Density — Page 37, Lesson 31

Let’s start with the definition. Density is mass per unit volume. That’s the core idea — how much stuff is packed into a given space. We can express it in grams per cubic metre, as a percentage of the standard surface density (which we call relative density), or as the altitude in the standard atmosphere that corresponds to the observed density — that’s density altitude. Density altitude is a particularly important concept for you as a pilot because it directly affects aircraft performance: the higher the density altitude, the poorer the performance. Now, let’s look at what changes density. First, pressure. If you increase pressure on a volume of air, you compress it — the volume shrinks, so the same mass occupies less space, and density goes up. If you decrease pressure, the air expands, volume increases, and density goes down. So we say density is directly proportional to pressure. In the atmosphere, as you go up in altitude, pressure decreases, so density also decreases. Conversely, if you descend, pressure increases and density increases. Next, temperature. If you heat a volume of air, it expands. That means the same mass now fills a larger volume, so the mass per unit volume — the density — goes down. So density is inversely proportional to temperature: as temperature goes up, density goes down; as temperature goes down, density goes up. Then there’s humidity. Water vapour molecules are lighter than nitrogen and oxygen molecules. If you add water vapour to a fixed volume of air, you’re replacing some of those heavier nitrogen and oxygen molecules with lighter water molecules. The total mass of that volume decreases, so density decreases. So density is inversely proportional to water vapour content — more moisture means less dense air. Now, altitude. In the troposphere, as altitude increases, both temperature and pressure decrease. Pressure decreasing tends to lower density; temperature decreasing tends to raise density — they pull in opposite directions. But the effect of pressure is much stronger, so overall density decreases as altitude increases. To give you a sense of scale: in the International Standard Atmosphere, density is 100% at sea level, 50% at 20,000 feet, 25% at 40,000 feet, and 10% at 60,000 feet. Also, density changes by about 1% for every 3 degrees Celsius change in temperature, or for every 10 hectopascals change in pressure. Finally, latitude. At the surface, as you move from the Equator toward the poles, temperature decreases, so density increases. But the story changes with height. At the Equator, surface temperatures are high, so the rate at which pressure decreases with height is relatively low. At the poles, temperatures are low, so pressure decreases with height more rapidly. That means at, say, 50,000 feet, the pressure over the Equator is relatively high compared to the pressure at the same altitude over the poles. Also, temperatures at 50,000 feet are actually lower at the Equator than at the poles. So the density at 50,000 feet over the poles ends up being less than at 50,000 feet over the Equator. To summarise: at the surface, density increases as latitude increases. At about 26,000 feet, density stays roughly constant with increasing latitude. Above 26,000 feet, density decreases as latitude increases, with the maximum deviation from standard occurring around 50,000 feet. That figure shows the effect of latitude on density visually — take a moment to look at how the density contours change with latitude and altitude.