Velocity - Dynamic Pressure Relationship — Page 83, Lesson 92

Let's start with the heart of this lesson, because it's the single most important idea in the whole chapter: the relationship between velocity and dynamic pressure. I want you to understand that when we write force equations for an aircraft — like the lift equation — the "velocity" we plug in is not just any speed. It is specifically the speed of the aircraft relative to the air through which it is moving. That is the True Airspeed, which we abbreviate as TAS. So when you see a V in the lift equation, that V is the TAS. Now, here's the key relationship. At a given angle of attack, for a constant lift force, a constant dynamic pressure must be maintained. Let me unpack that. Dynamic pressure is the pressure you feel from the air rushing past you — it's what pushes on the wing. The formula for dynamic pressure is Q equals one-half rho V squared, where rho is the air density and V is the TAS. So if you want to keep the same lift, you must keep the same dynamic pressure Q. But here's the problem. When you climb to altitude, the air density rho decreases. If rho goes down and you want Q to stay the same, then V must go up to compensate. So with increasing altitude, the TAS must be increased to maintain the same dynamic pressure. That's the direct consequence of the formula Q = ½ρV². As density drops, you need more speed to push the same amount of air. Now let's move to the second big idea: Density Altitude. This is about how air density at take-off and landing can significantly affect aircraft performance. If air density is low, a longer take-off run will be needed. Why? Because with less dense air, you need a higher TAS to achieve the same dynamic pressure, and it takes more runway to get up to that speed. So what determines air density? Air density is a product of three things: pressure, temperature, and humidity. And here's a specific fact you need to remember: humidity reduces air density, because the density of water vapour is about five-eighths that of dry air. So moist air is lighter than dry air. Now, let's look at how this plays out with the altimeter. On an airfield at sea level with standard pressure, if you set 1013 hectopascals in the altimeter window, the altimeter will read zero. This is what we call the Pressure Altitude. And here's the trap: Pressure Altitude can be very misleading, because dynamic pressure depends on the TAS and air density, not just air pressure. Here's the scenario. If the temperature is above standard, the density of the air will be less — perhaps a lot less — and there's no direct indication of this fact visible to the pilot. Let's do the math they give us. If the temperature is 25 degrees Celsius, that's 10 degrees above standard, because standard sea level temperature is 15 degrees. So 25 minus 15 equals 10. The air density would be that which would exist at a higher altitude, and we give this condition the name "high density altitude." So in practical terms, what does this mean? The aircraft will need a higher TAS for a given dynamic pressure, and hence a longer take-off run to achieve the required speed. The altimeter might say you're at sea level, but the air is behaving as if you were at a much higher altitude — thinner, less dense — and your aircraft performance suffers accordingly. Let me tie it all together for you. The velocity in the force equation is always TAS. Dynamic pressure Q equals one-half rho V squared. To keep lift constant at a given angle of attack, you must keep Q constant. So when density drops — whether from altitude or from high temperature — you must increase TAS. And that increased TAS requirement is exactly why you need a longer take-off run in high density altitude conditions. The altimeter reading of pressure altitude won't warn you about this, because it only measures pressure, not density. That's the complete picture of the velocity-dynamic pressure relationship and density altitude.