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The length of runway under standard conditions is 2000 m. The elevation of airport site is 300 m. Its reference temperature is 33.05°C. if the runway is to be constructed with an effective gradient of 0.25 percent, the correct runway length will be
- a)2500 m
- b)2600 m
- c)2700 m
- d)2800 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The length of runway under standard conditions is 2000 m. The elevatio...
Correction for elevation
Corrected length
= 2000 + 140 = 2140 m
Standard atmospheric temp at given elevation
= 15 - 0.0065 x 300 = 13.05°C
Correction for temperature
Corrected.Jength = 2140 + 428 = 2568 m
Correction for gradient
Corrected length
= 2568 + 128.4 = 2696.4 m = 2700 m
Corrected length
= 2000 + 140 = 2140 m
Standard atmospheric temp at given elevation
= 15 - 0.0065 x 300 = 13.05°C
Correction for temperature
Corrected.Jength = 2140 + 428 = 2568 m
Correction for gradient
Corrected length
= 2568 + 128.4 = 2696.4 m = 2700 m
Most Upvoted Answer
The length of runway under standard conditions is 2000 m. The elevatio...
°C. The airport is located at a place where the pressure altitude is 4000 ft. Determine the available takeoff distance for an aircraft whose takeoff weight is 80,000 kg. Assume that the runway surface is dry and the wind is calm.
Solution:
Given:
Airport elevation = 300 m
Reference temperature = 33.05°C
Pressure altitude = 4000 ft
Runway length = 2000 m
Takeoff weight of the aircraft = 80,000 kg
To find: Available takeoff distance
Step 1: Calculate the pressure at the airport using the pressure altitude.
Using the standard atmosphere model, we can find the pressure at the airport as follows:
P = P0 x (1 - Lh/T0)^((g0M) / (RL))
Where:
P0 = Sea level pressure = 1013.25 hPa
L = Standard lapse rate = 0.0065 K/m
h = Pressure altitude = 4000 ft = 1219.2 m
T0 = Standard temperature at sea level = 15°C = 288.15 K
g0 = Standard acceleration due to gravity = 9.80665 m/s^2
M = Molar mass of air = 0.0289644 kg/mol
R = Gas constant for air = 8.31432 J/mol/K
Substituting the values, we get:
P = 1013.25 x (1 - (0.0065 x 1219.2 / 288.15))^((9.80665 x 0.0289644) / (8.31432 x 0.0065))
P = 898.79 hPa
Step 2: Calculate the density of air at the airport using the pressure and temperature.
Using the ideal gas law, we can find the density of air at the airport as follows:
ρ = P / (RT)
Where:
R = Gas constant for air = 287.058 J/kg/K
T = Temperature in Kelvin
Substituting the values, we get:
ρ = 898.79 / (287.058 x 306.20)
ρ = 1.056 kg/m^3
Step 3: Calculate the corrected runway length using the density altitude.
Using the following formula, we can find the corrected runway length:
Lc = L x (ρc / ρs)^0.5
Where:
L = Runway length = 2000 m
ρc = Density of air at the airport under standard conditions = 1.225 kg/m^3
ρs = Density of air at the airport under non-standard conditions = 1.056 kg/m^3
Substituting the values, we get:
Lc = 2000 x (1.225 / 1.056)^0.5
Lc = 2262.86 m
Step 4: Calculate the takeoff distance.
Using the following formula, we can find the takeoff distance:
TOD = (1.67 x W / S) x (1 / ρ) x (Lc + 0.3 x CLmax x h)
Where:
W = Takeoff weight of the aircraft = 80,000 kg
S = Wing area of the aircraft = 150 m^2
CLmax = Maximum lift coefficient of the aircraft =
Solution:
Given:
Airport elevation = 300 m
Reference temperature = 33.05°C
Pressure altitude = 4000 ft
Runway length = 2000 m
Takeoff weight of the aircraft = 80,000 kg
To find: Available takeoff distance
Step 1: Calculate the pressure at the airport using the pressure altitude.
Using the standard atmosphere model, we can find the pressure at the airport as follows:
P = P0 x (1 - Lh/T0)^((g0M) / (RL))
Where:
P0 = Sea level pressure = 1013.25 hPa
L = Standard lapse rate = 0.0065 K/m
h = Pressure altitude = 4000 ft = 1219.2 m
T0 = Standard temperature at sea level = 15°C = 288.15 K
g0 = Standard acceleration due to gravity = 9.80665 m/s^2
M = Molar mass of air = 0.0289644 kg/mol
R = Gas constant for air = 8.31432 J/mol/K
Substituting the values, we get:
P = 1013.25 x (1 - (0.0065 x 1219.2 / 288.15))^((9.80665 x 0.0289644) / (8.31432 x 0.0065))
P = 898.79 hPa
Step 2: Calculate the density of air at the airport using the pressure and temperature.
Using the ideal gas law, we can find the density of air at the airport as follows:
ρ = P / (RT)
Where:
R = Gas constant for air = 287.058 J/kg/K
T = Temperature in Kelvin
Substituting the values, we get:
ρ = 898.79 / (287.058 x 306.20)
ρ = 1.056 kg/m^3
Step 3: Calculate the corrected runway length using the density altitude.
Using the following formula, we can find the corrected runway length:
Lc = L x (ρc / ρs)^0.5
Where:
L = Runway length = 2000 m
ρc = Density of air at the airport under standard conditions = 1.225 kg/m^3
ρs = Density of air at the airport under non-standard conditions = 1.056 kg/m^3
Substituting the values, we get:
Lc = 2000 x (1.225 / 1.056)^0.5
Lc = 2262.86 m
Step 4: Calculate the takeoff distance.
Using the following formula, we can find the takeoff distance:
TOD = (1.67 x W / S) x (1 / ρ) x (Lc + 0.3 x CLmax x h)
Where:
W = Takeoff weight of the aircraft = 80,000 kg
S = Wing area of the aircraft = 150 m^2
CLmax = Maximum lift coefficient of the aircraft =
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The length of runway under standard conditions is 2000 m. The elevation of airport site is 300 m. Its reference temperature is 33.05°C. if the runway is to be constructed with an effective gradient of 0.25 percent, the correct runway length will bea)2500 mb)2600 mc)2700 md)2800 mCorrect answer is option 'C'. Can you explain this answer?
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