How do i calculate Dv?

[Waterlimon]

if you have an equation like

a=b^c

then a logarithm with base b lets you find c if you only have a (and you have b of course). (c = logOfBaseB (a))

here, a is whatever comes out of the ln

b = e = 2.7 or so (we call log of base e "ln", the natural logarithm)

c = the mass ratio

So

massratio = e^a

and you want to find "a" so you use ln (logarithm of base e), like you would use square root to find the x in "y=x^2" using y

[TheDarkStar]

To explain a bit more:

a^b means a * a * a * a * ... * a, where b is the number of a's. For example, 5⁴ is 5 * 5 * 5 * 5, which equals 625.

Logarithms are the opposite of this. It's like division and multiplication are opposites of each other - one undoes what the other does. The notation is log_basenumber, or log_ba. The best way to explain what it means with an example, log₅625.

log₅625 is similar to the other example because it is the reverse. Instead of finding a^b = x, you're finding log_ax = b. a is 5 and x is 625, so you look for what x is in 5^x = 625. Here, it's 4. 5⁴ = 625, so log₅625 = 4.

[Starman4308]

Not everything here is helpful: a lot of it is sarcasm.

The short version is that the equation involving a logarithm is the simple way to do it. For pure plug-and-chug, this is how you do it.

#1: Divide your starting mass (with fuel) by the ending mass (without fuel).

#2: Take the natural logarithm (ln) of the resulting number. For many calculators, you can just press an ln button after you calculate the above: otherwise, you might have to get it like the following and press enter.

ln(answer)

#3: Multiply by g (9.82) and Isp (dependent on engine type).

There, you're done.

If you wish to know what the natural logarithm is, a reasonable source of information is the 22'nd chapter of Feynman's lectures on physics. The very short version is that exponentiation is repeated multiplication: a^b is a multiplied by itself b times. As such, 3^4 = 3*3*3*3. The logarithm is the inverse operation: log base a of b = c, where a^c = b. To restate, the result of the logarithm is the number to which you must raise a, so as to get b. The natural logarithm, ln, is simply log base e, where e is a fairly special number in mathematics. It's coded into most calculators: for now, all you need to know is that you use the natural logarithm.