Question

Now break the rocket into two equal stages, with each stage containing half the propellant and half the structure of Part 1 (i.e., 50,000 kg of propellant and 5000 kg of structure in each stage). The 5000 kg of payload goes on the front of the second stage. Note: A diagram might be useful to help you keep track of the various quantities. Make sure you are very clear in your work about what variables correspond to what quantities. Remember that mf of the first stage includes the first stage structure, but mi of the second stage does not include the first stage structure, since that is lost during staging. Calculate ΔV from the first stage in m/s: unanswered Calculate ΔV from the second stage in m/s: unanswered Add the two values of ΔV together to get ΔVtotal in m/s for the two-stage rocket: unanswered How much extra ΔV in m/s is obtained by the two-stage rocket as compared with the single-stage rocket?

Answer 1

Answer:

Now break the rocket into two equal stages, with each stage containing half the propellant and half the structure of Part 1 (.e., 50,000 kg of propellant and 5000 kg of structure in each stage). The 5000 kg of payload goes on the front of the second stage. Note: A diagram might be useful to help you keep track of the various quantities. Make sure you are very clear in your work about what variables correspond to what quantities. Remember that my of the first stage includes the first stage structure, but m, of the second stage does not include the first stage structure, since that is lost during staging. Calculate AV from the first stage in m/s: Calculate AV from the second stage in m/s: Add the two values of AV together to get AViotal in m/s for the two-stage rocket: How much extra AV in m/s is obtained by the two-stage rocket as compared with the single-stage rocket? Date Subject Propellent mass fraction mprop mtotal mprap a 1000 00 kg motel ut Se r dard u mpa7laad 5000 +1000O + 100000 = 11500og 100000 0.87 PYopetlent mass froction 1U5000 payload fraction mpa7lond 5000 mtotas 115 000 O.04 DV from Tsiolkovsky rocket ean ma ss of stag iwhen al) psopelPent has busnt initial massof stage i -Dn AV= Veメ mitad-mpr goxIsp -In mpta J15000-100 000 9.81x 45ox -en 115000 Av e 8991. 81 mls

Answer 2

Answer:

2519 m/s

7910 m/s

10429 m/s

1437 m/s

Explanation:

In the first stage, the initial and final masses are:  

mi1=mprop1+mprop2+mstruct1+mstruct2+mpayload  

mf1=mprop2+mstruct1+mstruct2+mpayload

Substituting these quantities into the Rocket Equation gives:  

ΔV=g0 x Isp  ln(mi1/mf1)

In the second stage, the initial and final masses are:  

mi2=mprop2+mstruct2+mpayload  

mf2=mstruct2+mpayload

Substituting these quantities into the Rocket Equation gives:  

ΔV=g0 x Isp  ln(mi2/mf2)

Subtracting the single-stage ΔV value from the two-stage ΔV value, we see that there is an additional ΔV of (10429-8992 = 1437 m/s). This result confirms the importance of rocket staging.