Basic Aerodyamics Flashcards
What is the approximate formula for the speed of sound as a function of temperature?
LLS (local speed of sound) = 38.94 x sq.rt of (kelvin temp)
in knots = 38.94 x sq.rt (273 + temp degC)
Therefore at 0 degC (273 degC) the SoS = 331 meters per second
= 642 kt
15 degC / 661kt 30 degC/ 678kt 0 deg C / 644 kt -10 deg/ 632 kt -20 deg/ 620 kt - 30 deg/ 608 kt - 40 deg/ 595 kt - 50 deg/ 582 kt - 56.7 deg / 573 kt - 60 deg/ 569 kt
Altitude: (ISA). ISA temp. Speed of sound
0’. 15 deg C. 661 kt
5,000’. 5. 650
10,000’. -5. 638
15,000’. -15. 626
20,000’. -25. 614
25,000’. -35. 602
30,000’. -44. 589
35,000’. -56. 574
40,000’. -56.6. 573
45,000’. -56.6. 573
50,000’. -56.6. 573
A more technical formula is speed of sound (mps) = the sq.rt. of (a diabetic constant x gas constant x absolute temperature over/molecular mass of gas).
Other relevant formulas:
Speed of sound (in metres per second ) = 20 x the square root of temperature in degrees Kelvin.
(20.05 to be more precise)
What is the relationship between the following? - EAS - CAS (also known as RAS) - IAS - TAS ...?
The pitot system and it’s associated instruments detect dynamic air pressure (‘ram pressure’) and basically substructure the ambient static pressure to give pressure that is representative of the speed that that airplane ‘thinks’ it is flying. I.e. what the airplane ‘feels’ in terms or airflow. In terms of flying safe speeds, i.e. not too slow as to not stall and not too fast as to not over-speed, this, IAS, is the most important speed for the airplane and therefore the most important speed for the pilot to keep the airplane flying safely.
So, what the airplane ‘feels’ is displayed directly to the pilot on the airspeed indicator and is the IAS. For the pilot, this is really all we need to know.
In terms of calculating speed over the ground, GS is important. This is most easiest determined by GPS and is used for flight time and associated calculations.
However, for the purposes of calculating the speed of the aircraft though space, i.e. assuming nil wind (in which case the speed of the airplane through space would be exactly equal to GS) we need to start with the IAS and then make corrections for things such ‘position error’, instrument error, compressibility error and of course temperature/pressure/density.
CAS/RAS is derived from IAS by correcting for instrument error (inaccuracies in the airspeed indicator mechanics, mainly due to friction of moving parts) and pressure (aka configuration) error (I think due to minute shielding/deflection of airflow going into the pitot tube). So CAS/RAS, which is IAS corrected for these 2 factors, is a speed which would be for a perfect ASI system.
The next factor is air compressibility. (At low subsonic speeds, usually about Mach 0.3, we treat air as being incompressible. At higher speeds, particularly transonic and supersonic, air is considered compressible. What’s the significance? An incompressible fluid is considered an ideal fluid, i.e. ‘ideal’ properties, i.e. Bernoulli’s equation (faster fluid movement means less pressure) is not affected by density, ie changes in density do not affect streamlines. However at high airspeeds compressibility becomes a factor. So we correct CAS/RAS for compressibility error effects which gives us EAS.
If we then correct EAS or air density properties, i.e temperature and pressure, we get TAS.
The higher the air density the greater the resistance of motion so lower TAS. This is why we can achieve higher TASs at higher altitudes (assuming we’ve got the power to get up there). Warm air is less dense than cold air however the higher the altitude the lower the density and this effect predominates over the warm air at lower altitude effect.
At a constant IAS the TAS will increase with altitude or temperature because of the reduction in air density. As per the formula: Dynamic Pressure (IAS) = 1/2 R x V.sqrd (TAS) (R = ‘rho’ = air density)
How is Mach number calculated?
If flying at a MN of M0.85 at 40,000’ in ISA conditions, what is the IAS?
Mach No. = TAS/LSS. I.e. True Airspeed divided by the local speed of sound.
At 40,000’ in ISA conditions the temperate is -56.6 degC. Therefore the LSS is 573kt. Therefore the TAS is 487kt. But how to convert to IAS?????
