Thrust fights drag

Drag is the price of moving through air. Aircraft engineers split it into two kinds.

1. Parasite drag. This comes from the shape and the skin: the pressure drag of the fuselage, tyres and struts pushing air aside, and the skin friction of air rubbing along the surface. It behaves like the lift: D_p = ½ρV²S × C_D0. It grows with the square of the speed.

2. Induced drag. This is the price of making lift. A wing with finite span pushes air down, and the air curls around the wingtips into swirling wingtip vortices. That wasted energy shows up as a backwards force: D_i = ½ρV²S × C_L² / (π e AR). Here AR is the aspect ratio (span² divided by wing area; long thin wings have a high AR) and e is an efficiency factor below 1.

Put together, the total drag coefficient is C_D = C_D0 + C_L² / (π e AR).

The toy numbers. The toy plane has C_D0 = 0.03, e = 0.8 and AR = 7.5 (teaching values). In level flight L = W, so C_L = 2W / (ρV²S) and gets smaller as the speed rises. That means induced drag falls with speed (it goes as 1/V²), while parasite drag rises with speed (V²). The toy plane gives:

• 25 m/s: parasite 184 N, induced 834 N, total about 1,020 N. Slow flight is dominated by induced drag.
• 36.5 m/s: parasite 392 N, induced 391 N, total about 783 N. This is the minimum drag.
• 50 m/s: parasite 735 N, induced 208 N, total about 943 N.
• 80 m/s: parasite 1,882 N, induced 81 N, total about 1,963 N. Fast flight is dominated by parasite drag.

Plot total drag against speed and you get a U-shaped curve. At the bottom of the U the induced and parasite drag are equal. That is the speed of the best L/D: at 36.5 m/s the plane has L/D = 9,810 / 783 ≈ 12.5. For a jet aircraft this speed is close to the one that gives the longest range, although the exact best speeds also depend on the engine. A glider pilot flies near it to cover the most ground for each metre of height lost (World 6).

What the engine is for. In steady flight the thrust must equal the drag, so thrust is set by the drag curve. At best L/D the toy plane needs only about 785 N of thrust to carry a 9,810 N weight. Fly slower or faster and the thrust needed rises again.

How to reduce drag. Smooth shapes and retracting landing gear cut parasite drag. A longer, narrower wing (higher aspect ratio) cuts induced drag, since D_i is inversely proportional to AR. That is why gliders have such long wings and airliners have winglets (World 7). Engines come in two main families, propellers (which accelerate a large amount of air a little) and jets (a smaller amount a lot faster). World 4 explains how a jet makes thrust.