Definitions and Calculations — Page 33, Lesson 41

Let’s start with the big idea that drives this whole chapter: the position of the centre of gravity — the CG — decides how stable or how manoeuvrable your aircraft is. These two qualities pull in opposite directions, and I want you to hold that tension in your head for the whole lesson. Imagine the fuselage, and picture the CG sitting at the mid position. Now push the CG forward, towards the nose. Stability increases, step by step. But at the same time, manoeuvrability decreases, step by step. Now push the CG aft, towards the tail. The exact opposite happens: manoeuvrability increases, and stability decreases. So you have a sliding trade-off — nose-ward means more stable but less agile; tail-ward means more agile but less stable. Why does that matter to you as a pilot? Because too much stability means the flying control stick forces go up, and your workload rises as you fight to overcome them. Too much manoeuvrability, on the other hand, makes the aircraft unstable and genuinely difficult to control. So the CG position is a balance between two failure modes. Now, a critical point: for aeroplanes, the CG is not fixed. It moves in flight. What moves it? Fuel burn, flap positions, and crew and passenger movements. So the aircraft operator — that’s the organisation responsible for the operation — has the duty to ensure the CG movement stays within the limits the manufacturer has imposed. And why does the manufacturer set those limits? To make sure that the average pilot can control the aircraft safely through all stages of flight, with normal piloting effort, free of fatigue. That phrase “average pilot” is deliberate — the limits are set so a typical, competent pilot isn’t pushed beyond reasonable effort. Now I want to walk you through what happens if the CG is pushed outside the forward limit. Learn these effects well — they come up frequently in the exams. First, drag increases. And because drag increases, fuel consumption goes up, and range and endurance go down. Here’s the mechanism: to keep the nose from pitching downwards, the tailplane must produce a balancing down load — think of a see-saw. That down load requires elevator deflection, and the resulting elevator deflection increases drag, which in turn increases fuel consumption and reduces range and endurance. Second, longitudinal stability increases. That means higher control column forces during manoeuvres, and a corresponding increase in physical effort to overcome them — which leads to increased pilot fatigue. Third — and this is a subtle one — the increase in tail down force is equivalent to an increase in weight. So the stall speed increases. And an increased stall speed has knock-on effects on performance: take-off and landing speeds increase, the available speed range reduces, and the safety margin between low-speed and high-speed buffet narrows. Fourth, the ability to pitch the nose up or down decreases, because stability is so high. Fifth, the take-off speeds V1, VR, and VMU all increase. Let me unpack that. On the ground, the aeroplane rotates about the main wheels, and uses the elevators to raise the nose for take-off. The CG, being ahead of the main wheels, produces a down force that the elevators — together with the speed of the airflow passing over them — must overcome. The more forward the CG, the greater that down force, and for a particular elevator deflection, the greater the speed of the airflow required. So the aircraft must accelerate for longer to produce the airspeed required. That’s why V1, VR, and VMU all go up. Now look at the summary table at the end. With a forward CG: take-off and landing run increase, range and endurance increase, rate of descent increases, max horizontal speed increases, rate of climb decreases, max altitude decreases, fuel consumption increases, braking energy increases, tyre wear increases, and structural fatigue increases. Wait — I need to be careful with that table. Let me read it exactly as it’s laid out. The arrows are grouped: take-off and landing run, range and endurance, rate of descent, and max horizontal speed all show upward arrows. Then rate of climb, max altitude, fuel consumption, braking energy, tyre wear, and structural fatigue all show upward arrows as well. So every single item in that table increases with a forward CG. That’s the complete picture — every listed quantity goes up. So the forward CG is a cascade: more drag, more fuel burn, higher stall speed, higher take-off speeds, more pilot effort, and more wear and fatigue on the structure. That’s why the forward limit exists — to keep you out of that regime. One more thing to note: the figure in your materials shows a “couple” — two forces acting together to produce a turning motion. That’s the underlying physics of the tailplane down load and the elevator deflection working together to rotate the aircraft. Keep that image in mind as you think about the see-saw effect. That’s the forward CG story. The key relationships to remember: forward CG means more stability, less manoeuvrability, more drag, higher stall speed, higher take-off speeds, and more pilot fatigue. The operator’s job is to keep the CG within the manufacturer’s limits so the average pilot can handle the aircraft safely.