Engineering 25
Prob 2.41
AirCraft
Separation
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
P2.41 MidAir Collision(?)
 The position and velocity of
two AirCraft, A & B, are
shown as below
y
yB
D
vy
x
vx
xA
 AirCraft Position at 1pm
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
P2.41 Close Miss
 Goals for P2.41
a) Plot D vs. t until D reaches
the MINIMUM VALUE
b) Use the roots command to
find t such Dfirst = 30 mi
y
yB
D
vy
x
vx
xA
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
P2.41 GamePlan
 This is a PARAMETRIC
Problem
 TIME is the INDEPENDENT
variable
• For each moment in time, xA
and yB
• Thus for every value of t we
can calc xA and yB
• Then us Pythagorus to find
Dmin
• Finally, use the roots the
command to solve the
Pythagorean Quadratic Eqn
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
410 mph @ 160mph
Time Difference
At Start
800 mi @ 320mph
410 mph @ 160mph
A ½-Hour Later
800 mi @ 320mph
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
MATLAB CODE
(May have BOBBY TRAPS)
% Bruce Mayer, PE
% ENGR25 * 04ep10
% AirCraft NearMiss * AirCraft_NearMiss_Prob2_41_1109.m
%
%
% Find tmax using given speeds & distances
tmax = max(320/800, 160/410)
%
% divide guessed tmax in t0 500 pieces
t = linspace(0, tmax, 500);
%
% Calx xA & yB based on t, the starting-positions and speeds
xA = 800 - 320*t;
yB = 410 - 160*t;
%
% Calc the corresponding 500 D values with pythagorus
xsq = xA.^2; ysq = yB.^2; % sq xA & yB
SumxA = sum(xsq); SumyB = sum(ysq); % sum the x & y values
SumTot = SumxA + SumyB; % add the sums
D = sqrt(xA.^2 + xA.^2);
%
% Now find value & index (address) for minimum D
[Dmin, DminIndex] = min(D)
% next the value of t that corresponds to Dmin
tmin = t(DminIndex)
%
% Now Plot The Separation distance vs time
plot(t,D, 'linewidth', 3), xlabel('Hours after 1pm');,...
ylabel('AirCraft Separation Distance (mi)'),grid
%
% PART B
% must solve pythagorean eqn
% => 30 = [xA^2 + yB^2]
% subbing for t
%=> 30 = [(500-320t)^2 + (410-160t)^2]
%
% Can use conv command to square polynomial
PA = conv([-320 800], [-320,800])
PB = conv([-160 410], [-160,410])
Ptot = PA + PB
%
% Now subtract 900 from both sides then use roots
D30 = roots(Ptot - [0 0 -900])
%
%
%
% Now that we know the "close miss time is 2.4325 hrs Let "zoom in" on the
% plot
tz = linspace(2.4, 2.65, 500);
%
% Calx xA & yB based on t, the starting-positions and speeds
xAz = 800 - 320*tz;
yBz = 410 - 160*tz;
%
% Calc the corresponding 500 D values with pythagorus
xsqz = xAz.^2; ysqz = yBz.^2; % sq xA & yB
SumxAz = sum(xsqz); SumyBz = sum(ysqz); % sum the x & y values
SumTotz = SumxAz + SumyBz; % add the sums
Dz = sqrt(yBz.^2 + yBz.^2);
%
% Now find value & index (address) for minimum D
[Dminz, DminIndexz] = min(Dz)
% next the value of t that corresponds to Dmin
tminz = tz(DminIndexz)
%
%
disp('Getting ready to show ZOOMED plot"; Hit Any Key to continue')
pause
%
% Now Plot The Separation distance vs time
plot(tz,Dz, 'linewidth', 3), xlabel('Hours after 1pm');,...
ylabel('AirCraft Separation Distance (mi)'),grid
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx
Engineering-25: Computational Methods
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Bruce Mayer, PE
E ENGR-25_Chp2_AirCraft_Separation_.pptx