Misplaced Pages

#483516

60-421: The Deepak is used for primary training, observation, liaison and target towing. When it flies upside-down fuel flows from a collector tank in the fuselage and the inverted flight is limited to 1 min. Deepak has a theoretical glide ratio of 8.5:1. The IAF and HAL are looking into new safety systems such as Ballistic Recovery Systems to enable it to descend safely in the event of an engine failure. On 16 May 2010

120-476: A limit value of one, for large time t . In other words, velocity asymptotically approaches a maximum value called the terminal velocity v t : v t = 2 m g ρ A C D . {\displaystyle v_{t}={\sqrt {\frac {2mg}{\rho AC_{D}}}}.\,} For an object falling and released at relative-velocity v  = v i at time t  = 0, with v i < v t ,

180-665: A limit value of one, for large time t . Velocity asymptotically tends to the terminal velocity v t , strictly from above v t . For v i = v t , the velocity is constant: v ( t ) = v t . {\displaystyle v(t)=v_{t}.} These functions are defined by the solution of the following differential equation : g − ρ A C D 2 m v 2 = d v d t . {\displaystyle g-{\frac {\rho AC_{D}}{2m}}v^{2}={\frac {dv}{dt}}.\,} Or, more generically (where F ( v ) are

240-445: A fixed wing aircraft are wingspan and total wetted area . One method for estimating the zero-lift drag coefficient of an aircraft is the equivalent skin-friction method. For a well designed aircraft, zero-lift drag (or parasite drag) is mostly made up of skin friction drag plus a small percentage of pressure drag caused by flow separation. The method uses the equation where C fe {\displaystyle C_{\text{fe}}}

300-809: A fluid at relatively slow speeds (assuming there is no turbulence). Purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity. The equation for viscous resistance is: F D = − b v {\displaystyle \mathbf {F} _{D}=-b\mathbf {v} \,} where: When an object falls from rest, its velocity will be v ( t ) = ( ρ − ρ 0 ) V g b ( 1 − e − b t / m ) {\displaystyle v(t)={\frac {(\rho -\rho _{0})\,V\,g}{b}}\left(1-e^{-b\,t/m}\right)} where: The velocity asymptotically approaches

360-450: A fluid increases as the cube of the velocity increases. For example, a car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome aerodynamic drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speeds, the drag/force quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work . At twice

420-445: A given flightpath, so that doubling the L/D ratio will require only half of the energy for the same distance travelled. This results directly in better fuel economy . The L/D ratio can also be used for water craft and land vehicles. The L/D ratios for hydrofoil boats and displacement craft are determined similarly to aircraft. Lift can be created when an aerofoil-shaped body travels through

480-479: A glider it determines the glide ratio , of distance travelled against loss of height. The term is calculated for any particular airspeed by measuring the lift generated, then dividing by the drag at that speed. 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

540-422: A high angle of attack and a gentle stall are also important. As the aircraft fuselage and control surfaces will also add drag and possibly some lift, it is fair to consider the L/D of the aircraft as a whole. The glide ratio , which is the ratio of an (unpowered) aircraft's forward motion to its descent, is (when flown at constant speed) numerically equal to the aircraft's L/D. This is especially of interest in

600-693: A human body ( d {\displaystyle d} ≈0.6 m) v t {\displaystyle v_{t}} ≈70 m/s, for a small animal like a cat ( d {\displaystyle d} ≈0.2 m) v t {\displaystyle v_{t}} ≈40 m/s, for a small bird ( d {\displaystyle d} ≈0.05 m) v t {\displaystyle v_{t}} ≈20 m/s, for an insect ( d {\displaystyle d} ≈0.01 m) v t {\displaystyle v_{t}} ≈9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers

660-465: A small sphere with radius r {\displaystyle r} = 0.5 micrometre (diameter = 1.0 μm) moving through water at a velocity v {\displaystyle v} of 10 μm/s. Using 10 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. The drag coefficient of

SECTION 10

#1732883520484

720-623: A sphere can be determined for the general case of a laminar flow with Reynolds numbers less than 2 ⋅ 10 5 {\displaystyle 2\cdot 10^{5}} using the following formula: C D = 24 R e + 4 R e + 0.4   ;           R e < 2 ⋅ 10 5 {\displaystyle C_{D}={\frac {24}{Re}}+{\frac {4}{\sqrt {Re}}}+0.4~{\text{;}}~~~~~Re<2\cdot 10^{5}} For Reynolds numbers less than 1, Stokes' law applies and

