Runway Length Calculation Overview

The International Civil Aviation Organization (ICAO) provides specific recommendations for calculating the required runway length for airport design. These recommendations involve applying sequential corrections to the basic runway length for various factors like elevation, temperature, and effective gradient. This solution focuses on applying the corrections for elevation and temperature as per the question's requirement.

Understanding ICAO Runway Corrections

According to ICAO, the basic runway length needs to be adjusted based on the specific atmospheric and topographical conditions of the airport. These adjustments are applied in a particular sequence:

• Elevation Correction: The first correction is applied for the airport's elevation above mean sea level.
• Temperature Correction: The second correction accounts for the difference between the airport's reference temperature and the standard atmospheric temperature at the airport's elevation.
• Gradient Correction: The third correction (not required for this specific question) considers the effective gradient of the runway.

Given Parameters

Let's list the given parameters for our calculation:

Elevation Correction for Runway Length

The first step in calculating the corrected runway length is to adjust it for the airport's elevation. Air density decreases with altitude, which affects aircraft performance, requiring a longer runway.

1. Standard Temperature at Airport Elevation

First, we need to determine the standard atmospheric temperature at the airport's elevation. The standard temperature at Mean Sea Level (MSL) is $15^\circ \\text{C}$, and the standard temperature lapse rate is $6.5^\circ \\text{C}$ per $1000 \\text{ m}$ elevation rise.

Standard temperature at elevation ($T_s$) is calculated as:

$T_s = \\text{Standard Temperature at MSL} - \\left(\\text{Lapse Rate} \\times \\frac{\\text{Elevation}}{1000}\\right)$

Substituting the values:

$T_s = 15^\circ \\text{C} - \\left(6.5^\circ \\text{C/1000 m} \\times \\frac{535 \\text{ m}}{1000 \\text{ m}}\\right)$

$T_s = 15^\circ \\text{C} - \\left(6.5 \\times 0.535\\right)^\circ \\text{C}$

$T_s = 15^\circ \\text{C} - 3.4775^\circ \\text{C}$

$T_s = 11.5225^\circ \\text{C}$

2. Applying Elevation Correction

ICAO recommends an increase in runway length by $7\\%$ for every $300 \\text{ m}$ rise in elevation above mean sea level.

The formula for runway length corrected for elevation ($L_E$) is:

$L_E = L_0 \\times \\left(1 + \\frac{7}{100} \\times \\frac{E}{300}\\right)$

Substituting the values:

$L_E = 2000 \\text{ m} \\times \\left(1 + \\frac{7}{100} \\times \\frac{535 \\text{ m}}{300 \\text{ m}}\\right)$

$L_E = 2000 \\times \\left(1 + 0.07 \\times 1.78333\\right)$

$L_E = 2000 \\times \\left(1 + 0.1248331\\right)$

$L_E = 2000 \\times 1.1248331$

$L_E = 2249.6662 \\text{ m}$

Approximately, the runway length corrected for elevation is $2250 \\text{ m}$.

Temperature Correction for Runway Length

The second sequential correction is for temperature. Higher temperatures reduce air density, which again impacts aircraft lift and engine thrust, necessitating a longer runway.

1. Temperature Difference

We calculate the difference between the Airport Reference Temperature (ART) and the standard temperature at the airport's elevation ($T_s$).

Temperature difference ($T_d$) is calculated as:

$T_d = \\text{Airport Reference Temperature} - \\text{Standard Temperature at Elevation}$

$T_d = T_a - T_s$

Substituting the values:

$T_d = 22.65^\circ \\text{C} - 11.5225^\circ \\text{C}$

$T_d = 11.1275^\circ \\text{C}$

2. Applying Temperature Correction

ICAO specifies an increase in runway length by $1\\%$ for every $1^\circ \\text{C}$ rise of the Airport Reference Temperature above the standard atmospheric temperature at the airport elevation. This correction is applied to the length already corrected for elevation ($L_E$).

The formula for runway length corrected for temperature ($L_T$) is:

$L_T = L_E \\times \\left(1 + \\frac{1}{100} \\times T_d\\right)$

Substituting the values:

$L_T = 2249.6662 \\text{ m} \\times \\left(1 + \\frac{1}{100} \\times 11.1275\\right)$

$L_T = 2249.6662 \\times \\left(1 + 0.111275\\right)$

$L_T = 2249.6662 \\times 1.111275$

$L_T = 2500.22 \\text{ m}$

Final Corrected Runway Length

After applying sequential corrections for elevation and temperature, the length of the runway required is approximately $2500 \\text{ m}$. This value aligns with one of the provided options.