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# Local induced velocity distortion factor

## Local induced velocity distortion factor

(OP)
Greetings all,

I'm looking for a way of relating the local induced velocity distortion factor to speed, with an emphasis on low speed flight.

Prouty's 'Helicopter Performance, Stability and Control'  gives v_L = v_1(1+K*cos(phi)) and then sets K = 1 for speeds above 100 knots, K = 0 for hover.  However, I need a way of modelling K's behaviour between the two.

Any thoughts or recommended references?

take care,

-Paul

### RE: Local induced velocity distortion factor

Paul,

The following report was available free on the net.  It is still available, at a price, from NASA Technical Report Server.

NACA Technical Paper 3675 ~ A Survey of Theoretical and Experimental Coaxial Rotor Aerodynamic Research ~ March 1997

It talks briely about the Sikorsky ABC and the reason for the hard landing of the first craft, while traveling at 25-30 knots. It then goes on to discuss the "Glauert coef" 'K' and it references 'Advancing Blade Concept (ABC) Development. A.J Ruddell, May 1976', which you know of.

Dave J.

### RE: Local induced velocity distortion factor

(OP)
Dave - thanks for the further tips!  I should have expected to see you on the forums here. ;)

IRstuff - thanks for the link!  I'll take a look.

I'm rather surprised that relatively little work seems to have been done of wake distortion in low speed flight.  Is this something that just isn't very important in helicopters outside of my application?

-Paul

### RE: Local induced velocity distortion factor

(OP)
Just a quick update for anyone who is interested - here's a what I've found for low speed distortion factors.

"Classical Inflow Models", a powerpoint presentation found at http://www.ae.gatech.edu/~lsankar/AE6070.Spring2004 gives a suscinct model for k, which is very simply

k = 1/2 tan^-1 (mu/lambda) ~= mu/(2*lambda)

This is a straight-line approximation of the wake skew.  The reported low-speed k behaviour in Ruddel does exhibit near-linearity for speeds <20kts.

"Articulated Rotor Blade Flapping Motion at Low Advance Ratio" by Harris has alternative models, but I have yet to get hold of a copy.

By far my favourite model for k sor far is from "Modelling the Mutual Distortions of Interacting Helicopter and Aircraft Wakes" by Whitehouse and Brown:

vL = vi

ie. they simply ignore it for low speeds. :)  Actually, that isn't as great a simplification as might be thought - in low speed flight (mu < 0.01), k is very small.

Thoughts?

### RE: Local induced velocity distortion factor

Numerous Empirical values for K exist. The main reason for different values of K is due to the different methods of modelling it. Chen gives an excellent survey of Inflow models used for flight dynamic simulations "A survey of nonuniform inflow models for rotorcraft flight dynamics and control applications. VERTICA, Vol.14, No. 2-Chen, R.T.N.". It is the effect of the linear variation from the front of the rotor to the rear, that causes the 'hump' in lateral flapping and lateral vibrations at low speed.

%Glauert Model of Induced FLow--%
Xi = atan(ux_disc/uzd_disc); Wake skew angle
K = COLEMAN et al 1945 = tan(Xi/2)
= DREES MODEL 1949 = 4/3*(1-1.8*ux^2)*tan(Xi/2)
= PAYNE 1959 = (4/3*tan(Xi/2))/(1.2+tan(Xi/2))
= BLAKE/WHITE 1979 = sqrt(2)*sin(Xi)
= PITT/PETERS 1981 = (15*pi/32)*tan(Xi/2)
%--------------------------------

### RE: Local induced velocity distortion factor

(OP)
Thanks!  That's just what I'm looking for!  I'll have to find this paper by Chen.

-Paul

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