# Private Pilot | Lesson 9 - Aircraft Performance

**TABLE OF CONTENTS:**

9.1 DENSITY ALTITUDE EXPLAINED

9.2 DENSITY ALTITUDE COMPUTATIONS

9.3 CALCULATING TAKEOFF DISTANCE

9.4 SETTING CRUISE POWER

9.5 CROSSWIND COMPONENTS

9.6 CALCULATING LANDING DISTANCE

**9.1 Density Altitude Explained**

Density Altitude is a measurement of the density of the air expressed in terms of altitude. The main reason for calculating Density Altitude is to determine its effect on aircraft performance. Air density varies inversely with altitude, that is to say, air is very dense at low altitudes and becomes less dense as your altitude increases. Thus, Density Altitude increases as your true altitude increases.

However, the same indicated airspeed is used for takeoffs and landings regardless of altitude or air density because the airspeed indicator is also directly affected by air density.

In addition to altitude, temperature, humidity, and barometric pressure will also affect air density.

A standardized scale for the ratio of air density to altitude has been established using a standard temperature and pressure for each altitude.

When temperature and pressure are not at standard (which, in reality, is almost always), density altitude will not be the same as true altitude.

How Pressure Affects Density Altitude

As barometric pressure increases, the air becomes more compressed and compact (think of high pressure as the resultant force of this compression and compaction of the air in a given area). This is an increase in air density. Air density is higher for high pressure, so the Density Altitude is lower.

- Density Altitude increases with a decrease in pressure.
- Density Altitude decreases with an increase in pressure.
- Or, you can remember that pressure inversely affects Density Altitude.

Note: Pressure altitude is based on standard temperature. Therefore, density altitude will exceed pressure altitude if the temperature is above standard.

How Temperature Affects Density Altitude

As the air temperature increases, the air expands and therefore becomes less dense. This decrease in density means a higher Density Altitude.

- Density Altitude increases with an increase in temperature.
- Density Altitude decreases with a decrease in temperature.
- Or, just remember that temperature directly affects Density Altitude.

How Humidity Affects Density Altitude

As the relative humidity increases, the air becomes less dense (a given volume of moist air weighs less than the same volume of dry air). This decrease in density means a higher density altitude.

- Density Altitude increases with an increase in humidity.
- Density Altitude decreases with a decrease in humidity.
- Or, remember relative humidity directly affects Density Altitude.

Cold, dry air and higher barometric pressure = low Density Altitude and better performing aircraft.

Hot, humid air and lower barometric pressure = high Density Altitude and reduced performance of aircraft.

##### Ascent Quick Quiz - 9.1 Density Altitude Explained

**Question 1:**What are the standard temperature and pressure values for sea level?

**Answer**

**Question 2:**What effect, if any, does high humidity have on aircraft performance?

**Answer**

**Question 3:**Which factor would tend to increase the density altitude at a given airport?

**Answer**

**Question 4:**What effect does high density altitude, as compared to low density altitude, have on propeller efficiency and why?

**Answer**

**Question 6:**What effect does high density altitude have on aircraft performance?

**Answer**

**Question 7:**Which combination of atmospheric conditions will reduce aircraft takeoff and climb performance?

**Answer**

**Question 8:**If the outside air temperature (OAT) at a given altitude is warmer than standard, the density altitude is

**Answer**

**9.2 Density Altitude Computations**

The easiest way to calculate Density altitude is to find the pressure altitude and then adjust for the temperature. (Pressure altitude is simply found by setting the altimeter to 29.92, and reading the indicated altitude.) The adjustment for temperature may be made using either your flight computer or on a Density Altitude Chart.

During the FAA knowledge test, you'll use the same Density Altitude Chart provided below (figure 8).

To use the Density Altitude Chart:

- Adjust the airport elevation to pressure altitude. Do this by using the given altimeter setting to determine how many feet should be added or subtracted from airport elevation to convert it to pressure altitude.
- Adjust pressure altitude for nonstandard temperature. Do this by plotting the intersection of the actual outside air temperature (listed on the horizontal axis of the chart) with the pressure altitude lines (listed as the diagonally sloped upward lines).
- Determine the approximate density altitude. Do this by moving directly left horizontally to the edge of the graph, and read density altitude on the Approximate Density Altitude vertical axis of the chart.

