Question

Consider a thin, symmetric airfoil at 1.5° angle of attack. From the results of thin airfoil theory, calculate the lift coefficient and the moment coefficient about the leading edge. (Round the final answers to three decimal places.)

Answer 1

To calculate the lift coefficient, use the formula Cl = 2πα, where α is the angle of attack. The moment coefficient can be calculated using the formula Cm = -2πα/3.

Step-by-step explanation:

The lift coefficient of an airfoil can be calculated using the formula:

Cl = 2πα

where Cl is the lift coefficient and α is the angle of attack in radians. To convert the given angle of attack from degrees to radians, we multiply it by π/180. So, α = 1.5° * π/180 = 0.0262 radians.

Therefore, the lift coefficient is:

Cl = 2π * 0.0262 ≈ 0.164

The moment coefficient about the leading edge can be calculated using the formula:

Cm = -2πα/3

Therefore, the moment coefficient about the leading edge is:

Cm = -2π/3 * 0.0262 ≈ -0.055

Answer 2

1. The lift coefficient is 0.1646

2. The moment coefficient about the leading edge is - 0.04115

How to solve for the lift coefficient

1. The lift coefficient for a thin airfoil is given by:

`\[ C_L = 2\pi \alpha \]`

alpha is the angle. This is represented in radians

solving for the moment we have:

`\[ C_{M_{\text{LE}}} = -(1)/(4) C_L \]`

convert 1.5 to radians

`\[ \alpha = 1.5^\circ * (\pi)/(180^\circ) \]`

= 0.2619

`\[ C_L = 2\pi \alpha \]`

= 2 * π * 0.02619

= 0.1646

Hence the lift coefficient is 0.1646

2. Next we solve for the moment coefficient

`C_m=-(1)/(4) C_L`

=
`-(1)/(4) * 0.1646`

= -0.04115

The moment coefficient about the leading edge is - 0.04115