These motors do not look like a motor that usually, most bodinya not installed. In fact, part motorcycle spare part just placed improvised.
This motor is not in terms of appearance, but judging from his ability to race in the race.
Drag Races or commonly also called Track-race trekan is motor racing race through two tracks straight quarter of a mile between 2 drivers. The winner is who has the shortest time record over the finish line.
Drag Races developments in Indonesia is not as fast as other motor racing such as road race and motocross. Only a few areas in Java is often a contest like this event.
Rare event of a Drag Races officially make some biker down to the street with a wild race. Drag Races and it even has its own community, but there is no container in the international arena.
Read More..
The drag coefficient
The drag coefficient is a number that aerodynamicists use to model all of the complex dependencies of shape, inclination, and flow conditions on aircraft drag. This equation is simply a rearrangement of the drag equation where we solve for the drag coefficient in terms of the other variables. The drag coefficient Cd is equal to the drag D divided by the quantity: density r times half the velocity V squared times the reference area A.
Cd = D / (A * .5 * r * V^2)
The quantity one half the density times the velocity squared is called the dynamic pressure q. So
Cd = D / (q * A)
The drag coefficient then expresses the ratio of the drag force to the force produced by the dynamic pressure times the area.
This equation gives us a way to determine a value for the drag coefficient. In a controlled environment (wind tunnel) we can set the velocity, density, and area and measure the drag produced. Through division we arrive at a value for the drag coefficient. As pointed out on the drag equation slide, the choice of reference area (wing area, frontal area, surface area, ...) will affect the actual numerical value of the drag coefficient that is calculated. When reporting drag coefficient values, it is important to specify the reference area that is used to determine the coefficient. We can predict the drag that will be produced under a different set of velocity, density (altitude), and area conditions using the drag equation.
The drag coefficient contains not only the complex dependencies of object shape and inclination, but also the effects of air viscosity and compressibility. To correctly use the drag coefficient, we must be sure that the viscosity and compressibility effects are the same between our measured case and the predicted case. Otherwise, the prediction will be inaccurate. For very low speeds (< 200 mph) the compressibility effects are negligible. At higher speeds, it becomes important to match Mach numbers between the two cases. Mach number is the ratio of the velocity to the speed of sound. At supersonic speeds, shock waves will be present in the flow field and we must be sure to account for the wave drag in the drag coefficient. So it is completely incorrect to measure a drag coefficient at some low speed (say 200 mph) and apply that drag coefficient at twice the speed of sound (approximately 1,400 mph, Mach = 2.0). It is even more important to match air viscosity effects. The important matching parameter for viscosity is the Reynolds number that expresses the ratio of inertial forces to viscous forces. In our discussions on the sources of drag, recall that skin friction drag depends directly on the viscous interaction of the object and the flow. If the Reynolds number of the experiment and flight are close, then we properly model the effects of the viscous forces relative to the inertial forces. If they are very different, we do not correctly model the physics of the real problem and will predict an incorrect drag.
The drag coefficient equation will apply to any object if we properly match flow conditions. If we are considering an aircraft, we can think of the drag coefficient as being composed of two main components; a basic drag coefficient which includes the effects of skin friction and shape (form), and an additional drag coefficient related to the lift of the aircraft. This additional source of drag is called the induced drag and it is produced at the wing tips due to aircraft lift. Because of pressure differences above and below the wing, the air on the bottom of the wing is drawn onto the top near the wing tips. This creates a swirling flow which changes the effective angle of attack along the wing and "induces" a drag on the wing. The induced drag coefficient Cdi is equal to the square of the lift coefficient Cl divided by the quantity: pi (3.14159) times the aspect ratio AR times an efficiency factor e.
Cdi = (Cl^2) / (pi * AR * e)
The aspect ratio is the square of the span s divided by the wing area A.
