31 Altitude Definitions & Altitude Measurement

Introduction

As with its airspeed, measurements of the altitude of an aircraft is also critical to both its piloting and its engineering. Pilots are concerned about the altitude of an aircraft relative to sea level or above the ground, i.e., for takeoff and landing or terrain avoidance. Naturally, the altitude reference (datum) used is essential so that all aircraft fly at altitudes measured relative to the same standard reference, this being essential for air traffic control and collision avoidance. Pilots also need to be able to anticipate their aircraft’s performance, which depends on altitude and outside air temperature.

Engineers, however, are more interested in obtaining a measurement of air density at a given flight altitude, so altitude measurements must be related to the air density by measuring pressure and temperature and then calculating density by invoking the equation of state. In addition, an altimeter is a pressure-measuring instrument by design, so it is possible to determine the corresponding local air pressure by measuring altitude. Therefore, the proper basis of altitude measurement must be understood, and also how such measurements are used in engineering practice.

Objectives of this Lesson

  • Understand how an altimeter works and how to read one.
  • Appreciate the principles associated with altitude measurement.
  • Know the differences between pressure altitude and density altitude.
  • Be able to calculate density altitude from values of temperature and pressure altitude.

What is an Altimeter?

Like the airspeed indicator (ASI), an altimeter is a pressure-measuring (pneumatic) instrument. An altimeter responds to the local ambient static pressure, so the altimeter must be connected to the static pressure reference source on the aircraft, i.e., to the static port. However, unlike an airspeed indicator, which has two ports, one for total (ram) pressure and the other for static pressure, an altimeter has only a single port for static pressure. The mechanical design of an altimeter is shown in the schematic below. Although it looks relatively simple, it is a delicate and precise instrument and requires careful calibration to be used in practice.

The inner workings of an altimeter. The face of the altimeter has a circular scale like a clock with three pointers that allow for the measurement of altitude to an accuracy of about plus or minus 10 feet.

Inside the altimeter, the expansion and contraction of an evacuated aneroid wafer stack is detected by a system of levers and gears and then displayed by the rotational movement of pointer (needles) on a face with a scale, much like that of a clock. The display of an altimeter has three needles: One for 100s of feet, another for 1,000s of feet, and the third for 10,000s of feet. Notice from the figure above that the altimeter also has a setting window, usually called the Kollsman window. On the bottom left side of the altimeter is a knurled adjustment knob used to adjust the reference pressure displayed in the Kollsman window. The altimeter, therefore, will read differently depending on the reference value used in this window.

Reading an altimeter is relatively easy but does take some practice. In reference to the image below, the 10,000-foot pointer is the longest and narrowest needle on the altimeter; it rotates by one unit for each 10,000 feet change in altitude. The shortest and widest needle measures increments of 1,000 feet, so a full rotation of the needle is an altitude increment of 10,000 feet. The medium-length needle reads 100s of feet so that a full rotation would be an altitude increment of 1,000 feet. In this regard, the numbers on the dial each represent 100 feet increments, and the tick marks between the numbers represent increments of 20 feet. For example, in the case shown below, the 100 feet pointer is just past the number 4 (i.e., 410 feet), the 10,000-foot pointer has just moved from 0, and the 1,000-foot pointer is between the 1 and the 2, so 1,000 feet plus. Therefore, in this case, the altimeter, as shown, reads 1,410 feet relative to the pressure datum value set in the Kollsman window.

The face of altimeter, in this showing a reading of 1,410 ft.

All aviation altimeters are formally calibrated according to the pressure variations in the ISA. Typically, the mechanical design of an altimeter means that it can only be calibrated within a certain tolerance, \pm20 feet being typical for a GA aircraft, which is sufficient for piloting use. For engineering use, a formal calibration will be needed so that mechanical errors can be accounted for, just as in the case of the ASI, which is obtained by calibrating the altimeter relative to known pressure values or against a reference altimeter that has been previously calibrated. Again, the results for the correction are usually provided as a chart or a table of values.

Test your understanding of how to read an altimeter

Refer to the face of the three altimeters, A, B, and C, as shown below. What is the altitude reading in each case?

Answers: A: 10,500 feet. B: 14,500 feet. C: 9,500 feet

Pressure Altitude

As previously described, an altimeter is a calibrated pressure gauge, its basis of calibration being the International Standard Atmosphere (ISA). Therefore, it makes sense to use the altimeter to measure the pressure of the air the aircraft is flying, which is performed by determining the pressure altitude. By definition, the pressure altitude, h_p, is the altitude in the ISA that corresponds to the prevailing ambient local static pressure, the ISA being used as the basis of calibration. The advantage of using pressure altitude as a reference is that its value is a function of the ambient pressure alone.

