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114-528: The D.31 Turbulent was designed to be amateur-built and is a single-seat ultra-light aircraft with cantilever low-wing and fixed tailwheel landing gear. Designed to be powered by a 30 hp (1200cc) Volkswagen or similar engine. The fuselage and wings use wood construction with fabric covering. Rollason Aircraft & Engines Limited produced 26 factory-built D.31 aircraft in the United Kingdom and three D.31A models with strengthened wing spar in order to get

228-422: A Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong , electromagnetic , weak , and gravitational . High-energy particle physics observations made during

342-415: A ' brewery horse ' could produce 32,400 foot-pounds [43,929 J] per minute." James Watt and Matthew Boulton standardized that figure at 33,000 foot-pounds (44,742 J) per minute the next year. A common legend states that the unit was created when one of Watt's first customers, a brewer, specifically demanded an engine that would match a horse, and chose the strongest horse he had and driving it to

456-464: A constant mass m {\displaystyle m} to then have any predictive content, it must be combined with further information. Moreover, inferring that a force is present because a body is accelerating is only valid in an inertial frame of reference. The question of which aspects of Newton's laws to take as definitions and which to regard as holding physical content has been answered in various ways, which ultimately do not affect how

570-580: A different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result . If both of these pieces of information are not known for each force, the situation is ambiguous. Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate

684-482: A force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. When kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion. Some forces are consequences of

798-474: A force that existed intrinsically between two charges . The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction , was both attractive and repulsive (there was intrinsic polarity ), was independent of the mass of the charged objects, and followed the superposition principle . Coulomb's law unifies all these observations into one succinct statement. Subsequent mathematicians and physicists found

912-582: A frame of reference if it at rest and not accelerating, whereas a body in dynamic equilibrium is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa. Static equilibrium was understood well before the invention of classical mechanics. Objects that are not accelerating have zero net force acting on them. The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on

1026-619: A full British certificate of Airworthiness. Five Turbulents are operated by the Tiger Club in 2019. The rights to plans for the design are held by the UK Light Aircraft Association . The Tiger Club Turbulent displays have been a highlight of the UK air display scene since 1959 and, by remaining in sight of the crowd at all times, their displays are often regarded as the most rivetting. Reviewers Roy Beisswenger and Marino Boric described

1140-429: A group of engineers modified a dynometer to be able to measure how much horsepower a horse can produce. This horse was measured to 5.7 hp (4.3 kW). When torque T is in pound-foot units, rotational speed N is in rpm , the resulting power in horsepower is The constant 5252 is the rounded value of (33,000 ft⋅lbf/min)/(2π rad/rev). When torque T is in inch-pounds, The constant 63,025

1254-526: A healthy human can produce about 1.2 hp (0.89 kW) briefly (see orders of magnitude ) and sustain about 0.1 hp (0.075 kW) indefinitely; trained athletes can manage up to about 2.5 hp (1.9 kW) briefly and 0.35 hp (0.26 kW) for a period of several hours. The Jamaican sprinter Usain Bolt produced a maximum of 3.5 hp (2.6 kW) 0.89 seconds into his 9.58 second 100-metre (109.4 yd) sprint world record in 2009. In 2023

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1368-459: A key principle of Newtonian physics. In the early 17th century, before Newton's Principia , the term "force" ( Latin : vis ) was applied to many physical and non-physical phenomena, e.g., for an acceleration of a point. The product of a point mass and the square of its velocity was named vis viva (live force) by Leibniz . The modern concept of force corresponds to Newton's vis motrix (accelerating force). Sir Isaac Newton described

1482-479: A level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a normal force ). The situation produces zero net force and hence no acceleration. Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because

1596-432: A straight line will see it continuing to do so. According to the first law, motion at constant speed in a straight line does not need a cause. It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time . If