AR = s^2 / A
For a rectangular wing this reduces to the ratio of the span to the chord. Long, slender, high aspect ratio wings have lower induced drag than short, thick, low aspect ratio wings. Lifting line theory shows that the optimum (lowest) induced drag occurs for an elliptic distribution of lift from tip to tip. The efficiency factor e is equal to 1.0 for an elliptic distribution and is some value less than 1.0 for any other lift distribution. A typical value for e for a rectangular wing is .70 . The outstanding aerodynamic performance of the British Spitfire of World War II is partially attributable to its elliptic shaped wing which gave the aircraft a very low amount of induced drag. The total drag coefficient Cd is equal to the drag coefficient at zero lift Cdo plus the induced drag coefficient Cdi.
Cd = Cdo + Cdi
The drag coefficient in this equation uses the wing area for the reference area. Otherwise, we could not add it to the square of the lift coefficient, which is also based on the wing area. Read More..
Drag (physics)
In fluid dynamics, drag (sometimes called air resistance or fluid resistance) refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces act in a direction opposite to the oncoming flow velocity.[1] Unlike other resistive forces such as dry friction, which is nearly independent of velocity, drag forces depend on velocity.[2]
For a solid object moving through a fluid, the drag is the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of the movement. The component perpendicular to this direction is considered lift. Therefore drag opposes the motion of the object, and in a powered vehicle it is overcome by thrust.
In astrodynamics, and depending on the situation, atmospheric drag can be regarded as an inefficiency requiring expense of additional energy during launch of the space object or as a bonus simplifying return from orbit.
Types of drag
Types of drag are generally divided into the following categories:
* parasitic drag, consisting of
o form drag,
o skin friction,
o interference drag,
* lift-induced drag, and
* wave drag (aerodynamics) or wave resistance (ship hydrodynamics).
The phrase parasitic drag is mainly used in aerodynamics, since for lifting wings drag is in general small compared to lift. For flow around bluff bodies, drag is most often dominating, and then the qualifier "parasitic" is meaningless. Form drag, skin friction and interference drag on bluff bodies are not coined as being elements of parasitic drag, but directly as elements of drag.
Further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in the aviation perspective of drag, or in the design of either semi-planing or planing hulls. Wave drag occurs when a solid object is moving through a fluid at or near the speed of sound in that fluid — or in case there is a freely-moving fluid surface with surface waves radiating from the object, e.g. from a ship. Also, the amount of drag experienced by the ship is decided upon by the amount of surface area showing the direction youre heading and the speed you are going.
For high velocities — or more precisely, at high Reynolds numbers — the overall drag of an object is characterized by a dimensionless number called the drag coefficient, and is calculated using the drag equation. Assuming a more-or-less constant drag coefficient, drag will vary as the square of velocity. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid mass density, the cross sectional area of the specified item, and the square of the velocity.
Wind resistance is a layman's term used to describe drag. Its use is often vague, and is usually used in a relative sense (e.g., a badminton shuttlecock has more wind resistance than a squash ball).
Drag at high velocity
Main article: Drag equation
194144main 022 drag.ogg
Play video
Explanation of drag by NASA.
The drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000), also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (L being some length). The force on a moving object due to a fluid is:
F_D\, =\, \tfrac12\, \rho\, v^2\, C_d\, A,
see derivation
where
\mathbf{F}_d is the force of drag,
\mathbf{} \rho is the density of the fluid,[3]
\mathbf{} v is the speed of the object relative to the fluid,
\mathbf{} A is the reference area,
\mathbf{} C_d is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car)
The reference area A is often defined as the area of the orthographic projection of the object — on a plane perpendicular to the direction of motion — e.g. for objects with a simple shape, such as a sphere, this is the 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.
In case of a wing, comparison of the drag to the lift force is easiest when the reference areas are the same, since then the ratio of drag to lift force is just the ratio of drag to lift coefficient.[4] Therefore, the reference for a wing often is the planform (or wing) area rather than the frontal area.[5]
For an object with a smooth surface, and non-fixed separation points — like a sphere or circular cylinder — the drag coefficient may vary with Reynolds number Re, even up to very high values (Re of the order 107). [6] [7] For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for Re > 3,500.[7] Further the drag coefficient Cd is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere).
