Using Tail Volume Coefficients in Airplane Design

[Air-headed Aviator]

If you ever designed an airplane yet was never sure how big to make your horizontal and vertical stabilizers, you could use tail volume coefficients to give you a frame work. TCVs are a dimensionless value that describe how effective the stabilizing fins are on an aircraft. There is a specific formula for calculating TCVs of an aircraft, and you can reconfigure those formulas to figure out the area they should be for a desired TCV.

The Formula for configuring the Horizontal Stabilizer Area is:

V_H stands for Horizontal Volume Coefficient. M.A.C stands for Mean Aerodynamic Chord, and of the main wing. And Length refers to the distance between the intended center of gravity for the wing and the aerodynamic center of the horizontal stab (typically 20% of the stabilizer mean aerodynamic chord).

The Formula for configuring the the Vertical Stabilizer Area is:

V_v stands for Vertical Volume Coefficient. Length refers to the distance between the intended center of gravity of the main wing and the aerodynamic center of the vertical stabilizer. (typically 20% of the stabilizer mean aerodynamic chord).

The size of both the Horizontal and Vertical stabilizer are dependent on how far away they are placed from the wing center of gravity, the area of the wing, and the chord for horizontal while wing span for vertical. The farther the stabs are from the wing the smaller they can be to produce the same effect. The larger the wing is the larger the stabilizers need to be to achieve the desired effect. The Tail Volume Coefficients are the third ingredient to tailplane sizing.

Below are examples of graphs sourced from Hamburg University of Applied Science that lists various TVCs of a variety of aircraft:

The graphs list out calculations from various aerodynamicists over the years, some listing specific values and others ranges. You can see how larger values are associated for larger aircraft, and smaller values for either small or extremely fast aircraft - some jet fighter values are actually lower than home built aircraft values for horizontal stability, though higher for vertical stability.

From these graphs one may assume that to have an RC design with stability/agility characteristics of a Jet Fighter that those listed TCVs should be used in one's calculations, however one must consider that RC aircraft are slow. The TCVs of Jet Fighters, Jet Transports, and Airliners are considering cruising speeds above Mach 0.75-0.8. RC planes are typically flying at Mach 0.07, significantly slower. It is my recommendation that the coefficients associated for Homebuilt aircraft or even commuters is the best match for RC plane designs, whether slow flight or sport/speed planes.

When you're going about using these formulas the process as always begins with the wing. The wing determines the capability of the aircraft. After the wing is chosen a designer can decide how long or short the airframe can be to best fit their goals. There are limitations to how short you can make an aircraft, as if the tailplane is too close to the wing it can be blanketed by wing wake and cause the aircraft to spin out of control. Going too long introduces diminishing returns on drag, weight, and strength. With these decisions made a designer can then use the formulas above to find the area of their stabilizers. If doing aircraft with twin tails, the area found for the vertical stab is duplicated between them. If a design introduces dihedral or angles to the stabilizers the designer has to accommodate that angle with Pythagorean Theorem, using trigonometric equivalents with the angle in use. These formulas work also for Canard aircraft, but not for tailless aircraft that lack either horizontal stabs, vertical stabs, or both.

 

[Mr NCT]

If you ever designed an airplane yet was never sure how big to make your horizontal and vertical stabilizers, you could use tail volume coefficients to give you a frame work. TCVs are a dimensionless value that describe how effective the stabilizing fins are on an aircraft. There is a specific formula for calculating TCVs of an aircraft, and you can reconfigure those formulas to figure out the area they should be for a desired TCV.

The Formula for configuring the Horizontal Stabilizer Area is:

View attachment 256151
V_H stands for Horizontal Volume Coefficient. M.A.C stands for Mean Aerodynamic Chord, and of the main wing. And Length refers to the distance between the intended center of gravity for the wing and the aerodynamic center of the horizontal stab (typically 20% of the stabilizer mean aerodynamic chord).

The Formula for configuring the the Vertical Stabilizer Area is:

View attachment 256152

V_v stands for Vertical Volume Coefficient. Length refers to the distance between the intended center of gravity of the main wing and the aerodynamic center of the vertical stabilizer. (typically 20% of the stabilizer mean aerodynamic chord).

The size of both the Horizontal and Vertical stabilizer are dependent on how far away they are placed from the wing center of gravity, the area of the wing, and the chord for horizontal while wing span for vertical. The farther the stabs are from the wing the smaller they can be to produce the same effect. The larger the wing is the larger the stabilizers need to be to achieve the desired effect. The Tail Volume Coefficients are the third ingredient to tailplane sizing.