1710-745: A surface up to the limit specified by the coefficient of static friction ( μ s f {\displaystyle \mu _{\mathrm {sf} }} ) multiplied by the normal force ( F N {\displaystyle \mathbf {F} _{\text{N}}} ). In other words, the magnitude of the static friction force satisfies the inequality: 0 ≤ F s f ≤ μ s f F N . {\displaystyle 0\leq \mathbf {F} _{\mathrm {sf} }\leq \mu _{\mathrm {sf} }\mathbf {F} _{\mathrm {N} }.} The kinetic friction force ( F k f {\displaystyle F_{\mathrm {kf} }} )

1824-413: A system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained. Some textbooks use Newton's second law as a definition of force. However, for the equation F = m a {\displaystyle \mathbf {F} =m\mathbf {a} } for

1938-484: A unidirectional force or a force that acts on only one body. In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero: F 1 , 2 + F 2 , 1 = 0. {\displaystyle \mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but

2052-513: Is torque , which produces changes in the rotational speed of an object. In an extended body, each part often applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress . In equilibrium these stresses cause no acceleration of the body as the forces balance one another. If these are not in equilibrium they can cause deformation of solid materials, or flow in fluids . In modern physics , which includes relativity and quantum mechanics ,

2166-400: Is a unit of measurement of power , or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are the imperial horsepower as in "hp" or "bhp" which is about 745.7 watts , and the metric horsepower as in "cv" or "PS" which is approximately 735.5 watts. The term

2280-424: Is a coefficient of theoretical brake horsepower and cylinder pressures during combustion. Nominal horsepower (nhp) is an early 19th-century rule of thumb used to estimate the power of steam engines. It assumed a steam pressure of 7 psi (48 kPa). Force A force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. The concept of force makes

2394-421: Is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at

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2508-420: Is also used in many places to symbolize brake horsepower. Drawbar power (dbp) is the power a railway locomotive has available to haul a train or an agricultural tractor to pull an implement. This is a measured figure rather than a calculated one. A special railway car called a dynamometer car coupled behind the locomotive keeps a continuous record of the drawbar pull exerted, and the speed. From these,

2622-417: Is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of

2736-460: Is equivalent to a boiler heat output of 33,469 Btu/h (9.809 kW). Present industrial practice is to define "boiler horsepower" as a boiler thermal output equal to 33,475 Btu/h (9.811 kW), which is very close to the original and revised definitions. Boiler horsepower is still used to measure boiler output in industrial boiler engineering in the US. Boiler horsepower is abbreviated BHP, which

2850-450: Is equivalent to a boiler heat output of 33,485 Btu/h (9.813 kW). A few years later in 1884, the ASME re-defined the boiler horsepower as the thermal output equal to the evaporation of 34.5 pounds per hour of water "from and at" 212 °F (100 °C). This considerably simplified boiler testing, and provided more accurate comparisons of the boilers at that time. This revised definition

2964-481: Is in psi, and flow rate is in US gallons per minute. Drilling rigs are powered mechanically by rotating the drill pipe from above. Hydraulic power is still needed though, as 1 500 to 5 000 W are required to push mud through the drill bit to clear waste rock. Additional hydraulic power may also be used to drive a down-hole mud motor to power directional drilling . When using SI units, the equation becomes coherent and there

3078-465: Is needed to pull a drawbar load of 2,025 pounds-force at 5 miles per hour? { P } h p = 2025 × 5 375 = 27. {\displaystyle \{P\}_{\mathrm {hp} }={\frac {2025\times 5}{375}}=27.} The constant 375 is because 1 hp = 375 lbf⋅mph. If other units are used, the constant is different. When using coherent SI units (watts, newtons, and metres per second), no constant

3192-507: Is needed, and the formula becomes P = Fv . This formula may also be used to calculate the power of a jet engine, using the speed of the jet and the thrust required to maintain that speed. Example: how much power is generated with a thrust of 4000 pounds at 400 miles per hour? { P } h p = 4000 × 400 375 = 4266.7. {\displaystyle \{P\}_{\mathrm {hp} }={\frac {4000\times 400}{375}}=4266.7.} This measure