780-410: A viscous fluid such as air. The aerofoil is often cambered and/or set at an angle of attack to the airflow. The lift then increases as the square of the airspeed. Whenever an aerodynamic body generates lift, this also creates lift-induced drag or induced drag. At low speeds an aircraft has to generate lift with a higher angle of attack , which results in a greater induced drag. This term dominates

840-558: Is about v t = g d ρ o b j ρ . {\displaystyle v_{t}={\sqrt {gd{\frac {\rho _{obj}}{\rho }}}}.\,} For objects of water-like density (raindrops, hail, live objects—mammals, birds, insects, etc.) falling in air near Earth's surface at sea level, the terminal velocity is roughly equal to with d in metre and v t in m/s. v t = 90 d , {\displaystyle v_{t}=90{\sqrt {d}},\,} For example, for

900-455: 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 in the wake behind the body. Parasitic drag , or profile 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,

960-448: Is also defined in terms of the hyperbolic tangent function: v ( t ) = v t tanh ⁡ ( t g v t + arctanh ⁡ ( v i v t ) ) . {\displaystyle v(t)=v_{t}\tanh \left(t{\frac {g}{v_{t}}}+\operatorname {arctanh} \left({\frac {v_{i}}{v_{t}}}\right)\right).\,} For v i > v t ,

1020-619: Is asymptotically proportional to R e − 1 {\displaystyle \mathrm {Re} ^{-1}} , which means that the drag is linearly proportional to the speed, i.e. the drag force on a small sphere moving through a viscous fluid is given by the Stokes Law : F d = 3 π μ D v {\displaystyle F_{\rm {d}}=3\pi \mu Dv} At high R e {\displaystyle \mathrm {Re} } , C D {\displaystyle C_{\rm {D}}}

1080-399: Is determined by Stokes law. In short, 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. The equation for viscous resistance or linear drag is appropriate for objects or particles moving through

1140-424: Is dominated by pressure forces, and streamlined if the drag is dominated by viscous forces. For example, road vehicles are bluff bodies. For aircraft, pressure and friction drag are included in the definition of parasitic drag . Parasite drag is often expressed in terms of a hypothetical. This is the area of a flat plate perpendicular to the flow. It is used when comparing the drag of different aircraft For example,

1200-401: Is measured empirically by testing in a wind tunnel or in free flight test . The L/D ratio is affected by both the form drag of the body and by the induced drag associated with creating a lifting force. It depends principally on the lift and drag coefficients, angle of attack to the airflow and the wing aspect ratio . The L/D ratio is inversely proportional to the energy required for

1260-428: Is more or less constant, but drag will vary as the square of the speed varies. The graph to the right shows how C D {\displaystyle C_{\rm {D}}} varies with R e {\displaystyle \mathrm {Re} } for the case of a sphere. Since the power needed to overcome the drag force is the product of the force times speed, the power needed to overcome drag will vary as

SECTION 20

#1732883520484

1320-472: Is presented at Drag equation § Derivation . The reference area A is often the orthographic projection of the object, or the frontal area, on a plane perpendicular to the direction of motion. For objects with a simple shape, such as a sphere, this is the cross sectional area. Sometimes a body is a composite of different parts, each with a different reference area (drag coefficient corresponding to each of those different areas must be determined). In

1380-513: Is the Mach number. Windtunnel tests have shown this to be approximately accurate. Drag (aerodynamics) In fluid dynamics , drag , sometimes referred to as fluid resistance , is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid . This can exist between two fluid layers, two solid surfaces, or between a fluid and a solid surface. Drag forces tend to decrease fluid velocity relative to

1440-578: Is the Reynolds number related to fluid path length L. As mentioned, the drag equation with a constant drag coefficient gives the force moving through fluid a relatively large velocity, i.e. high Reynolds number , Re > ~1000. This is also called quadratic drag . F D = 1 2 ρ v 2 C D A , {\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A,} The derivation of this equation

