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Question

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VIPSolutions · Accepted Answer

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**Required information**

Consider a positively cambered airfoil with a zero-lift angle of +4.00°.  
The lift slope is .1 per degree.

A virtual angle of attack must be made inside and/or be set to generate the same lift as that when it is right-side up at a 5° angle of attack.  
The angle is ___°.

---

VIPSolutions · Answer

# Calculation of Virtual Angle of Attack for a Positively Cambered Airfoil

## Given Data
- **Zero-lift angle ($\alpha_0$)**: +4.00°
- **Lift slope ($C_L/\alpha$)**: 0.1 per degree
- **Desired lift angle ($\alpha$)**: 5°

## Calculation Steps

1. **Calculate Lift Coefficient at 5° Angle of Attack**:
   $$
   C_L = C_L/\alpha \times (\alpha - \alpha_0)
   $$
   Substitute the values:
   $$
   C_L = 0.1 \times (5 - 4) = 0.1 \times 1 = 0.1
   $$

2. **Determine Required Angle of Attack**:
   To find the virtual angle of attack ($\alpha_v$) that achieves the same lift coefficient:
   $$
   0.1 = 0.1 \times (\alpha_v - 4)
   $$
   Rearranging gives:
   $$
   \alpha_v - 4 = 1 \quad \Rightarrow \quad \alpha_v = 5° + 4° = 9°
   $$

## Conclusion
The virtual angle of attack required to generate the same lift as when the airfoil is right-side up at a 5° angle of attack is **9°**.

VIPSolutions · Answer

# Aerodynamics of Airfoils

## Topic: Virtual Angle of Attack Calculation

### Overview
This section discusses how to determine the virtual angle of attack for a positively cambered airfoil to achieve the same lift as when positioned at a specified angle of attack.

### Key Concepts
- **Zero-lift Angle**: The angle of attack at which the lift coefficient is zero.
- **Lift Slope**: The rate of change of lift coefficient with respect to angle of attack.
- **Virtual Angle of Attack**: An angle that, when applied, produces the same lift as a given angle of attack.

### Calculation Example
1. **Parameters**:
   - Zero-lift angle ($\alpha_0$): +4.00°
   - Lift slope ($C_L/\alpha$): 0.1 per degree
   - Desired lift angle ($\alpha$): 5°

2. **Lift Coefficient Calculation**:
   $$
   C_L = C_L/\alpha \times (\alpha - \alpha_0) = 0.1 \times (5 - 4) = 0.1
   $$

3. **Determining Virtual Angle of Attack**:
   $$
   0.1 = 0.1 \times (\alpha_v - 4)
   $$
   This simplifies to:
   $$
   \alpha_v = 9°
   $$

### Conclusion
The required virtual angle of attack for the airfoil to generate the same lift as at a 5° angle of attack is **9°**.

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