Power-to-weight ratio (or specific power or power-to-mass ratio) is a calculation commonly applied to engines Engines come in many types, a common type is a heat engine such as an internal combustion engine which typically burns a fuel with air and uses the hot gases for generating power. External combustion engines such as steam engines use heat to generate motion via a separate working fluid and mobile power sources to enable the comparison of one unit or design to another. Power-to-weight ratio is a measurement of actual performance of any engine or power sources. It is also used as a measurement of performance of a vehicle A vehicle is a device that is designed or used to transport people or cargo. Most often vehicles are manufactured (e.g. bicycles, cars, motorcycles, trains, ships, boats, and aircraft) as a whole, with the engine's power output being divided by the weight (or mass) of the vehicle, to give a metric that is independent of the vehicle's size.

The inverse of power-to-weight, weight-to-power ratio (power loading) is a calculation commonly applied to aircraft, cars, and vehicles in general, to enable the comparison of one vehicle performance to another. Weight-to-power ratio is a measurement of the acceleration capability (potential) of any land vehicle or climb performance of any aircraft or space vehicle.

Power to weight (specific power)

The power-to-weight ratio (Specific Power) formula for an engine (power plant) is the power The dimension of power is energy divided by time. The SI unit of power is the watt , which is equal to one joule per second. Non-SI units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, generated by the engine divided by weight In one of the more common definitions, the weight of an object, often denoted by W, is defined as being equal to the force exerted on it by gravity. This force is the product of the mass m of the object and the local gravitational acceleration g. Expressed in a formula: W = mg. In the International System of Units, the unit of measurement for of the engine as follows:

A typical turbocharged V-8 diesel engine might have an engine power of 330 horsepower (250 kW) and a weight of 835 pounds (379 kg)^[1], giving it a power-to-weight ratio of 0.65 kW/kg (0.40 hp/lb).

Examples of high power-to-weight ratios can often be found in turbines. This is because of their ability to operate at very high speeds. For example, the Space Shuttle The Space Shuttle, part of the Space Transportation System , is an American spacecraft operated by NASA for orbital human spaceflight missions. The first of four test flights occurred in 1981, which were followed by operational flights beginning in 1982. The system is scheduled to be retired from service in 2010 after 134 launches. Major missions's main engines use turbopumps As the name suggests, a turbopump comprises basically two main components: a rotodynamic pump and a driving turbine, both mounted on the same shaft (machines consisting of a pump driven by a turbine engine) to feed the propellants (liquid oxygen and liquid hydrogen) into the engine's combustion chamber. The original liquid hydrogen turbopump is similar in size to an automobile engine (weighing approximately 775 pounds (352 kg)) and produces 72,000 hp Horsepower is the name of several units of measurement of power. The most common definitions equal between 735.5 and 750 watts (53.6 MW The watt is a derived unit of power in the International System of Units (SI), named after the Scottish engineer James Watt (1736–1819). The unit measures the rate of energy conversion. It is defined as one joule per second)^[2] for a power-to-weight ratio of 153 kW/kg (93 hp/lb).

Physical Interpretation

In classical mechanics In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces, instantaneous power The dimension of power is energy divided by time. The SI unit of power is the watt , which is equal to one joule per second. Non-SI units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, is the limiting value of the average rate of change of work done per unit time as the time interval Δt approaches zero.

If the work to be done is rectilinear motion of a body with constant mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties , whose center of mass The center of mass of a system of particles is the point at which the system's whole mass can be considered to be concentrated for the purpose of calculations. The center of mass is a function only of the positions and masses of the particles that compose the system. In the case of a rigid body, the position of its center of mass is fixed in is to be accelerated along a straight line In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by to a speed and angle with respect to the centre and radial In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its inclination angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane of a gravitational field A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms by an onboard powerplant In a motor vehicle, the term powertrain or powerplant refers to the group of components that generate power and deliver it to the road surface, water, or air. This includes the engine, transmission, driveshafts, differentials, and the final drive . Sometimes "powertrain" is used to refer to simply the engine and transmission, including, then the associated kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude to be delivered to the body is equal to

where:

is mass of the body

is speed of the center of mass The center of mass of a system of particles is the point at which the system's whole mass can be considered to be concentrated for the purpose of calculations. The center of mass is a function only of the positions and masses of the particles that compose the system. In the case of a rigid body, the position of its center of mass is fixed in of the body, changing with time.

