Aviation is as much art as science. In many aspects of aviation, math is needed to precisely fly the airplane. Few pilots want to constantly do calculations with an E-6B flight computer or handheld calculator. Fortunately there is an easier way. Over the years, many rules of thumb have been developed to help pilots fly with more precision, but without the hassle. Here are a few that I frequently use flying jets. Many can be used in piston airplanes as well.
One simple rule of thumb is how to smoothly level off from a climb or descent. When changing altitudes, lead the level off by 10 percent of the vertical speed. If the airplane is climbing at 500 feet per minute, start the level off 50 feet before the altitude is reached to avoid an overshoot or undershoot. If the thought of percentages is daunting, just drop the last zero from the rate of climb.
Similarly, a good rule of thumb for planning a cruising altitude is to use 10 percent of the trip length, multiplied by a thousand. If the flight is 200 miles, an efficient cruising altitude would be 20,000 feet. Obviously, the service ceiling of the airplane becomes a limiting factor as well. No matter how long the trip, a Cessna 172 is not likely to climb into the flight levels (18,000-60,000 feet).
It can be helpful to know how fast your airplane is traveling in nautical miles per minute to determine how quickly you will arrive at a fix. To determine your speed in miles per minute, simply divide the speed in knots by 60 minutes per hour. Some commonly used speeds in jets are 200 knots (3.3 nautical miles per minute) and 250 knots (4.1 miles per minute). A piston single that flies at 120 knots is also traveling at two miles per minute.
The figure above can be used in the formula, distance = rate x time, to determine the time to a fix. Time would be equivalent to distance divided by rate so the piston airplane traveling at 120 knots would take 50 minutes to fly to a fix 100 miles away (100 miles / 2 miles per minute). A jet flying at 250 knots would cover the same ground in about 25 minutes. (To make the calculation even simpler, round 4.1 miles per minute to four. The answer using 4.1 is 24.39 minutes. Twenty-five is close enough for government – or pilot – work.)
Descent planning is a common math problem in airplanes. In modern airplanes, the flight computer (FMS) can be programmed to initiate a descent, but it never hurts to double-check the computer. The first step in the process is to determine how much altitude the airplane will need to lose. In my Lear 45, we commonly cruise at FL400 (40,000 feet). If we were planning to descend into a sea level airport such as our home base at Houston Hobby, we would need to lose 40,000 feet. For airports at higher elevations, (such as Aspen, Colorado, field elevation 7,820 feet), we would need to plan on losing about 32,000 feet (40,000 – 8,000). Airport elevations are recorded in heights above mean sea level (MSL) and can be found on charts or websites such as Globalair.com’s airport directory.
One you have determined how much altitude to lose, divide that number by 300 to determine how far out to begin a descent in order to maintain a typical three degree glide path. This means that the airplane would be descending about 300 feet per nautical mile. To descend into Aspen, we would want to start 106 miles from our destination (32,000/300). To make the calculation easier, you can drop the last two zeros from both numbers (320/3). The longer descent into Houston would require 133 miles.
Now that we know how far out to start the descent, we need to know what rate of descent will yield a three degree glide path. This number varies with groundspeed, which in turn is affected by the winds aloft. The simple way to determine a three degree rate of descent is to multiply the groundspeed (typically read directly from cockpit instruments) in knots by 5. For example, if the airplane has a groundspeed of 450 knots, the descent rate must be 2,250 feet per minute (FPM) to maintain a three degree glide path.
Because ILS (instrument landing system) approaches are also based on a three degree glide path, this rule of thumb can also be used to determine what rate of descent will keep the airplane on the ILS glideslope. If you plan to fly the approach at 100 knots, you should plan to descend at about 500 FPM.
Since official weather reports and ATIS broadcasts give temperatures in Celsius, another useful rule of thumb helps to convert Celsius temperatures to the more familiar Fahrenheit temperatures for briefing passengers. Start with the Celsius temperature from the ATIS, 34 degrees today in Midland, Texas where I am writing this, and double it (34 x 2 = 68). Next, subtract 10 percent of the result (68 – 7 = 61). The final step is to add 32 to the result of the second step (61 + 32 = 93 degrees Fahrenheit). With a little practice, this conversion can be done easily in your head.
When considering fuel performance, jet pilots generally think in terms of weight rather than gallons. This can be confusing because most airport fuel trucks pump fuel by the gallon. There is a rule of thumb to help pilots quickly determine how much fuel to order so that they don’t buy too much or – worse yet – not enough.
To start the planning, two pieces of information are needed: the fuel required for the trip and how much is already on board the airplane. A one hour flight in the Lear 45 can be expected to require approximately 1,700 pounds of jet fuel. (This number is obtained from aircraft performance data and flight planning sources available online). If the airplane already has 1,000 pounds on board, we need to buy at least 700 pounds of fuel to complete the flight. Don’t stop there though. We don’t want to land with no fuel left in the tanks!
The FARs (federal aviation regulations) and company procedures specify that pilots must carry reserve fuel. A typical fuel reserve for the Lear 45 is 1,500 to 2,000 pounds. We should also plan for APU (auxiliary power unit) fuel usage of about 100 pounds. Therefore, the total fuel needed is 3,800 pounds (1,700 + 2,000 + 100). We would need to purchase 2,800 pounds since we already have 1,000 on board.
To convert jet fuel weight to gallons, divide by 6.7 pounds per gallon. This means that we would need to order 418 gallons from the fuel truck. A quick and dirty rule of thumb is that 150 gallons of jet fuel is approximately 1,000 pounds. This method can be used to check your math or for a quick estimate.
One last rule of thumb is that no rule of thumb that goes unused will be remembered. Practice using rules of thumbs to crosscheck the automation on every flight in order to keep yourself sharp.