Power
The power required to overcome the aerodynamic drag is given by:
P_d = \mathbf{F}_d \cdot \mathbf{v} = {1 \over 2} \rho v^3 A C_d
Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.
Velocity of a falling object
Main article: Terminal velocity
The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity v = 0 at time t = 0, is roughly given by a function involving a hyperbolic tangent (tanh):
v(t) = \sqrt{ \frac{2mg}{\rho A C_d} } \tanh \left(t \sqrt{\frac{g \rho C_d A}{2 m}} \right). \,
The hyperbolic tangent has a limit value of one, for large time t. In other words, velocity asymptotically approaches a maximum value called the terminal velocity vt:
v_{t} = \sqrt{ \frac{2mg}{\rho A C_d} }. \,
For a potato-shaped object of average diameter d and of density ρobj, terminal velocity is about
v_{t} = \sqrt{ gd \frac{ \rho_{obj} }{\rho} }. \,
For objects of water-like density (raindrops, hail, live objects — animals, birds, insects, etc.) falling in air near the surface of the Earth at sea level, terminal velocity is roughly equal to
v_{t} = 90 \sqrt{ d }, \,
with d in metre and vt in m/s. For example, for a human body ( \mathbf{} d ~ 0.6 m) \mathbf{} v_t ~ 70 m/s, for a small animal like a cat ( \mathbf{} d ~ 0.2 m) \mathbf{} v_t ~ 40 m/s, for a small bird ( \mathbf{} d ~ 0.05 m) \mathbf{} v_t ~ 20 m/s, for an insect ( \mathbf{} d ~ 0.01 m) \mathbf{} v_t ~ 9 m/s, and so on. Terminal velocity for very small objects (pollen, etc) at low Reynolds numbers is determined by Stokes law.
Terminal velocity is higher for larger creatures, and thus potentially more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This explains why small animals can fall from a large height and not be harmed.
Very low Reynolds numbers — Stokes' drag
Trajectories of three objects thrown at the same angle (70°). The black object doesn't experience any form of drag and moves along a parabola. The blue object experiences Stokes' drag, and the green object Newton drag.
Main article: Stokes' law
The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, Re < 1).[8] In this case, the force of drag is approximately proportional to velocity, but opposite in direction. The equation for viscous resistance is:[9]
\mathbf{F}_d = - b \mathbf{v} \,
where:
\mathbf{} b is a constant that depends on the properties of the fluid and the dimensions of the object, and
\mathbf{v} is the velocity of the object.
When an object falls from rest, its velocity will be
v(t) = \frac{(\rho-\rho_0)Vg}{b}\left(1-e^{-bt/m}\right)
which asymptotically approaches the terminal velocity \mathbf{} v_t = \frac{(\rho-\rho_0)Vg}{b}. For a given \mathbf{} b , heavier objects fall faster.
For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant,
b = 6 \pi \eta r\,
where:
\mathbf{} r is the Stokes radius of the particle, and \mathbf{} \eta is the fluid viscosity.
For example, consider a small sphere with radius \mathbf{} r = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity \mathbf{} v of 10 µm/s. Using 10−3 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water.
Drag in aerodynamics
Lift induced drag
Main article: lift-induced drag
Induced drag vs. lift
Lift-induced drag (also called induced drag) is drag which occurs as the result of the creation of lift on a three-dimensional lifting body, such as the wing or fuselage of an airplane. Induced drag consists of two primary components, including drag due to the creation of vortices (vortex drag) and the presence of additional viscous drag (lift-induced viscous drag). The vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air of varying pressure on the upper and lower surfaces of the body, which is a necessary condition for the creation of lift.
With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. For an aircraft in flight, this means that as the angle of attack, and therefore the lift coefficient, increases to the point of stall, so does the lift-induced drag. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow on the surface of the body.
