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Math Help - physics: model rocket altitude equation

  1. #1
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    physics: model rocket altitude equation

    I have an equation for predicting the altitude of a model rocket under specific impulse. I am struggling to understand some parts of it. Here is the one equation for a variable that I need, an the variable definitions:

    v = q*[1-exp(-x*t)] / [1+exp(-x*t)]

    v = velocity;
    q = [sqrt(T-M*g)/k]
    x = 2*k*q/M;
    M = mass;
    T = thrust;
    k = 0.5*0.75*rho*Area;
    rho = 1.2kg/m^3;
    t = burn time,
    g = 9.8m/sec/sec (gravitational constant).

    So I think I got them all. My question is the [1-exp(-x*t)] / [1+exp(-x*t)] portion,
    I assume -x is x * -1; t is self explanatory.
    what is exp in this case? I've never seen this before, and can't find anything that makes sense on the web. A web link and explanation would be very helpful... thank you!
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  2. #2
    Super Member Matt Westwood's Avatar
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    In this context: "exp" means "e to the power of".

    It saves having to write complicated stuff in superscript and can make an equation loads clearer.
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  3. #3
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    ok, so exp = exponent. for easy memorization.

    Ok... so another question. Is e another constant? It isn't defined anywhere in the fomulae, and I don't know if it offhand.
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  4. #4
    Super Member Matt Westwood's Avatar
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    Euler's constant: 2.71828182845045 ... or something like that. It's the value of p such that:

    \frac d {dx} p^x = p^x

    the next most famous irrational number after \pi.

    See here:

    Definition:Euler's Number - ProofWiki

    for some more info. Fascinating number.
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  5. #5
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    so, if I wanted to simplify the equation, I could use 2.71828182845045^(-x*t)
    for that particular part?
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  6. #6
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    Quote Originally Posted by kaloralros View Post
    so, if I wanted to simplify the equation, I could use 2.71828182845045^(-x*t)
    for that particular part?
    for ease in notation, just use e^{-xt} ... the constant e is available on most calculators and computer programs.
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  7. #7
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    I am actually writing a program to predict altitude as a way of learning new functions and mathematical processes... so I am trying to keep it close to what I know... I very much appreciate the help!
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