How do i calculate Dv?

[Souper]

So i went to the Tsiolkovsky rocket equation, but my problem is, i have utterly NO idea what ISP or a natural logarithm is, and have major problems interpreting the equation. Plus, it's algebra! That's WAY over my head!

so what i'd like is an alternate method of finding my delta V. remember, simpler means better!

(NOTE: i want to be able to do all the equations inside my head. No calculators.)

[Kryten]

(NOTE: i want to be able to do all the equations inside my head. No calculators.)

Good luck.

[Souper]

Ok, good news. i have a piece of paper and a functioning pencil!

plus, i can get these things:

My rocket's mass

My rocket's dry mass

My rocket's engine's ISP (OK, i know it means efficiency)(i lied for no reason)

[PakledHostage]

So i went to the Tsiolkovsky rocket equation, but my problem is, i have utterly NO idea what ISP or a natural logarithm is, and have major problems interpreting the equation. Plus, it's algebra! That's WAY over my head!

so what i'd like is an alternate method of finding my delta V. remember, simpler means better!

So you want a means of calculating delta-V using nothing more than about grade 6 or 7 level math, is that it? If so, that's a bit of a strange request. There is a price of admission... Why not pony up? We're not talking complex math here. We're talking plug and chug. There are many helpful people here who can probably help you raise your math skills to the requisite level. It may seem intimidating but that doesn't mean it is hard.

[Souper]

Actually, what i want to do is convert that equation into 7th grade level math. (I can't read equations.)

[ZetaX]

For a start, try to understand logarithm to base 2 and 10, and their relations to 2^x and 10^x. After that try to understand natural logarithm "ln" and e^x. And stop doing this with pencil and paper; it' wont work well.

[Kryten]

To get Delta-V of a rocket stage without using a calculator, you only need to add up the total mass of the rocket stage and any payload (including any upper stages) before launch, divide it by the total weight after launch (getting you what's called the mass ratio), get the natural log of that, and then multiply that by (I_spX9.981). To approximate the natural log without using a calculator, simply perform this formula;

(the one on the right, you can ignore the others)

with z=the mass ratio, a large number of times-to get the true value, an infinite number of times. Since powers are just repeated multiplication, it should be easy enough to do using just pen and paper.

[Souper]

...I JUST said i can't understand algebra.

[PakledHostage]

Actually, what i want to do is convert that equation into 7th grade level math. (I can't read equations.)

But that re-emphasizes my point. Help us understand where you're hung up and we'll try to help you raise your skills to the requisite level. ZetaX's post contains some good information to get you started. A typical scientific calculator has a "ln" button and an "e^x" button (it is often even the same button). Just try it out.

...I JUST said i can't understand algebra.

Kryten is being facetious but he's also illustrating the absurdity of your question. You need to understand some basics before you can proceed with what you're trying to do.

Edited December 15, 2014 by PakledHostage
Updated.

[Kryten]

That's not algebra, just a lot of multiplication and division. Let's say you work out the mass ratio to be four; what you would then have to work out is;

2X([3/5)]+[1/3X{3/5³}]+[1/5X{3/5⁵}]+[1/7X{3/5³}]+[1/9X{3/5⁹}]+[1/11X{3/5¹¹}]). Or a few more, if you want to be accurate.

[Souper]

I.....Can't understand that either.

[Kryten]

It's just multiplication, powers, and addition. Read it through one bit at a time.

[Waterlimon]

Here I copypasted a top precision approximation that is wrong if someone made a mistake, for you:

dv of stage = 2((mass0/mass1-1)/(mass0/mass1+1) + (1/3)(mass0/mass1-1)^3/(mass0/mass1+1)^3 + (1/5)(mass0/mass1-1)^5/(mass0/mass1+1)^5 + (1/7)(mass0/mass1-1)^7/(mass0/mass1+1)^7 + + (1/9)(mass0/mass1-1)^9/(mass0/mass1+1)^9 + (1/11)(mass0/mass1-1)^11/(mass0/mass1+1)^11 + (1/13)(mass0/mass1-1)^13/(mass0/mass1+1)^13 + (1/15)(mass0/mass1-1)^15/(mass0/mass1+1)^15) * Isp * 9.981

mass0 = mass of entire ship when stage is activated

mass1 = mass of entire ship when stage is finished

Isp = how much thrust u get per kg of fuel

You can probably work it out on paper using long division and really long multiplication

If you want to calculate dV, use a calculator (because by definition to calculate the ln you need to do an infinite number of arithmetic operations, so doing it by hand is pointless even if its just an approximation)

If you want to understand the equation, you need to understand how the equation was derived, meaning youd also have to probably understand what ln or e mean at some point. You cannot understand it by calculating ln using basic arithmetic, because still all you are doing is calculating ln, which doesnt really help you understand it. ln is not an abstraction of some intuitive simple calculation, the calculation is an approximation of ln. The ln is the simple thing here.

