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How can an all flying rudder be almost 100% more efficient than a vertical tail and rudder?

According to the Zenith school of aircraft design, a rule of thumb for the size of an all flying rudder is 7% of wing area. For a classic vertical tail and rudder, the rule is 12%. That's an increase in area of almost 100%!!

A classic rudder foil, something like a NACA0012, has a max cL of roughly 1.5.

A vertical stabilator and rudder is like a wing and an unslotted flap, which adds cL of about 0.7. That's a total cL of about 2.2, which works out to an increase in efficiency of 50%.

So... why is an all flying rudder 100% more efficient, if a vertical stab and rudder produce 50% more lift?

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  • $\begingroup$ Exactly what is happening? What are the conditions? Presumably your comparison does not involve a test of weathervane stability, with the pilot's feet off the rudder pedals! $\endgroup$ – quiet flyer Jul 25 '19 at 20:55
  • $\begingroup$ Yes, this would include weathervane stability with the pilot's feet on the rudder pedals. $\endgroup$ – Fred Aug 14 '19 at 16:39
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Because on the Zenith the massively slab sided fuselage is the vertical stabilizer, and the rudder is still the rudder. The surface area of the all flying rudder is about the same as the rudder on a normal plane, and it depends on the fuselage for weathervaning tendency. There's no free lunch. If you build a Zenith with a skinny boom tail and the all flying rudder, it will be quite marginally stable in yaw, like a Fokker DR-1.

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  • $\begingroup$ The slab sided fuselage would definitely be used in the tail volume calculation $\endgroup$ – Fred Aug 14 '19 at 16:38
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When we deflect the rudder to create an intentional sideslip, the net sideforce from the fin-rudder combination actually acts in the WRONG direction-- OPPOSITE to the direction that we are trying to shift the rear of the aircraft. The fin is "fighing" the rudder. Therefore we have more rudder power-- we can achieve a higher sideslip angle-- if we get rid of the fin.

This is explained in more detail in this highly related answer -- How is a sideslip maintained (aerodynamically)?

On the other hand if we are just trying to use the rudder to oppose some other yaw torque (such as P-factor) and maintain a zero slip angle as measured by a yaw string, then the fin isn't "fighting" the rudder any more and the rudder might be more efficient when the fin is present than when the fin is not. However, if we are talking about a fixed total area of fin and rudder combined, it's not hard to see even in the zero-slip condition, the all-moving rudder would have more power than a smaller rudder plus a fixed fin.

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  • $\begingroup$ For passive yaw stability, the rudder does nothing. It just wants to trail unless you hold it centered with your feet. You can add the rudder into the passive yaw stability equation by adding an anti-servo tab or installing bungee centering springs which tend to fix the rudder at neutral so it contributes to passive weathevaning to the extent of the spring stiffness. Cessna 180s and 185s use centering spring bungees to provide enough yaw stability to require no additional fin area when on floats. The force you have to apply to overcome the springs is a pain though. $\endgroup$ – John K Jul 25 '19 at 21:06
  • $\begingroup$ @JohnK -- true-- as noted in my comment under question, we have to ask exactly what is being tested. $\endgroup$ – quiet flyer Jul 25 '19 at 21:10
  • $\begingroup$ Future edit: add link to Zenair webpage-- "Rudder" section mentions virtues of all- moving vertical fin for exceptional crosswind performance ( i.e. ability to attain large sideslip angles). zenithair.com/stolch801/design/design.html $\endgroup$ – quiet flyer Aug 2 '19 at 0:49
  • $\begingroup$ I've flown the Zenith 750 with the demo pilot in Mexico Missouri and yes it had a lot of yaw power and I don't recall it being squirrely in yaw, so I guess the fuselage side area does the job. $\endgroup$ – John K Aug 2 '19 at 3:12
  • $\begingroup$ I still don't see how the fin is fighting the rudder. Deflection is lift. A classic NACA foil generates max lift at about 15deg at a cL of about 1.5. Add a stab with a gap and the vertical tail becomes a "slotted wing with a flap", which adds a cL of about 1.3 for a max cL of about 2.7. That's generating almost twice the lift, not less lift , providing you're deflecting the rudder at about 15 deg. $\endgroup$ – Fred Aug 14 '19 at 16:35
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I would caution against comparing the effectiveness of stabilizing surfaces using CLmax, or generally any surface using CLmax alone (see related question: What happens when you put vortex generators on both sides of a symmetrical vertical tail?). The efficiency of an aircraft is more than its maximum lift.

Sure, a rudder is a plain flap. But why do you need rudder, other than coordinated turn? I can think of two operational scenarios: crosswind landing (1), and trim for asymmetry (2).

In (1), the maneuver is initiated at zero sideslip, hardly CLmax which corresponds to high flow incidence. Once you are established in a steady-state wings-level skid (fully de-crabbed), the sideslip is actually opposite of the rudder deflection. The CLmax for plain flap is inapplicable.

In (2), the worst case is one engine inoperative. Sideslip here could be positive or negative, depending on whether banked into the live engine(s). Still, the sideslip is not near the maximum incidence.

Now onto the all moving rudder vs. traditional stab+rudder, all moving rudder has a larger surface area so it's a more effective rudder. However, I would caution against decreasing the overall tail volume since it affects your weathercock stability and dutch-roll. That's not accounting for other factors such as heavier actuators for all moving surfaces.

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  • $\begingroup$ You also need tail volume for yaw control, especially in slow flight, getting out of a spiral $\endgroup$ – Fred Aug 14 '19 at 16:42

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