[Stock] The Bare Minimun II

[Apotheosist]

EDIT: No longer applicable to 0.16

This is an altered version of my original 'The Bare Minimun' ship http://kerbalspaceprogram.com/forum/index.php?topic=11407.0 , which used landing legs for stage separation, which is no longer possible in 0.15. I initially thought that an extra half tank of fuel would be required make up for the aditional mass of normal decouplers, and I initially posted such a craft. However, it seems that with the new patched conics trajectory projection, it is possible to fly much more precisely and efficiently, wasting less delta-v. This craft should be 'update proof', in that it does not use any tricks or unbalanced parts that might get fixed or balanced in future updates.

Please give it a go and post back with your results!

[DrBurst]

You sir are a god among men

[Apotheosist]

You sir are a god among men

Hehe thank you . Funny you should say that, as my name, 'Apotheosist', I came up with from the word 'apotheosis', which means 'For man to become God' or something like that. So yes, I\'m suggesting I\'m a god amongst men, as you said . But you probably already knew that.

[xclusiv8]

This little thing can actually get to the mun and back

[closette]

An amazing craft, calling for impressive piloting skills. For those of us who are less coordinated, I have been wondering what a bare minimum craft would need to look like if you had to include an SAS or ASAS module, an RCS tank, and a parachute.

Specifically, how many additional LFEs would that require, and how would they be arranged? (Perhaps I could make this a Challenge but I pretty much know who would win it!).

[Apotheosist]

CHALLENGE ACCEPTED! Hehe, I\'m on it. I actually have a formula I developed recently to help me work out how many additional fuel tanks I need to carry a certain amount of mass a certain distance (delta-v). So I will make a ship with an ASAS, parachute, rcs tank and how many rcs blocks?. I suppose 2 rcs blocks would be the minimum. And I suppose the capsule and a parachute will have to separate from the rest of the craft for a super easy landing, unless you are ok with doing some propulsion for a safe landing.

[Apotheosist]

Ok so I built a rocket, and flew it to the Mun and back. I gave it 3 rcs blocks as I figured that would cover movement in all directions. One problem with this ship was that the second stage (lander) has a narrow base and tips over easily. So I\'m going to try modifying it a little. Until then, I\'ve posted pictures of my flight and the ship. This rocket was optimised, but It could probably be further improved, as this was my first try.

Also, the ascent plan I used for this was one I tried one day and found worked surprisingly well. It needs just two maneuvers, tilting to 45 degrees at ~13km (first colour change on the atmoshpere indicator), then tilting 90, horizontal at ~30km (second atmosphere indicator colour change). I then circularized for a 70km orbit.

[xclusiv8]

Y u no use landing gear?

[closette]

@Apotheosist - you win a 'fastest response time to a challenge' award as well - amazing. I\'ll give it a whirl later on when I get home.

I\'ve noticed that the ascent profiles used by you and Kosmo-not for these mini-ships are quite different from the usual bigger ones (e.g. those Mun ships in the stock repository thread), with pretty much full pitchover by 30 km. At first thought it appears that would put your ship through a long path-length of atmosphere at high speed, which would cause a lot of drag, but it seems to work well in these cases. Fewer parts means less drag and higher thrust/weight ratio I guess. It does show that the optimal ascent-to-orbit profile can be very different between spacecraft.

I think I can derive it, but care to share your payload vs. fuel delta-v formula with us? Might be a useful part of a tutorial at some point.

[colmo]

You might be able to use the structural supports instead of radial decouplers to shave some mass off. They don\'t have as much ejection force, but are half the mass. It would buy you some landing gear, easily!

[Apotheosist]

@ xclusiv8, that is one option, only two would be needed to keep it upright. Shouldn\'t affect the flight characteristics of the ship much either.

@ closette, Hehe, thanks. I love designing ships . I\'ll always be happy to help design a ship if needed. And yes, I think it might actually have been one of your own posts that stated that at 30km, the optimim velocity is equal to orbital velocity. So I figured that at this altitude, the craft should be trying to get as much orbital speed as possible, hence the horizontal pitch.

