Math Model


Princliples Math Model Computational Model


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  Appendixes .   Appendix A
  Appendix B
  Appendix C

     =W2 - W2 + SP2 - ratio*F2
     = SP2 - ratio*(W2 - SP2)			inserting W2- SP2 for F2
     = SP2 - ratio*W2 + ratio*SP2		distribution
     = W2/R2 - ratio*W2 + ratio*W2/R2	When solving for R2, it is found that 
SP2 = W2/R2
P2 = (1/R2 - ratio -ratio*R2)*W2/R2	distribution
********
P1 = (1/R1 - ratio -ratio*R1)*W1/R1 	The first stage is the same as the second 
********
W2 = P1					Next we insert P1 for W2
********
"	P2 = (1/R2 - ratio -ratio*R2)* (1/R1 - ratio -ratio*R1)*W!/R2*R1
**************
F = F1 + F2 
   = (W1-SP1) + (W2 - SP2)
  = (W1-W1/R1) + (W2-W2/R2)		substitution
  = (1-1/R1)*W1 + (1-1/R2)*W2		distribution 
  = (1-1/r1)*W1 + (1-1/R2)*P1
						from previous equation
  = (1-1/r1)*W1 + (1-1/R2)* (1/R1 - ratio -ratio*R1)*W1/R1 
"	F= {(1-1/r1) + (1-1/R2)* (1/R1 - ratio -ratio*R1)/R1}*W1 
*******
"	Payload = A*W1			when:
A = (1/R2 - ratio -ratio*R2)* (1/R1 - ratio -ratio*R1) R2*R1
*******
"	Fuel = B*W1 				when:
B = {(1-1/r1) + (1-1/R2)* (1/R1 - ratio -ratio*R1)/R1}
*******
W1 = payload/A
*******
fuel = B*W1
"	Fuel = B*payload/A
The above equations represent our program and the ability to find fuel from payload.

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