To calculate the maximum speed of the aircraft in straight and level flight, we can use the following principles and formulas.

Question

To calculate the maximum speed of the aircraft in straight and level flight, we can use the following principles and formulas.
### Given Data

- **Wing Area (S)**: 31.83 m²
- **Mass (m)**: 5156 kg
- **Thrust (T)**: 2 × 11 kN = **22 kN = 22000 N**
- **Cdo**: 0.025
- **k**: 0.0445

### Step 1: Calculate Lift at Sea Level

In straight and level flight, lift equals weight:

$$
L = W = m \cdot g
$$

Where $ g $ (acceleration due to gravity) is approximately $ 9.81 \, \text{m/s}^2 $.

$$
L = 5156 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 50553.96 \, \text{N}
$$

### Step 2: Calculate the maximum speed using the lift equation

Lift for a given speed can be represented as:

$$
L = \frac{1}{2} \cdot \rho \cdot V^2 \cdot S \cdot C_L
$$

Where:
- $ \rho $ (air density at sea level) is approximately $ 1.225 \, \text{kg/m}^3 $.
- $ V $ is the speed in m/s.
- $ C_L $ (Lift Coefficient) varies with angle of attack and is typically taken as $ 2\pi \cdot \alpha $ for small angles or can be assumed along with drag in some cases.

However, we also have to account for drag. The drag D can be expressed as:

$$
D = C_D \cdot \frac{1}{2} \cdot \rho \cdot V^2 \cdot S
$$

Where $ C_D = C_{D0} + k \cdot C_L^2 $.

### Step 3: Rearranging for Maximum Speed

The condition for maximum speed occurs when thrust equals drag:

$$
T = D
$$

Thus,

$$
T = \left( C_{D0} + k \cdot \frac{2L}{\rho \cdot S \cdot V^2}^2 \right) \cdot \frac{1}{2} \cdot \rho \cdot V^2 \cdot S
$$

### Step 4: Calculation

We can use numerical methods to solve for V using Python. Here's the code:

```python
import numpy as np
from scipy.optimize import fsolve

# Constants
S = 31.83 # Wing Area in m^2
m = 5156 # mass in kg
g = 9.81 # gravity in m/s^2
rho = 1.225 # air density in kg/m^3
Cdo = 0.025 # zero-lift drag coefficient
k = 0.0445 # coefficient for drag polar
T = 22000 # thrust in N

# Weight of the aircraft
W = m * g

# Climb angle calculation
def equations(V):
CL = (2 * W) / (rho * S * V**2) # Lift coefficient
CD = Cdo + k * CL**2 # Drag coefficient
drag = CD * (0.5 * rho * V**2 * S) # Drag force
return T - drag # Return thrust - drag

# Estimate max speed
initial_guess = 100 # Initial speed guess in m/s
max_speed_mps = fsolve(equations, initial_guess)[0]

# Convert speed from m/s to knots
max_speed_kts = max_speed_mps * 1.94384 # 1 m/s = 1.94384 knots
max_speed_kts
```

### Step 5: Calculate The Climb Angle

The climb angle (γ) can be calculated by relating the rate of climb to the weight and thrust:

$$
\text{Rate of Climb} = (T - D) \cdot V / W
$$

The angle can be calculated as:

$$
\gamma = \arctan\left( \frac{\text{Rate of Climb}}{V} \right)
$$

### Example Implementation

You may modify the earlier code to include the calculation of climb angle after finding $ V $.

### Conclusion

Use the provided code to calculate maximum speed in knots and the associated climb angle derived from the rate of climb under given thrust conditions. The output will give you the required values.
help me run this code, my python  doesnt work

GPT-4o mini · Answer

I can certainly help you with that! Here’s a breakdown of how to use the provided Python code to calculate the maximum speed of the aircraft, but since I'm unable to run the code directly, I will guide you through the steps you would need to take to execute it on your own system. If Python isn't working for you right now, you may also consider running it in an online Python interpreter such as Google Colab, Jupyter Notebook, or any other similar platform.

Steps to Run the Code

Install Required Libraries: Make sure that you have the necessary libraries (numpy and scipy) installed. You can do this using pip:
```
pip install numpy scipy
```
Create a Python Script: Open your favorite text editor or IDE (like VSCode, PyCharm, or an online editor) and create a new Python file, for example, aircraft_speed_calculation.py.

Copy the Following Code: Paste the code into your Python file:

import numpy as np
from scipy.optimize import fsolve

# Constants
S = 31.83 # Wing Area in m^2
m = 5156 # mass in kg
g = 9.81 # gravity in m/s^2
rho = 1.225 # air density in kg/m^3
Cdo = 0.025 # zero-lift drag coefficient
k = 0.0445 # coefficient for drag polar
T = 22000 # thrust in N

# Weight of the aircraft
W = m * g

# Function to calculate drag and find the maximum speed
def equations(V):
    CL = (2 * W) / (rho * S * V**2)  # Lift coefficient
    CD = Cdo + k * CL**2  # Drag coefficient
    drag = CD * (0.5 * rho * V**2 * S)  # Drag force
    return T - drag  # Return thrust - drag

# Estimate max speed
initial_guess = 100  # Initial speed guess in m/s
max_speed_mps = fsolve(equations, initial_guess)[0]

# Convert speed from m/s to knots
max_speed_kts = max_speed_mps * 1.94384  # 1 m/s = 1.94384 knots
print(f'Maximum Speed: {max_speed_kts:.2f} knots')

Run the Script: Save your file and run it. If you're using a command line or terminal, you can run the script by navigating to the folder containing it and typing:
```
python aircraft_speed_calculation.py
```
View the Output: If everything is set up correctly, the script will execute and print the maximum speed of the aircraft in knots.

Troubleshooting

If you encounter any errors regarding library imports, ensure that you've installed numpy and scipy correctly.
If you don't see any output, make sure to check for syntax errors or indentation issues in the code.

Alternative: Using Online Python Environments

If you prefer not to deal with local installations or errors, you may use an online Python interpreter:

Visit a site like Google Colab, Replit, or Jupyter Notebook Online.
Create a new notebook or Python file.
Copy and paste the code there and run it.

If you follow these instructions, you should be able to calculate the maximum speed of the aircraft successfully! If you have any issues or further questions, feel free to ask.