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Simple rocket speed calculation

  • 04-04-2010 4:33pm
    #1
    Registered Users, Registered Users 2 Posts: 90 ✭✭


    I would like to get to understand rocket formulas, not being that great at maths I'll start with something simple.

    If I have a rocket of 1000kg mass and its engine produces 1500kg thrust what speed would it reach in 60 seconds (it's starting from 0 speed, let's ignore gravity, drag and loss of rocket mass due to burning of fuel).

    a = F/m
    1.5 = 1500/1000

    is this 1.5 meters per second, so in 60 seconds it will travle 90 meters, is this right.

    I know speed is measured as velocity can it be determined from the mass and thrust above. Any help or alternative formulas would be apreciated.


Comments

  • Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    'fraid not.

    The net force upwards is 1500g - 1000g = 500g newtons. In this, g is the numerical value of "acceleration due to gravity" = 9.8 approx. (By the way, when you say a thrust of 1500 kg, I'm taking this to be "kilograms force"; the SI unit of force is the newton, and you need to multiply by g to turn kilograms force into newtons.)

    a = F/m = 500g/1000 = g/2 = 4.9 m/s/s.

    That is, its velocity is increasing by 4.9 m/s every second. After 60 seconds, the velocity will be 4.9*60 = 294 m/s.

    By the way, in practice, you couldn't ignore the mass of fuel being lost. As far as I'm aware, a high proportion of a rocket's mass is fuel, and a lot of it gets burned up in the early part of the journey.


  • Registered Users, Registered Users 2 Posts: 1,583 ✭✭✭alan4cult


    It's not rocket science...



















    :D Apologies, I just had to say it!


  • Moderators, Recreation & Hobbies Moderators, Science, Health & Environment Moderators, Technology & Internet Moderators Posts: 94,288 Mod ✭✭✭✭Capt'n Midnight


    By the way, in practice, you couldn't ignore the mass of fuel being lost. As far as I'm aware, a high proportion of a rocket's mass is fuel, and a lot of it gets burned up in the early part of the journey.
    http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

    Only a few 3% or so of the launch mass reaches orbit, which is about the same mass as the fuel used in the first few seconds. Saturn V got 15,000Kg lighter per second.

    By comparison n to get from the moon to lunar orbit you can get 50% of the original mass into orbit. In the case of the 1000Kg rocket the initial gravity drag would only be 1/6th that down here. So your rocket would have maybe 1,333Kg of thrust instead of 500Kg


    equations
    F=ma you know the force and the mass => acceleration
    height=ut + 0.5 at^2 u=initial speed = 0 t=time a= ^^
    speed is just acceleration by time

    in the real world mass changes A LOT , this increases your acceleration unless you throttle back the engines , which then changes your rate of loss of mass , which changes ....
    your acceleration is is limited by how many g the crew / structure can handle
    the thrust from the engines also varies with air pressure being higher in a vacuum


    in the real world air resistance changes , it goes up as you go faster , but goes down as the air gets thinner. Again the limit depends on how much weight you can spare for streamlining and structural support instead of fuel , and you ditch the covers as soon as you clear the atmosphere. On the Saturn V they also dropped the escape rocket very soon after launch. Air resistance can also vary according to the size of the rocket exhaust which depends on speed , thrust and altitude.




    Despite all the "progress" in rocketry the Russians are still using a design from the 1950's.


  • Registered Users, Registered Users 2 Posts: 90 ✭✭iioklo


    Thanks for the replys. It'll help me get to understand it a bit better.


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