Below are examples of graphs sourced from Hamburg University of Applied Science that lists various TVCs of a variety of aircraft:

View attachment 256155 View attachment 256156

The graphs list out calculations from various aerodynamicists over the years, some listing specific values and others ranges. You can see how larger values are associated for larger aircraft, and smaller values for either small or extremely fast aircraft - some jet fighter values are actually lower than home built aircraft values for horizontal stability, though higher for vertical stability.

From these graphs one may assume that to have an RC design with stability/agility characteristics of a Jet Fighter that those listed TCVs should be used in one's calculations, however one must consider that RC aircraft are slow. The TCVs of Jet Fighters, Jet Transports, and Airliners are considering cruising speeds above Mach 0.75-0.8. RC planes are typically flying at Mach 0.07, significantly slower. It is my recommendation that the coefficients associated for Homebuilt aircraft or even commuters is the best match for RC plane designs, whether slow flight or sport/speed planes.

When you're going about using these formulas the process as always begins with the wing. The wing determines the capability of the aircraft. After the wing is chosen a designer can decide how long or short the airframe can be to best fit their goals. There are limitations to how short you can make an aircraft, as if the tailplane is too close to the wing it can be blanketed by wing wake and cause the aircraft to spin out of control. Going too long introduces diminishing returns on drag, weight, and strength. With these decisions made a designer can then use the formulas above to find the area of their stabilizers. If doing aircraft with twin tails, the area found for the vertical stab is duplicated between them. If a design introduces dihedral or angles to the stabilizers the designer has to accommodate that angle with Pythagorean Theorem, using trigonometric equivalents with the angle in use. These formulas work also for Canard aircraft, but not for tailless aircraft that lack either horizontal stabs, vertical stabs, or both.

That's going to be useful! Why isn't it TVCs (tail volume coefficient)?

 

[Air-headed Aviator]

That's going to be useful! Why isn't it TVCs (tail volume coefficient)?

Because I was having a Dislexic moment 😅

 

[Mr NCT]

Because I was having a Dislexic moment 😅

On the positive side you're consistent!

 

[telnar1236]

Definitely a good tool to use for sizing the tail

 

[telnar1236]

From these graphs one may assume that to have an RC design with stability/agility characteristics of a Jet Fighter that those listed TCVs should be used in one's calculations, however one must consider that RC aircraft are slow. The TCVs of Jet Fighters, Jet Transports, and Airliners are considering cruising speeds above Mach 0.75-0.8. RC planes are typically flying at Mach 0.07, significantly slower. It is my recommendation that the coefficients associated for Homebuilt aircraft or even commuters is the best match for RC plane designs, whether slow flight or sport/speed planes.

One important thing to consider is that the Mach number is not the only thing affecting the TVC. The wing aspect ratio and the desired feel of the plane also plays a role. For example, a fighter jet like design might have a more close-coupled wing and tail resulting in a much lower TVC while still maintaining the same aerodynamic stability and pitch damping as a design with longer tail simply by having less mass behind the wing as well as a shorter moment arm.
Pretty much always, the "best" design for an RC plane will have a straight wing with a moderate aspect ratio wing and a longer tail - basically a warbird or trainer arrangement, but sometimes we want to build planes that fly interesting as much as fly well.

When you're going about using these formulas the process as always begins with the wing. The wing determines the capability of the aircraft. After the wing is chosen a designer can decide how long or short the airframe can be to best fit their goals. There are limitations to how short you can make an aircraft, as if the tailplane is too close to the wing it can be blanketed by wing wake and cause the aircraft to spin out of control. Going too long introduces diminishing returns on drag, weight, and strength. With these decisions made a designer can then use the formulas above to find the area of their stabilizers. If doing aircraft with twin tails, the area found for the vertical stab is duplicated between them. If a design introduces dihedral or angles to the stabilizers the designer has to accommodate that angle with Pythagorean Theorem, using trigonometric equivalents with the angle in use. These formulas work also for Canard aircraft, but not for tailless aircraft that lack either horizontal stabs, vertical stabs, or both.

Definitely a good approach for most planes to start with the wing. Something important to keep in mind with this approach is that it's essentially a more rigorous way to make your airplane similar to what has worked before - these recommended values are established by looking at large numbers of successful historical planes. That means that if you have a wild design that is well outside the norms, though, it doesn't work too great