Parasitic drag
Main article: parasitic drag
Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag (form drag), and drag due to surface roughness (skin friction drag). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag, which is sometimes described as a component of parasitic drag.
In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the induced drag becomes much less, but parasitic drag increases because the fluid is flowing faster around protruding objects increasing friction or drag. At even higher speeds in the transonic, wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance (minimum fuel consumption), or maximise gliding range in the event of an engine failure.
Power curve in aviation
The power curve: parasitic and induced drag vs. airspeed
The interaction of parasitic and induced drag vs. airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the power curve, and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires more thrust as speed decreases, rather than less. The consequences of being "behind the curve" in flight are important and are taught as part of pilot training. At the subsonic airspeeds where the "U" shape of this curve is significant, wave drag has not yet become a factor, and so it is not shown in the curve
Wave drag in transonic and supersonic flow
Qualitative variation in Cd factor with Mach number for aircraft
Main article: wave drag
Wave drag (also called compressibility drag) is drag which is created by the presence of a body moving at high speed through a compressible fluid. In aerodynamics, Wave drag consists of multiple components depending on the speed regime of the flight.
In transonic flight (Mach numbers greater than 0.5 and less than 1.0), wave drag is the result of the formation of shockwaves on the body, formed when areas of local supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air on a body increases when it accelerates over the body, in this case above Mach 1.0. Therefore, aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as transonic compressibility drag. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at these speeds.
In supersonic flight (Mach numbers greater than 1.0), wave drag is the result of shockwaves present on the body, typically oblique shockwaves formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large, unattached shockwaves, or bow waves will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic flow regimes, wave drag is commonly separated into two components, supersonic lift-dependent wave drag and supersonic volume-dependent wave drag.
The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the Sears-Haack Distribution. Similarly, for a fixed volume, the shape for minimum wave drag is the Von Karman Ogive.
Busemann's Biplane is not, in principle, subject to wave drag at all when operated at its design speed, but is incapable of generating lift.
d'Alembert's paradox
Main article: d'Alembert's paradox
In 1752 d'Alembert proved that potential flow, the 18th century state-of-the-art inviscid flow theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the Navier–Stokes equations for the description of viscous flow were developed by Saint-Venant, Navier and Stokes. And for the flow around a sphere at very low Reynolds numbers, Stokes was able to derive the drag — called Stokes law.[10]
However, in the limit of high-Reynolds numbers the Navier–Stokes equations approach the inviscid Euler equations; of which the potential-flow solutions considered by d'Alembert are solutions. While also at high Reynolds numbers all experiments showed there is drag. Attempts to construct inviscid steady flow solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.[10]
The notion of boundary layers — introduced by Prandtl in 1904, founded on both theory and experiments — explained the causes of drag at high Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important when the viscosity becomes very small (or equivalently the Reynolds number becomes very large).[10] Read More..
For a solid object moving through a fluid, the drag is the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of the movement. The component perpendicular to this direction is considered lift. Therefore drag opposes the motion of the object, and in a powered vehicle it is overcome by thrust.
In astrodynamics, and depending on the situation, atmospheric drag can be regarded as an inefficiency requiring expense of additional energy during launch of the space object or as a bonus simplifying return from orbit.
Types of drag
Types of drag are generally divided into the following categories:
* parasitic drag, consisting of
o form drag,
o skin friction,
o interference drag,
* lift-induced drag, and
* wave drag (aerodynamics) or wave resistance (ship hydrodynamics).
The phrase parasitic drag is mainly used in aerodynamics, since for lifting wings drag is in general small compared to lift. For flow around bluff bodies, drag is most often dominating, and then the qualifier "parasitic" is meaningless. Form drag, skin friction and interference drag on bluff bodies are not coined as being elements of parasitic drag, but directly as elements of drag.
