A Very Brief Introduction to Aeronautical Engineering

Chapters 5 and 6 are devoted to problems which could be understood most easily by applying the energy balance, and this chapter is devoted to other problems, which could be understood most easily by applying the momentum balance. Some problems are most easily understood by applying both the energy and th momentum balances. A very interesting example is the elementary analysis of flight, which helps explain the behavior of airplanes and helicopters and birds and insects. 

Since not all the air comes in or goes out at the same velocity, the two V s in this equation must be some appropriate average velocities, obtained by an integral of the flow per unit surface area over the entire surface of the system. However, we need not worry about this integration, if we merely think of these velocities as some appropriate average. 

In the direction of the +y axis, F is negative. The flow through m is positive, so Vy — Vy must be negative the air must be accelerated in the —y direction, downward. Thus, we see that, to stay in level flight, the airplane must accelerate the surrounding air downward. This is precisely what a swimmer does in treading water by accelerating the water downward, the swimmer stays up. 

Example 7.13. An airplane with a mass of 1000 kg (and thus a weight of 9810 N) is flying in constant-velocity, horizontal flight at 50m/s. Its wingspread is 15 m, and we assume that it influences a stream of air as wide as its wingspread and 3 m thick. How much average vertical downward velocity must it give this air Assume that the air comes in at zero vertical velocity. 

From the balance of forces in the x direction we see that, in order to fly, the plane must oyerconie the air resistance, which is called drag. In constant-velocity level flight, the drag is equal and opposite to the forward force, or thrust, developed by the power plant. 

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