Information about Drag Equation
The drag equation is a practical formula used to calculate the force of drag experienced by an object due to a fluid that it is moving through. The equation is attributed to Lord Rayleigh, who originally used 
in place of 
(L being some linear dimension). The force on a moving object due to a fluid is:
where
The reference area A is the area of the projection of the object on a plane perpendicular to the direction of motion (ie cross-sectional area). Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given. The reference for a wing would be the plane area rather than the frontal area.
Of particular importance is the v² dependence on velocity, meaning that fluid drag increases with the square of velocity. When velocity is doubled, for example, not only does the fluid strike with twice the velocity, but twice the mass of fluid strikes per second. Therefore the change of momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid friction, which generally has very little velocity dependence.
In aerodynamics, a stall is a sudden reduction in the lift forces generated by an airfoil. This most usually occurs when the critical angle of attack for the airfoil is exceeded.
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in place of (L being some linear dimension). The force on a moving object due to a fluid is:
where
- Fd is the force of drag,
- ρ is the density of the fluid (Note that for the Earth's atmosphere, the density can be found using the barometric formula. Air is 1.293 kg/m3 at 0°C and 1 atmosphere),
- v is the velocity of the object relative to the fluid,
- A is the reference area, and
- Cd is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car).
The reference area A is the area of the projection of the object on a plane perpendicular to the direction of motion (ie cross-sectional area). Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given. The reference for a wing would be the plane area rather than the frontal area.
Discussion
The equation is based on an idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up stagnation pressure over the whole area. No real object exactly corresponds to this behavior. Cd is the ratio of drag for any real object to that of the ideal object. In practice a rough unstreamlined body (a bluff body) will have a Cd around 1, more or less. Smoother objects can have much lower values of Cd. The equation is precise--it simply provides the definition of Cd (drag coefficient), which varies with the Reynolds number and is found by experiment.Of particular importance is the v² dependence on velocity, meaning that fluid drag increases with the square of velocity. When velocity is doubled, for example, not only does the fluid strike with twice the velocity, but twice the mass of fluid strikes per second. Therefore the change of momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid friction, which generally has very little velocity dependence.
References
- Huntley, H. E. (1967). Dimensional Analysis. Dover. LOC 67-17978.
See also
drag (sometimes called resistance) is the force that resists the movement of a solid object through a fluid (a liquid or gas). Drag is made up of friction forces, which act in a direction parallel to the object's surface (primarily along its sides, as friction forces at the
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FLUID (Fast Light User Interface Designer) is a graphical editor that is used to produce FLTK source code. FLUID edits and saves its state in text .fl files, which can be edited in a text editor for finer control over display and behavior.
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Lord Rayleigh
John William Strutt, 3rd Baron Rayleigh
Born 12 November 1842
Langford Grove, Maldon, Essex, UK
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John William Strutt, 3rd Baron Rayleigh
Born 12 November 1842
Langford Grove, Maldon, Essex, UK
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(See Huntley 1967)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.
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
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Earth's atmosphere is a layer of gases surrounding the planet Earth and retained by the Earth's gravity. It contains roughly (by molar content/volume) 78% nitrogen, 20.95% oxygen, 0.93% argon, 0.
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The barometric formula, sometimes called the exponential atmosphere or isothermal atmosphere, is a formula used to model how the pressure (or density) of the air changes with altitude.
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Standard atmosphere is a pressure defined as 101 325 Pa and used as unit of pressure (symbol: atm). Standard atmosphere is a non-SI unit that is internationally recognized.
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velocity is defined as the rate of change of position. It is a vector physical quantity, both speed and direction are required to define it. In the SI (metric) system, it is measured in meters per second (m/s). The scalar absolute value (magnitude) of velocity is speed.
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Area is a physical quantity expressing the size of a part of a surface. The term Surface area is the summation of the areas of the exposed sides of an object.
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Units
Units for measuring surface area include:- square metre = SI derived unit
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The drag coefficient (Cd, Cx or Cw, depending on the country) is a dimensionless quantity that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation.
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In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number.
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In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. This is in contrast to a variable, which is not fixed.
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Unspecified constants
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In geometry, a cross section is the intersection of a body in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross sections.
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The drag coefficient (Cd, Cx or Cw, depending on the country) is a dimensionless quantity that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation.
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In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions.
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Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
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momentum (pl. momenta; SI unit kg m/s, or, equivalently, N•s) is the product of the mass and velocity of an object. For more accurate measures of momentum, see the section "modern definitions of momentum" on this page.
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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Friction is the force of two surfaces in contact. It is not a fundamental force, as it is derived from electromagnetic forces between atoms. When contacting surfaces move relative to each other, the friction between the two objects converts kinetic energy into thermal energy, or
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Angle of attack (AOA, , Greek letter alpha) is a term used in aerodynamics to describe the angle between the airfoil's chord line and the relative airflow, wind, effectively the direction in which the aircraft is currently moving.
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- For other uses, see stall.
In aerodynamics, a stall is a sudden reduction in the lift forces generated by an airfoil. This most usually occurs when the critical angle of attack for the airfoil is exceeded.
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terminal velocity is the velocity at which the drag force of a falling object equals the weight of the object minus the acting force due to air, which halts acceleration and causes speed to remain constant.
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