SPOTLIGHT - Effects of Density Altitude

[Darren Hill]

Introduction

An important aspect of flight planning is to calculate the performance of the aircraft for the day of the flight. The performance of the aircraft depends on a multitude of factors – the predominant factors being mass and balance, aircraft wear and tear, and density altitude.

Wear and tear on the airframe and engine can generally be considered the least significant, as the degradation is slow and rarely changes between two successive flights.

The effects of mass and balance are extensive and will be covered in a later article.

 

Wear and Tear

Wear and tear on an aircraft is most prevalent in the engine. A factory new or refurbished engine will generally provide higher power output than an engine nearing time before overhaul (TBO).

It is rather unusual to see a degradation in performance due to the airframe over time, unless the airframe has sustained physical damage such as a bird strike or “hanger rash”.

Density Altitude

Effects of Air Density

Drag

Drag is the surface friction an object experiences as it moves through a fluid medium due to direct contact with that medium. Being a force, drag is a vector with direction opposite to the direction of motion and magnitude defined by the drag equation

Lift

Lift is the resultant force of the pressure differential between the upper and lower surfaces of the wing. The vector of lift is directed perpendicular to the chord line and towards the upper surface of the wing. The magnitude of lift is defined by the lift equation

Influence of Density Altitude

The concepts of lift and drag are directly linked to the density of the air that an object is passing through. In both equations, air density is represented by ρ (rho) and there is direct proportionality between Lift/Drag and air density.

If the air is less dense, then less lift will be produced by both the wings and less thrust by the propellor. Additionally, the engine will take in less oxygen molecules per unit time, reducing the combustion potential and thus power output if the fuel mixture is not adjusted by the pilot.

As the aircraft climbs, air becomes less dense and the aircraft will perform worse. However, if the air density is “artificially” reduced by atmospheric factors, the performance of the aircraft will be further limited – potentially creating a safety risk.

To better define and understand how an aircraft will perform on a given day, the concept of density altitude is introduced. Density altitude refers to the altitude the aircraft “thinks” it is at – a measure of the actual density of the air molecules passing over the wing – which is calculated using QNH, altitude, and temperature.

 

International Standard Atmosphere

The performance of an aircraft in any situation is dependent on the air it is passing through. To set a standard for measuring aircraft performance, an International Standard Atmosphere is defined:

• Sea Level Temperature: 15°C
• Sea Level Pressure: 1013.25hPa or 29.92 inHg
• Standard Lapse Rate: 1.98°C per 1000ft until 36090ft
• Density: 1.225 kg/m³

An obvious question exists: what if the atmosphere does not conform to ISA?

The atmosphere is a constantly changing fluid, affected by pressure systems, variances in moisture, and a variety of other factors. As such, the atmosphere at a given point rarely conforms to ISA, as basic factors like sea level pressure change. This is significant for aircraft and its performance.
 

Pressure Altitude

Pressure altitude is the vertical displacement relative to the standard reference datum of 1013hPa. In aircraft, the measurement is taken by simply setting the subscale of the altimeter to 1013hPa and is referred to as a flight level. Similarly, any elevation above mean sea level can be adjusted to a displacement above the standard reference datum.

Pressure Altitude is often used by pilots to calculate aircraft performance using performance graphs and tables in the Pilot’s Operating Handbook. Usually, graphs and tables are given in terms of Pressure Altitude, requiring the pilot to also input Temperature.

For every 1hPa, there is a change of around 27ft which is often simplified and rounded up to 30ft. Thus, for every 1hPa deviation from the ISA standard pressure of 1013hPa, the elevation or altitude will deviate from the Pressure Altitude by 30ft.

If the QNH is above 1013hPa, the Pressure Altitude will be lower than the elevation or altitude.
If the QNH is below 1013hPa, the Pressure Altitude will be higher than the elevation or altitude.

This inverse proportionality is shown in the Pressure Altitude Formula

Example 1

An aircraft is travelling at 8700ft on the local QNH of 1003hPa. What is the aircraft’s pressure altitude?

 

Example 2

The elevation of a remote airfield is 2350ft. The pilot uses his altimeter on the ground to measure a pressure altitude of 3100ft. What is the local QNH at the airport?

ISA Temperature and Deviation

Standard Lapse Rate

The International Standard Atmosphere is defined with a standard lapse rate of 1.98°C per 1000ft. Standard lapse rate refers to the decrease in temperature as altitude increases – a direct result of moving further from the ground which radiates heat – while assuming a dry atmosphere. The phenomenon continues until an altitude of approximately 36090ft known as the tropopause, above which the temperature remains a constant -57.5°C.

ISA Temperature

Using the ISA defined sea level temperature of 15°C, the ISA temperature at a given pressure altitude can be easily calculated. ISA defines the sea level pressure as 1013hPa and thus pressure altitude is used, as it gives the vertical displacement above the standard reference datum.

ISA temperature is calculated by subtracting the lapse rate for a given altitude from 15°C.

 

ISA Deviation

The outside air temperature is very rarely equal to the ISA temperature, which can be the result of a multitude of factors. The ISA deviation is the difference between the outside air temperature and the calculated ISA Temperature.

