# How can I calculate the moment coefficient around the center of gravity?

Hi guys I was wondering if you could help me with the following problem:

• Wing surface area= 260m2 (sw)

• MAC= 6.608m (cw)

• horizontal stabilizer surface area=69.5m2 (st)

• distance from the cog till the aerodynamic center of the horizontal stabilizer=30m (lt)

• change in downwash angle vs angle of attack de/da=0.5

• distance from wing til aerodynamic center (hacw) = 26% of mac angle (hacw)

• of the wing is 0.12 per degree (aw)

• angle of the stabilizer = 0.07 per degree (at)

• downwash stabilizer at an angle of attack of 0 is e0=0

• moment coefficient of the wing in the aerodynamic center is Cmacw=-0.04

• CoG=31%

Calculate the moment coefficient around the CoG(Cmcg) of the entire airplane when the angle of attack is 3 degrees and the angle of the stabilizer is 1.5 degrees aircraft nose up.

I know the answer which should be Cmcg=-0.022 but I have no idea how it is calculated.

I am sorry, what i did was the following: I calculated the tail volume coficiency which is 1.213564, the position of the neutral point being it 0.61396. I am trying to use the following formula:

$C_{mcg}=C_{macw} + a_w a_w (h-h_{acw}-{a_t\over a_w} V_h (1-{\Delta e\over\Delta a})) + a_t V_h (i_t+e_0)$

when filling in I do the following

$-0.04+a_w A_w (0.31-0.26-{a_t\over a_w} 1.213564 (1-0.5) + a_t × 1.213564(i_t+e_0)$

for aw and at I am not sure to use the 0.12 and 0.07 or do it times 3 and 1.5 for the degrees. it seems to be angle of the stabilizer but I am not sure. e0 I think is 0 but again not sure.

• I am sorry, what i did was the following:
– Jay
Jun 28, 2016 at 14:05
• @Jay I tried making your maths slightly more readable, don't know if I succeeded, feel free to revert the edit if it's no longer accurate. Jun 28, 2016 at 18:26
• @falstro thanks, as you can see I am as green as they come. I'll do better next time!
– Jay
Jun 28, 2016 at 18:42
• Yeah, no worries this MathJax stuff looks pretty much like gibberish if you don't know LaTeX (markup format mostly used for scientific papers) Jun 28, 2016 at 18:57

$-0.04+0.12*3 (0.31-0.26-{0.07\over 0.12} 1.213564 (1-0.5) + 0.07 × 1.213564(1.5+0)=-0.022$