# How do you calculate the vertical and horizontal tail volume if you have Vvbar and Vhbar?

I know the general formulas for calculating the horizontal and vertical tail volumes. Unfortunately, I only have Vvbar and Vhbar. I’ve checked through multiple textbooks and I don’t know why I can’t find an expression for Vvbar.

This is what I have.

The 'bar' volumes are the same volumes but taken with respect to the wing-body aerodynamic centre (AC) rather than CG. This is more convenient because this is a constant reference, whereas CG may move.

The difference between them is only the arm: $$\overline{c}(h-h_{n_{wb}})$$, which leads to your last expression for $$V_H$$.

For the yaw motion, the aerodynamic centre of the wing is much less relevant(*), and thus the 'plain' $$V_V$$ (with respect to CG) is commonly used. This is why you can't find an expression for $$\overline{V_V}$$.

Nevertheless, if we want to relate it to the same wing-body AC as for $$V_H$$, we can do it. However, in lateral motion the generic reference is the wing span $$b$$ rather than the MAC $$\overline c$$ (as you can see from your first two definitions). Thus $$\overline c$$ is not eliminated, and we have an uglier expression:

$$\overline{V_V} = V_V + \frac{S_{VT}} S \frac {\overline c} b (h-h_{n_{wb}})$$

(*) It could be related to AC of the body alone (which is typically near the very front of the fuselage), but this is also not very sensible: the wing (and the wing-body interaction) does play a major role. I've never seen $$\overline{V_V}$$ defined like that for airplanes.

• Thank you so much. I really appreciate it. I went in circles for a few days. Commented Aug 2, 2019 at 0:44
• You're welcome. You can select the green tick beside the answer to mark it accepted.
– Zeus
Commented Aug 2, 2019 at 5:09

You need to multiply the cg moment arm ($$h-h_{n_{wb}}$$) by the MAC then divide by reference span.

• Thank you so much. I really appreciate it. Commented Aug 2, 2019 at 0:45