EXAMPLE:[ Show me this in a step-by-step example video] Find the Density Altitude given the following variables:

Outside air temperature 70°F,

Altimeter setting 30.10" Hg,

Airport elevation 5,883 ft.This is found as follows:

The altimeter setting of 30.20 requires a –165 altitude correction factor. Subtract 165 from field elevation of 5,883 ft. to obtain pressure altitude of 5,718 ft.- Locate 70°F on the bottom axis of the chart and move up to intersect the diagonal pressure altitude line of 4,468 ft.
- Move horizontally to the left axis of the chart to obtain the density altitude of about 7,700 ft.
So, you've determine the Density Altitude in this example to be approximately 7,700 ft.

Notice that while the airport elevation is 5,883 ft., the Density Altitude is approximately 7,700 ft!

Finally, note that you may determine the effects of temperature changes on density altitude simply by following the above chart procedure and substituting different temperatures.

##### Ascent Quick Quiz - 9.2 Density Altitude Computations

**Question 1:**(Refer to figure 8.) Determine the density altitude for these conditions:

**Answer**

Altimeter setting . . . 30.35,

Runway temperature . . . +25°F,

Airport elevation . . . 3,894 ft MSL

**Question 2:**(Refer to figure 8.) What is the effect of a temperature increase from 30 to 50°F on the density altitude if the pressure altitude remains at 3,000 feet MSL?

**Answer**

**Question 3:**(Refer to figure 8.) Determine the pressure altitude at an airport that is 3,563 feet MSL with an altimeter setting of 29.96.

**Answer**

**Question 4:**(Refer to figure 8.) What is the effect of a temperature decrease and a pressure altitude increase on the density altitude from 90°F and 1,250 feet pressure altitude to 55°F and 1,750 feet pressure altitude?

**Answer**

**Question 5:**(Refer to figure 8.) Determine the pressure altitude at an airport that is 1,386 feet MSL with an altimeter setting of 29.97.

**Answer**

**Question 6:**(Refer to figure 8.) What is the effect of a temperature increase from 25 to 50°F on the density altitude if the pressure altitude remains at 5,000 feet?

**Answer**

**Question 7:**(Refer to figure 8.) Determine the pressure altitude with an indicated altitude of 1,380 feet MSL with an altimeter setting of 28.22 at standard temperature.

**Answer**

**Question 8:**(Refer to figure 8.) Determine the density altitude for these conditions:

**Answer**

Altimeter setting . . . 29.25,

Runway temperature . . . +81°F,

Airport elevation . . . 5,250 ft MSL

**9.3 Calculating Takeoff Distance**

As we've been discussing, the conditions that will reduce aircraft takeoff and climb performance are:

- High altitude
- High temperature
- High humidity

In order to know to what degree any these conditions will affect the aircraft's takeoff distance, we must turn to the Performance section of the Pilot's Operating Handbook. Takeoff distance performance is depicted in the airplane operating manual either in chart form or on a graph. If a graph, it is usually depicted in terms of Density Altitude. So, you must first calculate Density Altitude from your airport's elevation, the current pressure altitude, and temperature. (As you just learned from above!)

In the graph used on the FAA written exam (see figure 41), the first section on the left uses outside air temperature and pressure altitude to obtain density altitude.

To use the Takeoff Distance chart:

- Start with the given Outside Air Temperature, move directly up the graph until you intercept the given pressure altitude guide line (note that the pressure altitude guide lines curve a bit, and you'll have to estimate for the appropriate curvature intercept point). Then move horizontally right to the next Reference Line.
- Adjust for the given takeoff weight by moving parallel to the weight guide lines until you intercept the given weight. From that point, move horizontally right to the next Reference Line.
- Adjust for the wind component by moving parallel (either up for a tailwind, or down for a headwind) to the wind guide lines until you intercept the given wind component. From that point, move horizontally right to the next Reference Line.
- Adjust for a obstacle height, if necessary.

- If an obstacle height is given, move parallel up the obstacle height guide lines until you intercept the given obstacle height. From that point, move horizontally right to the edge of the graph. Read the takeoff distance from the vertical axis of the graph. Note, a 50 ft. obstacle will take you to the edge of the graph as you move up the guide line.
- If there is no obstacle height given or if the question asks for the 'ground roll' as well, simply move horizontally right from the point that you hit the Obstacle Height Reference Line and read the takeoff distance off the edge of the graph.

