Flying by the Numbers

This article is a compilation of some calculations and rules of thumb that I’ve found useful in my career as a private pilot. The article is intended for pilots; for non-pilots who would like to learn more about flying, I recommend the FAA Airplane Flying Handbook and John Denker’s excellent See How It Flies.

In general, my goal is to derive and memorize a relatively small set of numbers which I can use for a wide variety of flight planning situations. I use these numbers to answer questions such as “When should I start my descent?” and “Where should I turn base?”. I fly Cessna 172s and 182s, but these numbers should apply equally well to many other piston singles.

Of course, this can all be precisely pre-calculated for any specific flight (incorporating exact aircraft performance, atmospheric conditions, and routing)… but in practice, it is impossible to predict every situation in advance, so I find the rules of thumb to be far more useful than a precomputed flight plan.

Climbs and descents

When planning climbs and descents, it’s useful to have an idea of what distance will be required for a given altitude change.

Flight type Airspeed Vertical speed Distance per 1000 feet
Normal climb 90 knots ↑ 500 fpm 3 nautical miles
Normal descent 120 knots ↓ 500 fpm 4 nautical miles
Cruise climb 110 knots ↑ 200 fpm 9 nautical miles
Cruise descent 120 knots ↓ 200 fpm 10 nautical miles

Exceptions

Headwinds make things take less distance. Tailwinds make things take more distance. A reasonable estimate is to allow an extra nautical mile per 1000 feet of altitude change per 10 knots of tailwind. In a headwind, I’ll simply reduce my climb rate.

In high-density-altitude conditions, climb performance gets really bad. In these cases, there’s nothing to do except fly at the best climb speed and accept whatever performance results.

Approach to landing

Light aircraft allow substantial pilot choice in the approach to land. We can use full flaps or no flaps. We can approach at a flat 20:1 slope under partial power (the same as the large jets), or we can make a much steeper power off approach (typically around 6:1, depending on the aircraft). We have a wide range of airspeeds to choose from. To a certain extent, the selection of an approach profile depends on runway length and wind conditions – but I think there’s a great safety benefit to selecting and practicing a standard approach which can be applied to the vast majority of landings.

I’ve decided to fly visual approaches at the same slope as my power-off glide, to permit gliding to a runway landing from an engine failure on approach. For normal operations, there is no reason to fly an approach any steeper than this – steeper approaches are less comfortable for passengers and carry a greater risk of botching the landing flare. For the purpose of establishing some standard numbers to commit to memory, I’ve decided that all of my visual approaches will be flown at a slope of 9 to 1.

Approach type Airspeed Vertical speed
Short field 60 knots ↓ 700 fpm
Normal 70 knots ↓ 800 fpm

In the presence of a headwind, the airspeed and vertical descent rate will remain constant, but the ground speed and distance covered will decrease. (There is also a weak dependence on airspeed, which I ignore.)

Headwind Distance per 1000 feet
0 knots 1.5 nautical miles
10 knots 1.25 nautical miles
20 knots 1.0 nautical miles

The application of these rules of thumb to a straight-in approach is simple. For example: if there is a 10 knot headwind, and I am flying at 1000 feet AGL, I will maintain altitude until I am 1.25 nautical miles from the runway threshold and then set up a 800 fpm descent at 70 knots. From this point forward I will fly the approach visually, maintaining airspeed but allowing the descent rate to vary as needed to reach the aiming point.

Exceptions

If there is a headwind stronger than 20 knots, I won’t steepen my approach track beyond 1000 feet per mile over the ground. Instead, I will fly the approach with partial flaps, a slightly greater airspeed, and a lesser rate of vertical descent. In this rare case, I trade away my ability to glide to a landing in exchange for improved handling and increased stall margin in strong winds.

When flying into an obstructed short field, I will fly a power-off approach (which ends up somewhere around a 6 to 1 slope). In this case, the extra risk of a steeper approach is outweighed by the increased safety of having more runway available.

Traffic patterns

I like to fly my traffic patterns at 80 knots with 10 degrees of wing flaps. In this configuration, visibility and maneuverability are good and power requirements are low. (Another reason for selecting this airspeed is that some of the older Cessnas don’t allow flap extension above 85 knots.) The traffic pattern should be as small as possible without compromising safety, which means:

Putting these numbers together leads to the “4000 foot” traffic pattern: the downwind leg should be offset from the runway by 4000 feet, the base turn should begin 4000 feet past abeam the touchdown point, and the final approach should be 4000 feet long.

The rule of thumb for wind is to shorten the downwind and final legs by 500 feet for every 10 knots of wind. So if there is going to be a 20 knot headwind when landing, the final approach will only be 3000 feet long. This keeps the airspeed and vertical descent rate the same.

Here’s what it looks like if we take the usual traffic pattern diagram and redraw it to scale:

The usual traffic pattern diagram… but this time, it’s drawn to scale.

The usual traffic pattern diagram… but this time, it’s drawn to scale.

I always struggled to get my traffic patterns to be the right size until I started flying them “by the numbers”. Landing somewhere with a shorter runway, I would end up much too high on final due to the scaled-down visual cues. Now that I know all the distances and altitudes, it’s effortless to fly a perfect pattern every time.