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We can see that the range will be maximum when the value of is the highest (i.e. when it is equal to 1). Clearly, 2 θ {\displaystyle 2\theta } has to be 90 degrees. That is to say, θ {\displaystyle \theta } is 45 degrees.
The maximum range condition is obtained at maximum lift/drag ratio (L/DMAX) The maximal total range is the maximum distance an aircraft can fly between takeoff and landing . Powered aircraft range is limited by the aviation fuel energy storage capacity (chemical or electrical) considering both weight and volume limits. [ 1 ]
The range and the maximum height of the projectile do not depend upon its mass. Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontal range d of the projectile is the horizontal distance it has traveled when it returns to its initial height ( y = 0 {\textstyle y=0} ).
The maximum range for a given initial speed is obtained when =, i.e. the initial angle is 45. This range is v 2 / g {\displaystyle v^{2}/g} , and the maximum altitude at the maximum range is v 2 / ( 4 g ) {\displaystyle v^{2}/(4g)} .
The angle at which maximum lift coefficient occurs is the stall angle of the airfoil, which is approximately 10 to 15 degrees on a typical airfoil. The stall angle for a given profile is also increasing with increasing values of the Reynolds number, at higher speeds indeed the flow tends to stay attached to the profile for longer delaying the ...
The corresponding maximum range condition is the maximum of C L 3/2 /C D, at C L 2 = 3.C D0 /K, and so the optimum speed is 244 km/h (152 mph). The effects of the approximation C L0 = 0 are less than 5%; of course, with a finite C L0 = 0.1, the analytic and graphical methods give the same results.
In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, [b] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function.
Thus, we have from the two equations = (). The location of the orifice that yields the maximum horizontal range is obtained by differentiating the above equation for with respect to , and solving / =. Here we have