Transmitter antenna height = 50m, receiver antenna height = 80m. Radius of earth = 6400 km. Find maximum distance between for LOS communication.

Answer

To find the maximum distance for Line of Sight (LOS) communication between a transmitter and a receiver, we can use the formula for the distance based on the heights of the antennas and the radius of the Earth. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Height of the transmitter antenna (HT) = 50 m
- Height of the receiver antenna (HR) = 80 m
- Radius of the Earth (R) = 6400 km = 6400 × 10^3 m

### Step 2: Convert the radius of the Earth to meters
Since the heights of the antennas are given in meters, we need to convert the radius of the Earth into meters:
- R = 6400 km = 6400 × 10^3 m = 6400000 m

### Step 3: Use the formula for LOS distance
The maximum distance (D) for LOS communication can be calculated using the formula:
\[ D = \sqrt{2 \cdot R \cdot HT} + \sqrt{2 \cdot R \cdot HR} \]

### Step 4: Calculate the distance for the transmitter antenna
Substituting the values for the transmitter antenna:
\[ D_T = \sqrt{2 \cdot (6400000) \cdot (50)} \]
\[ D_T = \sqrt{640000000} \]
\[ D_T = 8000 \text{ m} \]

### Step 5: Calculate the distance for the receiver antenna
Now, substituting the values for the receiver antenna:
\[ D_R = \sqrt{2 \cdot (6400000) \cdot (80)} \]
\[ D_R = \sqrt{1024000000} \]
\[ D_R = 10120 \text{ m} \]

### Step 6: Calculate the total maximum distance for LOS communication
Now, add the two distances:
\[ D = D_T + D_R \]
\[ D = 8000 + 10120 \]
\[ D = 18120 \text{ m} \]

### Step 7: Convert the distance to kilometers
To convert the distance from meters to kilometers:
\[ D = \frac{18120}{1000} = 18.12 \text{ km} \]

### Final Answer
The maximum distance for LOS communication is approximately **18.12 km**.

---