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These vary with speed, so the results are typically plotted on a 2-dimensional graph. In almost all cases the graph forms a U-shape, due to the two main components of drag. The L/D may be calculated using computational fluid dynamics or computer simulation. It is measured empirically by testing in a wind tunnel or in free flight test. [1] [2] [3]
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
In the center of mass frame the kinetic energy is the lowest and the total energy becomes = ˙ + The coordinates x 1 and x 2 can be expressed as = = and in a similar way the energy E is related to the energies E 1 and E 2 that separately contain the kinetic energy of each body: = = ˙ + = = ˙ + = +
A different area rule, known as the supersonic area rule, developed by NACA aerodynamicist Robert Jones in "Theory of wing-body drag at supersonic speeds", [2] is applicable at speeds beyond transonic, and in this case, the cross-sectional area requirement is established with relation to the angle of the Mach cone for the design speed.
[1] [2] [3] The Kármán–Moore theory indicates that the wave drag scales as the square of the second derivative of the area distribution, [″ ()] (see full expression below), so for low wave drag it is necessary that () be smooth. Thus, the Sears–Haack body is pointed at each end and grows smoothly to a maximum and then decreases smoothly ...
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Form drag follows the drag equation, meaning that it increases with the square of the velocity, and thus becomes more important for high-speed aircraft. Form drag depends on the longitudinal section [clarification needed] of the body. A prudent choice of body profile is essential for a low drag coefficient.
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