> #mathematics , #aviation , #physics > Given an airplane located at sea level with current barometric pressure of 29.92 inches of mercury and temperature of 20 degree Celsius,calculate attitude and density attitude?
Apr 19

# Given an airplane located at sea level with current barometric pressure of 29.92 inches of mercury and temperature of 20 degree Celsius,calculate attitude and density attitude?

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Apr 19
To calculate the altitude and density altitude, we can use the following formulas:

Altitude (in feet) = (1 - (pressure / 1013.25) ^ 0.190284) * 145366.45

Density Altitude (in feet) = altitude + (120 * (OAT - ISA))

Where:
- pressure is the current barometric pressure in inches of mercury (29.92 in this case)
- OAT is the outside air temperature in degrees Celsius (20 degrees Celsius in this case)
- ISA is the International Standard Atmosphere temperature at sea level, which is 15 degrees Celsius

First, let's calculate the altitude:

Altitude = (1 - (29.92 / 29.92) ^ 0.190284) * 145366.45
Altitude = (1 - 1) ^ 0.190284 * 145366.45
Altitude = 0 * 145366.45
Altitude = 0 feet

Next, let's calculate the density altitude:

Density Altitude = 0 + (120 * (20 - 15))
Density Altitude = 0 + (120 * 5)
Density Altitude = 0 + 600
Density Altitude = 600 feet

Therefore, the altitude of the airplane is 0 feet and the density altitude is 600 feet.
1
Apr 19
1. Altitude

Altitude can be calculated using the barometric formula:

```
Altitude = 44330 - (1 - (P / P0)^0.190284)
```

where:

- Altitude is in feet
- P is the current barometric pressure in inches of mercury (inHg)
- P0 is the sea level barometric pressure in inHg (29.92 inHg)

Plugging in the given values:

```
Altitude = 44330 - (1 - (29.92 / 29.92)^0.190284)
= 0 feet
```

Therefore, the airplane is currently at sea level.

2. Density Altitude

Density altitude takes into account both pressure and temperature to determine the effective altitude at which the air has the same density as at a given altitude under standard atmospheric conditions. It is calculated using the following formula:

```
Density Altitude = Altitude + 120 - (OAT - ISA_OAT)
```

where:

- Density Altitude is in feet
- Altitude is the altitude calculated in step 1
- OAT is the current outside air temperature in degrees Celsius
- ISA_OAT is the International Standard Atmosphere (ISA) temperature at the current altitude

At sea level, the ISA temperature is 15°C. Plugging in the given values:

```
Density Altitude = 0 + 120 - (20 - 15)
= 600 feet
```

Therefore, the density altitude is 600 feet.
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