Jonzza,
Hopefully this will enable you to understand the basis for the four finger rule.
INDICATED AIRSPEED (IAS)
IAS is the speed shown on the Airspeed Indicator (ASI). It includes instrument errors.
CALIBRATED AIRSPEED (CAS)
CAS is the IAS corrected for position (pressure sensing errors) errors which are caused by the location of the pitot static probes and changes in the aircraft attitude.
EQUIVALENT AIRSPEED (EAS)
As true airspeed increases, the increasing dynamic pressure compresses the air in the pitot probe. This increases the air density in the pitot tube, thereby causing theASI to over read at high speeds. EAS is the CAS corrected for this compressibility error.
TRUE AIRSPEED (TAS)
TAS is the true speed of the aircraft relative to the air around it. TAS is CAS corrected for density errors. ASIs are calibrated such that IAS is equal to TAS at mean sea level inthe ISA. As altitude increases, the decreasing air density causes the TAS at any given IAS to increase.
MACH NUMBER
Mach Number is theTAS expressed as a fraction of the local speed of sound.
Mach Number = TAS/ Local speed of Sound.
EFFECTS OF CHANGESIN ALTUDE
The difference between IAS and CAS is generally not great and is not affected significantly by changes in altitude. For the purposes of the explanation below the differences between IAS and CAS have been assumed tobe zero.
The airspeed indicator produces an Indicated Airspeed output (IAS) that is proportional to ½rVsquared. Where r is air density and V is TAS.
Any given valueof ½ rVsquared will always produce the same IAS, regardless of altitude. Climbing at constant IAS therefore means climbing at constant ½ rVsquared. But r decreases with increasing altitude, so the TAS equating to any given IAS must increase, such that the rate of decrease in ρ is equal to the rate of increase in (TAS)squared . At 40000 feet in the standard atmosphere, ρ is approximately ¼ of its sea level value, so TAS is approximately twice IAS.
As altitude increases, the reducing air density makes the air easier to compress. This enables the air in the pitot probe to become compressed, making its density increase. This increased air density in the pitot probe increases the impact pressure that is sensed by the ASI. This in turn causes the ASI to over-indicate, such that the IAS becomes slightly greater than the EAS.
The Airspeed Indicator is calibrated such that at mean sea level in the ISA, the EAS, IAS and TAS are equal. But as described above,as altitude increases, the EAS becomes slightly less than the IAS and the TAS becomes greater than the IAS. If the three speeds were plotted against altitude they would take the form of three lines. Using speed increasing from left to right on the X axis and altitude increasing from ISA MSL at the bottom of the Y axis, these lines would start at a single point on the X axis (at mean sea level) and would fan out as altitude increases. The order of these lines reading from left toright would be EAS, IAS, TAS. Although the shapes of the lines are quite complex, straight lines are probably sufficient for the purposes of the questions posed in this thread.
As altitude increases in the ISA up to the tropopause at 36000 feet, air temperature gradually decreases. Local Speed Of Sound (LSS) isproportional to the square root of the absolute temperature, so as altitude increases, the reduction in temperature causes the LSS to decrease. Mach number = TAS / LSS so for any given Mach number, the TAS decreases as altitude increases up to the tropopause. The deacreasing TAS causes the IAS and EAS to decrease, so when climbing at constant mach number the EAS, IAS and TAS all decrease up to 36000 feet.
Combining all of the above factors permits the relationships between the various speeds to be represented by four lines on a graph. If the purpose of the graph is to illustrate the qualitative bahaviour of the four speed,rather than their absolute values, the four lines can originate at a single pointon the X axis and fan out as they move up the altitude scale. To test the effect of climbing or descending with any one of the speeds held constant simply rotate the fan until the line representing the constant speed is vertical. The slopes of the lines will then indicate whether the other speeds are increasing (sloping to the right) or decreasing (sloping to the left).
Above 36000 feet the temperature remains constant, so the Mach number at any given TAS also remains constant. But the EAS, IAS and TAS will continue to diverge as described above. This effect can be illustrated by removing the Mach line from the graph and using the TAS line to represent both MACH and TAS.
In an inversion the temperature increases with increasing altitude. This causes the relationship between changes in TAS and Mach to bereversed. This can be illustrated by using the four-line graph but with the order or the TAS and Mach lines reversed.
Last edited by keith williams; 24th August 2013 at 16:55.