### Question: 9.81 m/s^2 in delta V calculations?

Isn't that figure the acceleration due to gravity on Earth at sea level?

I'm assuming that the devs used an earth-like parameter for Kerbin, and obviously this math is working for you; but do you use a different acceleration parameter when calculating the delta-V of your Munar return stage? --Hovissimo (talk) 19:45, 25 December 2012 (UTC)

<P> No, the 'g' is a standard unit of measurement. Changing it would be like changing the length of a metre because the Mun "has less of them". Kahlzun (talk) 07:37, 2 January 2013 (UTC)

Isn't that kind of arbitrary, though? Wouldn't Δv = Isp · ln(m0/m1) make more sense? Ninenineninefour (talk) 14:48, 23 March 2013 (CDT)
Wait, I just answered my own question: It's not the equation that is arbitrary, it's the definition of specific impulse itself, which is the exhaust velocity divided by standard gravity. What would make more sense, in fact, is Δv = Ve · ln(m0/m1). The reason why Isp is used instead of exhaust velocity is so that the efficiency of engines can be easily compared, even when they are measured with the imperial system instead of the (much better) metric system.
Oh I didn't saw this post when I undid this change. At first I also find this very strange until Scott Manley uploaded a video an explained it. After this it “meh” of course ;). Actually sometimes the Isp is given in ${\displaystyle {\frac {Ns}{kg}}}$ which is equal to ${\displaystyle {\frac {m}{s}}=kg\cdot {\frac {m}{s^{2}}}\cdot {\frac {s}{kg}}}$ (with ${\displaystyle N=kg\cdot {\frac {m}{s^{2}}}}$). That is also why I added extra explanation everywhere Isp is used. — xZise [talk] 11:38, 29 April 2013 (CDT)

## Cleaning Explanation of Delta V calculations?

In the "Calculating Transfer Maneuvers" section could we make it more clear that R1 and R2 are the radius from the center of the planet and so you need to add 600km to the altitude to get correct numbers. Also, it might be useful to include that the solutions to the two delta-V calculations are 73.65 m/s for burn #1 and 71.23 m/s for burn #2 for a total delta-V of 144.88 m/s.--lancastrian (talk) 22:16 CST, 29 December 2013 (CST)

Good point, I added the radius into the formula. I don't know if the ${\displaystyle r_{1}+R+r_{2}+R}$ should be simplified to ${\displaystyle r_{1}+r_{2}+2R}$ because I try to make in the first clear that you need the distance to the center not the surface. I've also validated and added the calculated Δv values. — xZise [talk] 05:44, 30 December 2013 (CST)

I wonder if we could keep the equation the same as it was before but specify that R1 and R2 are the radius from the center of the planet. So, the explanation for R1 would read:

• ${\displaystyle r_{1}}$= The radius of our first orbit from the center of the orbited body (in this case 700km, or our orbital altitude of 100 km plus Kerbin's radius of 600km).

--lancastrian (talk) 22:16 CST, 29 December 2013 (CST)

This is of course possible, but I was thinking as everything in KSP is showing the distance relative to the surface it should be made clear that the distance to the center is important. But as you can simply redefine what r1 you can also say that it is the distance from the center. — xZise [talk] 07:25, 31 December 2013 (CST)

## Formula graphs might make the formulas easier to understand.

It might be a good idea to add graphs of the some of the formulas here, this way people could visually see what the pattern is, which makes estimating rocket builds a lot easier. Is there someone good with computer math software that wants to do this, or should I? (I can get Maxima set up and render the graphs in a few hours, however someone more experienced with computer math systems could clearly do a far better job in far less time.) --Ruedii (talk) 08:57, 20 February 2014 (CST)

## Rocket equation correction for ascents

Note that the rocket equation ${\displaystyle \Delta v=I_{sp}\ln {\frac {m_{0}}{m_{1}}}}$ assumes no external forces, in particular abscence of gravity. That makes it sufficient for short maneuvers, but less well-suited for ascent, which is strongly affected by gravity. If gravity is included, the formula looks like this:

${\displaystyle \Delta v=I_{sp}\ln {\frac {m_{0}}{m_{1}}}+\int {\vec {g}}\,dt}$

where ${\displaystyle \int {\vec {g}}\,dt}$ is the integrated gravitational acceleration during the ascent (or any other maneuver). As it is hard to compute, we can conservatively estimate it by

