Flight Theory and Aerodynamics. Joseph R. Badick

Flight Theory and Aerodynamics - Joseph R. Badick


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       Pressure altitude (P.A.) = 2005 ft is found using Figure 2.3.

       Referencing Table 2.1 for P.A. 2000 ft, δ = 0.9298

       Using Eq. 2.2, θ = 1.031

       Using Eq. 2.5, solve for the density ratio

       

       Using Table 2.1, it can be interpolated that with a density ratio of 0.902, the resultant density altitude is 3500 ft. This makes sense as the sea level pressure is lower than standard and the temperature is above standard for that altitude, which results in lower air density (higher density altitude).As discussed, density altitude influences aircraft performance; the higher the density altitude, the lower the aircraft performance. So, in the previous problem, even though the aircraft is at an indicated altitude of 1800 ft, the density altitude for performance calculations is 3500 ft. Low air density equals a higher density altitude; high air density equals a lower density altitude. Therefore, aircraft performance charts are provided for various density altitudes.

       Application 2.2

      A non‐pressurized, single‐engine aircraft departs for a cross‐country flight at 6500 ft. A portion of the route crosses rising terrain with peaks at 5000 ft. The pilot is only concerned with maintaining an indicated altitude of 6500 ft as filed on the visual flight rules (VFR) flight plan.

      What other altitudes must the pilot consider along the route of flight? What are the implications of failing to adjust the altimeter setting if the barometric pressure is decreasing along the route? Consider the FAA definition of Maximum Elevation Figure (MEF) on VFR Sectionals and if nonstandard pressure and temperature may impact obstacle clearance.

      The mass airflow symbol Q is the product of the density, the area, and the velocity:

      (2.6)equation

      The continuity equation states that the mass airflow is a constant:

      (2.7)equation

      The continuity equation is valid for steady‐state flow, both in subsonic and supersonic flow. For subsonic flow, the air is considered to be incompressible, and its density remains constant. The density symbols can then be eliminated; thus, for subsonic flow,

      (2.8)equation

      Velocity is inversely proportional to cross‐sectional area: as cross‐sectional area decreases, velocity increases.

Schematic illustration of the flow of air through a pipe.

      The continuity equation explains the relationship between velocity and cross‐sectional area. It does not explain differences in static pressure of the air passing through a pipe of varying cross sections. Bernoulli, using the principle of conservation of energy, developed a concept that explains the behavior of pressures in flowing gases.

      The energy of an airstream is in two forms: It has a potential energy, which is its static pressure, and a kinetic energy, which is its dynamic pressure. The total pressure of the airstream is the sum of the static pressure and the dynamic pressure. The total pressure remains constant, according to the law of conservation of energy. Thus, an increase in one form of pressure must result in an equal decrease in the other.

      Static pressure is an easily understood concept (see the discussion earlier in this chapter). Dynamic pressure, q, is similar to kinetic energy in mechanics and is expressed by

      where V is measured in feet per second. Pilots are much more familiar with velocity measured in knots instead of in feet per second, so a new equation for dynamic pressure, q, is used in this book. Its derivation is shown here:

Schematic illustration of the pressure change in a venturi tube.

      Source: U.S. Department of Transportation Federal Aviation Administration (2018).

equation

      (2.10)equation

      Bernoulli’s equation can now be expressed as

      Total pressure (head pressure), H = Static pressure, P + Dynamic pressure, q:

      (2.11)equation


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