Using the relationships for the ISA then the value of the pressure altitude, h_p, as measured in feet (ft), is given by

(1)   \begin{equation*} h_p = \frac{T_0}{B} \left[ 1 - \left( \frac{p}{p_0} \right)^{0.1903} \right] = \frac{518.4}{0.00357} \left[ 1 - \left( \frac{p}{p_0} \right)^{0.1903} \right] \end{equation*}

Remember that the unit of feet (ft) is used universally in all of aviation, and most altimeters are calibrated in ft. If required, then the reading can be converted from ft to meters (m) by multiplying by 0.3048.

Pressure altitude can be read directly by using an altimeter, which is calibrated according to the ISA model, but only when the reference value of pressure on the altimeter is set to the standard MSL value of pressure. In practice, this is done by setting the reading in the reference setting window of the altimeter to p_0 equals 29.92 inches of mercury or 1013.2 millibars (depending on the specific altimeter), which are equivalent to the ISA MSL values of 2116.4 lb/ft^2 or 101,325 Pa, respectively, in engineering units. The value of h_p can then be directly measured because it can be read off the altimeter installed in the aircraft’s cockpit. Always remember that an altimeter is calibrated according to the pressure variations in the ISA.

Density Altitude

While pressure altitude can be measured directly, ultimately, what affects the aircraft’s performance and its powerplant(s) is the density of the air in which it is flying. To this end, a measurement of the density of the air is required for aircraft performance work. By definition, the density altitude, h_{\rho}, is the altitude in the ISA that corresponds to the prevailing ambient density. The value of the density altitude (again, measured in units of feet) is defined using the ambient density in the relation

(2)   \begin{equation*} h_{\rho} = \frac{T_0}{B} \left[ 1 - \left( \frac{\rho}{\rho_0}\right)^{0.235}\right] = \frac{518.4}{0.00357} \left[ 1 - \left( \frac{\rho}{\rho_0}\right)^{0.235}\right] \end{equation*}

where again this relationship comes from the ISA model.

Unlike pressure altitude, which can be directly measured on an altimeter when the reference is set to the standard ISA MSL value, density altitude must be calculated from measurements of pressure altitude and then corrected for non-standard ambient temperature conditions relative to the ISA temperature standard. In this regard, the term “nonstandard” means that the local temperature deviates (higher or lower) from the ISA standard value of temperature at that given pressure altitude, e.g., for a temperature that is higher than the ISA standard temperature, then the density altitude will be greater than the pressure altitude.

The density ratio in the ISA can be obtained from

(3)   \begin{eqnarray*} \sigma = \frac{\rho}{\rho_0} & = & \frac{T_0}{(T+273.16)} \left( 1 - \frac{B h_p}{T_0} \right)^{5.252} \nonumber \\ & = &\frac{288.16}{(T+273.16)} \left( 1 - \frac{0.001981~h_p}{288.16} \right)^{5.252} \end{eqnarray*}

where the pressure altitude, h_p, is in feet and T is in ^{\circ}C or using

(4)   \begin{equation*} \sigma = \frac{\rho}{\rho_0} = \frac{518.4}{(T+459.4)} \left( 1 - \frac{0.001981~h_p}{288.16} \right)^{5.252} \end{equation*}

where h_p is in feet and T is in ^{\circ}F. Notice that pressure altitude and density altitude are identical if the local temperature at that pressure altitude conforms to local standard conditions. As a rule of thumb, density altitude exceeds pressure altitude by about 60 ft per ^{\circ}F (30 ft per ^{\circ}C) that the temperature exceeds the standard value at a given pressure altitude.
This result means that the air density can be measured (estimated) from measurements of pressure altitude and outside air temperature. In aviation terminology, the outside air temperature (OAT) refers to the air surrounding an aircraft during its flight. However, its value is assumed to be unaffected by the passage of the aircraft through it, i.e., it is often referred to as a static temperature.

Outside Air Temperature

A measurement of the outside air temperature (OAT) is required to determine the air density for engineering purposes. Below a Mach number of 0.3 (the incompressible flow regime), a simple OAT gauge can be used, as shown in the photograph below, which provides a relatively accurate measurement of the static air temperature. In this application, the probe is shrouded from the airflow, which minimizes temperature errors from any heating caused by direct sunlight. The probe typically protrudes through the aircraft’s windshield or the side of the fuselage at the cockpit so the probe can be exposed to the atmospheric air. The instrument head is mounted just inside the windshield in a suitable location where the pilot can easily read it.

A simple temperature probe, which can be suitably mounted to read out outside air temperature (OAT).

At higher airspeeds, the compressibility of the flow makes accurate air temperature measurements somewhat more challenging. In this case, the total air temperature (TAT) is measured, which is the static air temperature plus any rise in temperature caused by the effects of the airflow, i.e., a total temperature. TAT probes are constructed to measure this temperature value accurately and transmit the signals for cockpit indication as airspeed and/or Mach number, as well as for use in various engine and aircraft systems, as shown in the figure below.

Outside air temperature (OAT) or total temperature (TAT) probes are needed to measure the local ambient air temperature, which can be displayed on a variety of cockpit instruments.