3306-434: Is no dividing constant. where pressure is in pascals (Pa), and flow rate is in cubic metres per second (m ). Boiler horsepower is a boiler 's capacity to deliver steam to a steam engine and is not the same unit of power as the 550 ft lb/s definition. One boiler horsepower is equal to the thermal energy rate required to evaporate 34.5 pounds (15.6 kg) of fresh water at 212 °F (100 °C) in one hour. In

3420-506: Is ordinarily stated in watts or kilowatts. In the United States, the power output is stated in horsepower which, for this purpose, is defined as exactly 746 W. Hydraulic horsepower can represent the power available within hydraulic machinery , power through the down-hole nozzle of a drilling rig , or can be used to estimate the mechanical power needed to generate a known hydraulic flow rate. It may be calculated as where pressure

3534-481: Is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of m {\displaystyle m} will experience a force: F = m g . {\displaystyle \mathbf {F} =m\mathbf {g} .} For an object in free-fall, this force

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3648-397: Is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If Δ x {\displaystyle \Delta x}

3762-515: Is the coefficient of kinetic friction . The coefficient of kinetic friction is normally less than the coefficient of static friction. Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and do not stretch. They can be combined with ideal pulleys , which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action–reaction pairs so that if two objects are connected by an ideal string, any force directed along

3876-432: Is the mass and v {\displaystyle \mathbf {v} } is the velocity . If Newton's second law is applied to a system of constant mass , m may be moved outside the derivative operator. The equation then becomes F = m d v d t . {\displaystyle \mathbf {F} =m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}.} By substituting

3990-738: Is the approximation of Assuming the third CGPM (1901, CR 70) definition of standard gravity , g n = 9.80665 m/s , is used to define the pound-force as well as the kilogram force, and the international avoirdupois pound (1959), one imperial horsepower is: Or given that 1 hp = 550 ft⋅lbf/s, 1 ft = 0.3048 m, 1 lbf ≈ 4.448 N, 1 J = 1 N⋅m, 1 W = 1 J/s: 1 hp ≈ 745.7 W The various units used to indicate this definition ( PS , KM , cv , hk , pk , k , ks and ch ) all translate to horse power in English. British manufacturers often intermix metric horsepower and mechanical horsepower depending on

4104-410: Is the displacement, the force exerted by an ideal spring equals: F = − k Δ x , {\displaystyle \mathbf {F} =-k\Delta \mathbf {x} ,} where k {\displaystyle k} is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to

4218-410: Is the distance between the two objects' centers of mass and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointed in the direction away from the center of the first object toward the center of the second object. This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the solar system until

4332-468: Is the electromagnetic force, E {\displaystyle \mathbf {E} } is the electric field at the body's location, B {\displaystyle \mathbf {B} } is the magnetic field, and v {\displaystyle \mathbf {v} } is the velocity of the particle. The magnetic contribution to the Lorentz force is the cross product of the velocity vector with

4446-488: Is the force of body 1 on body 2 and F 2 , 1 {\displaystyle \mathbf {F} _{2,1}} that of body 2 on body 1, then F 1 , 2 = − F 2 , 1 . {\displaystyle \mathbf {F} _{1,2}=-\mathbf {F} _{2,1}.} This law is sometimes referred to as the action-reaction law , with F 1 , 2 {\displaystyle \mathbf {F} _{1,2}} called

4560-581: Is the magnitude of the hypothetical test charge. Similarly, the idea of the magnetic field was introduced to express how magnets can influence one another at a distance. The Lorentz force law gives the force upon a body with charge q {\displaystyle q} due to electric and magnetic fields: F = q ( E + v × B ) , {\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right),} where F {\displaystyle \mathbf {F} }

4674-591: Is the momentum of object 1 and p 2 {\displaystyle \mathbf {p} _{2}} the momentum of object 2, then d p 1 d t + d p 2 d t = F 1 , 2 + F 2 , 1 = 0. {\displaystyle {\frac {\mathrm {d} \mathbf {p} _{1}}{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {p} _{2}}{\mathrm {d} t}}=\mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} Using similar arguments, this can be generalized to

