INTRODUCTION TO HELICOPTERS Course Presentation on

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INTRODUCTION TO HELICOPTERSCourse Presentation on

• Momentum theory of Vertical Flight
• J.Divahar
• Dept of Aerospace, Indian Institute of Science
• Bangalore, India

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What is a Helicopter Rotor?

• ROTOR ? Rotating wing

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Blade Motion

• Flapping motion
• Lead lag motion
• Pitching motion

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Types of Rotor

• Articulated rotor
• Teetering Rotor
• Hingeless Rotor
• Bearingless Rotor

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Modes of Helicopter Flight

• Vertical flight
• Hover
• Ascending Descending
• Forward
• Level
• Ascending Descending

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Rotor Aerodynamics Analysis Methods

• Momentum theory
• Vortex theory
• Blade element theory
• Combined blade element theory
• Computational fluid dynamics

Actuator disk theories
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Momentum Theory

• Developed for marine propellers by Rankine
  (1865), Froude (1885).
• Extended to include swirl in the slipstream by
  Betz (1920)

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Notations and Non-dimensional Variables
Thrust Coeffiecient CT T/rA(WR)2 Power
Coeffiecient CP P/rA(WR)3 Induced Inflow
Ratio li vi/ WR Total Inflow Ratio ?
(Vvi)/ OR Thrust Loading T/A Power
Loading P/T Blade Loading
T/Ab Solidity Ratio N c /pR
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Momentum Theory - Model

• Rotor is modeled as an actuator disk which adds
  momentum and energy to the flow.
• concerns with the global balance of mass,
  momentum, and energy.
• It does not concern with details of the flow
  around the blades.
• It gives a good representation of what is
  happening far away from the rotor.

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Momentum Theory - Model

• Disk drives the flow through it
• Reaction ? Thrust
• Energy ? Induced Power

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Assumptions

• Disk is of zero thickness
• There is a well defined smooth slipstream
• Flow is incompressible.
• Flow is steady, inviscid, irrotational.
• Flow is one-dimensional, and uniform through the
  rotor disk, and in the far wake.
• There is no swirl in the wake.

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Momentum theory -- Hover

• Mass conservation
• Momentum Conservation

0
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Momentum theory -- Hover

• Energy Conservation

0
Note Same result as for elliptically loaded
fixed wing !
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Momentum theory -- Hover

• Through Bernoullis eqn...
• From station 0 ? 1
• From Station 2 ? 3

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Momentum theory -- Hover

• Pressure always decreases along the slipstream
  except at the rotor
• From station 0 ? 1
• From Station 2 ? 3

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Pressure Velocity variation
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Results
Thrust
Power
Induced Inflow ratio
Basic Characteristic of Helicopters
Power Loading
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Results and Discussions

• The induced power estimate is always less than
  the actual
• Non uniform inflow
• Finiteness of no. of blades
• Swirl in the wake
• Unsteady flow
• Not a detailed analysis
• Tip losses due to vortices
• The induced velocity can be used in blade element
  theory

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Actual difficulties and uncertainties
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Momentum theory -- Ascending Flight

• Mass conservation
• Momentum Conservation

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Momentum theory -- Ascending Flight

• Energy conservation

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Momentum theory -- Ascending Flight
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Momentum theory -- Descending Flight

• The right model should be used in momentum theory
  for every phase !!!
• Descending flight can not be modeled by letting
• V-V in climb model

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Wrong Descent Model
W2v
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Momentum theory -- Descending Flight
Sign Convention Downward is positive v, w, T
? positive (downward) V ? negative (upward)
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Momentum theory -- Descending Flight

• Mass conservation
• Momentum Conservation

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Momentum theory -- Descending Flight

• Energy conservation

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Momentum theory -- Descending Flight
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Flow States in Descending
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Flow States in Descending
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Flow States in Descending
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Flow States in Descending
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Flow States in Descending
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Actual Induced Velocity For Descending
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Blade Element Theory

• Idea ? William Froude in 1878
• Major treatment ? Stefan Drzewiecki between
  1892-1920

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Blade Element Theory -- Model

• Lifting line theory applied to the rotating wing
• Each blade section act as a 2-D airfoil
• The induced angle of attack is provided by the
  momentum theory.
• Relates the characteristics to design variables
  in detail

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Blade Element Theory -- Assumptions

• Stall and compressibility effects are negligible
• Flow is inviscid.
• No free end vortices.
• Lifting line theory ? AR is high
• Necessitates low disk loading
• UNIFORM INFLOW

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Blade Element theory Vertical Flight
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Blade Element theory Vertical Flight
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Blade Element theory Vertical Flight
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Blade Element theory Vertical Flight
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Blade Element theory Vertical Flight
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Blade Element theory Linear Twist
?0 ? pitch at root ?tw? twist rate per unit blade
length (rad)
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Blade Element theory Ideal Twist
?t ? pitch at tip
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Blade Element theory Induced Velocity
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Blade Element theory Induced Velocity
In the same way for Ideally twisted blade,
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Blade Element theory Power Estimation
Induced Power
Profile Power
For untwisted blade with Constant cd
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Figure of Merit

• Factor for comparison of rotors of same disk
  loading