelling wing to create more lift.

Consider the following:

·         A Jabiru UL flying at a 100mph

·         A rate one turn (180deg in one minute)

·         Wingspan 10mtrs.

With these figures the difference in airspeed between the inner and outer wing is around 1%.  The lift difference between the inner and outer wing is around 2% .

Things become a lot more interesting if we now carry out a steeper turn say a 90 deg turn in 6 seconds at a lower airspeed of 60mph.

If you do the math the difference in airspeed between the inner and outer wing is now around 4%.

Since lift is a quadratic function of airspeed the difference in lift between the inner and out wing would be near to 9%.

This is one of the main reasons why, in a long span aircraft such as a glider, there is considerable amount of bank ‘hold off’ when turning steeply either way in a thermal.

A chap by the name of Daniel Chisholm has run similar numbers

but his conclusion was that in such a manoeuvre the effect was "pretty negligible".    QUOTE:

"With respect to the difference in speed over the wings, let's run some numbers and see:

• small aircraft flying at 100knots/100mph (50m/s in round terms)
• A comfortable turn rate - 180 degrees in one minute
• wingspan 33'/10m (so 5m from a/c centreline to each wing tip)

Turning 3 degrees per second means that the wingtips have a speed difference of tan(3 degrees)/sec * 10m, which is 0.52m/s or 1%. Even with the fact that lift is proportional to the square of the airspeed (so the lift at the wingtips differs by 2%), this is still a pretty small and pretty negligible effect in cruising-like maneuvers like this."

And yes, he did go to say that:

Where thing get more interesting is with lower speeds and higher turn rates (for example during an approach to landing, with the last 90 degree turn onto final approach). If the airspeed is 60knots (0.6X the above) and the turn rate 90 degrees in 6s (so 15deg/s or 5X the above), then the difference in airspeed between wingtips will be about 8.3 times as much or about 4.4% Based on a the lift being a quadratic function of speed this indicates a 9% difference in lift, and in fact closer to the stall speed like this the lift-vs-angle-of-attack curve is nonlinear and increases the effect further.

answered Jan 4 '12 at 17:03
Daniel Chisholm

Edited by Garfly
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