Answer :
To determine the corrected runway length, you need to account for the elevation of the airport, reference temperature, and the gradient of the runway.
Elevation Correction: Runway length needs to be increased due to higher elevation because aircraft performance decreases at higher altitudes. For every 300 meters (approximately 1000 feet) of elevation above sea level, runway length should typically be increased by about 7%. In this case, the elevation is 270 meters, which means an approximate increase of 6.3% in the runway length for elevation correction.
Temperature Correction: Higher temperatures can also reduce aircraft performance, requiring longer runway lengths. The reference temperature of 32.9°C suggests the need for further correction, often around 1% increase for every 1°C above a standard temperature (around 15°C). So, the temperature correction would be (32.9 - 15) °C = 17.9 °C, which translates to an approximate increase of 17.9%.
Gradient Correction: Runways with gradients can affect the aircraft's ability to take off, and correction is typically needed. The problem states an effective gradient of 0.2 percent. The general rule is to increase the runway length by about 10% for every 1% gradient, resulting in a 0.2% runway length increase in this case.
Let's calculate the total corrections and the corrected length:
- Initial runway length = 1602 m
- Elevation correction: 1602 m * 6.3% = 100.926 m
- Temperature correction: 1602 m * 17.9% = 286.758 m
- Gradient correction: 1602 m * 0.2% = 3.204 m
Adding these corrections to the original runway length:
[tex]\text{Corrected Length} = 1602 + 100.926 + 286.758 + 3.204[/tex]
[tex]= 1992.888 \, \text{meters}[/tex]
Therefore, the corrected runway length should be approximately 1992.89 meters under the given conditions. This ensures safe takeoff and landing operations considering the elevation, temperature, and gradient adjustments.
