Item 1117

OTHER: Aerodynamics - Rotor Theory - Momentum Method

This is just the single rotor calculations which are developed further in the twin rotor pages. It is probably temporarily here

Power:

P = Tv_ind ≡ Tv_hov = T√(T/2ρA_S)= (2T^3/2)/(√2ρA_S) = 2ρA_Sv_ind³ [Source ~ PHA p.41]

A_S is the area of a single disk.

v_hov is the induced velocity in hover.

FORM: Momentum Method ~ Code

Hover:

Public Sub Hover()

'Calculation of info for hovering.

On Error GoTo hover_Err

''DL = Forms![Helicopter].Form![DL] 'Disk loading

Me!DL = GW / AT 'I am going with the Total Disk Area for the momentum method; as per Prouty.

'and the Effective disk area for the Blade element.

Me!vv1hov = Sqr((1 / (2 * rho))) * Sqr(Me!DL) 'Induced velocity at rotor disk. [Ref: RWP1, p. 4 & RWA, book I, p. 52, (2.13)]

Me!P = hp_by_momentum_method(GW) 'Power [hp]

Me!PLh = GW / Me!P 'Thrust or Weight per horsepower in hover.

'## DOES THE FOLLOWING LINE SERVE ANY PURPOSE??

mm = rho * AT * Me!vv1hov 'Mass flux through the disk. Used in blade_element_moment_of_inertia()

hover_Exit:

Exit Sub

hover_Err:

MsgBox Err.Description

Resume hover_Exit

End Sub

_______________________

Public Function hp_by_momentum_method(GW As Single) As Single

' Required horsepower; by momentum method. [Ref: RWP1, p. 7 & RWA, book I, p. ??, (2.??)]

Dim T As Single ' Thrust [lb]

Dim DV As Single ' Drag - Vertical

Dim hpi As Single ' Induced horsepower

Dim hpact As Single ' Actual horsepower

On Error GoTo hp_by_momentum_method_Err

DV = 0.3 * PA * Me!DL ' Drag-Vertical is 30% of projected area (plan view of fuselage under downwash) times disk loading.

T = (1 + (DV / GW)) * GW

hpi = (T * Sqr(Me!DL / (2 * rho))) / 550

hpact = hpi / FM ' Actual hp is induced hp divided by figure of merit.

hp_by_momentum_method = hpact

hp_by_momentum_method_Exit:

Exit Function

hp_by_momentum_method_Err:

MsgBox Err.Description

Resume hp_by_momentum_method_Exit

End Function

Vertical:

 States: Climb, Descent and Vortex ring.

Forward:

Notes:

Froudes' Momentum Theory: (Actuator Disk Theory)

From a PPRuNe Posting:

As an aside;

Momentum Theory is a reasonable method of performing an initial assessment of rotor performance. This is because all single rotors are basically the same except for the nuances such as; twist, taper, etc., plus blade count.

However, IMHO, Momentum Theory totally breaks down when it come to the consideration of multiple, aerodynamically interactive main rotors.

This is why I express my disappointment that Igor led rotorcraft away from the aerodynamically superior twin rotors. It should be noted that virtually all of the research and development followed along behind the single rotor.

Rotorcraft have always been inefficient. However, when electric drives start permeating the fields of transportation the rotorcraft industry must look back to the past for it to move forward.

Dave

The PPRuNe posting on the thread [2007: Centennial of the Helicopter] appears to support the above.

Downloadable Books on Momentum Theory, and more:

· Aerodynamics of the Helicopter: ~ Gessow and Myers

· Helicopter Theory ~ Wayne Johnson

Preamble re Consideration of the Validity of Momentum Theory:

· The idea of BET [blade element theory] was apparently first suggested by Drzewiecki (1892, 1920) for the analysis of airplane propellers …….. At the beginning of twentieth century, there was considerable scientific debate about the theoretical analysis of propellers and helicopter rotors …… [Principles of Helicopter Aerodynamics ~ Leishman]

Induced Power Factor: Induced Power Correction Factor: (Κ)

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Last Revised: 9 October 2012