Further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in the aviation perspective of drag, or in the design of either semi-planing or planing hulls. Wave drag occurs when a solid object is moving through a fluid at or near the speed of sound in that fluid — or in case there is a freely-moving fluid surface with surface waves radiating from the object, e.g. from a ship. Also, the amount of drag experienced by the ship is decided upon by the amount of surface area showing the direction youre heading and the speed you are going.
For high velocities — or more precisely, at high Reynolds numbers — the overall drag of an object is characterized by a dimensionless number called the drag coefficient, and is calculated using the drag equation. Assuming a more-or-less constant drag coefficient, drag will vary as the square of velocity. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid mass density, the cross sectional area of the specified item, and the square of the velocity.
Wind resistance is a layman's term used to describe drag. Its use is often vague, and is usually used in a relative sense (e.g., a badminton shuttlecock has more wind resistance than a squash ball).
Drag at high velocity
Main article: Drag equation
194144main 022 drag.ogg
Play video
Explanation of drag by NASA.
The drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000), also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (L being some length). The force on a moving object due to a fluid is:
F_D\, =\, \tfrac12\, \rho\, v^2\, C_d\, A,
see derivation
where
\mathbf{F}_d is the force of drag,
\mathbf{} \rho is the density of the fluid,[3]
\mathbf{} v is the speed of the object relative to the fluid,
\mathbf{} A is the reference area,
\mathbf{} C_d is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car)
The reference area A is often defined as the area of the orthographic projection of the object — on a plane perpendicular to the direction of motion — e.g. for objects with a simple shape, such as a sphere, this is the 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.
In case of a wing, comparison of the drag to the lift force is easiest when the reference areas are the same, since then the ratio of drag to lift force is just the ratio of drag to lift coefficient.[4] Therefore, the reference for a wing often is the planform (or wing) area rather than the frontal area.[5]
For an object with a smooth surface, and non-fixed separation points — like a sphere or circular cylinder — the drag coefficient may vary with Reynolds number Re, even up to very high values (Re of the order 107). [6] [7] For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for Re > 3,500.[7] Further the drag coefficient Cd is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere).
Power
The power required to overcome the aerodynamic drag is given by:
P_d = \mathbf{F}_d \cdot \mathbf{v} = {1 \over 2} \rho v^3 A C_d
Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.
Velocity of a falling object
Main article: Terminal velocity
The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity v = 0 at time t = 0, is roughly given by a function involving a hyperbolic tangent (tanh):
v(t) = \sqrt{ \frac{2mg}{\rho A C_d} } \tanh \left(t \sqrt{\frac{g \rho C_d A}{2 m}} \right). \,
The hyperbolic tangent has a limit value of one, for large time t. In other words, velocity asymptotically approaches a maximum value called the terminal velocity vt:
v_{t} = \sqrt{ \frac{2mg}{\rho A C_d} }. \,
For a potato-shaped object of average diameter d and of density ρobj, terminal velocity is about
v_{t} = \sqrt{ gd \frac{ \rho_{obj} }{\rho} }. \,
For objects of water-like density (raindrops, hail, live objects — animals, birds, insects, etc.) falling in air near the surface of the Earth at sea level, terminal velocity is roughly equal to
v_{t} = 90 \sqrt{ d }, \,
with d in metre and vt in m/s. For example, for a human body ( \mathbf{} d ~ 0.6 m) \mathbf{} v_t ~ 70 m/s, for a small animal like a cat ( \mathbf{} d ~ 0.2 m) \mathbf{} v_t ~ 40 m/s, for a small bird ( \mathbf{} d ~ 0.05 m) \mathbf{} v_t ~ 20 m/s, for an insect ( \mathbf{} d ~ 0.01 m) \mathbf{} v_t ~ 9 m/s, and so on. Terminal velocity for very small objects (pollen, etc) at low Reynolds numbers is determined by Stokes law.
Terminal velocity is higher for larger creatures, and thus potentially more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This explains why small animals can fall from a large height and not be harmed.
Very low Reynolds numbers — Stokes' drag
Trajectories of three objects thrown at the same angle (70°). The black object doesn't experience any form of drag and moves along a parabola. The blue object experiences Stokes' drag, and the green object Newton drag.
