How does one calculate the required deltaV for the highest (atmospheric) stage

[xendelaar]

Hi everybody,

I like to plan my expeditions using excel. I made this sheet that calculates the lightest engine setup for a given:

• Payload
  
• TWR
  
• desired delta V budget
  
• current altitude from kerbin (because the ISP changes as a function of the atmospheric height)
  

Calculating a setup in vacuum is easy with my sheet. However. Getting into LKO is a little bit more difficult. Below approximately 10-15km, the ISP for vacuum engines drop rapidly. In that case atmospheric engines are better suited.

I tried to calculate how much delta V I need to get from 70km to 15km and from 15km to 0 km, but I'm not able to figure out all the math. The ascend profile and drag losses make it too difficult for me. So I'm still stuck at guessing the required vacuum delta V (say 1800 m/s) and then slapping an atmospheric engine with a budget of 1700 or something on the bottom of my setup (my total delta V is approximately 3500 m/s to get in to orbit). Although this approach always works, it doesn't feel like a very efficient way of designing a rocket.

So here's my question:

I was wondering how you boys and girls calculate the "best" rocket setup to get a given payload to orbit. With "best" I mean lightest setup. Do you use a rule of thumb to get the right setup, like 40% atmospheric engine(s) and 60(%) vacuum engine(s)? Or even better: is there a way of calculating the delta V budget to get to a certain altitude (at a certain flight angle and set TWR). I would love to expand my excel sheet with more maths... XD

Also, how many stages do you guys normally use to get to orbit?

[Steelsunoa]

Wow, just reading your post makes me feel inefficient! Haha...I guess I just "feel it out" and tweak things as I build and re-launch. Don't get me wrong though, I'm a math nerd and love that you can actual apply math to this game, I just like to use KSP a little more casually I guess. Have you tried using actual orbital mechanics and equations? I'm not sure how you can find some of the values, but I think it's doable. Perhaps the KSP wiki page would be a good starting point to help? http://wiki.kerbalspaceprogram.com/wiki/Tutorial:_Basic_Orbiting_(Math)

I typically have 2 stages to obtain my orbit, one for the ascent and another for the gravity turn/orbit & transfer. I try for 2 usually, but it depends on the design and how I want the rocket to look. I sacrifice some efficiency for aesthetics more often than not, but try to find a balance. Generally I like my 3rd stage to be my transfer stage and drop it as I obtain orbit around the SOI that I'm targeting, but I suspect it would really be for the return trip in most cases depending on design. Sorry that I don't have a real answer, but hopefully the wiki link will get you moving in the right direction. Fly safe!

Edited September 7, 2015 by Steelsunoa
spelling

[mhoram]

Calculating the ideal setup of rockets is something that is very complex and not a single formula can do that.

This site has information about an iterative process to reach this.

This post by Temstar goes into the depths of asparagus staging setup.

Also recommendable is the Payload-Fraction challenge. You can see lots of high-efficiency designs there.

About my manual way to build rockets:

First I create my payload and have a DV-reserve for circularizing in LKO.

The stage before payload has around 1000-2000 m/s DV with a TWR > 0.6 (depending on payloadmass and used engines)

The initial 1-3 phases I build according to how much DV I still need, fiddle around with different engine setups and add some solid boosters. ... I know not very scientific and mostly experience-based.

Edit: Regarding selection of best engines you might find this site interesting:

http://forum.kerbalspaceprogram.com/threads/127691

Edited September 7, 2015 by mhoram

[Steelsunoa]

Nice, thanks for the links...even though this wasn't my thread. Those should prove rather useful!

Edited September 7, 2015 by Steelsunoa

[cantab]

Knowing the atmosphere curve will help. By 5 km up your engines are already closer to vacuum than sea-level performance. By about 11 km they're 90% of the way to their vacuum performance. So atmosphere figures are only relevant pretty low down.

[GoSlash27]

Knowing the atmosphere curve will help. By 5 km up your engines are already closer to vacuum than sea-level performance. By about 11 km they're 90% of the way to their vacuum performance. So atmosphere figures are only relevant pretty low down.

^ This. I ignore the atmosphere entirely for everything above 8km. A single "booster" stage that operates in that region is calculated at 1/2 atm.