The instantaneous mechanical pushing/pulling power delivered to the body from the powerplant is then

where:

is acceleration of the center of mass The center of mass of a system of particles is the point at which the system's whole mass can be considered to be concentrated for the purpose of calculations. The center of mass is a function only of the positions and masses of the particles that compose the system. In the case of a rigid body, the position of its center of mass is fixed in of the body, changing with time.

is linear force - or thrust - applied upon the center of mass of the body, changing with time.

is velocity In physics, velocity is the rate of change of displacement . It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system of the center of mass of the body, changing with time.

is torque Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist applied upon the center of mass of the body, changing with time.

is angular velocity In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc. When measured in cycles or of the center of mass of the body, changing with time.

Along an obstacle free positive inclined straight road steering an automobile An automobile, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor. Most definitions of the term specify that automobiles are designed to run primarily on roads, to have seating for one to eight people, to typically have four wheels, and to be constructed principally for the straight ahead, positive linear acceleration will change the speed but not the direction of the vehicle.

The weight In one of the more common definitions, the weight of an object, often denoted by W, is defined as being equal to the force exerted on it by gravity. This force is the product of the mass m of the object and the local gravitational acceleration g. Expressed in a formula: W = mg. In the International System of Units, the unit of measurement for of the body is the force applied to the body to support it at rest in a uniform gravitational field A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms, g. Using Newton's Second Law of Motion Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are:, then

where:

is mass of the body

is gravitational field (acceleration) vector

For large changes in altitude or with a body of mass significant when compared with the gravitational field A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms source mass, then the gravitational field A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms may no longer be considered uniform and therefore g also changes with time.

The torque Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist from the powerplant In a motor vehicle, the term powertrain or powerplant refers to the group of components that generate power and deliver it to the road surface, water, or air. This includes the engine, transmission, driveshafts, differentials, and the final drive . Sometimes "powertrain" is used to refer to simply the engine and transmission, including is accelerating the body to a desired velocity of motion whilst lifting the weight of the body, overcoming friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, or material elements sliding against each other. It may be thought of as the opposite of "slipperiness" through the powerplant and upon the surface of the body (e.g. rolling resistance Rolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tire rolls on a flat surface. It is caused mainly by the deformation of the object, the deformation of the surface, or both. Additional contributing factors include wheel radius, forward speed, surface adhesion, and skin friction), and overcoming other drag In fluid dynamics, drag refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces act in a direction opposite to the oncoming flow velocity. Unlike other resistive forces such as dry friction, which is nearly independent of velocity, drag forces depend on velocity from the motion of the body through fluids (e.g. air, water). The degree in which the deliverable torque associated with the body overcomes the force of gravity Gravitation, or gravity, is one of the four fundamental interactions of nature , in which objects with mass attract one another. In everyday life, gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, thus accounting for upon the body and yields a net positive linear climbing acceleration, or mechanical advantage In physics and engineering, mechanical advantage is the factor by which a mechanism multiplies the force or torque applied to it. Generally, the mechanical advantage is defined as follows:, is then

where:

is mass of the body

is linear speed of the center of mass The center of mass of a system of particles is the point at which the system's whole mass can be considered to be concentrated for the purpose of calculations. The center of mass is a function only of the positions and masses of the particles that compose the system. In the case of a rigid body, the position of its center of mass is fixed in of the body, changing with time.

is powerplant acceleration of the center of mass of the body, changing with time.

is gravitational acceleration of the center of mass of the body.

is force of friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, or material elements sliding against each other. It may be thought of as the opposite of "slipperiness" within powerplant and upon surface of the body.

is force of drag In fluid dynamics, drag refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces act in a direction opposite to the oncoming flow velocity. Unlike other resistive forces such as dry friction, which is nearly independent of velocity, drag forces depend on velocity.

