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= θ_{0}+ r/R θ_{1}= θ_{0 }+ x θ_{1 }

and, C_{D}= 0.0087-0.0216α+ 0.4α^{2 }

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

## a)

The equation of thrust and thrust coefficient is given by,

T= C_{T}* (ρ*A(ω*R)^{2})

Where ρ is density which is given by 0.002378 lbs^{2}/ft^{4,} A is the area of the disk = pi*r^{2 }, ω is the rate of rotation which is denoted by rad/sec and R is the blade radius.

## b)

Resultant rotor torque and torque coefficient expression is given by,

dQ= (D-Lφ)ydy =0

It can be expressed simply as,

C_{T }= TГ/(0.5 ρ_{a}A_{T}V^{2}T)

Where, C_{T }is the coefficient of torque

## c)

The ideal power coefficient C_{p }can be expressed as, C_{P }= P/(0.5 ρ_{a}A_{R}V^{3})

## d)

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

C_{D}= 0.0087-0.0216α+ 0.4α^{2,} the blade twist is θ_{1=}-5^{0 }, 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

## a)

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*r^{2 }(ft^{2})

= 3.14*7.81^{2}*51^{2}

= 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

## b)

h=(T-D/W)V = P_{av}-P_{req }/W

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

## c)

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:

## a)

% 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

%INPUTS

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

%CALCULATED VALUES

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

%percentage

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};

end

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;

end

return

end

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;

end

function out = dCt(lami)

global r sigma Cla AoA

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

end

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## b)

### i)

### ii)

### iii)

### iv)

### V)

# References

Carlile, J., Hendricks, R. and Yoder, D. (1992). *Brush seal leakage performance with gaseous working fluids at static and low rotor speed condtitions*. [Washington, DC]: National Aeronautics and Space Administration.

D’Angelo, M. (1995). *Wide speed range turboshaft study*. [Washington, D.C.: National Aeronautics and Space Administration].

Fratta, D., Puppala, A. and Muhunthan, B. (2010). *GeoFlorida 2010*. [Reston, Va.]: American Society of Civil Engineers.

Frint, H. (1977). *Design Selection Tests for TRAC Retraction Mechanism*. Ft. Belvoir: Defense Technical Information Center.

Haddon, D. and Hughes, T. (1995). *Enhanced warning and intervention strategies for the protection of rotor speed following power failure*. London: Civil Aviation Authority.

Kahl, S. and Aktan, H. (2009). *Condition assessment and methods of abatement of prestressed concrete box-beam deterioration, phase II*. [Lansing, Mich.]: Michigan Dept. of Transportation.

Kolomvatsos, K., Anagnostopoulos, C. and Hadjiefthymiades, S. (2013). *Intelligent technologies and techniques for pervasive computing*. Hershey, Pa.: IGI Global (701 E. Chocolate Avenue, Hershey, Pennsylvania, 17033, USA).

Mace, W. (1993). *Investigation of the aerodynamic environment for an advanced lightweight rotor in forward flight*. Hampton, Va.: National Aeronautics and Space Administration, Langley Research Center.

Ohno, Y. and Fukada, T. (1978). *Heat transfer coefficient at the labyrinth seal of steam turbine rotor*. Tokyo: Central Institute of Electric Power Industry, Energy and Environment Laboratory.

Powell, R. (1959). *Maximum mean lift coefficient characteristics at low tip Mach numbers of a hovering helicopter rotor having an NACA 64**₁A012 airfoil section*. Washington [D.C.]: National Aeronautics and Space Administration.

Raletz, R. (1990). *Basic theory of the helicopter*. Toulouse, France: Cepadues Editions.