1-The A-4D Skyhawk has the following properties: S=28m^2,b=9m and bar (c)=3.54m . If the aircraft is flying at M=0.4 at sea level (a=340m/s,rho =1.225kg/m^3) , and C_(m_(q))=-3.6 determine the pitching moment change resulting from a change in pitch rate of +10deg/s

To determine the pitching moment change resulting from a change in pitch rate, we can use the following formula:<br /><br />$\Delta M = \frac{1}{2} \cdot S \cdot b \cdot \bar{c} \cdot \alpha \cdot \dot{\alpha}$<br /><br />Where:<br />- $\Delta M$ is the change in pitching moment<br />- $S$ is the wing area<br />- $b$ is the mean chord length<br />- $\bar{c}$ is the mean aerodynamic chord<br />- $\alpha$ is the angle of attack<br />- $\dot{\alpha}$ is the rate of change of angle of attack<br /><br />Given:<br />- $S = 28m^2$<br />- $b = 9m$<br />- $\bar{c} = 3.54m$<br />- $M = 0.4$<br />- $a = 340m/s$<br />- $\rho = 1.225kg/m^3$<br />- $C_{m_{q}} = -3.6$<br />- $\dot{\alpha} = +10deg/s$<br /><br />First, we need to calculate the angle of attack ($\alpha$) using the Mach number ($M$) and the speed of sound ($a$):<br /><br />$\alpha = \frac{M}{\sqrt{M^2 + (\frac{a}{340})^2}}$<br /><br />Substituting the given values:<br /><br />$\alpha = \frac{0.4}{\sqrt{0.4^2 + (\frac{340}{340})^2}} = \frac{0.4}{\sqrt{0.16 + 1}} = \frac{0.4}{\sqrt{1.16}} = \frac{0.4}{1.077} \approx 0.371$<br /><br />Next, we can calculate the pitching moment coefficient ($C_{m_{q}}$) using the given value:<br /><br />$C_{m_{q}} = -3.6$<br /><br />Now, we can calculate the pitching moment change ($\Delta M$):<br /><br />$\Delta M = \frac{1}{2} \cdot S \cdot b \cdot \bar{c} \cdot \alpha \cdot \dot{\alpha}$<br /><br />Substituting the given values:<br /><br />$\Delta M = \frac{1}{2} \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\Delta M = 0.5 \cdot 28 \cdot 9 \cdot 3.54 \cdot 0.371 \cdot 10$<br /><br />$\