Code not working, velocity comes back the same each time

ive finally got to the point where my code actually runs without bringning back error messages, however now whatever values i plug in my answer comes out the same and the answer seems way too high for the impact velocity of a spacecraft hitting earth. if anyone could please correct this that would be great, thank you :) my code is below

% M = 850;
% As = 5;
% Ap = 150;
% Hs = 150000;
% Hp = 3000;
% U = 0;
promptA = 'What is the mass of the Spacecraftt in Kg? ';
M = input(promptA);
promptB = 'What is the Cross Sectional Area of the Spacecraft in m^2? ';
As = input(promptB);
promptC = 'What is the Cross Sectional Area of the Parachute in m^2? ';
Ap = input(promptC);
promptD = 'What is the Initial Height of the Spacecraft in m? ';
Hs = input(promptD);
promptE = 'What is the parachute deployment height in m? ';
Hp = input(promptE);
promptF = 'What is the initial velocity of the Spacecraft in m/s? ';
U = input(promptF);

%Constants
C=0.7; % Drag Coefficient
Ha=100000; % Height of the Atmosphere in m
Tstep=1; % Time step in seconds


% Initialisation of Increments
i=1;
H(i)=Hs;
V(i)=0;
S(i)=0;
t(i)=0;

% Freefall above the atmosphere

while (i <= length(H) && H(i) > Ha)
    Tstep=1;
    Fd=0;
    g(i)=(40*(10^7))/(6371+H(i));
    a(i)=g(i); 
    V(i+1)=V(i)+(a(i)*Tstep); % Velocity at next i
    S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2); % Displacement at next i
    t(i+1)=t(i)+Tstep; % Time at next incriment
    i=i+1;
    continue
end

% Freefall within the Atmosphere (No parachute)

while (i <= length(H) && H(i) > Hp )
    Tstep=1;
    p(i)=(H(i)/71)+1.4; % Drag Coefficient for Fd
    Fd(i)=(0.5*C*p(i)*As*(V(i)^2)); % Air Resistance
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2);
    t(i+1)=t(i)+Tstep; 
    i=i+1;
    continue
end

% Freefall within the Atmosphere with a parachute

while (i <= length(H) && H(i)> 0)
    Tstep=1;
    p(i)=(H(i)/71)+1.4; % Drag Coefficient for Fd
    Fd(i)=(0.5*C*p(i)*Ap*(V(i)^2)); % Air Resistance
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2);
    t(i+1)=t(i)+Tstep; 
    i=i+1;
    continue
end

display (V(i))

[darova]

Please edit your code according following instructions

No one will input those values

[Oliver Stericker-Taylor]

this wont change that its not working will it though? im currently inputting these values myself as the code needs to show me answers for different parachute heights

[darova]

Yes. It will not change anything. It's for me

[Oliver Stericker-Taylor]

no worries ill put them in for you one sec pal

[Oliver Stericker-Taylor]

M = 850;
As = 5;
Ap = 150;
Hs = 150000;
Hp = 3000;
U = 0;

%Constants
C=0.7; % Drag Coefficient
Ha=100000; % Height of the Atmosphere in m
Tstep=1; % Time step in seconds


% Initialisation of Increments
i=1;
H(i)=Hs;
V(i)=0;
S(i)=0;
t(i)=0;

% Freefall above the atmosphere

while (i <= length(H) && H(i) > Ha)
    Tstep=1;
    Fd=0;
    g(i)=(40*(10^7))/(6371+H(i));
    a(i)=g(i); 
    V(i+1)=V(i)+(a(i)*Tstep); % Velocity at next i
    S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2); % Displacement at next i
    t(i+1)=t(i)+Tstep; % Time at next incriment
    i=i+1;
    continue
end

% Freefall within the Atmosphere (No parachute)

while (i <= length(H) && H(i) > Hp )
    Tstep=1;
    p(i)=(H(i)/71)+1.4; % Drag Coefficient for Fd
    Fd(i)=(0.5*C*p(i)*As*(V(i)^2)); % Air Resistance
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2);
    t(i+1)=t(i)+Tstep; 
    i=i+1;
    continue
end

% Freefall within the Atmosphere with a parachute

while (i <= length(H) && H(i)> 0)
    Tstep=1;
    p(i)=(H(i)/71)+1.4; % Drag Coefficient for Fd
    Fd(i)=(0.5*C*p(i)*Ap*(V(i)^2)); % Air Resistance
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2);
    t(i+1)=t(i)+Tstep; 
    i=i+1;
    continue
end

display (V(i))

[darova]

Thank you. Very generous of you!