Main article: Stokes' law
The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, Re < 1).[8] In this case, the force of drag is approximately proportional to velocity, but opposite in direction. The equation for viscous resistance is:[9]
\mathbf{F}_d = - b \mathbf{v} \,
where:
\mathbf{} b is a constant that depends on the properties of the fluid and the dimensions of the object, and
\mathbf{v} is the velocity of the object.
When an object falls from rest, its velocity will be
v(t) = \frac{(\rho-\rho_0)Vg}{b}\left(1-e^{-bt/m}\right)
which asymptotically approaches the terminal velocity \mathbf{} v_t = \frac{(\rho-\rho_0)Vg}{b}. For a given \mathbf{} b , heavier objects fall faster.
For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant,
b = 6 \pi \eta r\,
where:
\mathbf{} r is the Stokes radius of the particle, and \mathbf{} \eta is the fluid viscosity.
For example, consider a small sphere with radius \mathbf{} r = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity \mathbf{} v of 10 µm/s. Using 10−3 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water.
Drag in aerodynamics
Lift induced drag
Main article: lift-induced drag
Induced drag vs. lift
Lift-induced drag (also called induced drag) is drag which occurs as the result of the creation of lift on a three-dimensional lifting body, such as the wing or fuselage of an airplane. Induced drag consists of two primary components, including drag due to the creation of vortices (vortex drag) and the presence of additional viscous drag (lift-induced viscous drag). The vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air of varying pressure on the upper and lower surfaces of the body, which is a necessary condition for the creation of lift.
With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. For an aircraft in flight, this means that as the angle of attack, and therefore the lift coefficient, increases to the point of stall, so does the lift-induced drag. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow on the surface of the body.
Parasitic drag
Main article: parasitic drag
Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag (form drag), and drag due to surface roughness (skin friction drag). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag, which is sometimes described as a component of parasitic drag.
In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the induced drag becomes much less, but parasitic drag increases because the fluid is flowing faster around protruding objects increasing friction or drag. At even higher speeds in the transonic, wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance (minimum fuel consumption), or maximise gliding range in the event of an engine failure.
Power curve in aviation
The power curve: parasitic and induced drag vs. airspeed
The interaction of parasitic and induced drag vs. airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the power curve, and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires more thrust as speed decreases, rather than less. The consequences of being "behind the curve" in flight are important and are taught as part of pilot training. At the subsonic airspeeds where the "U" shape of this curve is significant, wave drag has not yet become a factor, and so it is not shown in the curve
Wave drag in transonic and supersonic flow
Qualitative variation in Cd factor with Mach number for aircraft
Main article: wave drag
Wave drag (also called compressibility drag) is drag which is created by the presence of a body moving at high speed through a compressible fluid. In aerodynamics, Wave drag consists of multiple components depending on the speed regime of the flight.
In transonic flight (Mach numbers greater than 0.5 and less than 1.0), wave drag is the result of the formation of shockwaves on the body, formed when areas of local supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air on a body increases when it accelerates over the body, in this case above Mach 1.0. Therefore, aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as transonic compressibility drag. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at these speeds.
In supersonic flight (Mach numbers greater than 1.0), wave drag is the result of shockwaves present on the body, typically oblique shockwaves formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large, unattached shockwaves, or bow waves will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic flow regimes, wave drag is commonly separated into two components, supersonic lift-dependent wave drag and supersonic volume-dependent wave drag.
The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the Sears-Haack Distribution. Similarly, for a fixed volume, the shape for minimum wave drag is the Von Karman Ogive.