EXAMPLE 1:(Refer to figure 41.) Determine the total distance required for takeoff to clear a 50-foot obstacle. Given:

Outside air temperature of 15°C,

Pressure altitude of 5,650 ft.,

Takeoff weight of 2,950 lb.,

Headwind component of 9 kts.The solution to the example problem is marked with the dotted arrows on the chart above, and can be found as follows:

- Move straight up from 15°C (which is also where the standard temperature line begins) to the pressure altitude of 5,650 ft. Then horizontally right to the next Reference Line.
- In this example, it is not necessary to adjust for weight because the airplane is at maximum weight of 2,950 lb. Move horizontally right to the next Reference Line.
- Adjust for wind component, the headwind component of 9 kt. means an adjustment downward parallel to the guide lines until you intercept 9 kts.
- Then adjust for the obstacle and determine the ground roll.

- For the takeoff distance over the 50-foot obstacle, move parallel up the obstacle guide lines until you reach the edge of the graph. Read the takeoff distance from the vertical axis of the graph, approximately 2,300 ft.
- Go back to the intercept point with the Obstacle Height Reference Line and move horizontally right until you reach the edge of the graph, and read the takeoff distance, approximately 1,375 ft.

EXAMPLE 2:[ Show me this in a step-by-step example video] (Refer to figure 41.) Determine the total distance required for takeoff to clear a 50-foot obstacle. Given:

Outside air temperature of 22°C,

Pressure altitude of 2,000 ft.,

Takeoff weight of 2,600 lbs.,

Headwind component of 6 kts.This is found as follows:

- Move straight up from 22°C to the pressure altitude of 2,000 ft. Then horizontally right to the next Reference Line.
- Then adjust for the takeoff weight by moving parallel down the weight guidelines until you intercept 2600 lbs. Then horizontally right to the next Reference Line.
- Then adjust for the wind component. A headwind was given so you'll have to move parallel downward until you intercept 6 kts. Then horizontally right to the next Reference Line.
- Then adjust for the obstacle and determine the ground roll.

- For the takeoff distance over the 50-foot obstacle, move parallel up the obstacle guide lines until you reach the edge of the graph. Read the takeoff distance from the vertical axis of the graph, approximately 1200 ft.
- For the ground roll, go back to the intercept point with the Obstacle Height Reference Line and move horizontally right until you reach the edge of the graph, and read the takeoff distance, approximately 600 ft.

##### Ascent Quick Quiz - 9.3 Calculating Takeoff Distance

**Question 1:**(Refer to figure 41.) Determine the total distance required for takeoff to clear a 50-foot obstacle.

**Answer**

OAT . . . Std,

Pressure altitude . . . 4,000 ft,

Takeoff weight . . . 2,800 lb,

Headwind component . . . Calm

**Question 2:**(Refer to figure 41.) Determine the approximate ground roll distance required for takeoff.

**Answer**

OAT . . . 100°F,

Pressure altitude . . . 2,000 ft,

Takeoff weight . . . 2,750 lb,

Headwind component . . . Calm

**Question 3:**(Refer to figure 41.) Determine the total distance required for takeoff to clear a 50-foot obstacle.

**Answer**

OAT . . . Std,

Pressure altitude . . . Sea level,

Takeoff weight . . . 2,700 lb,

Headwind component . . . Calm

**Question 4:**(Refer to figure 41.) Determine the approximate ground roll distance required for takeoff.

**Answer**

OAT . . . 90°F,

Pressure altitude . . . 2,000 ft,

Takeoff weight . . . 2,500 lb,

Headwind component . . . 20 kts

**9.4 Setting Cruise Power**

Cruise power settings are also found in the Performance section of the Pilot's Operating Handbook (or, **POH**) and are displayed usually in a table format (see figure 36).

For the FAA written exam you will use figure 36 exclusively to calculate cruise power settings. It is based on 65% power, and it consists of three sections to adjust for varying temperatures:

- ISA -20°C (on left)
- Standard temperature (in middle)
- ISA +20°C (on right)

Values found on the table based on various pressure altitudes and temperatures include

- Engine RPM
- Manifold pressure (in. Hg)
- Fuel flow in gal. per hr. (with the expected fuel pressure gauge indication in pounds per square inch)
- True airspeed (kt. and MPH)

The FAA written exam questions gauge your ability to find values on the chart and interpolate between lines, for example, a pressure altitude of 9,500 ft would be produce fuel flow and TAS values that were 75% of those for a pressure altitude of 10,000 ft.

(If needed, see the How to Interpolate*** tutorial for instruction)

EXAMPLE:What is the expected fuel consumption for a 1,000-nautical mile flight under the following conditions:

A pressure altitude of 4,000 ft.,

a temperature of 25°C,

and calm wind.This is found as follows:

So, the expected fuel consumption is 72.3 gals.