1500-435: Is the equivalent skin friction coefficient, S wet {\displaystyle S_{\text{wet}}} is the wetted area and S ref {\displaystyle S_{\text{ref}}} is the wing reference area. The equivalent skin friction coefficient accounts for both separation drag and skin friction drag and is a fairly consistent value for aircraft types of the same class. Substituting this into

1560-755: Is the wind speed and v o {\displaystyle v_{o}} is the object speed (both relative to ground). 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 ) = 2 m g ρ A C D tanh ⁡ ( t g ρ C D A 2 m ) . {\displaystyle v(t)={\sqrt {\frac {2mg}{\rho AC_{D}}}}\tanh \left(t{\sqrt {\frac {g\rho C_{D}A}{2m}}}\right).\,} The hyperbolic tangent has

1620-550: Is wingspan. The term b 2 / S wet {\displaystyle b^{2}/S_{\text{wet}}} is known as the wetted aspect ratio. The equation demonstrates the importance of wetted aspect ratio in achieving an aerodynamically efficient design. At supersonic speeds L/D values are lower. Concorde had a lift/drag ratio of about 7 at Mach 2, whereas a 747 has about 17 at about mach 0.85. Dietrich Küchemann developed an empirical relationship for predicting L/D ratio for high Mach numbers: where M

1680-548: The Douglas DC-3 has an equivalent parasite area of 2.20 m (23.7 sq ft) and the McDonnell Douglas DC-9 , with 30 years of advancement in aircraft design, an area of 1.91 m (20.6 sq ft) although it carried five times as many passengers. 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

1740-459: The lift and drag coefficients C L and C D . The varying ratio of lift to drag with AoA is often plotted in terms of these coefficients. For any given value of lift, the AoA varies with speed. Graphs of C L and C D vs. speed are referred to as drag curves . Speed is shown increasing from left to right. The lift/drag ratio is given by the slope from the origin to some point on the curve and so

1800-445: The lift-to-drag ratio (or L/D ratio ) is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic drag caused by moving through air. It describes the aerodynamic efficiency under given flight conditions. The L/D ratio for any given body will vary according to these flight conditions. For an aerofoil wing or powered aircraft, the L/D is specified when in straight and level flight. For

1860-413: The order 10 ). 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. The further the drag coefficient C d is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere). Under the assumption that

HAL HPT-32 Deepak - Misplaced Pages Continue

1920-426: The span efficiency factor , a number less than but close to unity for long, straight-edged wings, and C D , 0 {\displaystyle C_{D,0}} the zero-lift drag coefficient . Most importantly, the maximum lift-to-drag ratio is independent of the weight of the aircraft, the area of the wing, or the wing loading. It can be shown that two main drivers of maximum lift-to-drag ratio for

1980-409: The wing or propeller of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices ( vortex drag ); and the presence of additional viscous drag ( lift-induced viscous drag ) that is not present when lift is zero. The trailing vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air from above and below

2040-533: The IAF cleared the installation of a parachute recovery system. The HPT-32 aircraft has been replaced by the Pilatus PC-7 Mk II in the IAF, as its workhorse as a Basic Trainer Aircraft (BTA) in 2013. In 17 Deepak crashes so far, 19 pilots have died. The Comptroller and Auditor General (CAG) of India has been reported as saying the aircraft is "technologically outdated and beset by flight safety hazards" when discussing

2100-413: The airflow and forces the flow to move downward. This results in an equal and opposite force acting upward on the wing which is the lift force. The change of momentum of the airflow downward results in a reduction of the rearward momentum of the flow which is the result of a force acting forward on the airflow and applied by the wing to the air flow; an equal but opposite force acts on the wing rearward which

2160-407: The airplane produces lift, another drag component results. Induced drag , symbolized D i {\displaystyle D_{i}} , is due to a modification of the pressure distribution due to the trailing vortex system that accompanies the lift production. An alternative perspective on lift and drag is gained from considering the change of momentum of the airflow. The wing intercepts

2220-424: The body which flows in slightly different directions as a consequence of creation of lift . With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. This means that as the wing's angle of attack increases (up to a maximum called the stalling angle), the lift coefficient also increases, and so too does the lift-induced drag. At the onset of stall , lift