Answer 1

[James Tursa]

Lines like this are wrong:

S(i+1)=S(i)+(V(i)*Tstep+0.5*a(i)*Tstep^2); % Displacement at next i

You are double booking the effect of gravity. Once for the V(i)*Tstep (which already includes the gravity effect) and then again for the 0.5*a(i)*Tstep^2. You only need the V(i) part in all three of your loops:

S(i+1)=S(i)+V(i)*Tstep; % Displacement at next i

Also, you never update H(i+1) in your loops. You need to update the height.

Gravity needs to be negative since it is an attractive force. So

g(i) = -(40*(10^7))/(6371+H(i));

And this g(i) calculation needs to be part of every loop. Gravity doesn't stop acting just because you are in the atmosphere.

Finally, I don't see the purpose of testing i <= length(H). Why would you exit the loop if i is greater than length(H)? Get rid of that part of the test and only test on height. If you want to limit the number of iterations, then put that test within the loop and generate an error if it fails. E.g., you could put something like this in each loop

if( i > maxi )
    error('Too many iterations, i > %d',maxi);
end

with an appropriate value of maxi set earlier in your code.

[Oliver Stericker-Taylor]

brilliant thank you, ive changed the S(i+1) values round and put g into each loop. sorry if this sounds really dumb (this is the first time ive used) this but how do i update the H(i+1). ive been left with very little resources to help me learn it so have been struggling to understand peoples answers too haha

[James Tursa]

H(i+1) = H(i) + V(i)*Tstep;

[James Tursa]

Also, the drag force always acts opposite of the velocity direction. I prefer to use abs(v)*v instead of v^2 so that the equation always works regardless of the sign of v. E.g., change this

    Fd(i)=(0.5*C*p(i)*As*(V(i)^2)); % Air Resistance
    a(i)=(g(i)-(Fd(i)/M));

to this

    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;

Same for the last loop.

[Oliver Stericker-Taylor]

thank you, should i put this new value of H(i+1) inside each loop or does it just go before the first loop?

[Oliver Stericker-Taylor]

ive re-input the code like this however am now getting the "index exceeds array elements" error message again

M = 850;
As = 5;
Ap = 150;
Hs = 150000;
Hp = 3000;
U = 0;

%Constants
C=0.7; % Drag Coefficient
Ha=100000; % Height of the Atmosphere in m
Tstep=1; % Time step in seconds


% Initialisation of Increments
i=1;
H(i)=Hs;
V(i)=0;
S(i)=0;
t(i)=0;

% Freefall above the atmosphere

while (i <= length(H) && H(i) > Ha)
    Tstep=1;
    Fd=0;
    g(i)=-(40*(10^7))/(6371+H(i));
    a(i)=g(i); 
    V(i+1)=V(i)+(a(i)*Tstep); % Velocity at next i
    S(i+1)=S(i)+V(i)*Tstep; % Displacement at next i
    t(i+1)=t(i)+Tstep; % Time at next incriment
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

% Freefall within the Atmosphere (No parachute)

while (i <= length(H) && H(i) > Hp )
    Tstep=1;
    g(i)=-(40*(10^7))/(6371+H(i));
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep; 
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

% Freefall within the Atmosphere with a parachute

while (i <= length(H) && H(i)> 0)
    Tstep=1;
    g(i)=-(40*(10^7))/(6371+H(i));
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep;
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

display (V(i))

[James Tursa]

Well, should the height change inside of each loop? Yes, of course. So this line needs to go inside each loop.

[Oliver Stericker-Taylor]

it is in each loop however now im just recieving the same error again

[James Tursa]

Please post your current code.

