Aircraft deplaning and centre of gravity

Hi guys, I have the following so far:

a=30;
b=3;
A=rand(a,b)<0.85;
B=zeros(30,1);
C=A;
D=[A B C]

I am working on aircraft deplaning and how the centre of gravity changes when passengers start to deplane the aircraft. I am simulating the A320 as a 30*7 matrix as it can be seen from the above. I am new to Matlab and would like to know how to perform the following:

1-the 30*7 matrix shows passengers seated in different seats where 1 is and empty seats are zeros. I want to simulate passengers getting off the aircraft and the ones become zeros. 2- a code that can calculate and track where the centre of gravity is and how it changes with respect to time.

Any help is very highly appreciated because I am stuck and need help with it.

Regards,

Answer 1

[Walter Roberson]

I showed simulation code for passengers deplaning at http://www.mathworks.com/matlabcentral/answers/301930-random-numbers-and-matrix#answer_233804

You cannot meaningfully calculate changes in center of gravity without modeling the existing weight distribution of the fixed portions, and the weight of the individual passengers (including luggage), and indeed the dynamic motion of the passengers moving through the plane, taking into account that they never simply deplane one at a time with the others staying seated until the previous is gone.

[Ahmad Al-jelali]

Yah Walter that is 100% correct but because I am new to my Matlab your example was confusing me more because I couldn't get it to run. What I am doing is deplaning the aircraft one by one and seeing how the centre of gravity changes with respect to time. Each passenger weights 77 Kg and has 7 kg luggage with them. Can you please show me how to make the code and run it correctly.

[Walter Roberson]

I have repaired the code in http://www.mathworks.com/matlabcentral/answers/301930-random-numbers-and-matrix#answer_233804

Answer 2

[Image Analyst]

Try this for a start:

a=30;
b=3;
A=rand(a,b)<0.85;
B=zeros(30,1);
C=A;
D=[A B C]
[rows, columns] = size(D)
for row = 1 : rows
  % Empty right side
  D(row, 1:3) = 0;
  % Compute center of gravity
  % I'll let you do this.  Let us know if you can't figure it out.
  [xCOG(row), yCOG(row)] = FindCOG(D)
  % Now empty left side.
  D(row, 5:7) = 0;
  % Compute center of gravity again.
  [x(row), yCOG(row)] = FindCOG(D)
end

I assume you know how to find the center of gravity. It's not hard but let us know if you can't figure that out.

[Ahmad Al-jelali]

Thanks guys for the help I really appreciate it. I know how to calculate the centre of gravity by hand but how do I compute it into the Matlab code assuming each passenger weights 77 Kg and has 7 kg luggage with them and leave the plane one by one using the 30 by 7 matrices.

[Ahmad Al-jelali]

Would it be like this: cog = sum(row .* 1:3) / sum(1;3); would that be correct.

[Image Analyst]

No, of course not. You said you knew. Think again. There is only one thing right about that and that is that the weight does not enter into it, but your formula is wrong. Think harder.

[Walter Roberson]

The weight only does not matter because the weights are equal and no other weight is being taken into account.

While passengers are sitting, their luggage is stored overhead; I estimate about 1.8 meters above the floor. That exerts a torque that needs to be taken into account by extending the model to 3D. But where exactly is the luggage stored? Typically spread out a bit and more over the outermost (window) seat.

[Ahmad Al-jelali]

Centre of gravity would be the sum of passengers left in the row and column divided by the total seats there. Would be CoG = sum(1:3 * 5:7) / sum(1:7). How many lines of coding do I need to code the COG.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/48451-find-the-center-of-gravity-of-an-array

https://www.mathworks.com/matlabcentral/answers/109455-calculate-the-center-of-gravity

[Ahmad Al-jelali]

Hi Image Analyst, I really appreciate your help for helping me with the code for finding the CoG for an aircraft but sadly I was unable to finish the code and I am running into a lot of trouble because I am new to Matlab. Would you guys be able to help me further to help me finish the code and get it to run? Any help is very highly appreciated.

thanks.

[Walter Roberson]

You need to be more specific. You have a certain weight of passenger and a certain weight of luggage. Should the passenger and luggage together be modeled as a point mass as long as they are seated, and both are removed instantaneously when the passenger deplanes? Or is the luggage for a group of three people centered above the window seat belonging to the group of three, so the effective weight of both that seat and another must be modified when the passenger deplanes?

[Image Analyst]

You only need to take the weight into account if the passengers and luggage are different weights. If so, you'll need rand() again to get different passenger weights and different luggage weights. Otherwise, if they're all the same weight, just ignore the weight.