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4788-438: Is the momentum of the system, and F {\displaystyle \mathbf {F} } is the net ( vector sum ) force. If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time. In common engineering applications

4902-449: Is the velocity of the object and r {\displaystyle r} is the distance to the center of the circular path and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object is always directed toward the center of the curving path. Such forces act perpendicular to

5016-437: Is typically independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals: F k f = μ k f F N , {\displaystyle \mathbf {F} _{\mathrm {kf} }=\mu _{\mathrm {kf} }\mathbf {F} _{\mathrm {N} },} where μ k f {\displaystyle \mu _{\mathrm {kf} }}

5130-442: Is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward. Newton's contribution to gravitational theory

5244-464: The Aristotelian theory of motion . He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction . Galileo's idea that force is needed to change motion rather than to sustain it, further improved upon by Isaac Beeckman , René Descartes , and Pierre Gassendi , became

5358-400: The action and − F 2 , 1 {\displaystyle -\mathbf {F} _{2,1}} the reaction . Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies. and thus that there is no such thing as

5472-476: The center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system. Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved in any closed system . In a system of two particles, if p 1 {\displaystyle \mathbf {p} _{1}}

5586-749: The kilowatt as the official power-measuring unit in EEC directives. Other names for the metric horsepower are the Italian cavallo vapore (cv) , Dutch paardenkracht (pk) , the French cheval-vapeur (ch) , the Spanish caballo de vapor and Portuguese cavalo-vapor (cv) , the Russian лошадиная сила (л. с.) , the Swedish hästkraft (hk) , the Finnish hevosvoima (hv) ,

5700-501: The 1926 Iowa State Fair , they reported that the peak power over a few seconds has been measured to be as high as 14.88 hp (11.10 kW) and also observed that for sustained activity, a work rate of about 1 hp (0.75 kW) per horse is consistent with agricultural advice from both the 19th and 20th centuries and also consistent with a work rate of about four times the basal rate expended by other vertebrates for sustained activity. When considering human-powered equipment ,

5814-409: The 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines . The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for

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5928-425: The 20th century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet , moon , comet , or asteroid . The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed. The electrostatic force was first described in 1784 by Coulomb as

6042-820: The Estonian hobujõud (hj) , the Norwegian and Danish hestekraft (hk) , the Hungarian lóerő (LE) , the Czech koňská síla and Slovak konská sila (k or ks ), the Serbo-Croatian konjska snaga (KS) , the Bulgarian конска сила , the Macedonian коњска сила (KC) , the Polish koń mechaniczny (KM) ( lit.   ' mechanical horse ' ), Slovenian konjska moč (KM) ,

6156-648: The Ukrainian кінська сила (к. с.) , the Romanian cal-putere (CP) , and the German Pferdestärke (PS) . In the 19th century, revolutionary-era France had its own unit used to replace the cheval vapeur (horsepower); based on a 100 kgf ⋅m/s standard, it was called the poncelet and was abbreviated p . Tax or fiscal horsepower is a non-linear rating of a motor vehicle for tax purposes. Tax horsepower ratings were originally more or less directly related to

6270-486: The acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law . Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass ( m ⊕ {\displaystyle m_{\oplus }} ) and

6384-399: The applied force is opposed by static friction , generated between the object and the table surface. For a situation with no movement, the static friction force exactly balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and

6498-430: The applied load. For an object in uniform circular motion , the net force acting on the object equals: F = − m v 2 r r ^ , {\displaystyle \mathbf {F} =-{\frac {mv^{2}}{r}}{\hat {\mathbf {r} }},} where m {\displaystyle m} is the mass of the object, v {\displaystyle v}

6612-502: The atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids , differences in pressure result in forces being directed along the pressure gradients as follows: F V = − ∇ P , {\displaystyle {\frac {\mathbf {F} }{V}}=-\mathbf {\nabla } P,} where V {\displaystyle V}

6726-428: The constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles , such as the flight of arrows. An archer causes the arrow to move at the start of the flight, and it then sails through the air even though no discernible efficient cause acts upon it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries

6840-406: The constant forward velocity. Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity. A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction . In such a situation,

6954-515: The construct of the electric field to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical " test charge " anywhere in space and then using Coulomb's Law to determine the electrostatic force. Thus the electric field anywhere in space is defined as E = F q , {\displaystyle \mathbf {E} ={\mathbf {F} \over {q}},} where q {\displaystyle q}

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7068-408: The crucial properties that forces are additive vector quantities : they have magnitude and direction. When two forces act on a point particle , the resulting force, the resultant (also called the net force ), can be determined by following the parallelogram rule of vector addition : the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that

7182-417: The definition of acceleration , the algebraic version of Newton's second law is derived: F = m a . {\displaystyle \mathbf {F} =m\mathbf {a} .} Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if F 1 , 2 {\displaystyle \mathbf {F} _{1,2}}

7296-566: The design in a 2015 review, saying, "the controls are wonderfully light, and although not aerobatic, the aircraft has been used by the Tiger Club Display Team for formation flying displays in the UK, since 1959. On 31 August 2019 the Tiger club celebrated 60 years of operating the Turbulent. In 1960, Rollason Turbulent G-APNZ was flown by Prince Philip, Duke of Edinburgh , making the Turbulent

7410-406: The early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light and also provided insight into the forces produced by gravitation and inertia . With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised

7524-652: The early days of steam use, the boiler horsepower was roughly comparable to the horsepower of engines fed by the boiler. The term "boiler horsepower" was originally developed at the Philadelphia Centennial Exhibition in 1876, where the best steam engines of that period were tested. The average steam consumption of those engines (per output horsepower) was determined to be the evaporation of 30 pounds (14 kg) of water per hour, based on feed water at 100 °F (38 °C), and saturated steam generated at 70 psi (480 kPa). This original definition

7638-428: The elements earth and water, were in their natural place when on the ground, and that they stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as

7752-522: The engine's bore size, number of cylinders, and a (now archaic) presumption of engine efficiency. As new engines were designed with ever-increasing efficiency, it was no longer a useful measure, but was kept in use by UK regulations, which used the rating for tax purposes . The United Kingdom was not the only country that used the RAC rating; many states in Australia used RAC hp to determine taxation. The RAC formula

7866-499: The engine. The situation persisted for several generations of four- and six-cylinder British engines: For example, Jaguar's 3.4-litre XK engine of the 1950s had six cylinders with a bore of 83 mm (3.27 in) and a stroke of 106 mm (4.17 in), where most American automakers had long since moved to oversquare (large bore, short stroke) V8 engines . See, for example, the early Chrysler Hemi engine . The power of an engine may be measured or estimated at several points in

7980-403: The equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. When this experiment

8094-568: The everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N) , and force is often represented by the symbol F . Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion . Types of forces often encountered in classical mechanics include elastic , frictional , contact or "normal" forces , and gravitational . The rotational version of force

8208-612: The first and only single-seat aircraft to have been flown by a member of the royal family. In the same year, the same aircraft won the King's Cup air race, flown by John Severne . G-APNZ is subject to a restoration at Derby Airfield . Data from A.J.Jackson, British Civil Aircraft since 1919 Volume 2, Putnam & Company, London, 1974. ISBN   0-370-10010-7 General characteristics Performance Aircraft of comparable role, configuration, and era Plans from LAA.<ref> [1] Horsepower Horsepower ( hp )

8322-424: The force directly between them is called the normal force, the component of the total force in the system exerted normal to the interface between the objects. The normal force is closely related to Newton's third law. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of

8436-417: The force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever ; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his Three Laws of Motion . Dynamic equilibrium

8550-400: The force vectors preserved so that graphical vector addition can be done to determine the net force. As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields

8664-401: The fundamental ones. In such situations, idealized models can be used to gain physical insight. For example, each solid object is considered a rigid body . What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo

8778-484: The horse could pull with a force of 180 pounds-force (800 N). So: Engineering in History recounts that John Smeaton initially estimated that a horse could produce 22,916 foot-pounds (31,070 J) per minute. John Desaguliers had previously suggested 44,000 foot-pounds (59,656 J) per minute, and Thomas Tredgold suggested 27,500 foot-pounds (37,285 J) per minute. "Watt found by experiment in 1782 that

8892-637: The implementation of the EU Directive 80/181/EEC on 1 January 2010, the use of horsepower in the EU is permitted only as a supplementary unit. The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner's Friend : The idea was later used by James Watt to help market his improved steam engine. He had previously agreed to take royalties of one-third of

9006-410: The interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light . This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum . When objects are in contact,

9120-456: The laws governing motion are revised to rely on fundamental interactions as the ultimate origin of force. However, the understanding of force provided by classical mechanics is useful for practical purposes. Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines , but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part, this

9234-450: The limit. In that legend, Watt accepted the challenge and built a machine that was actually even stronger than the figure achieved by the brewer, and the output of that machine became the horsepower. In 1993, R. D. Stevenson and R. J. Wassersug published correspondence in Nature summarizing measurements and calculations of peak and sustained work rates of a horse. Citing measurements made at

9348-404: The load. Such machines allow a mechanical advantage for a corresponding increase in the length of displaced string needed to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine. A simple elastic force acts to return a spring to its natural length. An ideal spring

9462-427: The magnetic field. The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs . These " Maxwell's equations " fully described the sources of the fields as being stationary and moving charges, and

9576-432: The magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right angles to

9690-440: The mass in a system remains constant allowing as simple algebraic form for the second law. By the definition of momentum, F = d p d t = d ( m v ) d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}={\frac {\mathrm {d} \left(m\mathbf {v} \right)}{\mathrm {d} t}},} where m

9804-551: The mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. A modern statement of Newton's second law is a vector equation: F = d p d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},} where p {\displaystyle \mathbf {p} }

9918-438: The motion of all objects using the concepts of inertia and force. In 1687, Newton published his magnum opus, Philosophiæ Naturalis Principia Mathematica . In this work Newton set out three laws of motion that have dominated the way forces are described in physics to this day. The precise ways in which Newton's laws are expressed have evolved in step with new mathematical approaches. Newton's first law of motion states that

10032-644: The natural behavior of an object at rest is to continue being at rest, and the natural behavior of an object moving at constant speed in a straight line is to continue moving at that constant speed along that straight line. The latter follows from the former because of the principle that the laws of physics are the same for all inertial observers , i.e., all observers who do not feel themselves to be in motion. An observer moving in tandem with an object will see it as being at rest. So, its natural behavior will be to remain at rest with respect to that observer, which means that an observer who sees it moving at constant speed in

10146-566: The normal force in action is the impact force on an object crashing into an immobile surface. Friction is a force that opposes relative motion of two bodies. At the macroscopic scale, the frictional force is directly related to the normal force at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction . The static friction force ( F s f {\displaystyle \mathbf {F} _{\mathrm {sf} }} ) will exactly oppose forces applied to an object parallel to

10260-466: The object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction. Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. In real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together

10374-446: The object. A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances . For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that

10488-457: The origin of the engine in question. DIN 66036 defines one metric horsepower as the power to raise a mass of 75 kilograms against the Earth's gravitational force over a distance of one metre in one second: 75 kg × 9.80665 m/s × 1 m / 1 s = 75  kgf ⋅m/s = 1 PS. This is equivalent to 735.49875 W, or 98.6% of an imperial horsepower. In 1972, the PS was replaced by

10602-481: The original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on

10716-409: The other two. When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium . Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero. A body is in static equilibrium with respect to

10830-670: The power generated can be calculated. To determine the maximum power available, a controllable load is required; it is normally a second locomotive with its brakes applied, in addition to a static load. If the drawbar force ( F ) is measured in pounds-force (lbf) and speed ( v ) is measured in miles per hour (mph), then the drawbar power ( P ) in horsepower (hp) is { P } h p = { F } l b f { v } m p h 375 . {\displaystyle \{P\}_{\mathrm {hp} }={\frac {\{F\}_{\mathrm {lbf} }\{v\}_{\mathrm {mph} }}{375}}.} Example: How much power