As for the formula, it\'s quite a simple one that I\'m not fully sure works. I was thinking of making a topic asking for help on it. I asked a few of my friends in school about it but they couldn\'t do much more with it than I :/ I\'m going to take a last look over it and will come back when I\'m ready.

@ colmo, yes, there are many advantages to using the C7 parts. The more efficient aerospike engine for one. However, I dont like to use C7 parts as many I believe are unbalanced, and may be balanced in future updates, thus altering the charactersistics of my craft. I\'m very much a stock purist, so much so that I\'m even sticking to the older stock parts! Hehe.

[Apotheosist]

I have made alterations to my first EZ rocket, giving it a much more stable base to land on, and I\'ve also reduced the weight a bit and taken an engine off. The craft attached has not been tested, I tested one with 2 extra half tanks on the bottom of the first stage and I had plenty of fuel left over, so I\'m confident this rocket can make it. If you\'re not sure, just add two half tanks on the bottom of the first stage (adding them on the bottom gives more delta-v than if you add them on the top due to the lower density of the fuel in the half tanks)

Edit: I have now tested the rocket, and I made it back to kerbin just fine.

[closette]

Finally I got to try your EZ Mun ships. The EZ Minimun II was much easier to control, and I managed to get out to the Mun and back safely, even though I was probably not very efficient.

I\'m not sure if this was supposed to be part of the flight plan, but when landing on the Mun with some uncorrected horizontal speed, I 'cleverly' managed to scrape off both empty side tanks, while the RCS kept the ship itself from toppling over. This made the trip home easy with the downsized ship:

I\'m not sure if I could do that again!

I encourage others to try this ship - it was a lot of fun to fly.

Apotheosist, I think you should request it be added to the Stock Repository thread so that more people will notice it. Great work!

[Apotheosist]

Bravo! What a brilliant mission closette! I have often tried to deliberately break off a few tanks on the Mun, but with no such results as you!

Thanks, I will request right away.

[Apotheosist]

This is the equation I came up with to help me find the number of tanks that need to be added to have a certain delta-v (if I know how much delta-v I want, then I can easily work out the mass ratio required to acheive said delta-v) . I just started off by describing what the mass ratio is equal to. So this is what I ended up with:

Mr=(a+n. / (a+n.c)

Where Mr=Mass ratio. (Initial mass/empty mass)

a=Mass you start off with (including mass of any stages above and mass of all engines in this stage)

b=Initial mass of one full fuel tank

c=dry mass of one fuel tank

n=number extra fuel tanks I need

So I have this equation where I know Mr, a, b, c, but not n. I tried and tried to rearrange it to get n on it\'s own, but with no luck. I asked many of my friends in school, but they couldnt find a way either. I would very much appreciate if someone can rearrange it, showing all of the steps. I actually have an equation with n on one side, which I got with help fom Wolfram alpha. I just typed in my mass ratio equation, and it gave me different forms of the equation, and it showed what n was equal to. I then ran some numbers through it for a rocket I was familiar with, and the result worked. So I have the equation, but I want to know how to rearrange my mass ratio equation to end up with the equation for n. I won\'t post the equation here yet, so that those trying to rearrange the equation start off with a blank sheet. Please give it a go if you think you can do it.

[mknote]

I get:

n = a*(1 - Mr)/(c*Mr -

As to how it\'s done, it\'s quite simple:

1. Multiply both sides by (a + c*n)

2. Multiply Mr through (a + c*n)

3. Subtract both a and Mr*c*n from both sides

4. Pull the n in common from all terms on the right

5. Divide by the remainder [b - Mr*c] to get n alone

6. Play around with negatives to get the above expression

7. ? ? ?

8. Profit!

[closette]

@ Apotheosist: As I thought, I could not easily repeat my double-tank-scraping trick on the Mun surface.

One more suggestion for the EZ Minimun II (which would make it a IIa I guess): I would put the RCS tank+thruster blocks above the stack decoupler, attached to the pod. That way, if and when you run out of fuel for the LFEs on the way home, you can at least get rid of the dead weight and use the pod+RCS+parachute as a 'lifeboat' to get back home.

