Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Acceleration to reach space

  1. Oct 18, 2016 #1
    The distance from the earths surface to the boundary of space is 100km. What i was wondering is how to calculate the acceleration you would need, incorporating air resistance and gravity to travel this distance. If you were being launched by a canon.

    So the initial acceleration, if someone knows the formulas that you could use that would be awesome, thanks! :)
     
  2. jcsd
  3. Oct 18, 2016 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try googling for "escape velocity".
     
  4. Oct 18, 2016 #3

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Google escape velocity

    [edit] Ha !

    Note that it's not a matter of acceleration: a simple ##g## is enough to get started
     
  5. Oct 18, 2016 #4

    russ_watters

    User Avatar

    Staff: Mentor

    If you are using a cannon, the acceleration is a function of the length of the barrel.
     
  6. Oct 18, 2016 #5

    jbriggs444

    User Avatar
    Science Advisor

    If the cannon is 100 km in height, one can call it an "elevator" and use negligible acceleration.
     
  7. Oct 18, 2016 #6

    Bystander

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

  8. Oct 18, 2016 #7
    If you are actually thinking of sending humans up that way, forget it. Suppose you had a 100 meter long cannon. Escape velocity is about 40,000 km/hr or about 11 km/second. It would take at least twice that velocity out the cannon to get to escape velocity because of atmospheric friction. Lets suppose you could achieve escape by doubling the cannon velocity to 22 km/second you would need to get to in 100 meters. The formula says it would take about 2000 g and the time in the cannon would be about 1/10th of a second. Of course, if a human was inside, she would be a mass of bloody skin and bones at the bottom of the vehicle and be quite dead before leaving the cannon.

    But if you did 2000 g's for 1/10th of a second you would be up to about 80,000 km/hr in 100 yards. That would be double escape velocity and you would also have to have extremely good insulation to keep from burning up the craft before it ever reached 100 km.

    Not many electronic boxes can take 2000 g's either. You could imagine sending fruit up that way, it would puree itself all over the bottom of the craft.

    You could certainly send metal that way or other materials but not anything you want to be alive when it leaves the cannon.

    Which is why they use very large rockets which limits acceleration to about 3 g's so humans can survive entry into orbit.
     
  9. Oct 18, 2016 #8
    I was wondering how to do the math because you would half to be in a constant state of acceleration. Wondering how to do that math taking gravity and air resistance into account.

    Also isn't escape velocity the minimum velocity you would need to leave earth implying a constant velocity. Im taking about the velocity it would take with one single push that it would take to leave earth.


    Thanks every one for the replies !
     
  10. Oct 18, 2016 #9

    jbriggs444

    User Avatar
    Science Advisor

    1. Set up a differential equation which includes air resistance as a function of altitude and velocity and gravity as a function of altitude.
    2. Solve said equation.

    The air resistance will depend on the size and shape of your projectile. Gravity will depend on its mass.

    It is likely to be a difficult equation to solve. So a numerical approach may be easier. Solve the problem in time-reversed fashion. Drop the projectile at zero velocity at the edge of the atmosphere and iterate backwards in time as air resistance and gravity both accelerate it toward the Earth. Read out the final velocity just prior to impact.
     
  11. Oct 18, 2016 #10

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You would not necessarily have to be in a constant state of acceleration (at least: not upwards ..). Witness the term escape velocity. But, just for assistance purposes, are you familiar with the basic equations for projectile trajectories ? SUVAT and such ?
     
  12. Oct 19, 2016 #11
    But that will give you the terminal velocity of free falling object, quite a bit lower than escape velocity (by a factor of approx. 25)

    from: https://www.grc.nasa.gov/www/k-12/airplane/termv.html
     
  13. Oct 19, 2016 #12

    jbriggs444

    User Avatar
    Science Advisor

    We are not asked for escape velocity, but only the velocity to reach "the boundary of space". Escape velocity is irrelevant to the question at hand.
     
  14. Oct 19, 2016 #13

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Good point. Actually, post #1 asks for an acceleration -- which we transmogrified to velocity. Once poster understands escape velocity, the step to velocity to reach 100 km is a small step for man ...
     
  15. Oct 19, 2016 #14

    jbriggs444

    User Avatar
    Science Advisor

    Right. Calculating required acceleration in the cannon barrel is easy if you know the muzzle velocity (and barrel length, as @russ_watters has pointed out).
     
  16. Oct 19, 2016 #15
    I was asking the question for the math point of view i know that its not escape velocity. I was asking with in 100km for an example, because i wanted to account for air resistance. I don't know the math of how to determine the initial velocity well accounting for an air resistance. That will be reduced as you go higher. Same with the variable of gravity.

    Yes.. don't see how i could use those. In grade 12 so my knowledge is limited.

    Thanks every one !
     
  17. Oct 19, 2016 #16

    jbriggs444

    User Avatar
    Science Advisor

    Do you feel that you know enough to attempt a calculation assuming a fixed acceleration of gravity and negligible air resistance?
     
  18. Oct 19, 2016 #17
    Yes.
     
  19. Oct 19, 2016 #18

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Come to think of it, gravity at 100 km isn't much less than at 0 km height (100 km is only 1/60 th of earth radius). So if you keep g constant things will simplify considerably. Ignoring air resistance, the SUVAT equations (or an energy balance) give you a value (1.4 km/s) to start with.

    Then, using trial and error you could take air drag into account (my estimate: a hefty increase in velocity required) to work towards a ground-level muzzle velocity.

    Biggest (range) guns built had 140 km horizontal range, so the odds you can build something that shoots upwards to 100 km aren't favorable. Methinks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Acceleration to reach space
  1. Acceleration in space? (Replies: 7)

Loading...