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

Let’s pick this up right where the numbers left off. That “+0.454 inches aft of datum” was the final CG position in our worked example, and it sat inside the limits. But before we move on, I want you to hold onto one operational habit that the book flags with a note: you must always check that both the take‑off mass and CG position, and the landing mass and CG position, are within the acceptable limits for the trip. Two separate checks, because fuel burn changes both mass and CG between take‑off and landing. Now we’re starting a new way of expressing CG position. Up to now, we’ve been giving CG position and CG limits as distances from a datum — inches aft of a reference point. That works fine, but many swept‑wing airliners don’t do it that way. They state the CG position and its limits as a percentage of something called the Mean Aerodynamic Chord — MAC for short. And the twin‑jet we’re about to study is exactly one of those aircraft, so this is the method we’ll be using from here on. Let me define MAC properly, because the name matters. The mean aerodynamic chord 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 of the wing to the trailing edge, measured parallel to the airflow. But a wing isn’t a rectangle — the chord changes along the span. The MAC is the single representative chord that stands in for the whole wing’s aerodynamic behaviour. Why do we care? Because the CG affects many aerodynamic considerations, and stability in particular. If we know where the CG sits relative to the aerodynamic forces, we can judge whether the aircraft will be stable. So it’s useful to express CG position in relation to those aerodynamic forces, not just to a datum. Here’s the geometry. The length of the MAC is constant — it doesn’t change — and it sits at a fixed distance from the datum. The CG is located at some point along that MAC. We then give the distance of the CG from the leading edge of the MAC as a percentage. 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. Not from the datum — from the leading edge of the MAC. Let me show you the calculation, and I’ll define the three quantities. We have A, which is the distance of the CG from the datum. We have B, which is the distance of the MAC leading edge from the datum. And we have C, which is the length of the MAC. The CG as a percentage of MAC is A minus B, divided by C, all multiplied by 100. In words: you find how far the CG sits aft of the MAC’s leading edge — that’s A minus B — then you express that as a fraction of the whole MAC length, C, and convert to a percentage by multiplying by 100. Let’s run the worked example so you see it live. 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 take A minus B: 66 minus 40, which is 26 inches — that’s how far the CG sits aft of the MAC leading edge. Divide by C, the MAC length, 152 inches. That gives 0.171, roughly. Multiply by 100, and we get 17.1%. So the CG is at 17.1% MAC. Notice what this does for us. The percentage tells us where the CG sits along the aerodynamic chord, which is exactly the information we need for stability considerations. And because the MAC length and its position relative to the datum are fixed for a given aircraft, once you know the CG’s distance from the datum, you can always convert it into this percentage form. That’s the bridge between the two systems — datum‑based and MAC‑based — and it’s the one we’ll use for the twin‑jet.