+ 0.454 inches aft of datum (within limits) — Page 50, Lesson 67

Let’s pick this up right where the numbers left off. That figure, +0.454 inches aft of datum, is the CG position we just calculated for the twin jet, and it sits within the acceptable limits. Before we move on, I want you to hold onto one operational habit that the book stresses right here: you must always check that the take-off mass and CG position, and the landing mass and CG position, are all within the acceptable limits for the trip. That’s a two-point check — take-off and landing — because fuel burn shifts the CG as the flight progresses. Now we’re switching to a different way of expressing CG position. Up to now, we’ve been giving CG position and CG limits as distances from a datum — like that +0.454 inches. But there’s an alternative method: stating the CG position and its limits as a percentage of the Mean Aerodynamic Chord, which we abbreviate MAC. This is common practice with many swept wing airliners, and it’s exactly what we’ll use for the twin jet we’re about to study. Let me define the mean aerodynamic chord properly. It is one particular chord on the wing, calculated from the aerodynamic characteristics of that particular wing. A chord, remember, is the straight-line distance from the leading edge to the trailing edge of the wing. But the MAC isn’t just any chord — it’s the one that represents the wing’s aerodynamic behaviour. Why do we care? Because the CG affects many aerodynamic considerations, particularly stability. So it’s useful to know the CG position in relation to the aerodynamic forces, not just in relation to a datum. Here’s the key geometry. The length of the MAC is constant, and it sits at a fixed distance from the datum. The CG is located at some point along the MAC. We express the CG’s position as a percentage of the MAC’s length, measured from the leading edge of the MAC. So a CG position of 25% MAC means the CG is positioned at one quarter of the length of the MAC, measured from the leading edge. Now let’s look at how we actually calculate that percentage. I’ll introduce three quantities. A is the distance of the CG from the datum. B is the distance of the MAC leading edge from the datum. And C is the length of the MAC. The CG as a percentage of MAC equals A minus B, divided by C, multiplied by 100. In other words, you take the CG’s distance from the datum, subtract the MAC leading edge’s distance from the datum — that gives you how far the CG is aft of the MAC’s leading edge — then you divide that by the MAC length, and multiply by 100 to turn it into a percentage. Let me walk you through Example 4 to make this concrete. Suppose the MAC is 152 inches long, its leading edge is 40 inches aft of the datum, and the CG is 66 inches aft of the datum. What’s the CG position as a percentage of MAC? We plug in: A is 66, B is 40, C is 152. So we have 66 minus 40, which is 26, divided by 152, times 100. That gives us 17.1%. So the CG sits at 17.1% MAC — just over one-sixth of the way back from the leading edge of the mean aerodynamic chord. That figure shows you the geometry — A, B, and C laid out on the wing relative to the datum. The key takeaway is that this percentage method ties the CG directly to the wing’s aerodynamics, which is why swept-wing airliners prefer it. The datum-based method we used earlier is fine, but the MAC method tells you where the CG sits relative to the aerodynamic forces that govern stability.