DeltaV calculation

[Palaceviking]

Hey,  does anyone know of a rough n' ready way of getting deltaV without using ln,  ie I just want to do it on paper and get an approximate Value??

[MajorMushroom]

I'm fairly certain the calculation is quite complicated, I think it would be easiest if you just get a mod that tells you the exact number 

[Spricigo]

https://math.stackexchange.com/questions/820094/what-is-the-best-way-to-calculate-log-without-a-calculator

 

But since you are using a computer to play you can just use some of those online calculator. (e.g. http://www.quantumg.net/rocketeq.html )

[OhioBob]

Nope, natural logarithm is part of the formula, you can't just take it out.  You can always memorize several values of natural log for the range of mass ratios you're likely to be dealing with.  Mass ratio can't be less than 1, and in KSP likely not more than 5 or so.

LN(1) = 0
LN(2) = 0.7
LN(3) = 1.1
LN(4) = 1.4
LN(5) = 1.6

For values in between you can interpolate.  Should get you in the ballpark.

[Kerbart]

The classic way is using a logarithmic table (which in itself where invented to turn the dreaded task of multiplication into addition)

[OhioBob]

Easier yet, if you just want a rough number, memorized this table:

Mass ratio	Delta-V
2	Isp * 7
3	Isp * 11
4	Isp * 14
5	Isp * 16

[Human Person]

Ehm, or just use a calculator.

[Snark]

3 hours ago, Palaceviking said:

Hey,  does anyone know of a rough n' ready way of getting deltaV without using ln,  ie I just want to do it on paper and get an approximate Value??

As folks have said, in general the answer is "no".  You need to use ln.  If you don't have a calculator handy, you'll need a logarithm table, or memorize some simple numbers for an approximation, or the like.

If the mass ratio of the ship is only a very small amount above 1-- that is, if you have a ship with a very massive dry weight, carrying only a very small amount of fuel-- then you can calculate the answer approximately linearly, since the mass of the ship doesn't change much during the burn.  Just take the Isp of the ship, multiply by 9.81, multiply by fuel mass, then divide by dry mass.  That will get you an approximate answer.  But I emphasize that that works only in the special case where the fuel mass is a lot lower than the dry mass of the ship, which is usually not the case in KSP (with the possible exception of ion-drive ships).

[Kryxal]

It's probably better to divide by (wet mass + dry mass) so as to lowball the delta-v figure ... having too much tends to be less of a problem than not enough.

[Cunjo Carl]

@Palaceviking

Oh, I have an interesting one to add to the pile. For many of the standard functions, you can make approximations using other natural functions. It's mostly an act of mathmatical tomfoolery, but if you know the range you're working with, I often find it easier than trying to memorize and interpolate. In this case, we can take advantage of peculiar relationship between the logs and exponents.

My favorite voicing of the rocket equation is:

deltaV = g_0^* I_sp^* ln(m_wet/m_dry)  and when using it this way, you often end up with ln arguments between 1.5-3.5 . My phone doesn't have a ln(x) button, so instead I use:

sqrt(x-1)-.31  = ~ln(x) , and in the range of x=1.5 - 3.5 it matches ln(x) within about 1.5% . Let me grab a plot:

I also plotted the linear interpolation for 2-3 for comparison in yellow. Also the actual version of the equation is sqrt(x-1)-(1-ln(2)) so the minus bit is... .306853.... I just use .31!

We could of course make even better approximations by instead using cube roots or quartic roots and ever onwards! But my phone has a sqrt button on it, so I guess it's good enough for me . Have fun mathing!

[Palaceviking]

On 30/09/2017 at 10:40 PM, OhioBob said:

Nope, natural logarithm is part of the formula, you can't just take it out.  You can always memorize several values of natural log for the range of mass ratios you're likely to be dealing with.  Mass ratio can't be less than 1, and in KSP likely not more than 5 or so.

LN(1) = 0
LN(2) = 0.7
LN(3) = 1.1
LN(4) = 1.4
LN(5) = 1.6

For values in between you can interpolate.  Should get you in the ballpark.

Spot on! Thank you

[Reactordrone]

On 10/1/2017 at 7:30 AM, Palaceviking said:

Hey,  does anyone know of a rough n' ready way of getting deltaV without using ln,  ie I just want to do it on paper and get an approximate Value??

"n" is the keyboard shortcut for ln in the windows scientific calculator if you don't have a handheld calculator handy.