- Determine which section of the Cruise Power Settings chart you should use. This example gives an outside air temperature of 25°C, so the far right section ISA +20 should be used.
- Then determine the True Air Speed (TAS). Under the ISA +20 section of the chart, at 4,000 ft. pressure altitude, the TAS is 159 kts.
- Next divide the distance of the trip by the TAS to get the total time of the trip (1000 NM ÷ 159 kts/hr = 6.29 hrs).
- Finally multiply the total time by the fuel flow gallons per hour (GPH) to get the total fuel consumption (6.29 hrs × 11.5 gal/hr = 72.3 gals).

##### Ascent Quick Quiz - 9.4 Setting Cruise Power

**Question 1:**(Refer to figure 36.) What fuel flow should a pilot expect at 11,000 feet on a standard day with 65 percent maximum continuous power?

**Answer**

**Question 2:**(Refer to figure 36.) What is the expected fuel consumption for a 1,000-nautical mile flight under the following conditions?

**Answer**

Pressure altitude . . . 8,000 ft,

Temperature . . . 22°C,

Manifold pressure . . . 20.8" Hg,

Wind . . . Calm

**Question 3:**(Refer to figure 36.) What is the expected fuel consumption for a 500-nautical mile flight under the following conditions?

**Answer**

Pressure altitude . . . 4,000 ft,

Temperature . . . +29°C,

Manifold pressure . . . 21.3" Hg,

Wind . . . Calm

**Question 4:**(Refer to figure 36.) Determine the approximate manifold pressure setting with 2,450 RPM to achieve 65 percent maximum continuous power at 6,500 feet with a temperature of 36°F higher than standard.

**Answer**

**Question 5:**(Refer to figure 36.) Approximately what true airspeed should a pilot expect with 65 percent maximum continuous power at 9,500 feet with a temperature of 36°F below standard?

**Answer**

**9.5 Crosswind Components**

When landing, you should always to plan to land the aircraft into the wind, however, in reality nature only sometimes sends a wind directly down the runway. Usually, you will be landing with a least some crosswind component. Airplanes have a limit to the amount of direct crosswind in which they can land. When the wind is blowing at a shallow (acute) angle to the runway, only a component of that wind is acting as a direct crosswind.

A crosswind component chart (figure 37) may be used to determine the amount of direct crosswind. The variables required too solve for the crosswind component are:

- Angle between wind and runway
- Wind velocity

The vertical axis of the graph indicates the headwind component, and the horizontal axis indicates the crosswind component of a quartering wind.

To use the crosswind component chart:

- Determine the angle between the wind direction and the landing runway.
- Starting at outer edge of the appropriate wind angle line, move toward the center of the wind angle line until you intercept the appropriate wind speed arc.
- Drop vertically straight down to determine the crosswind component.
- Move horizontally left to determine the headwind component.

EXAMPLE:Find the direct crosswind component of a 40 kt. wind at a 30° angle to the runway.

- Find the 30° wind angle line. This is the angle between the wind direction and landing runway, e.g., runway 12 and wind from 150°.
- Starting at the outer edge of the 30° wind angle line, move toward the center of the line until you intercept the 40 kt. wind speed arc.
- Drop straight down to determine the crosswind component of 20 kt. So, landing in this situation would be like having a direct crosswind of 20 kt.
- Move horizontally to the left to determine the headwind component of 35 kt. And, this is like having a headwind of 35 kt.

##### Ascent Quick Quiz - 9.5 Crosswind Components

**Question 1:**(Refer to figure 37.) What is the crosswind component for a landing on Runway 18 if the tower reports the wind as 220° at 30 knots?

**Answer**

**Question 2:**(Refer to figure 37.) What is the headwind component for a landing on Runway 18 if the tower reports the wind as 220° at 30 knots?

**Answer**

**Question 3:**(Refer to figure 37.) Determine the maximum wind velocity for a 45° crosswind if the maximum crosswind component for the airplane is 25 knots.

**Answer**

**Question 4:**(Refer to figure 37.) With a reported wind of north at 20 knots, which runway (6, 29, or 32) is acceptable for use for an airplane with a 13-knot maximum crosswind component?

**Answer**

**Question 5:**(Refer to figure 37.) What is the maximum wind velocity for a 30° crosswind if the maximum crosswind component for the airplane is 12 knots?

