Advance ratio
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In aeronautics and marine hydrodynamics, the ''advance ratio'' is the ratio of the freestream fluid speed to the propeller,
rotor Rotor may refer to: Science and technology Engineering * Rotor (electric), the non-stationary part of an alternator or electric motor, operating with a stationary element so called the stator *Helicopter rotor, the rotary wing(s) of a rotorcraft ...
, or
cyclorotor A cyclorotor, cycloidal rotor, cycloidal propeller or cyclogiro, is a fluid propulsion device that converts shaft power into the acceleration of a fluid using a rotating axis perpendicular to the direction of fluid motion. It uses several blades wi ...
tip speed. When a propeller-driven vehicle is moving at high speed relative to the fluid, or the propeller is rotating slowly, the advance ratio of its propeller(s) is a high number; and when it is moving at low speed, or the propeller is rotating at high speed, the advance ratio is a low number. The advance ratio is a useful non-dimensional velocity in helicopter and propeller theory, since propellers and rotors will experience the same angle of attack on every blade airfoil section at the same advance ratio regardless of actual forward speed. It is the inverse of the
tip speed ratio 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 speed of the wind, v. The tip-speed ratio is related to efficiency, with the optimum varying with blade design. Higher ...
used for wind turbines.


Mathematical definition


Propellers

The advance ratio J is a non-dimensional term given by:Prof. Z. S. Spakovszky


'' MIT turbines'', 2002
Thermodynamics and Propulsion, main page
/ref> :J = \frac, where :


Helicopter rotors and cyclorotors

The advance ratio μ is defined as: : \mu = \frac, where :


Significance


Helicopters

Single rotor helicopters are limited in forward speed by a combination of sonic tip speed and
retreating blade stall Retreating blade stall is a hazardous flight condition in helicopters and other rotary wing aircraft, where the retreating rotor blade has a lower relative blade speed, combined with an increased angle of attack, causing a stall and loss of lift ...
. As the advance ratio increases, the relative velocity experienced by the retreating blade decreases so that the tip of the blade experiences zero velocity at an advance ratio of one. Helicopter rotors pitch the retreating blade to a higher angle of attack to maintain lift as the relative velocity decreases. At a sufficiently high advance ratio, the blade will reach the stalling angle of attack and experience retreating blade stall. Specially designed airfoils can increase the operating advance ratio by utilizing high lift coefficient airfoils. Currently, single rotor helicopters are practically limited to advance ratios less than 0.7.


Propellers

The advance ratio allow to calculate the performance of the propeller for any flight conditions. For a specific propeller geometry, charts can be used, providing the traction coefficient Kt and the torque coefficient Kq given as a function of the advance number J. These dimensionless numbers allows to calculate the actual
thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that sys ...
&
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
of the propeller. These coefficients are experimentally determined for boat by: by so-called open water tests, usually performed in a cavitation tunnel or a towing tank. The
thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that sys ...
can be calculated as: T = where : The
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
can be calculated as: Q = where :


Relation to tip speed ratio

The advance ratio is the inverse of the
tip speed ratio 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 speed of the wind, v. The tip-speed ratio is related to efficiency, with the optimum varying with blade design. Higher ...
, \lambda , used in wind turbine aerodynamics: : \mu = \lambda^. In operation, propellers and rotors are generally spinning, but could be immersed in a stationary fluid. Thus the tip speed is placed in the
denominator A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
so the advance ratio increases from zero to a positive non-infinite value as the velocity increases. Wind turbines use the reciprocal to prevent infinite values since they start stationary in a moving fluid.


See also

*
Axial fan design An axial fan is a type of fan that causes gas to flow through it in an axial direction, parallel to the shaft about which the blades rotate. The flow is axial at entry and exit. The fan is designed to produce a pressure difference, and hence forc ...
*
Retreating blade stall Retreating blade stall is a hazardous flight condition in helicopters and other rotary wing aircraft, where the retreating rotor blade has a lower relative blade speed, combined with an increased angle of attack, causing a stall and loss of lift ...
* Helicopter rotor * Slowed rotor *
Aircraft propeller An aircraft propeller, also called an airscrew,Beaumont, R.A.; ''Aeronautical Engineering'', Odhams, 1942, Chapter 13, "Airscrews". converts rotary motion from an engine or other power source into a swirling slipstream which pushes the propeller ...


Notes

{{Reflist


External links


Propeller Aircraft Performance and The Bootstrap Approach


Aerospace engineering