2280-453: The case of a wing , the reference areas are the same, and the drag force is in the same ratio as the lift force . Therefore, the reference for a wing is often the lifting area, sometimes referred to as "wing area" rather than the frontal area. 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 , up to extremely high values ( Re of

2340-527: The design and operation of high performance sailplanes , which can have glide ratios almost 60 to 1 (60 units of distance forward for each unit of descent) in the best cases, but with 30:1 being considered good performance for general recreational use. Achieving a glider's best L/D in practice requires precise control of airspeed and smooth and restrained operation of the controls to reduce drag from deflected control surfaces. In zero wind conditions, L/D will equal distance traveled divided by altitude lost. Achieving

2400-678: The drag coefficient C D {\displaystyle C_{\rm {D}}} as a function of Bejan number and the ratio between wet area A w {\displaystyle A_{\rm {w}}} and front area A f {\displaystyle A_{\rm {f}}} : C D = 2 A w A f B e R e L 2 {\displaystyle C_{\rm {D}}=2{\frac {A_{\rm {w}}}{A_{\rm {f}}}}{\frac {\mathrm {Be} }{\mathrm {Re} _{L}^{2}}}} where R e L {\displaystyle \mathrm {Re} _{L}}

2460-487: The drag coefficient approaches 24 R e {\displaystyle {\frac {24}{Re}}} ! In aerodynamics , aerodynamic drag , also known as air resistance , is the fluid drag force that acts on any moving solid body in the direction of the air's freestream flow. Alternatively, calculated from the flow field perspective (far-field approach), the drag force results from three natural phenomena: shock waves , vortex sheet, and viscosity . When

HAL HPT-32 Deepak - Misplaced Pages Continue

2520-616: The drag constant: b = 6 π η r {\displaystyle b=6\pi \eta r\,} where r {\displaystyle r} is the Stokes radius of the particle, and η {\displaystyle \eta } is the fluid viscosity. The resulting expression for the drag is known as Stokes' drag : F D = − 6 π η r v . {\displaystyle \mathbf {F} _{D}=-6\pi \eta r\,\mathbf {v} .} For example, consider

2580-562: The equation for maximum lift-to-drag ratio, along with the equation for aspect ratio ( b 2 / S ref {\displaystyle b^{2}/S_{\text{ref}}} ), yields the equation ( L / D ) max = 1 2 π ε C fe b 2 S wet , {\displaystyle (L/D)_{\text{max}}={\frac {1}{2}}{\sqrt {{\frac {\pi \varepsilon }{C_{\text{fe}}}}{\frac {b^{2}}{S_{\text{wet}}}}}},} where b

2640-455: The event of an engine failure. Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation : F D = 1 2 ρ v 2 C D A {\displaystyle F_{\mathrm {D} }\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{\mathrm {D} }\,A} where The drag coefficient depends on

2700-504: The fluid is flowing more quickly around protruding objects increasing friction or drag. At even higher speeds ( 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 maximize gliding range in

2760-441: The fluid is not moving relative to the currently used reference system, the power required to overcome the aerodynamic drag is given by: P D = F D ⋅ v = 1 2 ρ v 3 A C D {\displaystyle P_{D}=\mathbf {F} _{D}\cdot \mathbf {v} ={\tfrac {1}{2}}\rho v^{3}AC_{D}} The power needed to push an object through

2820-448: The forces acting on the object beyond drag): 1 m ∑ F ( v ) − ρ A C D 2 m v 2 = d v d t . {\displaystyle {\frac {1}{m}}\sum F(v)-{\frac {\rho AC_{D}}{2m}}v^{2}={\frac {dv}{dt}}.\,} For a potato-shaped object of average diameter d and of density ρ obj , terminal velocity

2880-402: The grounding of the fleet in 2009. HAL HTT-40 is going replace HAL HPT-32 Deepak as primary trainer. Data from Jane's Aircraft Recognition Guide General characteristics Performance Armament Four hardpoints; 255 kg warload; machine gun pods; bombs; rockets Related HAL development: Comparable or Related Basic Trainers: Glide ratio In aerodynamics ,

2940-632: The low-speed side of the graph of lift versus velocity. Form drag is caused by movement of the body through air. This type of drag, known also as air resistance or profile drag varies with the square of speed (see drag equation ). For this reason profile drag is more pronounced at greater speeds, forming the right side of the lift/velocity graph's U shape. Profile drag is lowered primarily by streamlining and reducing cross section. The total drag on any aerodynamic body thus has two components, induced drag and form drag. The rates of change of lift and drag with angle of attack (AoA) are called respectively

