Here are some aviation-related rules of thumb from various nooks and crannies. These are not meant to be 100% accurate, but are useful in the cockpit where you have to work quickly in your head or using an E6B or a calculator on a kneeboard.
An angle of 1° represents a deviation of approximately 1/60. For example, if two planes fly a course 1° different, after 60 nm they should be roughly 1 nm apart.
This is an astoundingly useful rule in aviation because it works in so many different places. For example, a nautical mile is (conveniently) about 6,000 ft. That means that every 100 ft AGL altitude 1 nm from a runway threshold represents 1° of glidepath. To approach at a 3° glidepath, you need to be 300 ft above the runway elevation 1 nm back, 600 ft above 2 nm back, and so on.
To calculate distance to an NDB or VOR transmitter, turn perpendicular to your course and time how long it takes your bearing to the station to change by a fixed number of degrees. Divide the time by the number of degrees and multiply by 60 to get the time to the transmitter. For example, if it takes 5 minutes for the bearing to change by 10 degrees, then you are 5 / 10 * 60 or 30 minutes from the transmitter.
If you are 15 nm from your destination airport flying directly towards it and you want to arrive 2 nm to one side of it instead of directly overhead (say, to enter a circuit/pattern), alter your course left or right by 8°: 15 is 1/4 of 60, so multiple 2 * 4.
Assuming a standard lapse rate, an airplane's altimeter will over- or underread by 4 ft per 1°C deviation from ISA per 1,000 ft above the station reporting the altimeter setting.
For example, if you are flying at 11,000 ft indicated altitude using an altimeter setting from a station at 1,000 ft elevation and the outside air temperature is -20°C, your altimeter will be off by -520 ft (4 * -13 * 10), and your true altitude will be slightly below 10,500 ft.
Airplane performance depends on density altitude. To estimate density altitude (at least at lower altitudes), start with pressure altitude and add 120 ft for every degree Celsius above ISA temperature, or subtract 120 ft for every degree Celsius below ISA.
For example, at 3,000 ft pressure altitude, the ISA temperature is 9°C. If the actual temperature is 20°C, add 1,320 ft (11 * 120) to get an approximate density altitude of 4,320 ft.
Humidity also affects density altitude, but not enough to worry about in a rule of thumb.
The International Standard Atmosphere is the reference point for most aircraft performance data. When the real atmosphere varies from ISA, it is necessary to adjust the altimeter for pressure altitude and to modify cruise speeds, power settings, takeoff and landing distances for density altitude.
The ISA has an air pressure of 29.92 inHg at sea level, decreasing by 1.00 inHg for every thousand feet (at lower altitudes), a temperature of 15°C, decreasing by 2°C for every 1,000 ft (ditto), and no humidity.
For example, ISA predicts that the air pressure should be 19.92 inHg at 10,000 ft and that the outside air temperature should be -5°C. If the temperature is different than that, or if there is a non-standard pressure lapse rate, there will be a (possibly serious) altimeter error.
To calculate pressure altitude, set your altimeter to 29.92 inHg and read the value from your altimeter (write down the current altimeter setting first, if you're in the air), or alternatively, subtract 1,000 ft from indicated for every inHg above 29.92, or add 1,000 ft to indicated altitude for every inHg below 29.92 (remember, pressure decreases as you go up, so lower pressure seems like higher altitude).
For example, if the indicated altitude is 3,000 ft and the altimeter setting is 28.50, add 1,420 ft ((29.92 - 28.50) * 1,000) to get the pressure altitude of 4,420.
To get the bank angle for a standard-rate (2 minute) turn, divide your airspeed in knots by 10 and add 7. For example, if your airspeed is 120 kt, your bank angle will be 19° (12 + 7)
VHF and UHF transmitters work by line-of-sight. To calculate the maximum line-of-sight distance over the horizon in nautical miles for receiving a VHF or UHF radio signal (such as ATC or a VOR or DME transmitter), use
1.23 * sqrt(deltaAltitude_ft)
For example, if your plane is 10,000 ft higher than a VOR transmitter, you will have a good chance of picking it up from 123 nm away (1.23 * sqrt(10,000)). If you are 5,000 ft higher, the range will be 87 nm. Of course high terrain, interference from other transmitters on the same frequency, or a low-power transmitter can reduce that range significantly.
True airspeed is calibrated airspeed + 1.6% for every 1,000 ft of density altitude, or 8% for every 5,000 ft. For example, if your calibrated airspeed is 145 kt and your density altitude is 5,000 ft, your true airspeed will be 145 * 1.08, or 157 kt.
The following table contains of approximate values for wind components. Note that it is symmetrical around 45°, so it is necessary to remember only the first three rows, and even then, you can count 9/10 and 19/20 as basically all of it: just remembering that 15° is 1/4, 30° is 1/2, and 45° is 2/3 should be enough.
| Wind Angle | Crosswind | Headwind |
|---|---|---|
| 15° | 1/4 | 19/20 |
| 30° | 1/2 | 9/10 |
| 45° | 2/3 | 2/3 |
| 60° | 9/10 | 1/2 |
| 75° | 19/20 | 1/4 |
A wind angle of 45° has approximately a 2/3 crosswind component and a 2/3 headwind component (or a tailwind component, if it's behind you). If you are landing on runway 12 and the wind is from 165 deg at 18 kt, you will have a headwind of 12 kt and a crosswind of 12 kt.
For example, if you are landing on runway 12 with a wind speed of 12 kt, the crosswind component will be 3 kt if the wind is from 135° (15° angle), 6 kt if the wind is from 150° (30° angle), 9 kt if the wind is from 165°, and basically all of it if the wind is from 180° or more. The headwind component will be basically all of it up to 150°, 9 kt at 165°, 6 kt at 180°, and 3 kt at 195°.