Question 5.3: Consider tests of an unswept wing that spans the wind tunnel......

First, we need to calculate the section lift coefficient. We will assume that the lift is a linear function of the angle of attack and that it is independent of the Reynolds number (i.e., the viscous effects are negligible) at these test conditions. That these are reasonable assumptions can be seen by referring to Fig. 5.12. Thus, the section lift coefficient is

C_l=C_{l, \alpha}\left(\alpha-\alpha_{0 l}\right)       (5.9)

Using the values presented in the discussion associated with Fig. 5.12,

C_l=0.104(4.0-(-1.2))=0.541

At an angle of attack of 4^{\circ}, the experimental values of the section lift coefficient for an NACA 23012 airfoil section range from 0.50 to 0.57 .

To calculate the corresponding lift force per unit span, we rearrange equation (5.8)

C_l=\frac{l}{q_{\infty} c}    (5.8)

to obtain

l=C_l q_{\infty} c

To calculate the dynamic pressure \left(q_{\infty}\right), we need the velocity in \mathrm{m} / \mathrm{s} and the density in \mathrm{kg} / \mathrm{m}^3.

U_{\infty}=360 \frac{\mathrm{km}}{\mathrm{h}} \frac{1000 \mathrm{~m}}{\mathrm{~km}} \frac{\mathrm{h}}{3600 \mathrm{~s}}=100 \frac{\mathrm{m}}{\mathrm{s}}

Given the density altitude is 3 \mathrm{~km}, we refer to Table 1.2 to find that

\frac{\rho}{\rho_{\mathrm{SL}}}=0.74225

(Note: The fact that we are given the density altitude as 3 \mathrm{~km} does not provide specific information either about the temperature or about the pressure.)

\rho=(0.74225) 1.2250 \frac{\mathrm{kg}}{\mathrm{m}^3}=0.9093 \frac{\mathrm{kg}}{\mathrm{m}^3}

Thus, the lift per unit span is