Re: need help fast


alex macaskill wrote:
> How would i write this using matlab?

Aside from the fact that you haven't told us how far you've
gotten, you also forgot to post the actual question. You've
got a couple of equations and a lot of hints from your
instructor on how to implement things in Matlab. But
I don't see anywhere here what question you're supposed
to be answering.

> I know its drawn out but i have
> never used the program before and need this done quickly. Thanks for
> the help.

We can't "help" till you ask a question.

> Ra(t+dt)=Ra(t)+Va(t)dt (2)

This looks like a standard time-evolution equation. Given
current position, current velocity, and a time increment,
you use this to calculate the next position.

As your instructor told you, Matlab can represent these
vectors with a single symbol, an array of three elements.

Ra = Ra + Va*dt

will do the above.

> Va=((GAMMA/2pi)iz)x([(Ra-Rb)/((Ra-Rb)^2)]-[(Ra-Rc)/((Ra-Rc)^2)]+[(Ra-R
> d)/((Ra-Rd)^2)])

If some of those things are magnitudes (squared) and cross
products, your instructor has told you the Matlab calls
to calculate those things.

> The span of this jumbo jet is approximately 60m, and the initial
> height of the vortices is assumed to be 100
> m above the runway. Based on a total weight of 4 x 106 N and a
> take-off speed of 67 m/s, the magnitude of
> the circulation is 815 m2/s at sea level, where r = 1.22 kg/m3. The
> remaining computations involve only
> the two vector equations (2) and (3), which require the following
> five basic operations:
> · the vectorial addition and subtraction,
> · computing the magnitude of a vector,
> · the product of a scalar and a vector and,
> · the cross product of two vectors.
>
> These operations are to be performed by calling subprograms vad,
> vsbt, vmag, pdsv, and vcross.

I would follow this instruction and use those calls to implement
those two equations.

> A vector is to be represented in the program as a one-dimensional
> array having three elements, which are
> used to store, in order, the x, y, and z components of that vector.

I would follow this instruction and define your variables in
this format.

> For instance, the unit vector iz, is to be
> given the name UNIVZ in the program,

I would follow this instruction and define UNIVZ to be the unit
vector iz:

UNIVZ = [0 0 1];

> and assigned to it are the three
> values 0, 0, and 1. When vector A
> is added to vector B, the sum of their corresponding elements, that
> is, A(1) + B(1), A(2)+B(2), and
> A(3)+B(3), are first calculated, and the values are stored in the
> three elements of the resultant vector C.
>
> Program Symbol Definition
> B Wingspan of the airplane b, m
> DRA DrA, equal to VA Dt, m
> DT Time increment Dt, s
> GAMMA Magnitude of circulation G, m2/s
> H Initial height h of vortices above runway, m
> m Time step counter
> RA, RB, RC, RD Position vectors rA, rB, rC, rD of the vortex pair and
> their images, m
> RAB, RAC, RAD Vectors rA - rB, rA - rC, and rA- rD, respectively, m
> T Time t, s
> UNIVZ Unit vector along z-axis, iz, m
> VA VA, velocity of the vortex at rA, m/s

I would follow this instruction and use these names for the
variables representing these quantities.

>
> Using the above analysis and program symbols, complete the program,
> compute the trajectory of the vortex
> pair and plot your results.

As you have been given all the pieces and only have a couple
of lines of code to implement, this shouldn't take too long.
We can help you with the plotting.

> A correct result should show that the two vortices first move almost
> vertically downward, with small
> influence from their images because of the large height, and then
> start to spread out as the ground is
> approached. When the distance between the two vortices becomes large,
> their mutual interaction
> diminishes so that each of them moves under the strong influence of
> its own image. During this period
> they move away from each other at a speed of approximately equal to
> G/4pd, where d is the height of the
> vortices above ground. The result should also show that the trailing
> vortices of this airplane will stay in the
> vicinity of the runway for a few minutes.
>
> Comment on the accuracy of your results and validate the obtained
> solution.

"Validate" means checking against something else of known
accuracy. I'm not sure what that would be in this case.
A hand calculation? Something in a handbook?

If you can't get started on a single line of code, I'd
go back to your instructor to get you started.

- Randy

.

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