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Learning hub · Performance · Lesson 1

Density altitude and take-off performance

The same aeroplane on the same runway can need twice the distance on a hot summer afternoon as on a cold winter morning. This lesson shows what changes the take-off run and how to plan for it.

About 12 minutes, plus the quiz. Part of Performance. It builds on Pressure, QNH and the altimeter.

1. Density altitude in one minute

Engines and wings need dense air. Density altitude is the altitude in the International Standard Atmosphere (ISA) at which the air would have the density you actually have. High density altitude means thin air, which means less power from the engine, less lift from the wing and less thrust from the propeller.

It goes up with a higher airfield, with lower pressure and with higher temperature. Humid air is also slightly thinner than dry air, because water vapour is lighter than the nitrogen and oxygen it displaces. This is why instructors say: hot, high and humid are the three enemies. The calculator does the sum for you.

2. What changes the take-off run

  • Density altitude. As a rule of thumb, the take-off run grows by roughly 10 per cent for each 1,000 ft of density altitude on a normally aspirated engine, and more at high density altitudes. (UK CAA guidance for light aeroplanes gives 10 per cent for each 1,000 ft of elevation and 10 per cent for each 10°C rise in temperature.) The aircraft manual tables are better than any rule.
  • Mass. A heavier aeroplane needs more speed to fly and accelerates more slowly. The effect is more than proportional: a 10 per cent increase in mass lengthens the run by roughly 20 per cent.
  • Wind. A headwind shortens the run because you reach flying speed over the ground sooner. A tailwind lengthens it by more than a headwind of the same size shortens it. Where a manual allows for wind, UK CAA guidance is to count no more than 50 per cent of a headwind and at least 150 per cent of a tailwind.
  • Runway. Wet or long grass, soft ground, snow and an uphill slope all lengthen the run.
  • Flaps and technique. Use the setting in the manual and rotate at the speed in the manual.

3. A worked example

This aircraft is invented, so that the numbers are easy to follow. Its manual says: take-off run 300 m at sea level in standard conditions.

  1. From the first lesson, the airfield has a density altitude of about 2,000 ft today. That is 2 × 10 per cent = +20 per cent, so 300 × 1.2 = 360 m.
  2. You are carrying a full load, 10 per cent over the mass used in the manual: another +20 per cent, so about 430 m.
  3. The runway is dry grass and slightly uphill. Add a further allowance as the manual says, for example 20 per cent for dry grass: about 520 m.

You started with 300 m in the brochure and ended with about 520 m on the day. Manual take-off distances are usually measured to a height of 50 ft (15 m). The distance available needs to be well above that, and you need a clear path for the climb out.

4. Leave a margin

The figures in the manual were achieved in test flights with a new aeroplane and a healthy engine, in good conditions. A tired aeroplane or a less practised pilot may not match them. Many instructors teach adding a generous margin to the book figure. Figures such as 25 to 50 per cent are often suggested (the UK CAA recommends multiplying unfactored take-off data by 1.33), but there is no single rule, so follow your school’s. Plan to take off, not to scrape the fence.

Check three things before every take-off: the distance you need (with the margin), the distance you have (the take-off run available, TORA, in the AIP), and the obstacles you have to clear. If the numbers do not fit with a margin, wait for cooler air, carry less fuel or fewer passengers, or choose a longer runway.

Use the performance data in your aircraft’s flight manual for a real flight. The rules of thumb here are for understanding how the factors act, not for planning.

5. Try it yourself

Work each one out on paper first, then open the answer to compare. The numbers are invented.

  1. This aircraft is invented. Its manual gives a take-off run of 400 m at sea level in standard conditions. Today the density altitude is 3,000 ft, and you are 5 per cent over the mass used in the manual. Estimate the run with the lesson’s rules of thumb, then apply the 1.33 margin. The usable runway is 700 m. Does it fit?
    Show the answer

    Density altitude: 3 × 10 per cent = +30 per cent, so 400 × 1.3 = 520 m.

    Mass: 10 per cent more mass gives about 20 per cent more run, so 5 per cent more gives about 10 per cent: 520 × 1.1 ≈ 572 m.

    Margin: 572 × 1.33 ≈ 760 m. The runway is 700 m, so it does not fit with a margin. Wait for cooler air, carry less fuel or fewer passengers, or use a longer runway.

  2. Take-off wind chart rules (UK CAA guidance as in the lesson): count no more than 50 per cent of a headwind and at least 150 per cent of a tailwind. The wind is 10 kt straight down runway 24. What headwind do you enter for runway 24, and what tailwind for the opposite runway 06?
    Show the answer

    Runway 24 has a 10 kt headwind: count no more than 50 per cent, so enter 5 kt of headwind.

    Runway 06 would have a 10 kt tailwind: count at least 150 per cent, so enter 15 kt of tailwind.

    The credit for a headwind is small and the penalty for a tailwind is large, which is why you avoid taking off with a tailwind whenever you can.

  3. After all the corrections, the take-off distance for the day is 420 m, measured (as manuals usually do) to a height of 50 ft. The take-off run available (TORA) is 600 m. Apply the 1.33 factor. What else must you check before you decide?
    Show the answer

    420 × 1.33 ≈ 560 m. That is less than the 600 m available, so the distance fits, with about 40 m to spare.

    The three checks are: the distance you need (with the margin), the distance you have (TORA from the AIP), and the obstacles you have to clear. Because the figure is to 50 ft, you still need a clear climb-out path past any obstacles. With only 40 m of spare runway, many pilots would think hard about waiting for cooler air or carrying less.

6. Watch

A short safety video on hot, high and humid conditions and what they do to performance. It is American, so wording and some rules differ from European (ICAO/EASA) practice.

Open on YouTube if the player does not load. Not made by VectorEFB; check what you learn against your flying school’s material and your instructor.

More to watch

Another explanation of pressure altitude, temperature and density altitude, and what they do to performance. This video is American, so wording and some rules differ from European (ICAO/EASA) practice.

Open on YouTube if the player does not load. Not made by VectorEFB.

7. Check yourself

Five original practice questions. Answer them, press Check answers and read each explanation.

1. Which combination gives the poorest take-off performance?

Each of heat, altitude and humidity lowers the air density, and the effects add up. Cold, low and dry gives the best performance.

2. What does a high density altitude do to the take-off run?

Thin air reduces both the engine power and the wing lift, so you accelerate more slowly and need a higher ground speed to fly. The run is longer and the climb is weaker.

3. The take-off mass is 10 per cent higher than the mass used for the table. The take-off run will be about:

The effect of weight is more than proportional: roughly 20 per cent more distance for 10 per cent more mass.

4. Compared with a headwind of 10 kt, a tailwind of 10 kt:

A tailwind hurts more than a headwind of the same size helps, so avoid taking off with a tailwind whenever you can.

5. The take-off run in the manual is 400 m. Which is the most sensible planning approach?

The manual figure is for specific conditions and an ideal technique. Correct it for the day, then add a margin, and make sure the runway and the obstacle clearance still fit.

Next: the wind triangle. Back to the learning hub.

For training and situational awareness only. Not certified for navigation. Always use official charts, the AIP, NOTAMs and a proper weather briefing for real flights.