General Principles - Climb — Page 202, Lesson 231

Let’s start with the question that opens this part of the climb chapter: how many speeds are there? The answer the book gives is one — the True Airspeed, the only speed there is, the speed of the aeroplane through the air. That’s a deliberate, slightly provocative statement, and it’s the key to everything that follows. When we talk about performance, the speed that actually matters physically is TAS, the True Airspeed, because that’s the aeroplane’s actual velocity relative to the air mass it’s flying through. From that, we get the fundamental relationship: Power Required equals Drag times TAS. Let me unpack that. Drag is the aerodynamic resistance the aeroplane must overcome, and power is the rate of doing work — the rate at which energy is used to overcome that drag. So if you multiply the drag force by the speed at which you’re moving through the air, you get the power required to sustain that condition. That’s the formula: Power Required = Drag × TAS. Now, the book asks us to take a Thrust Required curve — that’s the drag curve — in sea level ISA conditions, and multiply the drag at various airspeeds by the TAS, then plot the resulting Power Required curve on the same graph. ISA, by the way, is the International Standard Atmosphere, the standard sea-level reference conditions. The result is Figure 3.43, which shows both curves together. Here’s the crucial point: the shape of the Power Required curve is very similar to that of Thrust Required, but the significant difference is that the Power Required curve is displaced to the left. Because of that displacement, the speed for minimum Power Required — which we call VMP — is slower than the speed for minimum Thrust Required, which we call VMD. So VMP is the airspeed at which power required is at its minimum, and VMD is the airspeed at which thrust required — or drag — is at its minimum. And the relationship is that VMP is slower than VMD. It’s essential to be able to visualize the Power Required curve relative to the Thrust Required curve, together with the VMP and VMD relationship. The book notes that associated data will be presented later, so for now, just hold onto that visual and that ordering. Let me show you one practical use of the Power Required = Drag × TAS formula. If an aircraft climbs at a constant IAS — that’s Indicated Airspeed — drag remains constant, but TAS must be increased to compensate for decreasing air density as altitude increases. So when climbing at a constant IAS, Power Required increases. That’s a direct consequence of the formula: drag stays the same, TAS goes up, so the product — power required — goes up. Now let’s move to rate of climb. Rate of climb is the vertical speed of an aeroplane, measured in feet per minute, and it’s displayed in the cockpit on the vertical speed indicator, the VSI. Another way to think of it is as the TAS of the aeroplane along a gradient — that is, the component of the aeroplane’s speed that is directed upward along the climb path. Figure 3.44 shows two identical aeroplanes at the same angle of climb. The one on the right has a higher TAS along the gradient. In the same time, the aeroplane on the right will climb through a greater vertical distance than the aeroplane on the left. Therefore the aeroplane on the right has a higher rate of climb. This demonstrates that TAS is one important factor when considering rate of climb. Figure 3.45 shows two identical aeroplanes at the same TAS. The aeroplane on the right is climbing at a steeper angle. In the same time, the aeroplane on the right climbs through a greater vertical distance than the aeroplane on the left. Therefore the aeroplane on the right has a higher rate of climb. This demonstrates that angle of climb is also an important factor in the rate of climb. So, putting both figures together, rate of climb is a function of both angle of climb and TAS along the achieved gradient. Two factors, not one: the steeper the angle, the more vertical distance per unit of horizontal travel; and the faster the TAS along that gradient, the more distance you cover per unit of time. Both push the vertical speed up. That’s the core of this section: the single-speed concept, the Power Required = Drag × TAS relationship, the VMP versus VMD ordering, the constant-IAS climb consequence, and rate of climb as a function of angle of climb and TAS.