# Thread: physics: model rocket altitude equation

1. ## 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!

2. 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.

3. 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.

4. Euler's constant: 2.71828182845045 ... or something like that. It's the value of $\displaystyle p$ such that:

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

the next most famous irrational number after $\displaystyle \pi$.

See here:

Definition:Euler's Number - ProofWiki

for ease in notation, just use $\displaystyle e^{-xt}$ ... the constant $\displaystyle e$ is available on most calculators and computer programs.