The design of a TAT probe is complicated by the possibility of ice forming on it, just as it might do on a total pressure or Pitot probe. Therefore, the TAT probe must be heated. In this regard, the ambient airflow must be directed carefully through the probe to measure the actual outside air temperature without any effects from the heater. Several manufacturers specialize in TAT probes for aircraft applications.

Use of Pressure & Density Altitude

The ISA equations are used universally for aircraft performance standardization and flight test evaluations. The information in an aircraft’s operating manual is expressed as a function of density altitude or, more often, in terms of pressure altitude with a temperature correction relative to the ISA standard temperature. As previously discussed, pressure altitude can be measured directly on the altimeter; recall that the altimeter is calibrated according to the ISA model. In contrast, density altitude is determined by determining the measured pressure altitude and local temperature at the same altitude. Again, remember that the pressure altitude is only measured on the altimeter by setting it to the standard MSL reference pressure of 29.92 inches of Hg.

Consider the case where the local altimeter setting is 30.07 inches of Hg (e.g., the pressure at sea level for that time of day). Setting the altimeter reference to this value would allow the pilot to read the altitude on the altimeter relative to MSL. However, the pressure altitude (and not the elevation above MSL) is required to evaluate the density altitude. Density altitude affects the aircraft’s performance, not the altimeter reading MSL.

Based on a reported altimeter setting of 30.07 inches of Hg and an altimeter reading of 8,700 ft (i.e., what the pilot will read on the altimeter in the cockpit), then it can be shown using the equations of the ISA (or from tables or charts) that the actual pressure altitude corresponding to these conditions is approximately 8,500 ft. Based on the ISA, the standard temperature at 8,500 ft pressure altitude is approximately 28.6^{\circ}F. Remember that this is based on the standard temperature lapse rate of minus 3.57^{\circ}F per 1,000 ft of altitude and the standard temperature at MSL, which is 59^{\circ}F.

Consider another example where the local measured outside air temperature at 8,500 ft is 75^{\circ}F. This result means that the temperature is 75 - 28.6 = 46.4^{\circ}F over standard atmospheric temperature at these conditions. Therefore, with an estimated pressure altitude of 8,500 ft and a temperature 46.4^{\circ}F above the standard temperature at this altitude, the ISA equations will yield a density altitude of 11,400 ft, which can be confirmed using the chart below. This result means that even though the altimeter will read 8,700 ft, the aircraft will behave from a performance perspective as if it is flying at an altitude of 11,400 ft in the standard atmosphere.

A standard pressure/density altitude chart from which density altitude and be calculated from measurements of pressure altitude and temperature.

What reference pressure readings on the altimeter do pilots use?

To adjust the altimeter for variations in atmospheric pressure, the setting in the Kollsman window must be continuously adjusted by the pilot of an aircraft. In the U.S., the altimeter reference pressure is generally set to the local mean sea level (MSL) pressure so that all aircraft in the same vicinity will fly with respect to the local MSL reference. In this case, when the aircraft is on the ground, the altimeter should read the approximate field elevation, which is also a way to check if the altimeter is working as it should. The local value of MSL pressure at any time is available from air traffic control, weather stations, etc. Above 18,000 ft in the U.S., pilots are required to set the altimeter to the standard MSL reference pressure of 29.92 inches of Hg, in which case the altitude reading is referred to as a flight level. Therefore, a flight level of 230 is equivalent to a pressure altitude of 23,000 ft.

Summary & Closure

A measurement of the altitude of aircraft during flight is fundamental to both its piloting and engineering. However, like the airspeed, the exact type of altitude must be carefully qualified. The density altitude affects aircraft and powerplant performance, which is a measure of the density of the air in which the aircraft is flying. Density altitude, however, cannot be measured directly and must be calculated based on pressure altitude and air temperature measurements. The higher the temperature above the standard temperature at a given altitude, the higher the density altitude, i.e., the lower the value of air density. Both aircraft and powerplant performance will always be affected by the local density of the air.

5-Question Self-Assessment Quickquiz

For Further Thought or Discussion
  • An airplane is flying at a pressure altitude of 10,000 ft where the outside air temperature is minus 10 degrees F. What is the corresponding density altitude?
  • An ERAU aircraft is preparing to take off from Daytona Beach (identifier KDAB) in the summer where the outside air temperature is 95 degrees F. What is the density altitude and why does the pilot need to know this?
  • If a pilot wants to estimate the approximate value of density altitude before takeoff, explain how that should be done using the cockpit instruments.
  • When an aircraft flying from an area of warmer air into an area with colder air, how will reading on the altimeter change and why?

Other Useful Online Resources

There are many internet resources that discuss altimetry and the practical use of altimeters in aviation. Here are just a few worth investigating:

  • Read here what the FAA officially has to say about altimeters.
  • A good description from a pilot’s perspective on the importance of determining altitude.
  • This video goes into more detail on the difference between pressure altitude and density altitude.
  • Video explaining the inner workings of an altimeter.
  • A downloadable FAA document explaining the concept of density altitude.