13.1 Pressure Altitude, Density Altitude, and Performance Effects

ACS PA.I.F.K1 asks you to use charts, tables, and data to predict performance. PA.I.F.K2a names atmospheric conditions as the first factor that changes those numbers. Chapter 6 already defined pressure altitude and density altitude as weather vocabulary. This section is the performance half of the same words: how you compute them on a ramp, how you enter them on an AFM/POH chart, and what the airplane does when density altitude is high.

PHAK Chapter 11 is blunt. Instruments and manufacturer charts are calibrated to the International Standard Atmosphere. Sea-level ISA is 15 °C and 29.92 inHg. Temperature falls about 2 °C (3.5 °F) per 1,000 feet up to about 36,000 feet. Pressure falls about 1 inHg per 1,000 feet in the lower troposphere. Any other temperature or pressure is nonstandard, and the published takeoff or climb number is no longer the number you will get unless you correct for it.

Pressure altitude — two legal ways to the same number

Pressure altitude is height above the standard datum plane, the theoretical surface where pressure is 29.92 inHg. That surface sits at sea level only on a standard day. When the local altimeter setting is below 29.92, the datum plane is below you and pressure altitude is higher than indicated altitude. When the setting is above 29.92, pressure altitude is lower than field elevation.

Two methods, same answer:

1. Set 29.92 in the Kollsman window and read the altimeter. That reading is pressure altitude. This is what you do in the airplane, and what you do above 18,000 feet when everyone flies flight levels.
2. Correct field elevation (or indicated altitude) with the reported setting, using PHAK’s lower-atmosphere lapse of about one inch per thousand feet:

Pressure altitude ≈ indicated / field elevation + 1,000 × (29.92 − altimeter setting)

If the setting is below 29.92 you add. If it is above 29.92 you subtract. The 1,000-foot-per-inch factor is the same approximation AIM uses for altimeter-setting errors.

Worked PA example 1. Field elevation 2,200 feet MSL. ATIS altimeter 30.12 inHg. The setting is 0.20 inHg above 29.92, so subtract 200 feet:

Pressure altitude ≈ 2,200 − 200 = 2,000 feet.

Worked PA example 2. Field elevation 7,500 feet MSL. ATIS altimeter 29.42 inHg. The setting is 0.50 inHg below 29.92, so add 500 feet:

Pressure altitude ≈ 7,500 + 500 = 8,000 feet.

Do not walk to the takeoff chart with 2,200 or 7,500. Those are elevations. The chart’s first entry is pressure altitude or density altitude, depending on how that manufacturer drew the page.

Density altitude — PA corrected for temperature

PHAK’s definition is one sentence: density altitude is pressure altitude corrected for nonstandard temperature. It is the altitude in the standard atmosphere that has the same density as the air you are sitting in. Regardless of the elevation painted on the sectional, the airplane performs as though it were operating at the density altitude.

High density altitude is thin air. Contributors are high elevation, low pressure, high temperature, and high humidity. Low density altitude is dense air — cold, high pressure, low elevation, dry — and better performance.

PHAK tells you to find density altitude with a flight computer or a tabular / graphic chart (PHAK Figure 11-4 is the density-altitude graph). It does not publish a private-pilot “add N feet of density altitude per degree above ISA” rule. Do not invent one and do not treat a schoolhouse shortcut as if it were in the handbook. Compute pressure altitude, then look the density altitude up.

The table below is a teaching density-altitude table for this lesson. It is not a real AFM page and not a substitute for the PHAK graph or your E6B. Use it the way you will use those tools: enter pressure altitude and OAT, read density altitude.

DA lookup, example 1. PA 2,000 feet, OAT 32 °C. Teaching table: density altitude ≈ 4,500 feet. A 2,200-foot field on a hot afternoon is a 4,500-foot performance problem.

DA lookup, example 2. PA 8,000 feet, OAT 32 °C. Teaching table: density altitude ≈ 11,950 feet. The sectional still says 7,500. The wing, the propeller, and the normally aspirated engine are working in air that belongs near 12,000 feet on a standard day.

Standard temperature at 2,000 feet is about 11 °C; at 8,000 feet it is about −1 °C. Both of those OATs are far above ISA. That is why density altitude jumped thousands of feet above pressure altitude. Cold air does the opposite: density altitude falls below pressure altitude and performance improves.

What high density altitude actually changes

Thinner air hits the airplane three ways at once. The wing needs a higher true speed to make the same lift at the same angle of attack (L = CL × ½ ρ V² S — ρ is smaller, so V must grow). The propeller bites less air and produces less thrust. The normally aspirated engine ingests less mass of air and makes less power. PHAK: as density decreases, aircraft performance decreases.

The indicated takeoff and stall speeds stay about the same. The airspeed indicator is already a dynamic-pressure instrument. What grows is true airspeed at lift-off and at touchdown, so the ground roll grows even before you count the weaker engine and propeller. That is why a mountain arrival “at the same 65 knots” still uses more pavement.

Humidity makes air less dense because water vapor is lighter than dry air (PHAK 11). There is no published rule-of-thumb or chart that converts humidity into extra feet of density altitude. Expect a further performance loss on a muggy afternoon. Do not invent “add 200 feet for humidity.”

Charts, not vibes

PA.I.F.K1 is the skill of using the page. A density-altitude number that never enters a takeoff, climb, or landing chart is trivia. Typical AFM/POH takeoff graphs ask for pressure altitude and OAT (they do the density correction inside the grid) or they ask for density altitude after you computed it. Either way, the inputs are the two numbers you just made — not field elevation, not indicated altitude with the local setting still in the window, and not yesterday’s standard-day memory.

Scenario: Sam’s 2,200-foot airport

Sam’s home field is 2,200 feet MSL. This morning was 5 °C and 30.12; pressure altitude was 2,000 feet and the teaching table put density altitude near 1,300 feet. The airplane leapt off. This afternoon ATIS is still 30.12 but OAT is 32 °C. Pressure altitude is still 2,000 feet. Density altitude is now about 4,500 feet. Same runway paint. Same indicated rotation speed. A much longer roll, a much softer climb, and a higher TAS the moment the wheels leave the surface. Sam does not say “it’s only 2,200 feet.” Sam puts 2,000 feet and 32 °C on the chart and believes the new distance.