If the friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, or material elements sliding against each other. It may be thought of as the opposite of "slipperiness" and drag In fluid dynamics, drag refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces act in a direction opposite to the oncoming flow velocity. Unlike other resistive forces such as dry friction, which is nearly independent of velocity, drag forces depend on velocity loses are negligible, then the powerplant In a motor vehicle, the term powertrain or powerplant refers to the group of components that generate power and deliver it to the road surface, water, or air. This includes the engine, transmission, driveshafts, differentials, and the final drive . Sometimes "powertrain" is used to refer to simply the engine and transmission, including will convert essentially all its power to either delivering kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude to the body or lifting the weight of the body. To meet this ideal, techniques include low rolling resistance Rolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tire rolls on a flat surface. It is caused mainly by the deformation of the object, the deformation of the surface, or both. Additional contributing factors include wheel radius, forward speed, surface adhesion, tyres, sufficient tyre inflation, obstacle free path, straight asphalt Asphalt ( ˈæs.fɒlt ) is a sticky, black and highly viscous liquid or semi-solid that is present in most crude petroleums and in some natural deposits sometimes termed asphaltum. It is most commonly modelled as a colloid, with asphaltenes as the dispersed phase and maltenes as the continuous phase (though there is some disagreement amongst road, low automotive aerodynamic drag area Automotive aerodynamics is the study of the aerodynamics of road vehicles. The main concerns of automotive aerodynamics are reducing drag , reducing wind noise, minimising noise emission, and preventing undesired lift forces and other causes of aerodynamic instability at high speeds. For some classes of racing vehicles, it may also be important to, well lubricated powertrain In a motor vehicle, the term powertrain or powerplant refers to the group of components that generate power and deliver it to the road surface, water, or air. This includes the engine, transmission, driveshafts, differentials, and the final drive . Sometimes "powertrain" is used to refer to simply the engine and transmission, including and a low loss mechanical transmission A transmission or gearbox provides speed and torque conversions from a rotating power source to another device using gear ratios. In British English the term transmission refers to the whole drive train, including gearbox, clutch, prop shaft , differential and final drive shafts. The most common use is in motor vehicles, where the transmission to run the engine at a speed that corresponds with the engine peak output power. The mechanical advantage In physics and engineering, mechanical advantage is the factor by which a mechanism multiplies the force or torque applied to it. Generally, the mechanical advantage is defined as follows: is then simply

Power is only delivered if the powerplant is in motion, and is transmitted to cause the body to be in motion. It is typically assumed here that mechanical transmission allows the powerplant to operate at peak output power. This assumption allows engine tuning to trade power band The power band refers to the range of operating speeds under which the engine is able to operate efficiently. A typical gasoline automotive engine is capable of operating at a speed of between around 750 and 6000 RPM, but the engine's power band would be more limited. The engine would typically not generate maximum torque until higher operating width and engine mass for transmission complexity and mass. Electric motors do not suffer from this tradeoff. The power advantage or power-to-weight ratio is then

where:

is linear speed of the center of mass of the body.

Power-to-weight ratio is relative to a uniform gravitational field. Normalising to any arbitrary gravitational field yields the specific power or power-to-mass ratio which is then

The power-to-weight ratio is typically calculated from power and mass, although mass is usually measured as weight on a calibrated weighing scale. Values are then expressed in units power per unit force exerted on unit mass in standard gravity. Use of kg (kilogram) and lb (pound) rather than kgf (kilogram-force), SI unit N (Newton) or lbf (pound-force) is common. The value thus expressed is the power-to-mass ratio and not the power-to-weight ratio.

The actual useful power of any traction engine can be calculated using a dynamometer to measure torque and rotational speed. For jet engines there is often a cruise speed and power can be usefully calculated there, for rockets there is typically no cruise speed, so it is less meaningful.

Examples

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