How to convert IAS to TAS?
At sea level in IAS conditions, IAS=TAS (if we ignore a negligeable correct factor due to position and instrument error (CAS/RAS) and compressibility error (EAS).
Then correct pressure altitude for IAS deviation, eg ISA -5 (10 degC at sea level, or -61 deg at 40,000’) x 2 deg/1000’ would give a pressure altitude correction of minus 2,500’.
Then covert IAS to TAS by adding 2% per 1,000’ to the ISA deviation -corrected pressure altitude.
eg if you’re at 40,000’ ISA-5. Take this to be 37,500’ then TAS = 37.5 x 2% x IAS which = 175% x IAS. If IAS = 259kt then TAS = 453kt. (See later .. this is in fact quite inaccurate, ie about 30kt out).
(Question: have I got the =2500’ correct?? Would this still apply in the tropopause , ie above 36,100 feet (in ISA) in the flight levels that we fly)?? Eg ISA at 40,000’ = -56.6. And ISA at 37,000’ = -56.6
Apparently adding 2% per 1000’ is only valid for speeds < M0.3. A possible better method is +1.7% for each 1000’ and +/- 1% for each +/- 5% for ISA dev. So for the above example: 40,000, ISA-5, IAS 2(which will only be a few knots different from CAS and EAS): 40 x 1.7 = 68. 1.68 x 259. Less 1% = 430kt. This differs a bit from the calculation above (453kt) and from the hockwarth website (
Comparing to the calculator at hockwarth.com aviation calculator: Gives
Describe how you go from IAS to CAS (aka RAS) to TAS to GS
IAS is effectively 1/2/ rho. V. Sq and is a measure of the flow of molecules over the airplane. This is what the airplane feels it is flying. It is also what is displayed to the pilot (check that this is in fact the case for Airbus aircraft **).
IAS is a dynamic pressure indication. Dynamic pressure cannot be measured directly. It has to be derived by pitot (dynamic) pressure and static pressure.
IAS corrected for position error is called CAS (also called RAS). Position error si caused by installation and position of the pitot tube on the aircraft which results in slightly incorrect sensing of the dynamic and static pressures. This error is usually small and only noticeable with high angles of attack , eg stalk manoeuvres, or perhaps on short final with full flaps and gear. Conversion of IAS to CAS requires an aircraft-specific correction table (unless Airbus does it automatically??) - but I think the difference is minimal on modern jet aircraft. Have seen a table where CAS was 3kt below IAS at sea level at abotu 320kt, but then at FL200 CAS was 8kt higher than CAS.
EAS is CAS/RAS corrected for compressibility. This only becomes a factor above about 5,000’ and a speed above about 200kt / Mach 0.3. Flying after above that and the altiteter will over-read (ie air is starting to compress). At 10,000’ the error starts ar 160kt IAS with a 1/2 kt over-read. At 41,000’ at Mach 0.85 the over-read is about 17kt.
Air Speed Indicators are calibrated under ISA conditions. Some ASIs have a OAT know where an OAT subscale can be set to get a good approximation of TAS. Thisis effectively correcting CAS (or IAS, as an approximate in GA aircraft) for density, error. This is a correction for temperature and pressure. So, CAS corrected for temperature and pressure (density error) = TAS. TAS = IAS (or CAS to be more accurate ) x the sq. rt of (1.225kg per cubic meter over the actual air density at that altitude),
GS is is the speed over the ground, u.e. TAS corrected with wind. When there is no wind at all, TAS = GS.
What is the difference between: OAT, TAT and SAT?
OAT = Outside Air Temperature. It is the temperature of ambient air however it can only be determined in calm air.
TAT = Total Air Temperature. This is the what the temperature probe actually measures. It is the temperature of the ambient air plus the heating due to the ram effect of the air. When the aircraft is not moving and has had time to cool down, it is OAT.
SAA - Static Air Temperature. This value cannot be measured. It is calculated by an air data computer using the TAT and the Mach number. The static air temperature is used in flight and said to correspond to the OAT.
How to you calculate approximate cloud base from temperature and dew point?
(Temperature minus dew point)/2.5 x 1000 = Cloud base height
