ISA stands for International Standard Atmosphere, and MSL is Mean Sea Level — Page 109, Lesson 104

I want to walk you through the process of correcting airspeed indicator readings to get true airspeed, and I'll start with an important note about compressibility. The ASI, the airspeed indicator on your instrument panel, is already calibrated to allow for compressibility effects at ISA conditions at Mean Sea Level. ISA stands for International Standard Atmosphere, and MSL is Mean Sea Level. Under those specific conditions—ISA at sea level—no compressibility correction is necessary. In fact, compressibility correction is small at true airspeeds lower than 300 knots, and no correction is considered necessary below that threshold. So here's the practical sequence you will always follow. You will always calculate the Density Error correction first, and that gives you True Airspeed, or TAS. If the TAS you find is 300 knots or less, no further correction is needed. But if the TAS is greater than 300 knots, then you must apply the Compressibility Error correction on top of that. Let me give you the full summary of corrections to the airspeed indicator, which is laid out in a sequence. You start with Indicated Airspeed, or IAS. Then you apply Instrument Error and Pressure Error—also called Position Error—to get Calibrated Airspeed, or CAS. From CAS, you have two paths depending on speed. At low speed, you apply Density Error to get True Airspeed, TAS. At high speed, you first apply Compressibility to get Equivalent Airspeed, or EAS, and then Density Error to get TAS. But the key point is: if your TAS after the density correction is 300 knots or less, you stop there; if it's above 300, you add the compressibility correction. Now let's look at how you actually calculate TAS from CAS by correcting for Density Error. To correct CAS to TAS, you need to divide by the square root of the relative density. You'll recall this formula from Phase 1: CAS equals TAS multiplied by the square root of the relative density. So rearranged, TAS equals CAS divided by the square root of the relative density. Relative to what? The answer is that relative density is relative to ISA at Mean Sea Level, which has a density of 1225 grams per cubic metre. Let me give you a concrete example. Imagine we are flying at 100 knots CAS at Flight Level 200, or FL200, in an ISA atmosphere. FL200 means 20,000 feet pressure altitude. At that level, the ISA density is 653 grams per cubic metre. To calculate relative density, you take the density at your level and divide it by the sea-level density. So relative density equals 653 divided by 1225, which gives 0.5331. Then the square root of relative density is the square root of 0.5331, which is 0.7301. So with a CAS of 100 knots, TAS equals 100 divided by 0.7301, which gives 137 knots. Now, if we had an instrument that measured the density of the air we're flying through, we could calculate TAS this way directly. But in fact, there is no flight deck instrument that gives such a reading. So how do we get density? You should remember from your Principles of Flight lectures that pressure divided by density times temperature is a constant. More precisely, P over rho T equals a constant, or rho is proportional to P over T. Here P is pressure, T is temperature, and rho is density. So if we know any two of pressure, density, and temperature, we can find the third. You should also remember from your Piston Engine lectures that the Combined Gas Law is a combination of Boyle's Law and Charles' Law, and it represents the relationship between volume, pressure, and temperature. This can be shown as P times V over T equals K, or alternatively P times V equals K times T, or P2 times V2 over T2 equals P1 times V1 over T1. That relationship is what underpins the density calculations we use on the navigation computer. Let me show you the relevant diagrams. First, here is the CRP-5 navigation computer with its windows labelled. And here is how you align Flight Level 200 with minus 25 degrees Celsius on the computer. Finally, here is the CAS on the inner scale against TAS on the outer scale. You do not need to know or understand the theoretical explanation for that last one—all that is required is the practical use of the computer.