${\displaystyle \left|\int {\vec {g}}\,dt\right|\leq {\frac {g_{0}+g_{1}}{2}}\Delta t}$

where ${\displaystyle \Delta t}$ is the duration of the burn and ${\displaystyle g_{0},g_{1}}$ are the gravity acceleration at its begin and end (this assumes that g(t) is concave, which is the case for a constant burn near a single gravity source). Exploiting that the burn duration is given by the mass of the expelled fuel over the fuel flow rate, this yields the nice formula

${\displaystyle \Delta v\geq I_{sp}\left(\ln {\frac {m_{0}}{m_{1}}}-{\frac {|{\overline {F_{G}}}|}{|F_{T}|}}\right)}$

for ascent, where ${\displaystyle {\overline {F_{G}}}={\tfrac {1}{2}}(g_{0}+g_{1})(m_{0}-m_{1})}$ is kind of an average fuel weight estimation and ${\displaystyle F_{T}}$ is the thrust of the engine. Now finally you can see why you need stronger engines in presence of stronger gravity. -- Cami (talk) 11:57, 26 August 2014 (CDT)

First of all a nice addition, and feel free to add it. But doesn't thrust-to-weight ratio already explain partially why you need stronger engines to lift off of a surface? And isn't it explained because when the engines are more powerful, the rockets accelerate faster and thus the ascent time is lower? And for low orbits you could approximate ${\displaystyle {\tfrac {1}{2}}(g_{0}+g_{1})\approx {\tfrac {1}{2}}(g_{1}+g_{1})={\tfrac {1}{2}}2g_{1}=g_{1}}$ as long as you are close to the body. For example it's about 90% for a 70 km orbit. And you should make avoid confusion with the conversion factor between Isp in seconds and m/s. — xZise [talk] 06:43, 27 August 2014 (CDT)

## Last major edit 2013

All the stuff in this page is really useful information if you love doing nontrivial mathematics on paper or need to launch a rocket but don't have a computer handy. But I feel like the general KSP player would benefit more from a broad explanation of these concepts with less of a focus on how to calculate them. Because I doubt any large percentage of KSP players are actually going to calculate them. I think that many players (like me) are going to use a mod like KER or mechjeb to give these values for us, and as such, I think a mention of the existence of such mods would make this page less discouraging to the average reader, who might not be very mathematically inclined. — Preceding unsigned comment added by Kermen (talkcontribs) 20:58, 22 June 2015‎

Welcome to the wiki! Thanks for your feedback.  :-) While I agree with you that the majority of KSP players most likely don't bother with the formal maths, and just use tools like KER & MechJeb to do the number crunching the easy way, I think this page is an excellent bit of content for the wiki. I've not gone through it in detail to check if there's anything actually needing updated, but the last major edit can often be a very poor indicator of relevance or value. Some elements of the game change almost every release, others will likely never change. The fundamental maths behind rocket science have not changed since long before the world had seen the first electronic computer that was smaller than a building. Some of the maths for space flight actually go back to centuries before Babbage's mechanical Difference Engine (its applications included ballistics for artillery tables, and celestial navigation tables).
If you have spotted specific sections which are outdated or otherwise needing a refresh, please let us know exactly which bits they are. I certainly do not want to claim that the article is perfect or completely error free. You are probably correct that it could benefit from a short preamble to let people know that it's not compulsory to fully understand the maths.
You are quite welcome to edit articles to try to improve the overall quality of information. Don't worry about making your edit(s) perfect, just try to make them an overall improvement, and try to avoid damaging or removing any existing good information (but you are welcome to edit existing information to improve clarity, etc). Dropping suggestions and other feedback on the appropriate talk page, as you have done, is perfectly acceptable too, if you don't feel comfortable or confident editing any particular article.
--Murph (talk) 23:10, 22 June 2015 (UTC)
I agree with Murph and want to add that it always helps to know how stuff work. You might use KER/MechJeb instead of calculating the delta-v on your own. But knowing what delta-v is helps you understand rockets. E.g. that a more inefficient engine might have more delta-v if it's lighter for example. And if you are not interested in that I don't think that this tutorial is what you want as it looks to me like an explanation of various formulas (so maybe the page title is a bit misleading). — xZise [talk] 08:12, 23 June 2015 (UTC)