Worksheet #7 - Final Project Update Portion

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Final Project Worksheet #7. 

*** Place a comment at the top of your file that describes all the
    help you've received and its source. Also describe who you worked
    with, or who you have helped. Code should be your own, although
    you should work in groups and it is okay to get help on a sticky
    point from another student, but it must be documented. Plagiarism
    will be reported.

*** Name your cpp  lastname_firstname_finalproject.cpp
*** For example, ramsey_doc_finalproject.cpp

Our final project involves computing how much fuel is needed to
achieve certain deltaV given a specific payload. Our work in the
worksheets thus far is leading us towards this task. In this
extension, we'll be extending our program to include and save the
information into arrays. So let's walk through the structure of the
code.

You'll still have a while loop to let the user repeat all the code steps.

You'll still have a for loop to do a number of stages.

But, in worksheet #5, we were capable of asking how many stages were
on the rocket.  Unfortunately, we have to ignore this step in this
worksheet. But we'll add this capability back in during worksheet #8!
For now, assume there are 3 stages that we'll do every time we run the
program.

To keep all the information from our stages, we'll need many
arrays. For now, assume there are 3 stages. Here are the arrays that
we require:

  1) An array for the names of the stages.  
  2) An array for the total mass of the stages.  
  3) An array for the fuel masses of the stages.  
  4) An array for the deltaV of the stages.

Use your functions from Worksheet Update #5 to get the input into the
first 3 arrays and to perform the computation for each stage, but then
store the value into the arrays for later retrieval.

Once complete, find the total sum of the deltaV of all stages. This is
the actual deltaV of the entire spacecraft once all stages are
depleted of fuel.

In addition, find the average total mass and fuel masses of all the
stages. This doesn't have much useful information but it is
interesting and gives more practice with loops and arrays.

For the section outside of the for loop, we were using a loop to
compute the required fuel mass to reach a target deltaV. In that loop,
we incremented the fuel mass by 0.0001. If you still haven't found the
trick to do this very quickly, change this loop to increase the fuel
mass by 1 instead. This will make things much more speedy.

**UPDATE** In addition, any time the fuel mass is increased by 1,
there is an increase in the total mass by an extra .125. So the total
mass actually changes by 1.125 for every 1 of fuel. This total mass
increase is due to a required increase in the storage container
required to hold the fuel mass. Update your function to take this into
account. In the next worksheet, we'll ask the user for how many
payloads they wish to do this computation!


Some variables that we've been using:

 -craft name   	      	   	ex: Challenger
 -total mass			ex: 1995806.42
 -fuel mass  			ex: 1671487.88
 -ISP				ex: 269.1
 -gravity a constant value at 9.80665
 
 -dV				ex: 4300.2
 -target dV			ex: 6500.0
 -payload mass			ex: 27500.1


  dV = gravity * ISP * ln ( total_mass / ( total_mass - fuel_mass ) )

  Remember, payload mass, total mass, fuel mass, target dV, and ISP
   can never be below 0. Also, total mass must be larger than fuel
   mass. Write down any assumptions or decisions you make when you
   complete this process.