The temperature is then notated as ISA+<deviation> . For example, ISA+5 means the temperature is 5℃ higher than the ISA temperature for the given pressure altitude.

Calculating Density Altitude

Density altitude is pressure altitude corrected for ISA deviation.

Warmer air molecules, by definition, have higher kinetic energy. As such, the molecules have more space between them – a concept which is described by the kinetic energy model of matter. Density is defined as the amount of mass per unit volume – or mass divided by volume. Since the same number of atoms, and thus same amount of mass, occupy a larger volume, the density of warm air is less than the density of cold air.

Every +1°C of ISA deviation, the density altitude will increase above the pressure altitude by 120ft.
 

Practical Example 1

Let’s examine a practical example of density altitude negatively affecting the operation of a light aircraft:

A Piper Warrior II (PA28-161) is operating out of Rand airport (FAGM) near Johannesburg, where the airfield elevation is 5489ft. On this hot summer day, the QNH is 1024hPa and the OAT is 34°C. The instructor and his student are departing with around ¾ fuel load and minimal baggage. What is the density altitude at aerodrome level?

Firstly, we must calculate the Pressure Altitude:

We can also calculate the ISA Temperature and Deviation:

From these, we can calculate the Density Altitude:

Thus, the engine and airframe “think” they are operating at almost 9000ft above sea level!

Suppose we say that the aircraft is looking to practice stalls at 3000ft above Rand’s aerodrome level. Assuming that the lapse rate is ISA and there are no significant changes in humidity, this would require the aircraft to climb to a density altitude of 12000ft – only 2750ft below the service ceiling of 14750ft. As such, we would expect the climb rate to be very low, despite the aircraft being in the utility category.

 

Practical Example 2

Density altitude can, inversely, have a positive impact on aircraft performance.

A Slingsby Firefly is departing from Shoreham airport (EGKA) on the south coast. Shoreham has an airfield elevation of 148ft and Shoreham Tower is reporting a QNH of 1018hPa. On this 14°C day, a solo student is departing on their qualifying cross country navigation. What is the density altitude on the ground at Shoreham?

Firstly, we must calculate the Pressure Altitude:

In this example, the pressure altitude is indeed below mean sea level.

We can then calculate the ISA Temperature and Deviation:

From these, we can calculate the Density Altitude:

The density altitude is thus less than the airfield elevation. In this case, the performance advantage of only 120ft is not too significant. However, at airfields with higher elevation such as Rand the advantage can increase climb performance by hundreds of feet per minute.

 

Application of Density Altitude

Density altitude is used in the performance graphs and tables in aircraft Pilot’s Operating Handbooks. Generally, the pressure altitude is inputted along with temperature to effectively calculate the density altitude for the graph.

Example 1: Warrior II Takeoff Ground Roll (Graph)

A Warrior II is departing an airfield with a pressure altitude elevation of 5000ft and a temperature of 20°C. The headwind component is 5kt and the aircraft is loaded at 2200lbs. What is the ground roll of the takeoff and the lift off speed?

 

First, we input our known data. We start by drawing a line vertically upwards from 20°C until we hit 5000ft pressure altitude. We then draw the line across and follow the nearest curve until we pass the line vertical with 2200lbs. From here, we read off our first answer: lift off speed is 48kt.

We then draw the line to the right again. Since we have a headwind, we follow the nearest headwind line down until we hit the vertical 5kt line. We then draw the line across to read off our second answer: ground roll is 1750ft.

In doing this example, we can see visually see the effect of density altitude through its factors: pressure altitude and temperature. The pressure altitude curves are increasing functions with temperature, showing that a higher temperature will start us higher on the 2440lbs Reference Line. Similarly, higher pressure altitudes result in curves being placed higher on the graph.

 

Example 2: C172S Rate of Climb (Table)

A C172S is passing through FL70 where the pilot notes an outside air temperature of 10°C. Assuming a still atmosphere and a correctly leaned mixture, what is the expected rate of climb at 2550lbs?

To calculate out expected climb rate, we must interpolate between the 4 values shown in red. The final answer is independent of whether we choose to first average the temperature, or the pressure altitude values.

For this example, we will first calculate the expected climb rate at 10°C for FL60 and FL80.

At FL60, the expected climb rate is: fpm.
At FL80, the expected climb rate is:  fpm.

Thus, at FL70 and 10°C, the rate of climb is: fpm.

As with the previous example, the trend of temperature and pressure altitude is obvious from the table. Climb performance decreases left to right with an increase in temperature and decreases top to bottom with an increase in pressure altitude.

 

Conclusion

Density altitude plays a massive role in the performance of an aircraft. While this phenomenon is visible in airliners flying into Quito, the effect is far more pronounced and important in light aircraft.

Operating at high elevations during the hot summer may require less fuel or baggage to be loaded, or even moving the flight to the early morning to take advantage of lower temperatures. This may create issues with a pilot now requiring a night rating just to depart before legal daytime to make the takeoff safe.

Discussing and understanding the theory is the foundation to make better airmanship decisions through proper flight planning. Several fatal accidents occur annually due to a pilot expecting more performance from an aircraft. For a sobering and equally fascinating story, have a watch through this AOPA video: https://www.youtube.com/watch?v=8PBUVMCbmFQ.

Edited September 25, 2022 by Darren Hill