Generally for a 2 stager (which is all the staging I ever do on Kerbin), the lower stage is 1800 m/sec DV at 1/2 atm and the upper is 1600 m/sec at vacuum. Anywhere beyond 75km apo with atmospheric per is another stage and is all payload for launch purposes.

I do something similar to what it sounds like you're doing; I run a reverse rocket equation to simulate each engine simultaneously for the payload, t/w, and DV requirement. From there I can pick my best option for a stage by minimum mass, lowest cost, or simplest construction.

Best,

-Slashy

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Have you tried using actual orbital mechanics and equations?

Steelsunoa,

Oh, yeah. I have spreadsheets for calculating DV budgets for orbital transfers, burn timing, resonant orbits, transfer windows...

All the basic maths work in KSP.

Best,

-Slashy

Edited September 7, 2015 by GoSlash27

[xendelaar]

Hi everybody. First of all, thank you for all the quick and interesting responses. This community is a real special thing. Everybody is so friendly and eager to share their ideas. It's awesome!!!

Steelsunoa: Planning/designing my rockets in excel is half the fun for me. I just love fiddling around to create an even better way of designing my rockets. I already use the rocket equation to calculate most of my needs. Just like Slashy, I calculate the optimum engine using the reversed rocket equation on all engines simultaneously. I then choose which setup is best based on weight and complexity.

CanTab: 5 km is really low. If this is the case then perhaps it's not worth the hassle to find the physics and the math to solve this problem. On the other hand... It's still a nice puzzle I'll check my own ISP-Altitude graphs when I get home from my vacation abroad (which is tomorrow).

mhoran: thanks for the info. I'm going to read them right after finishing this post! I know it's really complex to solve this problem analytically, but I'm trying to find a way of better guesstamating the design of the highest stage. For me, anything is better than just doing stuff randomly as I'm doing right now...

Slashy: Your excel sheet looks a lot like mine! I think we're doing the same thing (more or less ). I also ignore the influence of the atmosphere mostly at the moment (save the initial TWR) but I'm hoping of optimizing my designs. Reading all these comments I doubt that I will be able to gain a little even if I'm able to "crack da code"... but we'll see.

As a first step.. I was thinking of calculating my vertical velocity at a given inclination with a fixed TWR. That way, I know how long it takes to reach the point where vacuum engines perform better. I believe the wiki info displays the fuel consumption rate per engine, so that way I'm able to calculate how much juice I need to get there. It's not perfect and it probably won't work, but it's something I will test it tomorrow when I get back.

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Slashy, you made sheets for calculating burn timing, resonant orbits and transfer windows??! Oh my Science! That's awesome. That must have been quite a lot of work!

[GoSlash27]

Slashy, you made sheets for calculating burn timing, resonant orbits and transfer windows??! Oh my Science! That's awesome. That must have been quite a lot of work!

xendelaar,

Thanks, but it's not really any big deal. It takes less mathing than what you've already done.

The equations are here and the constants are here.

It's like anything else; if you have the equations and constants, it's just a matter of using algebra to manipulate it to suit your needs.

Good luck and I'm very interested in seeing what you come up with!

-Slashy

[OhioBob]

The rough rule of thumb is that similar stages should produce the same ÃŽâ€v. So if your total ÃŽâ€v is 3500 m/s, you should aim for about 1750 m/s in the first stage and 1750 m/s in the second stage. When you have dissimilar stages, such as a kerosene fueled first stage and a liquid hydrogen fueled second stage, then you should give more ÃŽâ€v to the one with the higher ISP. However, that's not an issue in KSP because everything is similarly fueled (except for the "Nerv", but that's not an engine you'd use on a launcher).

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I had developed a group of rules that I used for rocket design pre-1.0 that worked very well. I optimize the design using computer simulations. I've been meaning to do the same thing for post-1.0 but haven't gotten around to it yet. My pre-1.0 rules were:

Payload fraction = 0.16

First stage TWR = 1.65

Second stage TWR = 1.30

Stage-2 thrust / Stage-1 thrust = 0.35

Edited September 7, 2015 by OhioBob

[cantab]

(except for the "Nerv", but that's not an engine you'd use on a launcher).

I wonder if that changes in enlarged solar systems. With such an enlarged system the upper stage has more delta-V to provide at a relatively low TWR and so the Nerv could be applicable. The real NERVA was planned as an upper stage engine.