Edited December 15, 2014 by Waterlimon

[Kryten]

Or you could divide m₀ by m₁, take that value, put it into windows calculator, and press the 'ln' button. If you're a wimp.

[Souper]

Tried it, couldn't do it. Can you just translate the whole equation into 3rd grader math?- you know what, no.

Let me try this: i know the wet mass and dry mass of my rocket, so i know the mass of the fuel. I do not however know the exhaust velocity of it, neither is my understanding of inertia advanced enough to know how mass, exhaust velocity, and rocket mass interact.

If i could understand that, my problems would be over!

[Kryten]

Exhaust velocity is I_sp divided by 9.81. You aren't going to get ÃŽâ€V without using some version of the Tsiolkovsky rocket equation, and the version with ln is going to be the easiest. Just suck it up and use a calculator, there should be a perfectly serviceable one as part of your computer's OS.

[ZetaX]

...I JUST said i can't understand algebra.

Then you need to learn basic algebra. It is not that hard, especially if you work with examples and a motivation in mind.

But closing your mind off by deciding "I can't do algebra" won't help.

[Souper]

Well, i'm an idiot. But i can at least use a calculator.

WAIT! Isp * 9.8 = exhaust velocity * fuel mass = Delta-V!

Edited December 15, 2014 by Souper

[Kryten]

No, because then your rocket would reach the same speed no matter how much payload you had on it.

[Waterlimon]

You cannot do this with a finite number of basic arithmetic operations.

The rate at which you gain dv depends on how much mass is left (less mass, faster gain of dv).

Thus as dv increases, the rate at which you gain it increases. This is a curve. You get this curve by doing someconstant * ln (x). You get dv by calculating the value of this thing for some specific value of x determined by how much mass you start with and how much mass you end with (mass1/mass0)

The reason you cant do it with finite arithmetic is because the properties of the curve are such that you can only approximate it (like you can only approximate pi). The approximation is done by doing a ton of arithmetic operations such that the error compared to doing an infinite amount is small enough to not matter.

[VincentS]

There is an easy (pen & paper) approximation :

dv = ISP*9.81 * ln (m_i/m_f)

ln(2) = 0.6931

dv = 6.8 * ISP (if m_i = 2 m_f)

dv = 6.8 * ISP * 2 (if m_i = 4 m_f)

dv = 6.8 * ISP * 3 (if m_i = 8 m_f)

dv = 6.8 * ISP * 4 (if m_i = 16 m_f)

I think that you get the idea : each time you double your m_i/m_f ratio, you add one to your dv multiplier (this property is caused by the log)).

(NB : fuel tank having m_i/m_f <= 9, you will probably get dv between 6.8*ISP*2 and 6.8*ISP*3)

With sqrt(2) = 1.414, you get two more (multiplying by sqrt(2) twice in a row is equivalent to multiplying by 2, so multiplying by sqrt(2) only add 0.5 to the multiplier):

dv = 6.8 * ISP * 1.5 (if m_i = 2.828 m_f) (because 2.828=2*sqrt(2))

dv = 6.8 * ISP * 2.5 (if m_i = 5.656 m_f) (because 5.656=4*sqrt(2))

Have fun !

[How2FoldSoup]

You can't ask people how to do something and then refuse the answer when they explain how to do it. There is a barrier to entry, some things just can't be explained at a 3rd grade level, this is why education isn't stopped at 3rd grade.

It's very easy use your pc calculator to do division between 2 values and then hit ln. Simple, even a 3rd grader could do it. Kryten has told you multiple ways how to calculate dv. If you're unwilling to do this, then you simply cannot calculate it.

[Souper]

Ok...i'm done acting like an idiot, let's finish this. i'm a 7th grader, i can do it if i try hard enough.

So...i'm DAMN close to finding out how it's done. you multiply your Isp by 9.81 the multiply it by ln. what I need to find out is what ln is.

[Kryten]

ln is a function, like finding the square root of something. You take the value you get by dividing the masses and do ln on it.

[Bill Phil]

Just hit the ln button on your calculator. Or, if you do want paper:

get mass ratio

Find nearest power of 3.

It should be a decent estimate.

After that, multiply be ISP and 9.8