Rotary Wing Aircraft-MAH_041214_2582_44606

Table of Contents

Task 1: 2

Task 2: 3

Task 3: 5

a) 5

b) 6

c) 6

d) 6

Task: 4. 7

a) 7

b) 8

c) 8

Task 5: 8

a) 8

b) 15

i) 15

ii) 16

iii) 17

iv) 18

V) 19

References. 20

Task 1:

         In this part of the question several kinds of blade elements velocity/ force will be showed which consists of three kinds of conditions such as when the rotor of the helicopter first encounters with the gust, after responding the rotor what effects on rotor on the lift and flapping position and after encountering behaviour of the helicopter.

The below figure depicts the various blade elements of a helicopter after encountering with the gust.

The below diagram showcases the rotor responds in lift and flapping of a helicopter after encountering with the gust.

              After responding of rotor includings lift anf flapping the opposzing forces of the rotor always should be zero. No unbalanced force can occur at the time of steady flight as it always follows the Newton’s Third Law which states that every action has an equal and opposite rectation or forces. As te four forces of the rotor are equal so the sum of the all forces are zero.

Task 2:

In this part of the question several kinds of blade element diagram will be analyzed to reduce the collective pitch at the time of engine failure of the helicopter.

Task 3:

For a helicopter rotor,

Radius = R, blades are b, c is the constant chord and linear twist is given by,

θ= θ0+ r/R θ1= θ0 + x θ1

and, CD= 0.0087-0.0216α+ 0.4α2

In this part of the question several kinds of velocity expressions will be derived.


The equation of thrust and thrust coefficient is given by,

T= CT* (ρ*A(ω*R)2)

Where ρ is density which is given by 0.002378 lbs2/ft4, A is the area of the disk = pi*r2 , ω is the rate of rotation which is denoted by rad/sec and R is the blade radius.


Resultant rotor torque and torque coefficient expression is given by,

dQ= (D-Lφ)ydy =0

It can be expressed simply as,

CT = TГ/(0.5 ρaATV2T)

Where,  CT is the coefficient of torque


The ideal power coefficient Cp can be expressed as, CP = P/(0.5 ρaARV3)


The radius of rotor (R)= 10.5m, rotational speed of the rotor= 250RPM, constant chord length C= 0.5 m, the airfoil lift curve slope is 5.73 rad and drag coefficient is given by

CD= 0.0087-0.0216α+ 0.4α2, the blade twist is θ1=-50 , in this part of the question a graph plot will be designed with the help of above given data. The below graph depicts the plot between thrust coefficient and power coefficient of a rotor.

Task: 4


Force which is required to lift the helicopter is given by= 2300 kg*9.81= 22563N

The area of the blades can be calculated by A= pi*r2 (ft2)

                                                                                = 3.14*7.812*512

                                                                                = 498163.688

Power loading PL= power/area = 391/498163.688

                       = 7.848825*10-4

Trust loading can be calculated by TL= 8.6859*PL(-0.3107)  

                                                     = 4.579

So, lift= TL*power = 35.93


h=(T-D/W)V = Pav-Preq /W

=(17.669-14.81/2300)= 1.24*10^-3


If the rotor RPM is reduced to 325 RPM then the climb rate will be h= (T-D/W)V = (17.669-14.81/2300)*325 =0.403.

Task 5:


%   Blade Element Momentum Theory analysis of a Single Rotor Helicopter

%   In Hover

%   Inputs: -Applied Angle of Incidence of the blade (Angle between the

%           chordline and the horizontal) (deg)

%           -RPM of the rotor

%           -BladeCharacteristics Structure containing:

%               -BChar.Cla  = Cl/Alpha slope of airfoil (1/deg)

%               -BChar.Cd   = Drag Coefficient of blade at Angle of

%                             Incidence

%               -BChar.Nb   = Number of Blades

%               -BChar.c    = Blade Chord Length  (m)

%               -BChar.Rmax = Max Radius of Blade (m)

%               -BChar.Rmin = Root Cutout Length (m)

%           -Number of Radial stations for calculation (n=100 is typical)

%   Outputs: [3×1 Vector, 2×1 Cell]

%               -[Thrust Generated, Power Required, Figure of Merit]

%               -[Radial Locations Vector, Non-Dimensional Inflow Vector]

function [ret,vect] = BEMTsingle(alpha, rpm, BChar, n)

       global Cla sigma AoA rev dr Nb r


    Cla = BChar.Cla;

    Cd = BChar.Cd;          %Drag Coefficient at AoA

    rho = 1.225;            %Density of Air

    Nb = BChar.Nb;          %Number of blades per rotor

    c = BChar.c;            %Blade Chord

    AoA = alpha;            %Angle of attack in degrees

    RPM = rpm;              %RPM

    Rmax = BChar.Rmax;      %Maximum Rotor Radius

    Rmin = BChar.Rmin;      %Root Cut out

    Nr = n;                 %Number of Radial Stations

                            %for calculation


    TipDeflection = 0.08*Cla*AoA;

    NormalR = sqrt((Rmax-Rmin)^2-TipDeflection^2);

    sigma = (Nb*c)/(pi*(Rmax));     %Solidity per rotor

    rev = RPM*(2*pi)/60;            %Radians per second

    dr = 1/Nr;                      %Radial incriment


    r = (dr:dr:1);                  %preallocating the r-range

    Cla = Cla*180/pi;               %Converting 1/deg to 1/rad

    AoA = AoA*pi/180;               %Converting deg to rad

    vz = 0;                         %Nondimensionalised vertical V (zero at the moment)

    Ad = pi*((Rmax-Rmin)^2);        %Disc Area

    laminf = vz*(ones(1,length(r)));

    lam = lam_calc(laminf);

%Calculation of the Coefficients

    dCt_on_dr = dCt(lam);

    Ct = sum(dr*dCt_on_dr);

    dCpo = (sigma*Cd*dr/2)*(r.^3);

    dCpi = dr*(dCt_on_dr.*lam);

    Cp = sum(dCpo + dCpi);

    Thrust = (NormalR/(Rmax-Rmin))*Ct*rho*Ad*((rev*Rmax)^2);

    Power = (NormalR/(Rmax-Rmin))*Cp*rho*Ad*((rev*Rmax)^3);

    FoM = (sum(dCpi))/(((Ct)^(3/2))/sqrt(2));

    ret = [Thrust,Power,FoM];

    vect = {r,lam};


function out = lam_calc(Laminf)

    global Cla sigma AoA r

    out = zeros(1,length(r));   %Preallocating  and initialising

                                %the out vector

    i = 1;

    while i <= 5

        A = (sigma*Cla/16)./(F(out)) – Laminf/2;

        B = (sigma*Cla*AoA/8)*(r./F(out));

        out = sqrt(A.^2 + B) – A;

        i = i + 1;




function out = F(v)

    global Nb r

    f = (Nb/2)*((1-r)./v);

    out = (2/pi)*acos(exp(-f));

    out(length(out)) = out(length(out)-1)/2;


function out = dCt(lami)

    global r sigma Cla AoA

    out = (sigma*Cla/2)*(AoA*(r.^2) – lami.*r);















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