Search results
The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... more
All wind turbines operate with a yaw error. In this case an extreme yaw error of 30 degrees is assumed. The flapwise blade root bending moment due to that ... more
Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to produce electrical power, windmills for mechanical ... more
A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheel energy storage works by accelerating a rotor to a very high ... more
Rotating unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass, or rotor, is said to be out of balance when its center ... more
Rotating unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass, or rotor, is said to be out of balance when its center ... more
In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more
A rotary variable differential transformer (RVDT) is a type of electrical transformer used for measuring angular ... more
A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheels have a significant moment of inertia and thus resist changes ... more
A stepper motor or step motor or stepping motor is a brushless DC electric motor that divides a full rotation into a number of equal steps. The ... more
The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.
The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)
Strategy
Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.
Solution for (a)
We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find Er . The angular velocity ω for 1 r.p.m is
and for 300 r.p.m
The moment of inertia of one blade will be that of a thin rod rotated about its end.
The total I is four times this moment of inertia, because there are four blades. Thus,
and so The rotational kinetic energy is
Solution for (b)
Translational kinetic energy is defined as
To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is
Solution for (c)
At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:
Discussion
The ratio of translational energy to rotational kinetic energy is only 0.380. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The 53.7 m height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.
Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to produce electrical power, windmills for mechanical ... more
The formula for the calculation of the angular velocity of a wind turbine rotor. The definition is according to the IEC 61400-2. ... more
The tip-speed ratio, λ, or TSR for wind turbines is the ratio between the tangential speed of the tip of a blade and the actual ... more
In turbomachinery, the slip factor is a measure of the fluid slip in the impeller of a compressor or a turbine, mostly a centrifugal machine. Fluid slip is ... more
An approximate formula given by Balje for radial-tipped (β2=900) blade impellers
... more
A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more
In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more
In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more
In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more
In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more
In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
Counter-electromotive force (abbreviated counter EMF or simply CEMF), also known as back electromotive ... more
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
A pendulum is a mass that is attached to a pivot, from which it can swing freely. Pendulum consisting of an actual object allowed to rotate freely around a ... more
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
...can't find what you're looking for?
Create a new formula
A typical small rescue helicopter, like the one in the Figure below, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades. (c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?