Derivation [edit]
The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object, according to a complicated (and not completely understood) law. Suppose that the variables involved – under some conditions – are the:
speed u,
fluid density ρ,
viscosity ν of the fluid,
size of the body, expressed in terms of its frontal area A, and
drag force FD.
Using the algorithm of the Buckingham π theorem, these five variables can be reduced to two dimensionless parameters:
drag coefficient CD and
Reynolds number Re.
Alternatively, the dimensionless parameters via direct manipulation of the underlying differential equations.
That this is so becomes apparent when the drag force FD is expressed as part of a function of the other variables in the problem:
This rather odd form of expression is used because it does not assume a one-to-one relationship. Here, fa is some (as-yet-unknown) function that takes five arguments. Now the right-hand side is zero in any system of units; so it should be possible to express the relationship described by fa in terms of only dimensionless groups.
There are many ways of combining the five arguments of fa to form dimensionless groups, but the Buckingham π theorem states that there will be two such groups. The most appropriate are the Reynolds number, given by
and the drag coefficient, given by
Thus the function of five variables may be replaced by another function of only two variables:
where fb is some function of two arguments. The original law is then reduced to a law involving only these two numbers.
Because the only unknown in the above equation is the drag force FD, it is possible to express it as
or
and
with 
Thus the force is simply ½ ρ A u2 times some (as-yet-unknown) function fc of the Reynolds number Re – a considerably simpler system than the original five-argument function given above.
Dimensional analysis thus makes a very complex problem (trying to determine the behavior of a function of five variables) a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number.
21. Write the formula of experimental aerodynamics for cross wind (lateral) force, to term values, which are contained in this formula.
22. Write the formula of experimental aerodynamics for normal force, to term values, which are contained in this formula.
23. Write the formula of experimental aerodynamics for longitudinal force, to term values, which are contained in this formula.
24. Write the formula of experimental aerodynamics for transversal force, to term values, which to be contained in this formula.
25. Write the formula of experimental aerodynamics for a pitching moment, to term values, which are contained in this formula.
26. Write the formula of experimental aerodynamics for rolling moment, to term values, which are contained in this formula.
27. Write the formula of experimental aerodynamics for a yawing moment, to term values, which are contained in this formula.
28. Give a definition of a lift coefficient.
29. Give a definition of drag force coefficient.
30. Give a definition of a cross-wind-force coefficient.
31. Give a definition of a normal force coefficient.
32. Give a definition of a longitudinal force coefficient.
33. Give a definition of a of transversal force coefficient.
34. Give a definition of a pitching-moment coefficient.
35.Give a definition of a rolling-moment coefficient.
36.Give a definition of a yawing-moment coefficient.
37.Give a definition of an aerofoil section.
38.Give a definition of a chord of an aerofoil section.
39.Give a definition of a center (mid) line of an aerofoil section.
40.Give a definition of relative thickness of an aerofoil section.
41.Give a definition of curvature and relative airfoil camber.
42.Give a definition of coordinate of maximum thickness of an aerofoil section.
43.Give a definition of coordinate of maximum airfoil camber.
44.Give a definition of an angle of attack of an aerofoil section.
45.Draw (approximately) chart of relation of a lift coefficient of an aerofoil section from an angle of attack, to mark on him reference points.
46.Write the formula for calculation of a lift coefficient, when the angles of attack are less than a permissible angle of attack. To term values, which are contained in this formula.
47.Approximately to draw relation of a pitching-moment coefficient of a profile to an angle of attack.
48.Give a definition of a centre of pressure of an aerofoil section.
49.Give a definition of an aerodynamic center of an aerofoil section.
50.Approximately to draw a polar of a kind I.
51.Approximately to draw a polar of a kind II.
52.Write the formulas for calculation of coefficients of normal and longitudinal forces, if the coefficients of lift force, drag force and angle of attack of a profile are known.
53.Write the formulas for calculation of coefficients of lift force, drag force, if the coefficients of normal and longitudinal forces and angle of attack of a profile are known.
54.Write the formula for ratio between coefficients of pressure in compressible and incompressible flows
55.Ggive a definition of a critical Mach number.
56.Influence (qualitative) relative thickness of a profile to a critical Mach number.
57.Influence (qualitative) relative camber of a profile to a critical Mach number.
58.Influence (qualitative) angle of attack of a profile to a critical Mach number.
59.What values of Mach numbers correspond to an incompressible flow?
60.What values of Mach numbers correspond to a compressible subsonic flow?
61.What values of Mach numbers correspond to a transonic flow?
62.What values of Mach numbers correspond to a supersonic flow?
63.Give a definition of a wave drag of an aerofoil section.
64.Give a definition of a span of wing.
65.Give a definition of a sweepback angle of a wing.
66.Give a definition of sweepback angle at the leading edge of a wing.
67.Give a definition of sweepback angle at the trailing edge of a wing.
68.Give a definition of forward and backward sweep of a wing.
69.Give a definition of aspect ratio of a wing.
70.Give a definition of wing taper ratio.
71.Give a definition of a bound vortex of a wing.
72.Give a definition of trailing vortexes of a wing.
73.Give a definition of a downwash by a wing.
74.Give a definition of a downwash angle.
75.Give a definition of an induced drag of a wing.
76.Write the formula for calculation of an aerodynamic coefficient of an induced drag, to term values, which are contained in this formula.
77.Influence (qualitative) ground proximity to an induced drag of a wing.
78.Influence (qualitative) ground proximity to a downwash angle of a wing.
79.Influence (qualitative) aspect ratio of a wing on a critical Mach number.
80.Influence (qualitative) of a sweepback angle of a wing to a critical Mach number.
81.Assignment of high-lift devices.
82.To term kinds of high-lift devices of a trailing edge of a wing.