10944-503: The projectile to its target. This explanation requires a continuous medium such as air to sustain the motion. Though Aristotelian physics was criticized as early as the 6th century, its shortcomings would not be corrected until the 17th century work of Galileo Galilei , who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus . Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove

11058-414: The radius ( R ⊕ {\displaystyle R_{\oplus }} ) of the Earth to the gravitational acceleration: g = − G m ⊕ R ⊕ 2 r ^ , {\displaystyle \mathbf {g} =-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {\mathbf {r} }},} where

11172-621: The same laws of motion , his law of gravity had to be universal. Succinctly stated, Newton's law of gravitation states that the force on a spherical object of mass m 1 {\displaystyle m_{1}} due to the gravitational pull of mass m 2 {\displaystyle m_{2}} is F = − G m 1 m 2 r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},} where r {\displaystyle r}

11286-547: The same amount of work . Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids . Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology . In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of

11400-408: The savings in coal from the older Newcomen steam engines . This royalty scheme did not work with customers who did not have existing steam engines but used horses instead. Watt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute). The wheel was 12 feet (3.7 m) in radius; therefore, the horse travelled 2.4 × 2π × 12 feet in one minute. Watt judged that

11514-423: The size of the engine; but as of 2000, many countries changed over to systems based on CO 2 emissions, so are not directly comparable to older ratings. The Citroën 2CV is named for its French fiscal horsepower rating, "deux chevaux" (2CV). Nameplates on electrical motors show their power output, not the power input (the power delivered at the shaft, not the power consumed to drive the motor). This power output

11628-400: The string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a configuration that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on

11742-410: The theory is used in practice. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach and Walter Noll . Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as " vector quantities ". This means that forces follow

11856-502: The transmission of the power from its generation to its application. A number of names are used for the power developed at various stages in this process, but none is a clear indicator of either the measurement system or definition used. In general: All the above assumes that no power inflation factors have been applied to any of the readings. Engine designers use expressions other than horsepower to denote objective targets or performance, such as brake mean effective pressure (BMEP). This

11970-487: The vector direction is given by r ^ {\displaystyle {\hat {\mathbf {r} }}} , is the unit vector directed outward from the center of the Earth. In this equation, a dimensional constant G {\displaystyle G} is used to describe the relative strength of gravity. This constant has come to be known as the Newtonian constant of gravitation , though its value

12084-412: The velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. More generally, the net force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates

12198-478: Was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses . It was later expanded to include the output power of other power-generating machinery such as piston engines , turbines , and electric motors . The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With

12312-521: Was due to an incomplete understanding of the sometimes non-obvious force of friction and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton . With his mathematical insight, Newton formulated laws of motion that were not improved for over two hundred years. By

12426-521: Was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic . Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame " did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of

12540-531: Was instituted by the Royal Automobile Club and was used to denote the power of early 20th-century British cars. Many cars took their names from this figure (hence the Austin Seven and Riley Nine), while others had names such as "40/50 hp", which indicated the RAC figure followed by the true measured power. Taxable horsepower does not reflect developed horsepower; rather, it is a calculated figure based on

12654-436: Was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as g {\displaystyle \mathbf {g} } and has a magnitude of about 9.81 meters per second squared (this measurement

12768-470: Was sometimes applied in British colonies as well, such as Kenya (British East Africa) . where Since taxable horsepower was computed based on bore and number of cylinders, not based on actual displacement, it gave rise to engines with "undersquare" dimensions (bore smaller than stroke), which tended to impose an artificially low limit on rotational speed , hampering the potential power output and efficiency of

12882-459: Was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion . Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that

12996-499: Was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of G {\displaystyle G} using a torsion balance ; this was widely reported in the press as a measurement of the mass of the Earth since knowing G {\displaystyle G} could allow one to solve for the Earth's mass given the above equation. Newton realized that since all celestial bodies followed

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