[Oliver Stericker-Taylor]

thank you, i realise it night be something realluy simple i appreciate your help on this

M = 850;
As = 5;
Ap = 150;
Hs = 150000;
Hp = 3000;
U = 0;
%Constants
C=0.7; % Drag Coefficient
Ha=100000; % Height of the Atmosphere in m
Tstep=1; % Time step in seconds
% Initialisation of Increments
i=1;
H(i)=Hs;
V(i)=0;
S(i)=0;
t(i)=0;
% Freefall above the atmosphere
while (i <= length(H) && H(i) > Ha)
    Tstep=1;
    Fd=0;
    g(i)=-(40*(10^7))/(6371+H(i));
    a(i)=g(i); 
    V(i+1)=V(i)+(a(i)*Tstep); % Velocity at next i
    S(i+1)=S(i)+V(i)*Tstep; % Displacement at next i
    t(i+1)=t(i)+Tstep; % Time at next incriment
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end
% Freefall within the Atmosphere (No parachute)
while (i <= length(H) && H(i) > Hp )
    Tstep=1;
    g(i)=-(40*(10^7))/(6371+H(i));
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep; 
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end
% Freefall within the Atmosphere with a parachute
while (i <= length(H) && H(i)> 0)
    Tstep=1;
    g(i)=-(40*(10^7))/(6371+H(i));
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep;
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end
display (V(i))

[James Tursa]

As I stated before, get rid of the i <= length(H) part of the test. You should have

while (H(i) > Ha)
    :
while (H(i) > Hp)
    :
while (H(i)> 0)

And you have too many lines here:

    a(i) = g(i) + Fd(i)/M;
    a(i)=(g(i)-(Fd(i)/M)); % New Acceleration formula inc. Fd

Get rid of that second a(i) = etc. line.

And in your parachute loop:

    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance

I think that As should be Ap.

[Oliver Stericker-Taylor]

thank you, again though im still getting the same error "index exceeds array elements" did i miss something?

M = 850;
As = 5;
Ap = 150;
Hs = 150000;
Hp = 3000;
U = 0;
%Constants

C=0.7; % Drag Coefficient
Ha=100000; % Height of the Atmosphere in m
Tstep=1; % Time step in seconds

% Initialisation of Increments

i=1;
H(i)=Hs;
V(i)=0;
S(i)=0;
t(i)=0;

% Freefall above the atmosphere

while (H(i) > Ha)
    Tstep=1;
    Fd=0;
    g(i)=-(40*(10^7))/(6371+H(i));
    a(i)=g(i); 
    V(i+1)=V(i)+(a(i)*Tstep); % Velocity at next i
    S(i+1)=S(i)+V(i)*Tstep; % Displacement at next i
    t(i+1)=t(i)+Tstep; % Time at next incriment
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

% Freefall within the Atmosphere (No parachute)

while (H(i) > Hp)
    Tstep=1;
    g(i)=-(40*(10^7))/(6371+H(i));
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep; 
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

% Freefall within the Atmosphere with a parachute

while (H(i)> 0)
    Tstep=1;
    g(i)=-(40*(10^7))/(6371+H(i));
    Fd(i) = -0.5 * C * p(i) * Ap * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep;
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

display (V(i))

[James Tursa]

You are missing your p(i) code in the last two loops. Also look at the fixes suggested by David.

[Oliver Stericker-Taylor]

thanks for your help. i still cant get it to work but thank you anyway

[James Tursa]

I'm still looking at this. There's issues with the gravity and drag forces. I'll let you know what I find out later today ...

[Oliver Stericker-Taylor]

brilliant thank you so much!!

Answer 2

[David Goodmanson]

Hello Oliver,

could you say where you got this problem? I am interesed in finding out since the problem keeps reoccurring on this website. See the link below, where I believe the calculation to be numerically correct.

This is a very badly posed problem, not in terms of what is being asked but in terms of units and dimensions. The expression for g should be

g(i)=(40*(10^7))/(6371+H(i))^2    not   g(i)=(40*(10^7))/(6371+H(i))   as you have it. 

However, in this expression, g is in m/sec^2 but H must be in km. This is not a good idea, rife with the possibility for error.

