Misplaced Pages

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58-513: When the USAAF started strategic bombing in Europe there were no fighters available to escort the bombers all the way to distant targets. The bombers carried several defensive guns and formed up in boxes so that they could provide mutually covering fire but there was interest in providing more firepower for the formation. The XB-41 Liberator was outfitted with 14 .50 caliber (12.7 mm) machine guns. This

116-476: 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 ,

174-665: 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

232-809: 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

290-450: 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

348-406: 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

406-547: A heavily armed escort capable of accompanying bombers all the way to the target and back. Of the initial order of 13, one (serial 43-5732) was lost on the delivery flight from Iceland to the UK in May 1943; it force-landed in a peat bog on a Scottish island after running out of fuel. Although removed to Stornoway and repaired, it never flew in combat. The remaining 12 were allocated to the 92d Bombardment Group (Heavy), being assigned to

464-423: 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 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

522-693: 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

580-457: A pair of YB-40s in the lead element of the strike to protect the mission commander. The original design concept of the YB-40 never played out as intended in practice. Luftwaffe fighter chief Adolf Galland considered the gunship's handful of combat victories to be "insignificant" and not worth the cost of the aircraft. The increased weight from the additional machine guns and ammunition nearly cut

638-468: 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

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696-623: 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

754-403: 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 the solid object in the fluid's path. Unlike other resistive forces, drag force depends on velocity. This is because drag force

812-483: 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 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

870-558: 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

928-448: 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 ,

986-625: 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}}}

1044-399: 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

1102-401: Is drag which occurs as the result of the creation of lift on a three-dimensional lifting body , such as 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

1160-428: 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

1218-472: 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

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1276-484: 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 the relative proportions of skin friction and form drag is shown for two different body sections: An airfoil, which

1334-583: 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

1392-755: 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

1450-409: The 327th Bombardment Squadron , stationed at RAF Alconbury (AAF-102) on 8 May 1943. YB-40s flew in the following operational missions: Altogether of the 59 aircraft dispatched, 48 sorties were credited. Five confirmed and two probable German fighter kills were claimed, and one YB-40 was lost, shot down on 22 June mission to Hüls, Germany. Tactics were revised on the final five missions by placing

1508-413: 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

1566-552: The prototype , Project V-139, began in September 1942 by converting the second production B-17F-1-BO (serial number 41-24341) built. Conversion work was done by Lockheed's Vega company. The aircraft differed from the standard B-17 in that a second manned dorsal turret was installed in the former radio compartment, just behind the bomb bay and forward of the ventral ball turret 's location. The single .50-caliber light-barrel (12.7 mm) Browning machine gun at each waist station

1624-558: The "gunship" concept remained, and the XB-41 program was abandoned. The prototype XB-41 was redesignated TB-24D; it served as an instructional airframe for training mechanics on the B-24. It was scrapped at Maxwell Field , Alabama on 2 February 1945. Data from General characteristics Performance Armament Related development Related lists Boeing YB-40 Flying Fortress The Boeing YB-40 Flying Fortress

1682-507: The XB-40 had the symmetrical waist windows of the standard B-17F and the second dorsal turret integrated into a dorsal fairing. In contrast, most of the YB-40s had the positions of the waist windows staggered for better freedom of movement for the waist gunners, and the aft dorsal turret was moved slightly backwards so that it stood clear of the dorsal fairing. The YB-40's mission was to provide

1740-554: The YB-40's climb rate in half from that of a B-17F, and in level flight it had difficulty keeping up with standard Flying Fortresses, especially after they had dropped their bombs. Despite the overall failure of the project as an operational aircraft, it led directly to the Bendix chin turret's fitment on the last 65 (86 according to some sources) Douglas-built aircraft starting with the B-17F-70-DL production block, and were part of

1798-479: The YB-40/TB-40 assembly job was transferred to Douglas. A variety of different armament configurations was tried. Some YB-40s were fitted with four-gun nose and tail turrets. Some carried cannon of up to 40 mm in caliber, and a few carried up to as many as 30 guns of various calibers in multiple hand-held positions in the waist as well as in additional power turrets above and below the fuselage. Externally,