Also, your formula assumes that all seats have people but that is not the case. You set it up so that some seats were empty. So your formula must take that into account. You can't say 1:3 if any of the seats is empty. You can only say that if all seats were occupied, which they weren't.

See if those hints help - that's all I have time for at the moment.

[Walter Roberson]

The weights "cancel out" in the case where the total weight per passenger (including luggage) is always the same and the weights are to be considered as point masses. If the total weight per passenger including luggage is always the same but the luggage is not to be considered to be in the same position as the passenger (e.g., because it is in the luggage compartment) then the weights do matter; if the total weight per passenger is not always the same then the weights do matter.

[Image Analyst]

I'm not sure if you're trying to get us to do the whole thing for you. I've fleshed it out a little more for you by assigning random weights for the passengers and their carry-on luggage.

airlineRows = 30;
airlineHalfSideSeats = 3;
occupancyFactor = 0.85;
% Create a seat map of the left side, middle asile, and right side.
rightSide=rand(airlineRows, airlineHalfSideSeats) < occupancyFactor;
middleAisle=zeros(30,1);
leftSide=rand(airlineRows, airlineHalfSideSeats) < occupancyFactor;
% Now make a seat map for the entire plane by combining them.
passengerMap = [rightSide, middleAisle, leftSide]
[rows, columns] = size(passengerMap)
% Make passenger weights uniformly distributed between 67 and 87:
passengerWeights = 67 + 20 * rand(size(passengerMap)) 
% Make passenger carry-on luggage weights uniformly distributed between 6 and 8:
luggageWeights = 6 + 2 * rand(size(passengerMap)) 
% Zero out empty seats.
passengerWeights = passengerWeights .* passengerMap
luggageWeights = luggageWeights .* passengerMap
timePoint = 1;
for row = 1 : rows
  % First assume that the left side empties first.
  % Start with seat 3, then 2, then 1
  for col = 3 : -1 : 1
    passengerMap(row, 3) = 0; % Empty the aisle seat only, seat #3.
    % Update passenger weight and luggage weight.
    passengerWeights = passengerWeights .* passengerMap
    luggageWeights = luggageWeights .* passengerMap
    % That passenger is now gone.
    % Remaining passengers shift to the right
    % See if you can figure out how to shift the arrays to the right.
    ; % Code.....
    % After the aisle passenger has left, and remaining passengers
    % has shifted right, re-compute center of gravity.
    % I'll let you do this.  Let us know if you can't figure it out.
    [xCOG(timePoint), yCOG(timePoint)] = FindCOG(passengerMap, passengerWeights, luggageWeights)
    timePoint = timePoint + 1;
  end
  
  % Now empty the right side.
  % Start with seat in column 5, then 6, and then finally 7
  for col = 5 : 7
    passengerMap(row, 5) = 0; % Empty the aisle seat only, seat #5.
    % Update passenger weight and luggage weight.
    passengerWeights = passengerWeights .* passengerMap
    luggageWeights = luggageWeights .* passengerMap
    % That passenger is now gone.
    % Remaining passengers shift to the left
    % See if you can figure out how to shift the arrays to the left.
    ; % Code.....
    % After the aisle passenger has left, and remaining passengers
    % has shifted left, re-compute center of gravity.
    % I'll let you do this.  Let us know if you can't figure it out.
    [xCOG(timePoint), yCOG(timePoint)] = FindCOG(passengerMap, passengerWeights, luggageWeights)
    timePoint = timePoint + 1;
  end
end

See if you can finish the simulation by shifting the passengers (the map, the passenger weights, and the carry-on luggage weights) over in the row after the aisle passenger exits, and computing the COG with the random weights applied.

To make it more realistic (and complicated) you'd have to put the aisle passenger into column 4 and march them forward one or more rows as people exit the plane at row 0. But don't worry about that at this early stage. Just get this working first.

To make it fancy and visual, show the passengerMap with imshow() and the COG with plot().

[Ahmad Al-jelali]

WOW, I was not even close to this in any way I need a month to understand this. I was told it's going to be a 3-4 lines coding. thanks guys

[Image Analyst]

Well, half the code is just comments. I don't know who told you 3-4 lines but ask them what the steps were. It is obviously overly simplistic. So is my code, but 3-4 lines -- wow, hard to see how that could even be remotely realistic even in the simplest circumstances.

[Ahmad Al-jelali]

Yah he made it sound so easy when I asked. I will try my best to finish it but what is the best way to learn Matlab.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/8026-best-way-s-to-master-matlab