The question requires us to determine the Airport Reference Temperature (ART) for a proposed airport site, utilizing the provided temperature data for the hottest month of the year.

Airport Reference Temperature Definition

The Airport Reference Temperature (ART) is a critical meteorological parameter used in the design and planning of airports, particularly for calculating the required runway length. It represents a standard temperature condition that helps predict aircraft performance during takeoff and landing. Higher temperatures lead to decreased air density, which reduces aircraft engine thrust and wing lift, thereby necessitating longer runways for safe operations. This temperature is specifically derived from data collected during the hottest month at the airport's location.

Given Airport Temperature Data

For the hottest month at the proposed airport site, the following temperature values are provided:

• The monthly mean of the average daily temperature (\(T_a\)) is given as \(39^\circ\text{C}\). This value is the average of all the daily average temperatures recorded over that hottest month.
• The monthly mean of the maximum daily temperature (\(T_m\)) is given as \(48^\circ\text{C}\) for the same hottest month. This value represents the average of all the daily maximum temperatures recorded during that month.

Airport Reference Temperature Formula

The standard formula used to calculate the Airport Reference Temperature (ART) is:

$$ \text{ART} = T_a + \frac{T_m - T_a}{3} $$

Where:

• \(\text{ART}\) is the Airport Reference Temperature, expressed in degrees Celsius (\(^\circ\text{C}\)).
• \(T_a\) is the monthly mean of the average daily temperature, also in \(^\circ\text{C}\).
• \(T_m\) is the monthly mean of the maximum daily temperature, also in \(^\circ\text{C}\).

Calculating Airport Reference Temperature

Let's apply the given temperature values to the formula to calculate the Airport Reference Temperature:

• Monthly mean of average daily temperature (\(T_a\)) = \(39^\circ\text{C}\)
• Monthly mean of maximum daily temperature (\(T_m\)) = \(48^\circ\text{C}\)

Substitute these values into the ART formula:

$$ \text{ART} = 39 + \frac{48 - 39}{3} $$

Step 1: Calculate the difference between the monthly mean of maximum daily temperature (\(T_m\)) and the monthly mean of average daily temperature (\(T_a\)):

$$ 48 - 39 = 9 $$

Step 2: Divide this difference by 3:

$$ \frac{9}{3} = 3 $$

Step 3: Add the result from Step 2 to the monthly mean of average daily temperature (\(T_a\)):

$$ \text{ART} = 39 + 3 $$

$$ \text{ART} = 42^\circ\text{C} $$

Final Airport Temperature Result

Based on the calculations, the Airport Reference Temperature for the proposed airport site is \(42^\circ\text{C}\). This temperature is a key factor in airport design, especially for determining the appropriate runway length required to ensure the safety and operational efficiency of aircraft under high-temperature conditions.