13.4 Wind, Gradient, Surface, and Crosswind Component

ACS PA.I.F.K2d is the airport: runway heading versus wind, slope, and what the surface will do to acceleration and braking. The knowledge test loves a wind-component chart because it is easy to pick the wrong angle and then read a perfectly calculated wrong number.

How to use a wind-component chart

The FAA/PHAK crosswind graph is a quarter-circle. One family of arcs is wind speed. One family of radials is degrees between the wind and the runway. You do not enter runway heading and wind direction as two raw numbers. You enter the difference.

1. Find the angle: |wind direction − runway heading|, reduced so it is between 0° and 90°. A 270° runway and a 240° wind is 30°, not 240° and not 270°.
2. Find the wind-speed arc (20 knots, 15 knots, whatever ATIS said).
3. Where that radial meets that arc, drop to the horizontal axis for the crosswind and to the vertical axis for the headwind (or tailwind if you are using the downwind runway).

A direct headwind is 0° off — all headwind, no crosswind. A 90° wind is all crosswind. A 45° wind splits into equal components of about 0.7 × wind speed each (sin 45° = cos 45° ≈ 0.707).

If you do not have the graph, the same geometry is:

Headwind = wind speed × cos(angle)
Crosswind = wind speed × sin(angle)

Worked example: runway 27, wind 240 at 20

Runway 27 is heading 270°. Wind 240° at 20 knots.

Angle = 270 − 240 = 30°.

Headwind = 20 × cos 30° = 20 × 0.866 = 17.3 knots (call it 17 knots on a chart).

Crosswind = 20 × sin 30° = 20 × 0.50 = 10 knots.

That is the whole item. The trap answers on the test are usually the components for 20°, 40°, or 60° — or someone who used 240° as the angle, or who called the entire 20 knots a crosswind because the wind was “not down the runway.” A 30° wind is still mostly a headwind.

Use the runway in use, not the one you wish you had. If you take runway 09 instead, the 240° wind becomes 240 − 090 = 150°, which is a 30° tailwind from the right (180 − 150 = 30°). Then you have about 17 knots of tailwind and still 10 knots of crosswind. Same crosswind, opposite and much more expensive headwind/tailwind sign. That is how a “the ramp is on this end” decision rewrites the takeoff chart.

Demonstrated crosswind is demonstrated

The AFM/POH usually publishes a maximum demonstrated crosswind. For many light trainers that number is about 15 knots. It is the largest 90°-component wind the manufacturer demonstrated during certification. It is not, by itself, a 14 CFR operating limitation. It is not a regulation that says “15.1 knots is illegal.” It becomes a limit only if the manufacturer puts it in the Limitations section of the AFM. Most trainers leave it in performance or handling-notes language: demonstrated, not limiting.

That does not make 20 knots of direct crosswind a good idea. It means the knowledge-test answer is “demonstrated, not a limit unless the AFM says so,” and the oral answer is “I will use a more into-wind runway, or I will not go, long before I treat 15 as a target.” Your personal minimum and your recent crosswind practice sit well inside the demonstrated number. The ACS skill standard for landing is a controllable airplane in the touchdown zone, not a legal debate on the numbers.

A common schoolhouse estimate you may hear — about 0.2 × VS0 as a rough maximum crosswind — is a rule of thumb, not a PHAK formula and not a substitute for the AFM. Do not write it as if the FAA published it as law.

Gust factor, conceptually

The Airplane Flying Handbook’s gust technique is conceptual, not a 14 CFR number: if the wind is 12 gusting 22, the gust increment is 10 knots, and you add about half of that increment (5 knots) to the normal approach speed. You are buying a margin so a sudden drop from 22 to 12 does not leave you below the target IAS in the flare. You are not authorized to add 15 knots “for the wind” and then float the length of the runway. Extra speed is extra landing distance (previous section). Add the gust increment, fly the airplane, and still be willing to go around.

Grass versus paved; gradient; contamination

Paved, dry, level is what most takeoff and landing charts assume. Dry grass adds rolling resistance — typical AFM notes add on the order of 15 percent to the takeoff ground roll (the 50-foot-obstacle number may use a different note). Landing on grass can be shorter if the turf is firm and you are light, or longer if the surface is wet and brakes do nothing. Wet or long grass is worse than dry short grass. Gravel and dirt chew acceleration and propellers. Standing water is hydroplaning plus a longer takeoff. Read the note under your chart.

Gradient again: percent slope is feet of height per 100 feet of length. Takeoff uphill lengthens the roll. Takeoff downhill shortens it but may aim you at obstacles or a drop-off. Landing uphill shortens the rollout; landing downhill lengthens it. A one-way strip that forces an uphill takeoff and a downhill landing in the same direction is a performance problem at both ends when density altitude is high.

The stacked takeoff — density, tailwind, uphill

None of these factors is exotic alone. Together they are how a “3,200-foot runway” disappears.

Combo scenario: Chen at midday. Field elevation 7,500 feet, altimeter 29.42, OAT 32 °C. From 13.1, pressure altitude is 8,000 feet and the teaching density-altitude table put the airplane near 12,000 feet. The teaching takeoff table at 12,000 feet density altitude was already 2,550 feet of paved, level, zero-wind ground roll and 4,600 feet to 50 feet, climbing at 180 fpm. Chen is near gross weight. The only usable direction is uphill about 2 percent on dry grass with a 6-knot tailwind because the wind favors the other end and that end has no taxiway. Apply, in the AFM’s order, the grass note, the tailwind note, and the slope (if the AFM even gives a slope note — many do not, which means the chart is silent, not generous). The 4,600-foot obstacle number was for a paved, level, zero-wind airplane. Chen does not have that airplane or that runway. 180 fpm will not outclimb rising terrain. This is a no-go, a wait for evening cool air and a headwind, or a departure after leaving people and bags on the ramp — not a “it looked long enough from the FBO window” takeoff.

The knowledge-test version of Chen’s day is shorter: high density altitude + tailwind + upslope + soft surface + high weight all move takeoff distance the same direction. None of them cancel. Headwind is the one that helps. If you cannot have a headwind, you need pavement, downhill or level, and a density altitude the climb chart can live with.

Scenario: Priya reads the chart, not the wind sock’s whole story

Priya has runway 27, wind 240 at 20 gusting 28. She computes 30°, 17 headwind, 10 crosswind — inside a 15-knot demonstrated number, with a gust increment of 8 knots and about 4 knots added to approach speed. She still chooses 27 rather than 09, because 09 would keep the 10-knot crosswind and replace the 17-knot headwind with a 17-knot tailwind. Demonstrated crosswind did not make 27 mandatory. Physics and the takeoff chart did.