MIT 16.687 · FAA PHAK Ch. 4 & 11 · Learning aid

Aircraft Performance Lab

Density altitude and the day-of factors that change takeoff and climb. Study home · Notes · Quiz · PHAK (FAA)

Before you play: what this is about

Aircraft performance is how the airplane behaves today—takeoff distance, climb, cruise, landing—not a single fixed number. A big part of that story is how dense the air is. Thin air means less oxygen mass for the engine, less “grip” for the propeller, and less lift from the wing at a given indicated airspeed.

Density altitude (DA)

Pilots summarize “how thin the air feels” as density altitude: the altitude in the standard atmosphere that has the same density as the air you are in right now. Formally (PHAK), DA is pressure altitude corrected for nonstandard temperature. When conditions match the standard atmosphere, DA equals pressure altitude.

What thins the air?

  • High elevation / low pressure — less air above you
  • High temperature — molecules spread apart
  • High humidity — water vapor is lighter than dry air, so moist air has less mass per volume

Heat and elevation often move DA by thousands of feet; humidity usually by hundreds. Still real—especially when margins are already tight.

Beyond the atmosphere

Even at the same density altitude, takeoff and climb change with weight, wind, runway surface and slope, and configuration (e.g. flaps). Most POH charts use pressure altitude and temperature (and weight/wind)—not a humidity axis. On hot, humid days, safety guidance often means adding extra margin (e.g. FAASTeam ~+10% takeoff distance).

What this tool is for

This lab is a mental-model sandbox, not a performance calculator. Use it to feel how the knobs interact and to build intuition before you open real AFM charts.

  1. Density — Change elevation, altimeter, temperature, and dew point. Watch pressure altitude, dry DA, humidity’s add-on, the “air in a box” mass picture, and the altitude tape.
  2. Mission — Stack weight, wind, surface, slope, and flaps on top of that DA. See a toy ground roll, climb, and engine/prop/wing meters (illustrative only).
  3. Guide — Walk a short story from standard day → hot/high/humid → heavy/tailwind/soft field, then check yourself with a few questions.

Suggested first pass: read this section → open Density and try the “Standard day” then “High + hot + humid” presets → switch to Mission and raise weight or add a tailwind → finish with Guide if you want the narrative path.

Anchored to FAA PHAK (FAA-H-8083-25C) Chapters 4 & 11 and related density-altitude safety guidance. Numbers in the lab are educational approximations—not substitute for your POH.

Skip to the interactive lab ↓

Atmosphere controls

Three knobs thin the air: pressure (elevation + altimeter), temperature, and humidity.

Pressure altitude
0 ft
ISA temp at PA
15 °C
DA (dry / chart-style)
0 ft
Humidity add
+0 ft
Density altitude (selected)
0 ft
PHAK: Density altitude is pressure altitude corrected for nonstandard temperature. Humidity also reduces density (water vapor is lighter than dry air) but is usually not a chart axis — still expect less performance when it is hot and humid.

Air in a box

Same volume. Primary truth is the mass % below (ideal-gas ρ/ρ₀). Dots are only a schematic decoration — not a molecular census.

Schematic — not to scale
Dry air (N₂ / O₂) Water vapor (H₂O) — few % of particles max
Air mass vs SL standard (ρ/ρ₀)
100%
Ideal gas · moist air · fixed volume
Vapor mole fraction (e/p)
0.0%
Density ρ
—
Dew-point ROT (compare)
~0 ft

Altitude tape

Field elev · pressure altitude · density altitude (dry vs humid).

Your airplane performs roughly as if it were at the density altitude — not just field elevation.

Scale check: Heat and elevation often move DA by thousands of feet; humidity usually by hundreds. Try presets, then isolate one slider at a time.

Mission factors

Density altitude from the atmosphere lab, plus weight, wind, runway, and configuration (PHAK Ch. 11).

Density altitude in use
0 ft
Humidity in DA
Off
At the same DA, try raising weight ~10% vs only raising dew point — weight often hurts the mission more.

Outcome theater

Toy trainer model for learning interactions — not AFM distances.

Ground roll vs available runway
Wind calm
✈
Toy ground roll
—
Toy climb rate
—
Climb angle (proxy)
—
Toy landing roll
—
OK

Guided story

Walk the full stack: atmosphere → humidity → weight → wind → surface.

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Operational loop: conditions → pressure altitude → density altitude → AFM/POH charts → margins. Humidity often lives in the “margins” step, not on the chart axes.

Check yourself

Five questions on performance and density altitude (including humidity).

About this model

  • Pressure altitude: (29.92 − altimeter) × 1000 + field elevation.
  • Dry density altitude: PA + 120 × (OAT − ISA temp at PA) °C — training approximation; at ISA, DA ≈ PA.
  • Humidity: simplified vapor-pressure → density reduction → feet of DA. Compare with dew-point ROT (~20 × Td °C). PHAK Ch. 4 example is a qualitative preset, not a certified reproduction of NOAA’s calculator.
  • Mission bars: illustrative scaling for weight, wind, surface, slope, flaps — not any specific POH.
  • Sources: FAA PHAK FAA-H-8083-25C Ch. 4 & 11; FAA-P-8740-2 Density Altitude (humid-day +10% takeoff heuristic); AC 00-6B framing of humidity as often negligible in the formal DA definition.