Messerschmitt Me-262 Schwalbe

Si consideri il primo jet a reazione da combattimento... e immaginate di volare! Ecco la relazione sul Me-262 (cliccate sul titolo del post per scaricarla) con tanto di allegato in MATLAB.

http://digilander.libero.it/Dany_Aerospace/Messerschmitt/Messerschmitt%20Me-262.pdf

http://digilander.libero.it/Dany_Aerospace/Messerschmitt/Me262_Mission.m

Prerequisiti: un minimo di conoscenze di Meccanica del Volo e di MATLAB. Per la Meccanica del Volo sono necessarie un minimo di Matematica (Analisi 1, ma neanche), un po' di Fisica (Meccanica del punto materiale) ed elementi di Aerodinamica. Per il MATLAB... un po' di informatica e conoscenza del linguaggio MATLAB.

Bibliografia (per la Meccanica del Volo):
Anderson, John D. Jr. - Introduction to Flight - McGraw-Hill International Edition
ISBN 007-123818-2

%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Messerschmitt Me-262 %%

%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all

clc

format short g

% Aircraft data

b = 12.50 % wingspan (m)

S = 21.70 % wing area (m^2)

hw = 1.5 % wing height from ground (m)

Wg = 6400*9.8 % gross weight (N)

W = 5000*9.8 % average weight (N)

We = 3800*9.8 % empty weight (N)

cL_max = 2.0 % max lift coefficient

cDo = 0.020 % zero-lift drag coefficient

e = 0.7 % Oswald efficiency factor

AR = b^2/S % aspect ratio

Ta_max = 2*900*9.8 % max trhust available (N)

%% Mission briefing:

%% 1) Takeoff

%% 2) Climb at 6,000 meters

%% 3) Cruise

%% 4) Gliding

%% 5) Landing

%% 1) Calculation of the takeoff distance on runway

rho = 1.225 % air density at sea level

g = 9.8 % gravity acceleration

mr = 0.02 % runway friction coefficient

Vmin = sqrt(2*Wg/(rho*S*cL_max)) % stall speed

Vto = 1.2 * Vmin % takeoff speed

phi = (16*hw/b)^2/(1+(16*hw/b)^2) % coefficient due to ground effect

D = 0.5*rho*(0.7*Vto)^2*S*(cDo+phi*cL_max^2/(pi*AR*e)) % average drag

L = 0.5*rho*(0.7*Vto)^2*S*cL_max % average lift

dto = 1.44*Wg^2/(rho*S*cL_max*g*(Ta_max-D-mr*(Wg-L))) % takeoff distance

%% 2) Calculation of the max rate of climb

h = 6000 % cruise altitude

rho_h = 0.66011 % air density at 6000 meters

for i = 1:300

V(i) = i;

q(i) = rho*V(i)^2/2; % dynamic pressure

cL(i) = Wg/(q(i)*S) ; % lift coefficient

cD(i) = cDo + cL(i)^2/(pi*e*AR); % drag coefficient

Pr_zl(i) = q(i)*S*V(i)*cDo; % power due to zero-lift drag

Pr_id(i) = q(i)*S*V(i)*cL(i)^2/(pi*AR*e); % power due to induced drag

Pr(i) = Pr_zl(i) + Pr_id(i); % power required at sea level

Pa(i) = Ta_max * V(i); % MAX power available at sea level

EoP(i) = (Pa(i) - Pr(i)); % excess of power

RC(i) = (EoP(i))/Wg; % R/C = excess of power / weight

RC_mpm(i) = RC(i) * 60; % meters per minute

RC_mpm_h(i) = RC_mpm(i) * rho_h/rho; % rate of climb at 6000 meters

end

RCmax = max(EoP)/Wg % max rate of climb at sea level

RCmax_mpm = RCmax * 60

RCmax_h = RCmax * rho_h/rho % max rate of climb at 6000 meters

RCmax_h_mpm = RCmax_h * 60

plot (V,Pa, 'r.')

hold on

plot (V,Pr_zl, 'g.')

hold on

plot (V,Pr_id, 'b.')

hold on

plot (V,Pr, 'k.')

grid on

title ('Me-262 - Power required and power available at sea level')

xlabel ('Velocity (m/s)')

ylabel ('Power (W)')

axis ([0 300 0 5e6])

legend ('MAX power available', 'power due to zero-lift drag',...

'power due to induced drag', 'power required')

figure

plot (V,RC_mpm, 'g.')

hold on

plot (V,RC_mpm_h, 'b.')

grid on

title ('Me-262 - Rate of Climb')

xlabel ('Velocity (m/s)')

ylabel ('Rate of Climb (m/min)')

axis ([0 300 0 2000])

legend ('sea level', '6000 meters')

av_RC = (RCmax + RCmax_h)/2 % average rate to climb

av_RC_mpm = av_RC * 60

time = h/av_RC % approx. time to climb

%% 3) Cruise flight

Ta = 0.8 * Ta_max * rho_h/rho % cruise thrust available at 6000 meters

for i = 1:300

V(i) = (i+34)*sqrt(rho/rho_h);

q(i) = rho_h*V(i)^2/2;

Tr_zl(i) = q(i)*S*cDo; % thrust due to zero-lift drag

Tr_id(i) = W^2/(q(i)*S*pi*e*AR); % thrust due to induced drag

Tr(i) = Tr_zl(i) + Tr_id(i); % thrust required

cL(i) = W/(q(i)*S);

cD(i) = cDo + cL(i)^2/(pi*e*AR);

E(i) = cL(i)/cD(i); % aerodynamic efficiency

end

figure

plot (V,Tr_zl, '.g')

hold on

plot (V,Tr_id, '.r')

hold on

plot (V,Tr, '.k')

hold on

plot (V,Ta, '.b')

grid on

axis ([0 300 0 1.5e4])

title ('Me-262 - Thrust required curves at 6000 meters')

xlabel ('Velocity (m/s)')

ylabel ('Thrust (N)')

legend ('thrust due to zero-lift drag','thrust due to induced drag',...

'thrust required', 'thrust available')

figure

plot (V,E, '.')

grid on

axis ([0 300 0 20])

title ('Me-262 - Aerodynamic efficiency')

xlabel (' Velocity (m/s)')

ylabel ('E = cL/cD')

Tmin = min(Tr) % min thrust

Emax = max(E) % max aerodynamic efficiency

VTmin = sqrt(Tmin/(rho_h*S*cDo)) % min thrust (max efficiency) airspeed

VTmin_KPH = VTmin * 3.6

%% 4) Calculation of the max range in gliding flight

theta = atand(1/Emax) % glide angle at max efficiency

range = h * Emax % max range in gliding at 6000 meters

%% 5) Calculation of the landing distance on the grass

Vmin = sqrt(2*We/(rho*S*cL_max)) % stall speed

Vl = 1.3 * Vmin % landing speed

mg = 0.60 % grass + brake friction coefficient

D = 0.5*rho*(0.7*Vl)^2*S*(cDo+phi*cL_max^2/(pi*e*AR)) % average drag

L = 0.5*rho*(0.7*Vl)^2*S*cL_max % average lift

dl = 1.69*We^2/(g*rho*S*cL_max*(D+mg*(W-L))) % landing distance