83.Draw the scheme of the plain flap.
84.Draw the scheme of the movable split flap.
85.Draw the scheme of the split flap.
86.Draw the scheme of the single slotted flap.
87.Draw the scheme of the duble slotted flap.
88.Draw the scheme of the extension flap.
89.Draw the scheme of the slat.
90.Draw the scheme of the aerofoil nose which can be deflected.
91.Influence (qualitative) deviations of mechanization of a trailing edge of a wing on the chart cl = f (α).
92.Influence (qualitative) deviations of mechanization of a leading edge of a wing on the chart cl= f (α).
93.Influence (qualitative) deviations of mechanization of a trailing edge of a wing on a drag coefficient.
94.Influence (qualitative) deviations of mechanization of a leading edge of a wing on a drag coefficient.
95.To draw (approximately) two charts cl = f (cd): one - when the mechanization is moved out, another - when the mechanization is removed.
96.To draw (approximately) two charts cl = f (cd): one with the count of ground proximity, another - without the count.
97.Write the formula for calculation of thrust force of a propeller, to term values, which to be contained in this formula.
98.Write the formula for calculation of power of a propeller, to term values, which to be contained in this formula.
99.For a fixed pitch angle of the propeller to draw (approximately) charts of relations of thrust coefficients, power, efficiency from relative advance, to mark on the chart reference points and ranges of relative advance.
100.Give a definition of an airscrew advance ratio.
101.Give a definition of an airscrew pitch.
102.Give a definition of normal force, longitudinal force, transversal force.
Problems of the second level
1.Concept about a velocity circulation. The theorem of the Stokes.
2.A supersonic flow near blunt angles. Originating of shock waves. Kinds of shock waves.
3.Two regimes of viscous flow.
4.Structure of viscous flow near to a solid body. A boundary layer. Types of boundary layers. The characteristics of a boundary layer.
5.To receive an integral-differential equation of a boundary layer.
6.Laminar boundary layer on a flat plate, velocity profile, thickness of a boundary layer, stress of friction on a wall, friction coefficient.
7.Turbulent boundary layer on a flat plate, velocity profile, thickness of a boundary layer, stress of friction on a wall, friction coefficient, influence of a roughness to a friction coefficient..
8.Mixed boundary layer on a flat plate. Compressibility effect on parameters of a boundary layer.
9.Boundary layer separation. Concept of the resistance of a pressure.
10.Principal physics of methods of control of a boundary layer.
11.Coordinate systems. Aerodynamic forces and moments which acting on a flight vehicle. Basic formulas of experimental aerodynamics. Aerodynamic coefficients and their relation to similarity parameters.
12.Connection between the main aerodynamic characteristics in wind-fixed and body-fixed coordinate systems.
13.The geometrical characteristics of a profile and finite-span wing.
14.Zhukovsky theorem. Relations between a velocity circulation and conditions of flow around an aerodynamic profile. The vortex systems of aerodynamic profile and wing.
15.Connection between the aerodynamic characteristics of an aerodynamic profile and the distribution of pressure coefficient.
16.Relation of the aerodynamic characteristics of an aerodynamic profile to an angle of attack. A stall angle, maximum lift force coefficient. Lift-to-drag ratio. Polars I and II of a kind.
17.Pitching-moment coefficient of an aerofoil section. Center of pressure, aerodynamic center of airfoil section. Influence of an angle of attack to relative coordinates of a position of a centre of pressure and aerodynamic center.
18.Influence to aerodynamic coefficients of an aerofoil section of its geometrical characteristics, Reynold's number, rate of turbulence.
19.Features of flow about the wing of finit span. The vortex schemes of an aerofoil section and a wing of finite span.
20.Downwash about a finite-span wing. An induced drag of a wing and its approximated calculation. A parabola of an induced drag.
21.The aerodynamic characteristics of a finite-span wing in an incompressible flow. Polars І and ІІ of a kind.
22.The aerodynamic characteristics of a aerodynamic profile in a subsonic compressed flow at Mach numbers smaller then critical value.
23.The aerodynamic characteristics of a finite-span wing in a subsonic compressed flow at Mach numbers smaller then critical value.
24.Critical Mach number of an aerofoil section and its relation to the geometrical characteristics and angle of attack of an aerofoil section.
25.Features of flow of an aerofoil section in a transonic flow.
26.The aerodynamic characteristics of an aerofoil section in a transonic flow.
27.The aerodynamic characteristics of a wing in a transonic flow.
28.Critical Mach number of a finite-span wing, relation of a critical Mach number to an angle of attack, geometrical characteristics of an aerofoil section and wing.
29.Features of flow about the wing of finit span.
30.Comparison of the aerodynamic characteristics of rectangular and swept wings.
31.Ways of decreasing of a wave drag and attenuation of wave crisis.
32.High-lift devices. Influence of high-lift devices to the aerodynamic characteristics of a wing.
33.Ground (screen) effect. Influence of screen effect to the aerodynamic characteristics of a wing.
34.The geometrical characteristics of body of revolutions. Features of the flow of a rounded body.
35.Types of control surfaces. The geometrical characteristics of control surfaces.
36.The aerodynamic characteristics of stabilizing and control surfaces.
37.Concept about hinge moments of control surfaces. Aerodynamic balance.
38.The aerodynamic characteristics of an airplane. Lift and resistance of an airplane with the count of an interference. Polars of an airplane at different Mach numbers.
39.Principle of operation of a propeller. Geometrical and kinematical characteristics of propellers.
40.The aerodynamic characteristics of propellers. The main operational regimes of propellers.
41.The theory of an ideal propeller (momentum theory of propulsion).
42.The theory of the isolated unit of a blade of a propeller.
43.Vortex models of a propeller.