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We used the basic rocket equation for this project:
v = c ln R
Where:
v = velocity gained by the vehicle during launch
c = the exhaust velocity of the engine
ln R is logR or the natural logarithm of R
R = the mass ration of the spacecraft, defined by
R = takeoff weight/burnout weight or,
R = S + F + P
S + P
S represents the weight of the structure of the rocket
P represents the payload weight
F represents the fuel weight
w is used further in the equation to represent the weights of each stage
Each stage has its own set of variables:
Stage one is represented by S1, P1, F1, v1, w1 and c1
Stage two is represented by S2, P2, F2, v2, w2 and c2; in this case P1 equals w2 because the payload of stage one is all of stage two. The payload (P2) in stage two is the actual payload the rocket is carrying. We then used the above variables and put then in an equation to find fuel when given payload (P2). We set S1 to 0.1(F1) and called the 0.1 "ratio".
The following are our equations and reasons.
P2 + F2 + S2 = W2
P2 = W2 - (F2 + S2)
=W2 - F2 - S2
=W2 - (W2 - SP2) - ratio*F2 SP2 = S2 + P2
F2 = W2 - SP2
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The images used were from the fallowing locations:
www.ender-design.com
www.gifanimations.com
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