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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

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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.

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

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

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