Consolidated XB-41 Liberator - Misplaced Pages Continue

1856-556: The aircraft were sent to reclamation, mostly at RFC Ontario in May 1945, being broken up and smelted. A couple of the YB-40s can be seen in the 1946 movie The Best Years of Our Lives , in the famous scene shot at the Ontario "graveyard". No airframes were sold on the civil market. Data from General characteristics Performance Armament Related development Drag (physics) In fluid dynamics , drag , sometimes referred to as fluid resistance ,

1914-468: The aircraft; on 21 March 1943, the Army declared the XB-41 as unsuitable for operational use; the conversion of thirteen Liberators to YB-41 service test aircraft was cancelled. Despite this, Consolidated continued to work on the XB-41 prototype; wide-blade propellers were fitted, and some of the armor was removed to reduce the aircraft's weight. Tests resumed at Eglin on 28 July 1943; however, the basic flaws of

1972-413: 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

2030-407: 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

2088-460: The burden this placed on the YB-40 is that while the B-17F on which it was based was rated to climb to 20,000 ft (6,100 m) in 25 minutes, the YB-40 was rated at 48 minutes. Part of the decreased performance was due to the weight increase, and part was due to the greater aerodynamic drag of the gun stations. The first flight of the XB-40 was on 10 November 1942. The first order of 13 YB-40s

2146-453: 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

2204-685: 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, 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 )

2262-678: 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}}

2320-487: 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

2378-620: 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

Consolidated XB-41 Liberator - Misplaced Pages Continue

2436-411: The flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air from above and below 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

2494-441: 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

2552-448: 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

2610-749: 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 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}}}

2668-408: 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 the event of an engine failure. Drag depends on the properties of the fluid and on the size, shape, and speed of

2726-462: The sides of the forward fuselage at the bombardier station), initially removed from the configuration, were restored in England to provide a total of 16 guns, and the bomb bay was converted to an ammunition magazine . Additional armor plating was installed to protect crew positions. The aircraft's gross weight was some 4,000 lb (1,800 kg) greater than a fully armed B-17. An indication of

2784-808: 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}}

2842-884: 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

2900-407: The stalling angle), the lift coefficient also increases, and so too 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 in the wake behind the body. Parasitic drag , or profile drag, is drag caused by moving a solid object through

2958-648: The standardized modifications conspicuous on the final production variant of the B-17, the B-17G : Once the test program ended, most of the surviving aircraft returned to the U.S. in November 1943 and were used as trainers. 42-5736 ("Tampa Tornado") was flown to RAF Kimbolton on 2 October 1943 where it was put on display and later used as a group transport. It was returned to the United States on 28 March 1944. All of

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3016-482: 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

3074-489: 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

3132-598: Was a modification for operational testing purposes of the B-17 Flying Fortress bomber aircraft, converted to act as a heavily armed gunship to support other bombers during World War II . At the time of its development, long-range fighter aircraft such as the North American P-51 Mustang were just entering quantity production, and thus were not yet available to accompany bombers all the way from England to Germany and back. Work on

3190-450: Was achieved by adding a second dorsal turret and a remotely operated Bendix turret (of the same type as fitted to the YB-40 ) under the chin to the standard twin gun tail turret and twin gun retractable ventral ball turret , plus twin mount guns at each waist window. The port waist mount was originally covered by a Plexiglas bubble; testing showed this caused severe optical distortion and it

3248-522: Was made in October 1942. A follow-up order for 12 more was made in January 1943. The modifications were performed by Douglas Aircraft at their Tulsa, Oklahoma center, and the first aircraft were completed by the end of March 1943. Twenty service test aircraft were ordered, Vega Project V-140, as YB-40 along with four crew trainers designated TB-40. Because Vega had higher priority production projects,

3306-467: Was removed. The XB-41 carried 12,420 rounds of ammunition, 4,000 rounds of which were stored in the bomb bay as a reserve. It was powered by four 1,250 hp (930 kW) Pratt & Whitney R-1830 -43 radial engines . On 29 January 1943, the sole XB-41 was delivered to Eglin Field , Florida. Tests were carried out for two months at Eglin during February 1943. These indicated significant problems with

3364-453: Was replaced by two of them mounted side by side as a twin-mount emplacement, with a mount for each pair of these being very much like the tail gun setup in general appearance. The bombardier 's equipment was also replaced by two .50-caliber light-barrel Browning AN/M2 machine guns in a remotely operated Bendix designed "chin"-location turret, directly beneath the bombardier's location in the extreme nose. The existing "cheek" machine guns (on

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