Busemann's Biplane is not, in principle, subject to wave drag at all when operated at its design speed, but is incapable of generating lift.
d'Alembert's paradox
Main article: d'Alembert's paradox
In 1752 d'Alembert proved that potential flow, the 18th century state-of-the-art inviscid flow theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the Navier–Stokes equations for the description of viscous flow were developed by Saint-Venant, Navier and Stokes. And for the flow around a sphere at very low Reynolds numbers, Stokes was able to derive the drag — called Stokes law.[10]
However, in the limit of high-Reynolds numbers the Navier–Stokes equations approach the inviscid Euler equations; of which the potential-flow solutions considered by d'Alembert are solutions. While also at high Reynolds numbers all experiments showed there is drag. Attempts to construct inviscid steady flow solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.[10]
The notion of boundary layers — introduced by Prandtl in 1904, founded on both theory and experiments — explained the causes of drag at high Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important when the viscosity becomes very small (or equivalently the Reynolds number becomes very large).[10] Read More..
2010 MotoGP Qatar Test Day 1
Rossi looks to dial in his M1 during preseason testing at Sepang.
As he has done in all the tests thus far in 2010, The Doctor once again led the way with over three-tenths in hand. Any thoughts of retirement from the Italian have been squashed by his performances this pre-season.
The MotoGP boys hit the sands of the Middle East for what will be their final pre-season test before the official 2010 season gets underway April 11. The two-day affair started with the man who’s been on top in the previous two tests, Valentino Rossi, topping the timesheets once again, showing that the 31-year-old has no plans of slowing down. His best time of 1:55.402 put the Fiat Yamaha rider just over three-tenths ahead of Ducati Marlboro’s Casey Stoner at 1:55.717.
“I am so happy today because this isn't one of our best tracks and to come here and be fastest shows what a great job Yamaha has done with this new M1," said Rossi in a team press release. "To start with the track was quite slippery but anyway we were still fast, and as the track started to improve I felt better and better. We are quite competitive and this gives me a good feeling and I was happy to make this quick lap right at the end."
But the big news of Day 1 may have been third-place rider Ben Spies. Despite a small crash, the rookie American clocked a blistering 1:55.954 on his satellite Tech 3 Yamaha, the final rider to get in the 1:55s, nipping at the heels of two of MotoGP’s top veterans. The Texan was able to break into the once believed to be untouchable “four aliens” group in what was his first ride at the Qatari circuit on a MotoGP bike. He raced at Losail last year for the first time on a Yamaha World Superbike, picking up both race wins. Based on pre-season testing so far, that group of "four aliens” could quickly become “five aliens” if he can translate his testing speed into race-pace. Amazing stuff from the Grand Prix newbie.
“I know this track from last year but riding under the floodlights is definitely a bit different and nothing I've experienced before," Spies said. "The perception of speed is much faster with it being at night but I'm having a lot of fun. It's really well lit up but there are a couple of darker spots on the track that you have to get used to, but I've not done too bad in adjusting to the lights."
Spies was followed by fellow Texan and Tech 3 Yamaha teammate Colin Edwards in fourth. But the American finished the day over a second back of Rossi with a best lap of 1:56.540, which was also half-a-second off Spies' time. Closely behind Edwards was LCR Honda’s Randy de Puniet. His best lap of 1:56.588 put the Frenchman in the top-five for the first time in '10 pre-season testing and is by far the best performance from the satellite Honda rider in quite some time.
Ducati Marlboros Casey Stoner was .395 of a second shy of Rossis Day 2 chart topping time.
Stoner continued his fine off-season form, ending Day 1 second-quickest overall.
Andrea Dovizioso was the first of the factory Repsol Honda riders in sixth at 1:56.811. Dovizioso is fresh off a nasty illness, which caused him to miss the team’s official press launch this week in Spain and is no doubt still feeling the effects.
Speaking of overcoming setbacks, seventh-quickest was Jorge Lorenzo. The Spanish star is riding with a still-healing broken right hand, requiring a special carbon fiber brace and one-off custom gloves. Lorenzo stated in a pre-test release that he would merely “try to ride.” But he did much more than that, posting a respectable 1:56.838.
