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=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
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P1 = (1/R1 - ratio -ratio*R1)*W1/R1 The first stage is the same as the second
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W2 = P1 Next we insert P1 for W2
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" P2 = (1/R2 - ratio -ratio*R2)* (1/R1 - ratio -ratio*R1)*W!/R2*R1
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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
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" Payload = A*W1 when:
A = (1/R2 - ratio -ratio*R2)* (1/R1 - ratio -ratio*R1) R2*R1
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" Fuel = B*W1 when:
B = {(1-1/r1) + (1-1/R2)* (1/R1 - ratio -ratio*R1)/R1}
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W1 = payload/A
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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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