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Density and Pressure Altitude

Hot summer flying makes for low density altitude.

When we go flying, we always calculate pressure and density altitude of our aerodrome and for our cruising altitude. Why do we do this? Recall the definitions of density altitude (DA) and pressure altitude (PA).

PA is the “height above sea level corresponding to a given barometric pressure under standard air conditions” (FGU, page 41).  What are standard air conditions?  Standard air conditions state that at sea level, the air has a pressure of 29.92″ Hg and temperature of 15 degrees C.  As we increase in altitude, the air cools at the adiabatic lapse rate of 1.98 degrees per 1000 feet.  This allows us to calculate our altitude for pressure given the pressure reading at our aerodrome. To calculate this, we always subtract our current altimeter reading from standard pressure of 29,92,  multiply by 1000 then add it to the actual AGL elevation of the aerodrome.

For example, at Springbank, when the altimeter reading is 30.15:

29.92 – 30.15 = -0.23 * 1000 = – 230  then add to the altitude of CYBW which is 3940:  3940 + (-230) = 3710.   This means that the actual pressure, at standard atmospheric conditions, is lower than actual field height.

The reason we need to know pressure altitude is because our altimeter is a pressure altimeter.  It is important to set the altimeter because knowing the actual height of the airplane is of vital importance.  An altimeter setting that is too high will give an altimeter reading that is too high, a low setting will show a reading that is lower than we actually are.   Generally, most standard altimeters doesn’t go above a pressure reading higher than 31.0 0″ Hg. Such high pressure readings are found in very cold, dry air masses.   To correct for this, the pilot can add 100 feet for each 0.10 ” reading above this figure.  This will give the true altitude of the aircraft.

So why do we need to know pressure altitude anyway? When we do flight planning, we need to calculate it for our departing aerodrome not only to have the proper pressure setting for our altimeter, but also because the performance of the aircraft is based on pressure altitude.  These are more direct engine performance things, like fuel burn, true airspeed and engine thrust. We always look at our POH to find the true airspeed which we base on pressure altitude, like climb and cruise performance.

Hot, hazy summer day produces high density altitude and reduced performance
Hot, hazy summer day produces high density altitude and reduced performance

Density altitude is based on pressure altitude. It is simply pressure altitude corrected for temperature.   Once we calculate pressure altitude, we use the following formula:

DA = PA + [ 100 * (Actual Temperature – Standard Temperature) ]

Actual temperature is self explanatory, if we are looking for temperature of our aerodrome it will be given in ATIS or if we are looking for the temperature of our cruising altitude that is available in the Upper Wind Forecasts (FD’s).  To get  standard temperature recall the definition of standard air conditions: cools at the adiabatic lapse rate of 1.98 degrees per 1000 feet. So we can calculate this ourselves to know what the standard temperature should be at our chosen altitude.  For instance, for my last flight I flew at 6000 feet and the standard temperature at this altitude is (6 * 2 = )12 degrees less than 15 degrees, or 3 degrees.  We can also refer to our aircraft’s POH, where standard temperature for the pressure altitude is listed.

Density altitude is important to know for lift and aerodynamics.  Have you ever taken off from an airport on a hot, hazy summer day and noticed the decrease in engine performance?  On these days it takes longer to accelerate and become airborne because the air density is behaving as if it were in much higher altitude – where there is less air for the aircraft to “grab” onto.  DA is important for calculating safe fuel and payload permissible for takeoff.

High density altitude makes take off and climb take longer. Last summer, on 30 degree days when flying circuits I noticed that I was consistently not reaching circuit altitude until I was well into my downwind leg. Typically, I reach the altitude on crosswind.

What gives good performance?  Low altitude (higher air density), cold and dry. Bad performance? High altitude (lower air density), hot and humid.

Also read how altitude affects performance.

 

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The “six pack” flight instruments: pitot-static

Flight instruments on a Cessna 172

Let’s do a review of the six main flight instruments: 

Detail is provided, of course, there is so much more we can add here!  The most important and basic flight instruments have remained the same for a long period of time, and are called the ‘six pack’.  Three of them are connected to the static port system which measures outside barometric pressure and the pitot tube which measures ram pressure.   The other three are gyroscopic.

The Pitot Tube on a Cessna 172
The Pitot Tube on a Cessna 172

The pitot tube, located on the leading edge of the wing, and the atmospheric pressure in the tube is increased by the dynamic pressure due to the forward motion of the aircraft while in flight.  The static pressure port is not affected by turbulence or ram air pressures.

The three instruments connected to the pitot-static system are:

(1) Airspeed Indicator (ASI) – pitot and static source; it measures the difference between the pressure in the pitot tube and the pressure in the static system. When the aircraft is on the ground the two pressures become equal, in motion the pressure difference causes the aneroid capsule inside the indicator to expand, moving the needle on the instrument.

The ASI shows indicated airspeed.  Indicated airspeed can be erroneous because of air density, which depends on pressure and temperature, and position error, which is caused by eddies that are formed when air passes over the wings and struts. This is the uncorrected reading from the dial and calibrated airspeed is the indicated airspeed corrected for position error (and installation error). Equivalent airspeed is the calibrated airspeed corrected for compressibility – this applies mainly to high speed airplanes.  Next we have true airspeed which is calibrated airspeed corrected for pressure and temperature. Roughly, to correct calibrated airspeed we add 2% to the indicated airspeed for every 1000 feet of pressure altitude.  We can gain more accurate readings using our flight computer – the E6B.

(2) Vertical Speed Indicator, static source. Operates on the principle that there is a change of barometric pressure with a change in altitude.  Atmospheric pressure is led into the capsule but slowed by a calibrated leak from entry into the case holding the capsule,  and this pressure differential causes the capsule to expand or compress.  There is a 6-9 second lag before it will indicate the correct rate of climb or descent.

(3) Altimeter, static source. Since pressure varies from place to place and the altimeter set to indicate height above sea level at the departure point may give a false reading after the aircraft has flown some distance.  To correct for this, the altimeter is equipped with a barometric scale (inches of mercury) which allows to set the current altimeter setting. We get this each time we depart our airport and can get it enroute.  If we fly to an airport that has a lower pressure than the one we departed from and we don’t change our altimeter setting, we will read higher than the actual height of the airplane. Temperature differences will also cause erroneous readings since the pressure altimeter is calibrated to indicate true altitude in standard atmospheric conditions.  When the temperature of the air beneath the airplane is colder than standard, the aircraft is lower than indicated, and vice versa for warmer than standard temperatures (higher than altimeter reading) .

Here are what we can expect from a compromised static-port system.

Instrument Pitot Tube Blocked Partially Blocked Static Port Fully Blocked Static Port
Altimeter Not connected Under-read in climb, over-read in descent Freezes
Vertical Speed Indicator Not connected Under-read in climb, less than true rate of descent Freezes at 0
Airspeed Indicator Acts like altimeter. Over-reads in climbs and under-reads in descents Under-read in climb, over-read in descent Under reads in climbs and over reads in descents.

Read about the other 3  instruments that are gyroscopes: the heading indicator, attitude indicator and turn and bank coordinator.

Do you have any other specialty instruments in your aircraft?