Calculations

How to calculate temperature?

ISA at sea level: 15° C

Temperature lapse rate 2° C or 3.5° F per 1000 feet.

Examples:

• Given FL270; 27 x -2 = -54° C. -54° C +15° C= -39° C
• Given 8000 ft => 15 - 2 x 8 = -1° C

How to calculate Pressure Altitude?

Determine pressure altitude by using this formula:

$$\text{PressureAltitude} = (\text{StandardPressure} - \text{CurrentPressure}) \times 1000 + \text{FieldElevation}$$

e.g. field elevation is 5,000 ft, pressure setting 29.45, density pressure is 5470 ft.

$$\text{PressureAltitude} = (29.92 - 29.45) \times 1000 + 5000 = 5470$$

How to calculate Density Altitude?

• OAT: Outside Air Temperature
• IST: Standard Temperature

$$\text{DensityAltitude} = \text{PressureAltitude} + [120 \times ( \text{OAT} - \text{IST})]$$

How to calculate the approximate base of the cumulus clouds?

What is the approximate base of the cumulus clouds if the surface air temperature at 1,000 feet MSL is 70 °F and the dewpoint is 48 °F?

As a rule of thumb, divide the difference between the temperature and dew point by 4.4 to determine the height of the cloud base.

E.g. 70° F - 48° F = 22. 22 / 4.4 = 5 (in thousands of feet). Add the field elevation of 1,000' to the 5,000' to find 6,000'.

How to get CAS from IAS?

Check POH.

How to calculate TAS from CAS?

Add 2 percent to the CAS for each 1,000 feet of altitude. At 10,000 feet, you are flying approximately 20% faster than your indicated airspeed.

$$\text{TAS} = \text{CAS} \times (1 + \text{Altitude} / 1000 \times 2\%)$$

Weight of fuel

100LL: ~6 lb per gallon.

How to estimate fuel burn?

lb per hour = power / 20;

e.g.

• Citabria 118 HP / 20 => ~6 ga / hour
• C172 180 HP / 20 => ~9 ga / hour.

How to calculate Maneuvering Speed?

$$V_A = V_{A_{max}} \times \sqrt{\text{CurWeight / MaxWeight}}$$

So if your current weight is 80% of MTOW, $V_A$ is ~90% of the $V_{A_{max}}$.

Estimate standard rate turn bank angle

Divide the true airspeed by 10 and add 7. e.g.

• 100 kt => 15.38; estimate: 100/10+7 = 17
• 300 kt => 39.5; estimate: 300/10+7=37

How to convert climb rate?

The vertical speed indicator (VSI) shows the rate of climb or descent in hundreds of feet per minute.

Departure procedures are using feet per NM instead. E.g. SFO Four Departure, Rwys 28L/R Takeoff minimums: "Standard with a minimum climb of 351' per NM to 1300."

To convert between the 2:

$$ft/nm \times \text{GroundSpeed} / 60 = ft/min$$

For example, in a small aircraft, assume ground speed is 90 nm/hour, we need a climb rate 1.5 times the ft/nm of the takeoff minimum, then you know if your aircraft is capable of flying this departure.

How to calculate a Visual Descent Point (VDP)?

Formula:

Height Above Touchdown (HAT) divided by 300

This essentially gives you the distance from the runway threshold where you can start your descent based on a standard 3-degree glide slope.

$$\tan 3^\circ = h / d = 0.0524$$

1 nm = 6076 ft, so d = h / 0.0524 / 6076 = h / 318

Example:

If your HAT is 600 feet, your VDP would be 2 nautical miles from the runway (600 / 300 = 2).