Figure 6.21 is drawn for sea level conditions, where TAS equals IAS — Page 131, Lesson 159

Let’s pick up with Figure 6.21, which is the heart of this part of the drag chapter. I want you to see exactly what this figure is telling us, because it introduces two speeds you’ll carry with you all the way through performance and into the glide work in Chapter 12. Figure 6.21 is drawn for sea level conditions, where TAS equals IAS. That’s a crucial simplification — at sea level, the two speeds are numerically the same, so the graph works cleanly. It’s also valid for one particular aircraft, for one weight, and only in level flight. So don’t generalise it — it’s a snapshot for a specific machine at a specific mass, in steady level flight. The figure shows two curves. One is the thrust required, or drag, in kilonewtons, plotted against TAS in knots. The other is power required, in kilowatts, also against TAS. And here’s the key construction: the power required curve is built from the drag curve by multiplying each value of drag by the appropriate TAS, and converting that product into kilowatts. So power required equals drag times TAS. That’s the relationship you must hold onto — power required is drag multiplied by true airspeed. Now, the two speeds. The speed for minimum power required is called VMP — that’s your notation, V sub M P — and it is an Indicated Airspeed, an IAS. The speed for minimum drag is VMD, V sub M D. And the note in the figure is this: VMP, the speed for minimum power, is slower than VMD, the speed for minimum drag. So on the speed scale, minimum power comes first, at a lower speed, and minimum drag comes later, at a higher speed. That’s a fact you should memorise cold — VMP is slower than VMD. Now let’s look at the effect of altitude, because this is where it gets interesting. An aircraft flying at VMD will experience constant drag at any altitude, because VMD is an IAS. Think about that — VMD is an indicated airspeed, and indicated airspeed is what the aerodynamics respond to, so the drag stays the same regardless of altitude. But at altitude, the TAS for a given IAS is higher — the air is thinner, so to hold the same indicated speed you’re actually moving faster through the air. And since power required equals drag times TAS, and TAS has gone up, the power required also increases. So the ratio of TAS to power required is unaffected, and VMP will remain slower than VMD. In other words, the relationship holds at any altitude — VMP stays below VMD — even though the actual power values climb with altitude. Now, why does this matter beyond the drag chapter? This information primarily concerns aircraft performance, but the relationship between VMP and VMD is important for the study of rate and angle of descent in a steady glide, which is outlined in Chapter 12. So keep these two speeds in your pocket — they’ll come back when you look at how an aircraft descends. Let me also give you the summary that closes this section, because it pulls together everything on drag. Parasite drag is made up of skin friction drag, form — or pressure — drag, and interference drag. And note this: skin friction drag plus form drag is known as profile drag. So parasite drag has three components, and two of them together are called profile drag. Parasite drag varies directly as the square of the Indicated Airspeed. Double the speed, and you get four times the parasite drag. Halve the speed, and you get one quarter the parasite drag. That’s the square law — speed squared. The designer can minimise parasite drag by streamlining, by filleting — that’s the fairing at junctions — and by the use of laminar flow wing sections. And flight crews have a role too: you must ensure the airframe, and the wing in particular, is not contaminated by ice, snow, mud, or slush. That contamination ruins the smooth airflow and drives parasite drag up. Now induced drag. Spanwise airflow generates wing tip vortices. The higher the CL — the lift coefficient — which corresponds to the lower the IAS, the stronger the wing tip vortices. So at low speed, high angle of attack, you get strong vortices. Those wing tip vortices strengthen downwash. The strengthened downwash inclines the wing lift rearwards. And the greater the rearward inclination of the wing lift, the greater the induced drag. So that’s the chain: spanwise flow, vortices, downwash, rearward-tilted lift, induced drag. Induced drag varies inversely as the square of the Indicated Airspeed. Halve the speed, and you get 16 times the induced drag coefficient, CDi, and four times the induced drag, Di. Double the speed, and you get one sixteenth of the CDi and one quarter of the Di. So note the asymmetry — induced drag is inverse square, parasite drag is direct square. The designer can minimise induced drag by using a high aspect ratio wing planform, and by using a tapered wing planform with wing twist and/or spanwise camber variation, or by incorporating wing end plates, tip tanks, winglets, or various wing tip shapes. All of those attack the vortices at the tips. So the whole picture: parasite drag grows with speed squared, induced drag shrinks with inverse speed squared, and the two speeds — VMP for minimum power, slower, and VMD for minimum drag, faster — are the landmarks you’ll use in performance and in the glide.