The expression for p should be

p(i) = -(H(i)/71) +1.4    not   p(i) = (H(i)/71) +1.4    as you have it

since I think you'll agree that air density increasing with height doesn't make sense. Here p is in kg/m^3 as it should be, but again H must be in km. [ The expression is ludicrously inaccurate as a model for air density vs. height in the atmosphere. But for problem purposes it's all right as long as people are aware of it. ]

In the link below, you can see how the signs are worked out and the height checks are done. But that calculation is done with velocity in m's, acceleration in m/sec^2 and height in km. You will see a couple of factors of .001 to make the conversion. That approach is tricky, and it's really better to go with meters everywhere, in which case H is in meters and

g(i) = (40e7)/(6371 +H(i)/1e3)^2      or equivalently    (40e13)/(6371e3 +H(i))^2
and
p(i)  = -(H(i)/71e3) +1.4

Then just go with

V(i+1) = V(i) +a(i)*Tstep;
S(i+1) = S(i) +V(i)*Tstep

at each stage, no conversion factors.

https://www.mathworks.com/matlabcentral/answers/385016-the-spacecraft-free-fall-math-model#answer_422743

[Oliver Stericker-Taylor]

brilliant thank you ill have a go at changing these values over. im a first year mechanichal engineer and this is our maths coursework, ill show you the questions we have as id imagine were all doing the exact same ones. weve been asked to do this with no prior knowledge of matlab and we have no resources to use to learn as were all stuck at home so im guessing everyones struggling with it. im gonna retry with these new values now although i think ill probably put them in wrong again haha, thank you for your help

[Oliver Stericker-Taylor]

im sorry to ask again but can you please explain what is wrong with this code again? ive had multiple people tell me to change things and none of it has worked. i have no background knowledge of matlab so im finding it very difficult to understand people ans what im supposed to be changing, this is my current code and im now very confused as to what is correct and what isn't. this is 60% of my grade and im really stressed as to why i cant get it to work. any help would be you could give would be really helpful. thank you.M = 850;

M = 850;
As = 5;
Ap = 150;
Hs = 150000;
Hp = 3000;
U = 0;

%Constants

C=0.7; % Drag Coefficient
Ha=100000; % Height of the Atmosphere in m
Tstep=1; % Time step in seconds

% Initialisation of Increments

i=1;
H(i)=Hs;
V(i)=0;
S(i)=0;
t(i)=0;

% Freefall above the atmosphere

while (H(i) > Ha)
    Tstep=1;
    Fd=0;
    g(i)=(40e7)/(6371+ H(i)/1e3)^2;
    a(i)=g(i); 
    V(i+1)=V(i)+(a(i)*Tstep); % Velocity at next i
    S(i+1)=S(i)+V(i)*Tstep; % Displacement at next i
    t(i+1)=t(i)+Tstep; % Time at next incriment
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

% Freefall within the Atmosphere (No parachute)

while (H(i) > Hp)
    Tstep=1;
    g(i)=(40e7)/(6371+ H(i)/1e3)^2;
    p(i)=-(H(i)/71e3)+1.4; % Drag Coefficient for Fd
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep; 
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

% Freefall within the Atmosphere with a parachute

while (H(i)> 0)
    Tstep=1;
    g(i)=(40e7)/(6371+ H(i)/1e3)^2;
    p(i)=-(H(i)/71e3)+1.4; % Drag Coefficient for Fd
    Fd(i) = -0.5 * C * p(i) * Ap * abs(V(i))*V(i); % Air Resistance
    a(i) = g(i) + Fd(i)/M;
    V(i+1)=V(i)+(a(i)*Tstep);
    S(i+1)=S(i)+V(i)*Tstep;
    t(i+1)=t(i)+Tstep;
    H(i+1) = H(i) + V(i)*Tstep;
    i=i+1;
    continue
end

display (V(i))

Answer 3

[James Tursa]

So here is a version of your code with the following changes:

Gravity model replaced with the model found here (also note that the sign of gravity in the code is negative):

https://www.vcalc.com/wiki/KurtHeckman/Gravity+Acceleration+by+Altitude

Atmosphere density model replaced with the simple isothermal model found here (using the exp(etc) model instead of truncated Taylor series):

https://www.spaceacademy.net.au/watch/debris/atmosmod.htm

Time step dropped significantly when the parachute opens to account for the large spike in acceleration due to the high velocity. This turns out to be extremely important to keep your simulation stable.

So, only a few changes made to your code, but extremely important ones. With these slight changes, the code seems to work OK and you should be able to manipulate it to answer your homework questions. At least now you can work on getting answers to the specific questions instead of spinning your wheels just getting things to work.