**Answer**

**Question 6:**(Refer to figure 37.) With a reported wind of south at 20 knots, which runway (10, 14, or 24) is appropriate for an airplane with a 13-knot maximum crosswind component?

**Answer**

**9.6 Calculating Landing Distance**

Just as with takeoff distance, the landing distance required to safely land an aircraft and bring it to a stop varies with altitude and temperature due to changes in air density. However, indicated airspeed for landing is the same at all altitudes - this is because the airspeed indicator is directly affected by changes in air density.

And, just as with takeoff distance, landing distance information is found in the Performance section of the Pilot's Operating Handbooks (POH) in table or graphical form. The landing distance charts and graphs used during the FAA written exam make adjustments to landing distance for variables of headwind, temperature, and dry grass runways.

An example of a landing distance graph is shown below (figure 38). It is used almost exactly the same as the takeoff distance graph.

Additionally, you must distinguish between landing distances for clearing a 50-ft. obstacle at the beginning of the runway, and landing distances without the 50-ft. obstacle.

An example of a landing distance chart is shown below (figure 39). It has been computed for landing with no wind, at standard temperature, and at pressure altitude.

The bottom "notes" tell you how to adjust for wind, nonstandard temperature, and a grass runway.

Note 1 says to decrease the distance for a headwind. Note that tailwind hurts much more than headwind helps, so you cannot use the headwind formula in reverse.

EXAMPLE:Given standard air temperature, 8-kt. headwind, and pressure altitude of 2,500 ft., find both the ground roll and the landing distance to clear a 50-ft. obstacle.

On the table for 2,500 ft., at standard temperature with no wind, the ground roll is 470 ft. and the distance to clear a 50-ft. obstacle is 1,135 ft. These amounts must be decreased by 20% because of the headwind (8 kt./4 x 10% = 20%).

Therefore, the ground roll is 376 ft. (470 x 80%) and the distance to clear a 50-ft. obstacle is 908 ft. (1,135 x 80%).

##### Ascent Quick Quiz - 9.6 Calculating Landing Distance

**Question 1:**(Refer to figure 38.) Determine the total distance required to land.

**Answer**

OAT . . . Std,

Pressure altitude . . . 10,000 ft,

Weight . . . 2,400 lb,

Wind component . . . Calm,

Obstacle . . . 50 ft.

**Question 2:**(Refer to figure 38.) Determine the approximate total distance required to land over a 50-ft. obstacle.

**Answer**

OAT . . . 90°F,

Pressure altitude . . . 4,000 ft,

Weight . . . 2,800 lb,

Headwind component . . . 10 kts.

**Question 3:**(Refer to figure 38.) Determine the total distance required to land.

**Answer**

OAT . . . 0°F,

Pressure altitude . . . 3,000 ft,

Weight . . . 2,900 lb,

Headwind component . . . 10 kts,

Obstacle . . . 50 ft.

**Question 4:**(Refer to figure 38.) Determine the total distance required to land.

**Answer**

OAT . . . 32°F,

Pressure altitude . . . 8,000 ft,

Weight . . . 2,600 lb,

Headwind component . . . 20 kts,

Obstacle . . . 50 ft.

**Question 5:**(Refer to figure 39.) Determine the approximate landing ground roll distance.

**Answer**

Pressure altitude . . . Sea level,

Headwind . . . 4 kts,

Temperature . . . Std

**Question 6:**(Refer to figure 39.) Determine the total distance required to land over a 50-ft. obstacle.

**Answer**

Pressure altitude . . . 3,750 ft,

Headwind . . . 12 kts,

Temperature . . . Std

**Question 7:**(Refer to figure 39.) Determine the approximate landing ground roll distance.

**Answer**

Pressure altitude . . . 5,000 ft,

Headwind . . . Calm,

Temperature . . . 101°F

**Question 8:**(Refer to figure 39.) Determine the approximate landing ground roll distance.

**Answer**

Pressure altitude . . . 1,250 ft,

Headwind . . . 8 kts,

Temperature . . . Std

**Question 9:**(Refer to figure 39.) Determine the total distance required to land over a 50-foot obstacle.

**Answer**

Pressure altitude . . . 7,500 ft,

Headwind . . . 8 kts,

Temperature . . . 32°F,

Runway . . . Hard surface

**Question 10:**(Refer to figure 39.) Determine the total distance required to land over a 50-foot obstacle.

**Answer**

Pressure altitude . . . 5,000 ft,

Headwind . . . 8 kts,

Temperature . . . 41°F,

Runway . . . Hard surface

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