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. enter image description here


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.

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

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

  • $\begingroup$ Thank you so much. I really appreciate it. $\endgroup$ – M.D. White Aug 2 at 0:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.