Do biplanes need bigger tail volume coefficients than monoplanes?

Question

Do biplane ultralights need bigger tail volume coefficients than monoplane ultralights?

Horizontal Tail Volume Coefficient

I understand that biplanes don't need a larger horizontal tail coefficients vs a monoplane of the same total wing area and same wing span. This is because the chord is would be half of the monoplane, but there are two wings, so the "total chord" is the same, so the horizontal tail volume coefficient does not need to increase. I'm told a typical tail volume coefficient for light airplanes is 35%.

I understand that the horizontal tail volume may actually be lower than that of a monoplane if the wings are staggered, the wings acting like a reflex wing and reducing the wing moment, so a smaller horizontal tail volume may be used in this specific case.

Vertical Tail Volume Coefficient

I understand that the vertical tail volume coefficient on a biplane is twice as large as that of a monoplane with the same span, as there are two sections of span that the vertical tail needs to control. I'm told a typical vertical tail volume coefficient is 3.5% for light aircraft.

Is this correct?

Answer 1

Tail volume is a measure for the ability of the tail to compensate for the destabilizing pitch moment created by the wing in case of the horizontal tail and for adverse yaw in case of the vertical tail. This pitch moment is proportional to the square of the wing chord (one factor comes from the area, the second from the lever arm), so if you compare two otherwise equal designs, one of which is a biplane and the other a monoplane of twice the chord, the dimensionful horizontal tail volume (expressed as tail surface times tail lever arm) of that monoplane needs to be twice that of the biplane. To counter adverse yaw, however, the dimensionful vertical tail volume is the same.

Tail volume is normally made dimensionless by referencing it to the wing area and the mean aerodynamic chord (for the horizontal) or wing span (for the vertical tail). Since the area of both designs is the same and the MAC of the monoplane twice as large as that of the biplane, both dimensionless horizontal and vertical tail volumes become equal even though the dimensionful horizontal tail volume of the monoplane is twice as large.

However, if you compare wings of the same aspect ratio (which might be a better basis), both the chord and the wing span of the monoplane are larger by a factor of √2 but there is only one wing to consider versus two in case of the biplane. Now the dimensionful horizontal and vertical tail volumes for the monoplane are larger by a factor of √2.

Only when you make the chord of both wings equal (doubling the span of the monoplane in the process) will the dimensionful horizontal tail volume of both designs be equal but now the vertical tail volume needs to be twice as large.

Wing stagger with the same incidence on both wings would move the biplane closer to the monoplane with twice the chord whereas a lower incidence on the rear wing would indeed create that reflex effect and reduce the instability of the wing. Still, you need control power to change angle of attack quickly enough for maneuvering, so I would be careful with any further reduction of tail volume even if the staggered biplane wing by itself is stable already.

Answer 2

Do biplanes need bigger tail coeefficients than monoplanes (of equal wing area)?

Here's where building free flight models and testing them in cross wind conditions is very helpful. As a designer, it is important to consider wing and tail functionality. Many "tailless" designs, such as deltas, have adequate stability without a separate and distinctive "tail". Reducing chord and increasing aspect increases the need for a separate, stabilizing "tail". Some designs put the "tail"(canard) in front to decrease stability and increase maneuverability.

You may find biplanes need a smaller vertical volume than a mono plane of similar wing area. This is consistent with designs of 100 years ago, where "slab sides" also aided in lateral stability.

The testing for for vertical tail volume can be done by releasing the plane in a cross wind, and seeing if it "points" into the wind or turns away. Many mono plane designs, particularly with excessive dihedral "effect", will roll and turn away from the wind. Biplanes seem to be less prone to this, possibly due to a shielding effect of the lower wing to the upper wing from the cross wind.

Tests for adequate horizontal stabilizer size will include adequate directional and static stabilility, but also there is one very important aspect of inertial rotation effect for larger aircraft. The horizontal stabilizer needs to be larger to arrest pitching momentum before it exceeds stall AOA and effectively reduce AOA faster than it increases from relative wind shift from downward acceleration as the plane "sinks" from loss of lift. This issue is much less common in GA sized aircraft unless aft CG limit is abused.

One may also find a wider wing, or 2 "staggered" wings, reduces the need for a horizontal stabilizer. But keep in mind using the wing as a stabilizer may reduce its efficiency of lifting, it's primary task. Notice "flying wings" have yet to replace the classic "wing and tail" design of modern sailplanes, though they can be very stylish looking.

There are many factors which go into the sizing of the vertical and horizontal stabilizer. For a (low Mach number) recreational aircraft, adequate "anhedralling" (side area below the CG) helps eliminate the need for excessive V stab area, as well as a longer torque arm (longer fuselage).

Evaluation of 120 years of existing and proven aircraft design, and choosing the parameters of desired performance, may be more useful than "rule of thumb". Essentially, it is a trade-off of stability, maneuverability, and drag before software is needed to keep one from crashing.