3000-451: The maximum L/D is not dependent on weight or wing loading, but with greater wing loading the maximum L/D occurs at a faster airspeed. Also, the faster airspeed means the aircraft will fly at greater Reynolds number and this will usually bring about a lower zero-lift drag coefficient . Mathematically, the maximum lift-to-drag ratio can be estimated as where AR is the aspect ratio , ε {\displaystyle \varepsilon }

3060-444: The maximum L/D ratio does not occur at the point of least drag coefficient, the leftmost point. Instead, it occurs at a slightly greater speed. Designers will typically select a wing design which produces an L/D peak at the chosen cruising speed for a powered fixed-wing aircraft, thereby maximizing economy. Like all things in aeronautical engineering , the lift-to-drag ratio is not the only consideration for wing design. Performance at

SECTION 50

#1732883520484

3120-442: The maximum distance for altitude lost in wind conditions requires further modification of the best airspeed, as does alternating cruising and thermaling. To achieve high speed across country, glider pilots anticipating strong thermals often load their gliders (sailplanes) with water ballast : the increased wing loading means optimum glide ratio at greater airspeed, but at the cost of climbing more slowly in thermals. As noted below,

3180-442: 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 angle of attack can be reduced and the induced drag decreases. Parasitic drag, however, increases because

3240-404: The relative proportions of skin friction and form drag is shown for two different body sections: An airfoil, which is a streamlined body, and a cylinder, which is a bluff body. Also shown is a flat plate illustrating the effect that orientation has on the relative proportions of skin friction, and pressure difference between front and back. A body is known as bluff or blunt when the source of drag

3300-458: The shape of the object and on the Reynolds number R e = v D ν = ρ v D μ , {\displaystyle \mathrm {Re} ={\frac {vD}{\nu }}={\frac {\rho vD}{\mu }},} where At low R e {\displaystyle \mathrm {Re} } , C D {\displaystyle C_{\rm {D}}}

3360-444: The solid object in the fluid's path. Unlike other resistive forces, drag force depends on velocity. This is because drag force is proportional to the velocity for low-speed flow and the velocity squared for high-speed flow. This distinction between low and high-speed flow is measured by the Reynolds number . Examples of drag include: Types of drag are generally divided into the following categories: The effect of streamlining on

3420-808: The speed, the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, 4 times the work done in half the time requires 8 times the power. When the fluid is moving relative to the reference system, for example, a car driving into headwind, the power required to overcome the aerodynamic drag is given by the following formula: P D = F D ⋅ v o = 1 2 C D A ρ ( v w + v o ) 2 v o {\displaystyle P_{D}=\mathbf {F} _{D}\cdot \mathbf {v_{o}} ={\tfrac {1}{2}}C_{D}A\rho (v_{w}+v_{o})^{2}v_{o}} Where v w {\displaystyle v_{w}}

3480-880: The square of the speed at low Reynolds numbers, and as the cube of the speed at high numbers. It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the Bejan number . Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of drag force it has been obtained: F d = Δ p A w = 1 2 C D A f ν μ l 2 R e L 2 {\displaystyle F_{\rm {d}}=\Delta _{\rm {p}}A_{\rm {w}}={\frac {1}{2}}C_{\rm {D}}A_{\rm {f}}{\frac {\nu \mu }{l^{2}}}\mathrm {Re} _{L}^{2}} and consequently allows expressing

3540-482: The terminal velocity v t = ( ρ − ρ 0 ) V g b {\displaystyle v_{t}={\frac {(\rho -\rho _{0})Vg}{b}}} . For a given b {\displaystyle b} , denser objects fall more quickly. 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

3600-489: The velocity function is defined in terms of the hyperbolic cotangent function: v ( t ) = v t coth ⁡ ( t g v t + coth − 1 ⁡ ( v i v t ) ) . {\displaystyle v(t)=v_{t}\coth \left(t{\frac {g}{v_{t}}}+\coth ^{-1}\left({\frac {v_{i}}{v_{t}}}\right)\right).\,} The hyperbolic cotangent also has

#483516