1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Space Mechanics

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data

    The dry mass fraction, F when multiplied by the propellant mass gives the dry mass of the vehicle (not counting its payload). This dry mass faction F, is a function of system design and lightness of the materials employed for its construction. So if F = 0.1, a ship carrying 90 tonnes of propellant would have a dry mass of 9 tonnes. If the mass ratio of the system had to be 10 to perform a certain ΔV, this would allow the craft to carry 1 tonne of payload. But if F = 0.11, the dry mass of the system would be 9.9 tonnes and the payload would fall by a factor of 10, to 0.1 tonne. If F = 0.12, the dry mass of the vehicle would be 10.8 tonnes, and the mission would be impossible even without any payload.

    I need help understanding where 0.1 tonne comes from. I know how they got 1 tonne of payload.


    2. Relevant equations

    [itex]\frac{M+P}{P}[/itex]= e[itex]^{ΔV/M}[/itex]

    M = Dry mass of vehicle without payload
    P = Mass of propellant


    3. The attempt at a solution

    Let x = payload

    (9 + 90)/9 - X = 10

    X = 1 tonne

    (9.9 + 90)/9.9 - X = 10

    X = 0.09090909~ tonne
     
    Last edited: Oct 22, 2012
  2. jcsd
  3. Oct 22, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You mean the 0.1T cargo for F=0.01?

    mass ratio has to be 10 to make a delta-vee.
    then a ship with 90T of fuel can still do the delta-vee if the combined dry-mass and cargo-mass is smaller than a certain amount. What is this amount?

    What is the dry-mass for a ship with F=0.01 and 90T of fuel?
    How much does this leave for cargo?
     
  4. Oct 22, 2012 #3
    Sorry, where did you get F=0.01 from? I'm confused.

    The amount of payload for a ship with F=0.1 and 90T of fuel will be 1T.

    I'm not sure where they came up with 0.1T of cargo for a ship with F=0.11 , 90T of fuel , and 9.9T of dry mass.

    The mass ratio is 10 = (M+P)/M right?
     
    Last edited: Oct 22, 2012
  5. Oct 22, 2012 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    F=0.11 is the example given but you seem to have found that confusing. The math is the same for any F. Here's the bit I guessed we were talking about:
    mass ratio = R
    mass of fuel = P
    dry mass = D
    cargo mass = C
    then mass-ratio is R = (P+D+C)/(D+C)

    so for P=90T, D+C=10T to get a mass-ratio: 100/10 = 10
    as a consequence: C = 10-D.

    If you like: since F=P/D, R=[(1+F)P+C]/[FP+C] solve for C
    But the above example does it in 3 steps ... thus:

    1. Given R and P you get D+C.
    2. Given F and P you get D
    3. combine 1 and 2 to get C.
     
  6. Oct 22, 2012 #5


    Does
    [itex]\frac{90T + 9.9T + C}{9.9T + C}[/itex] = 10T ?

    Then solving for C
    ....

    C = 0.1T
     
  7. Oct 22, 2012 #6

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Now you know where that 0.1 comes from?
     
  8. Oct 23, 2012 #7
    Yup, but uh..I'm not entirely sure where 10T comes from.

    Is D+C always going to be 10T when P=90T?


    EDIT:
    Or is it C = 0.1 because the units cancel out. Therefore that's why the Ratio is equal to [(1+F)P+C]/[FP+C].
    Sorry, I think I'm just going around in circles. ._.
     
    Last edited: Oct 23, 2012
  9. Oct 25, 2012 #8

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    There's a bunch of definitions:
    Dry mass, and mass ratio. These are separate.
    The 10T comes from a mass-ratio of 10, when the propellant mass is 90T.
    (You'd think a MR of 10 would mean "10:1" wouldn't you? But it doesn't.)

    Using above notation:
    if M = D+C+P is the total mass of the craft.
    MR = M/(M-P)

    So a 100T ship with MR=10 has P=90T and D+C=10T.

    Rocket design is actually quite complicated and these wee numbers help engineers make design decisions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Space Mechanics
  1. Spacing needed? (Replies: 5)

  2. Forces in space (Replies: 10)

  3. Satellite in space (Replies: 3)

  4. Motion in Space (Replies: 1)

Loading...