Rocket Equation

**blackskydreamer** · June 11th 2011, 04:31 PM

Hey all

Wasn't really sure where to post this, this thread seemed like a good start.
I've got a side project going on building a hybrid rocket engine for abit of fun, have been working from a few books I have which list all the equations and with the help of Excel have been writing a spreadsheet to help out the design, but I have just run into a bit of a road block where they list a quadratic equation that needs to be rearranged yourself. Its been a year or two since school where math was not my strong point and can't remember seeing one like this.

I've figured out Latex and this is the equation below. I have to solve for $w$

${w^2} + \frac{{2l + b}}{\pi }w - \frac{{mfuel}}{{NDLp\pi }} = 0$

Where:
$w$
$l$
$b$
$\pi$
$mfuel$
$N$
$D$
$Lp$
Are the seperate values.

Would you need the actual values or is it able to be solved like this?

Any help is greatly appreciated to get this project off the ground, quite literally!

**Also sprach Zarathustra** · June 11th 2011, 04:46 PM

Originally Posted by blackskydreamer

Hey all

Wasn't really sure where to post this, this thread seemed like a good start.
I've got a side project going on building a hybrid rocket engine for abit of fun, have been working from a few books I have which list all the equations and with the help of Excel have been writing a spreadsheet to help out the design, but I have just run into a bit of a road block where they list a quadratic equation that needs to be rearranged yourself. Its been a year or two since school where math was not my strong point and can't remember seeing one like this.

I've figured out Latex and this is the equation below. I have to solve for $w$

${w^2} + \frac{{2l + b}}{\pi }w - \frac{{mfuel}}{{NDLp\pi }} = 0$

Where:
$w$
$l$
$b$
$\pi$
$mfuel$
$N$
$D$
$Lp$
Are the seperate values.

Would you need the actual values or is it able to be solved like this?

Any help is greatly appreciated to get this project off the ground, quite literally!

It is a quadratic equation. Find the roots.

${w^2} + \frac{{2l + b}}{\pi }w - \frac{{ mfuel}}{{NDLp\pi }}=0$

Say, $\chi = \frac{{2l + b}}{\pi }$ and $\psi =\frac{{ mfuel}}{{NDLp\pi }}$ , then:

$w^2+\chi w+\psi=0$ , and the roots are:

$w_{1,2}=\frac{- \chi\pm \sqrt{ \chi^2-4\psi}}{2}$ ,

Real roots exist only when $\chi^2-4\psi\geqslant 0$

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