The final American, Nicky Hayden, was eighth on his factory Ducati, clicking off a 1:56.855. Pramac Racing Ducati’s Mika Kallio showed some speed to post the ninth-best time of the day at 1:56.923; the last rider under the 1:56 mark.
LCR Hondas Randy DePuniet was 13th fastest on Day 2.
Frenchman Randy de Puniet started the test off strong as the quickest Honda in fifth spot.
Rounding out the top-10 was Repsol Honda’s Dani Pedrosa, in a less-than-impressive performance from one of the so-called "aliens." Honda is expecting a championship out of the diminutive Spaniard this year and it looks as if he may have quite the hill to climb. Tomorrow is Day 2 and should reveal even more as it's the final time riders will see the track before the first race. Stay tuned…
P.S. Be sure to sign up for MotoUSA's Fantasy Racing now as the season starts soon! Read More..
Mazda2 Memang Oke
Selama tiga hari kami bercanda dengan The New Mazda2
OTOCOID, Jakarta – Dua minggu setelah peluncuran resminya, redaksi OTOCOID ditawari mencoba New Mazda2 oleh PT. Mazda Motor Indonesia. Maka, segeralah kami memanaj kesempatan terbaik ini dengan sebaik-baiknya. Sejumlah mitra terbaik OTO kami hubungi.
Jum’at (4/12) city car baru ATPM mobil Mazda itu kami jemput. Menghindari jalur 3 in 1, kami terpaksa harus ‘berhimpitan’ dengan kendaraan lain yang juga menjauh dari daerah yang mengharuskan mobil berpenumpang minimal 3 orang itu. Tapi, dengan dimensi yang ringkas, Mazda2 tetap lincah dan gesit menerobos kepadatan lalu lintas Kota Metropolitan pada saat jam sibuk.
Kelincahannya dalam bermanuver kami rasakan saat kami memasuki jalan bebas hambatan dalam kota. Mesin 1500 cc DOHC 16 valve benar-benar galak. Tenaga maksimalnya yang mencapai 103 dk pada saat putaran mesin mencapai 4000 rpm benar-benar kami rasakan. Injakan pedal akselerator yang belum masuk setengah itu sudah membuat roda berdecit.
Penasaran dengan keliaran tenaganya, kami mencobanya bercengkerama lebih dalam. Hasilnya, tenaganya luar biasa. Kecepatan 120 km/jam dengan mudah tercapai tanpa harus ada raungan pabrik tenaganya. Yang amat kami rasakan adalah kestabilan mobil ini saat dikebut. Traksinya sangat baik mencengkeram aspal jalan. Kebetulan mobil yang dipinjamkan Mazda itu dari jenis R dengan transmisi manual.
Mobil yang ditawarkan dengan harga Rp. 193 juta (on the road Jakarta) ini memang terhitung pendatang baru di segment yang dimainkan oleh sejumlah pesaingnya seperti Honda All New Jazz, Toyota Yaris, Suzuki Swift, Daihatsu Sirion, Hyundai i20 dan lainnya.
Namun melihat sosok dan performanya yang menantang ini, ke depan Mazda2 tentu akan menjadi pilihan anak muda yang aktif dan dinamis. Desain eksteriornya yang sangat sporty, tentu saja akan membuat penampilan si pengendaranya merasa jauh lebih muda. Apalagi, performanya yang gahar. Untuk membuktikan kehandalannya, tidak ada salahnya jika Mazda mencoba arena balap yang kini ramai diperebutkan Yaris dan All New Honda Jazz.
Masih di panggung yang digemari anak muda, Mazda2 juga dapat unjuk gigi dalam meningkatkan penampilannya di ajang kontes-kontes modifikasi. Lagi-lagi, di ajang yang mempertontonkan kreatifitas anak muda dalam mendandani mobil kesayangannya itu hanya dimainkan oleh Yaris dan All New Honda Jazz. Jadi, apa salahnya Mazda masuk ke dua sector yang digandrungi anak muda itu. Soalnya, Mazda2 memang jempol! Read More..
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