The fundamental problems I found in your latest code were:

1) Incorrect sign on the gravity

2) Incorrect density formula (that 71e3 simply isn't correct even for the truncated Taylor Series version)

3) Way too big of a stepsize, particularly when the parachute opens, to keep the simulation stable.

clear all

M = 850; % mass (kg)
As = 5; % s/c area (m^2)
Ap = 150; % parachute area (m^2)
Hs = 150 * 1000; % initial height (m)
Hp = 3 * 1000; % height at parachute open (m)
U = 0; % initial velocity (m/s)

%Constants

C = 0.7; % Drag Coefficient (dimensionless)
Ha = 100 * 1000; % Height of the Atmosphere (m)
Tstep = 1; % Time step in seconds

% Earth constants
g0 = 9.80665; % standard gravity (m/s^2)
Re = 6371 * 1000; % Earth radius (m)

% Initialisation of Increments

i = 1;
H(i) = Hs;
V(i) = U;
t(i) = 0;

% All units below are (m,kg,s)

% Freefall above the atmosphere

disp('Freefall outside atmosphere')
while (H(i) > Ha)
    Fd(i) = 0;
%    g(i) = -(40e7)/(6371+ H(i)/1e3)^2;
    g(i) = -g0 * (Re / (Re + H(i)))^2;
    a(i) = g(i) + Fd(i)/M;
    V(i+1) = V(i) + a(i)*Tstep; % Update velocity
    H(i+1) = H(i) + V(i)*Tstep; % Update height
    t(i+1) = t(i) +      Tstep; % Update time
    i = i + 1;
    continue
end

% Freefall within the Atmosphere (No parachute)

disp('Inside atmosphere')
while (H(i) > Hp)
%    p(i) = -(H(i)/71e3)+1.4; % Drag Coefficient for Fd
    p(i) = 1.3 * exp(-H(i)/7000);
    Fd(i) = -0.5 * C * p(i) * As * abs(V(i))*V(i); % Air Resistance
%    g(i) = -(40e7)/(6371+ H(i)/1e3)^2;
    g(i) = -g0 * (Re / (Re + H(i)))^2;
    a(i) = g(i) + Fd(i)/M;
    V(i+1) = V(i) + a(i)*Tstep; % Update velocity
    H(i+1) = H(i) + V(i)*Tstep; % Update height
    t(i+1) = t(i) +      Tstep; % Update time
    i = i + 1;
    continue
end

% Freefall within the Atmosphere with a parachute

disp('deploy parachute, changing stepsize');
Tstep = 0.05;
while (H(i)> 0)
%    p(i) = -(H(i)/71e3)+1.4; % Drag Coefficient for Fd
    p(i) = 1.3 * exp(-H(i)/7000);
    Fd(i) = -0.5 * C * p(i) * Ap * abs(V(i))*V(i); % Air Resistance
%    g(i) = -(40e7)/(6371+ H(i)/1e3)^2;
    g(i) = -g0 * (Re / (Re + H(i)))^2;
    a(i) = g(i) + Fd(i)/M;
    V(i+1) = V(i) + a(i)*Tstep; % Update velocity
    H(i+1) = H(i) + V(i)*Tstep; % Update height
    t(i+1) = t(i) +      Tstep; % Update time
    i = i + 1;
    continue
end

disp(V(i))

n = numel(t)-1;
m = 1;

figure;
plot(t(m:n),H(m:n),'.-');
grid on
title('Height')
xlabel('Time (s)');
ylabel('Height (m)');

figure;
plot(t(m:n),V(m:n),'.-');
grid on
title('Velocity')
xlabel('Time (s)');
ylabel('Velocity (m/s)');

figure;
plot(t(m:n),a(m:n),'.-');
grid on
title('Acceleration')
xlabel('Time (s)');
ylabel('Acc (m/s^2)');

[Oliver Stericker-Taylor]

you are a god of the matlab world. if ur ever in manchester i owe you a pint thank you

[Arqam Zaheer]

Hi Oliver Stericker-Taylor. Did you find the solution to this problem?

Can you please share it?

Regards

[James Tursa]

A working code is already posted and shared. Can you tell us what more you need?