For some reason I could not get this change to work in the VAB, but you may have better understanding of how the components fit. And this change does not affect the weight.

[Apotheosist]

@ mknote, thanks so much makes sense now. Very helpful indeed. The answer I got using Wolfram Alpha was n=a*(Mr-1)/(b-Mr*c), but I guess they\'re the same

@ Closette, indeed, I considered this arrangement, but decided against it as that last RCS stage would not have any SAS and would require thrusting with RCS on landing, which is easy enough, but further complicates things. I also would be tempted to utilize that extra delta-v from the rcs, to make the ship even smaller XD. but then it would be much more difficult to fly, so I decided not to tempt that minimalist side of my brain, and just leave it with the rest of the stage. However I did experiment with it in the VAB, and I\'ve attached a pic of the lander with detachable RCS stage. Couldn\'t get the side tanks to the same level as the bottom of the ASAS, so even harder to scrape them off, hehe. Oh, also in the pic it for some reason doesn\'t have a parachute :/

[closette]

Well I managed to switch the RCS tank and stack decoupler on my own, and personally I prefer it, since I can never make it all the way home with the LFEs alone.

I think most people can fly a pod+parachute+RCS fairly well, just not precisely. (The trick is to leave the pod\'s SAS 'on' to provide damping of one\'s control inputs).

As for landing back home, all my own ships have landed Soyuz-style (that is with parachute + retrofired RCS) which can be exciting over rough terrain, but I am used to it.

I even added SRBs to one version of this arrangent, and replaced two liquid booster tanks with half-tanks, since I noticed that the ascent speeds were slightly below optimal between 0 and 12 km. But I recognise that\'s moving away from the 'Minimun' concept.

Oh, on my last flight I tried scraping off the empty tanks (by frantic hopping around on the Mun) only to scrape off the engine instead! Serves me right!

As you can see I\'m having a great time with your designs!

[purple100]

I took the EZ MiniMun II into orbit with MechJeb, landed on Minmus, and returned safely. I\'m surprised at how little it takes to make that trip.

[Apotheosist]

Glad to see your\'e having fun with my designs! Also glad to see you making alterations to the rocket and sharing them! It can be a great help to many players to fly a rocket shared by someone else. And yes, I try to start off my rockets with a T/W of about 1.5, as it does not affect performance too much, and it minimizes engine weight. I then ensure I have enough fuel to keep my first stage going late into the burn to orbit, because the thrust to weight increases as fuel is used up, and is a good help. Above about 10k a T/W higher than 2 is optimal or so I\'ve heard. At a late stage in the burn, however, when the craft is in full pitchover, there is no need to carry those heavy engines, the small engines on the next stage are enough to circularize the orbit.

One of my next projects will be to create an EZ Minimun double-return capable ship, meaning it could go to the Mun, come back to Kerbin\'s surface safely, then use one of the the current EZ Minimun to go back to the Mun again and return to kerbin a second time. I have already made a Bare Minimun rocket capable of this, using 27 tanks in total. The creation of an easy to fly version of this would enable those who have never done a double mun return mission to try it if they so wished, without having a rocket too hard to fly, or having it so big as to considerably slow down their computer. A double Mun return mission is highly interesting and educational, involving a parachute assisted landing of a rocket on Kerbin. This type of mission could teach someone a lot about a Mars return type mission and prepare them for when another planet is added to the game.

Until then, have fun!

Also, @ purple 100, I have not taken it to Minmus myself, although I know Minmus missions need quite a bit less delta-v than mun missions. I have considered designing minimalist craft just for Minmus but I prefer working on Mun capable craft, and any craft that can go to the Mun can go to Minmus.

[Luke]

Are you saying it\'s easier to go to Minmus than the Mun? Darnit lol

[purple100]

The extra delta-v expended for the injection burn is made up by Minmus\' lack of gravity. It takes almost no power to break away and steer back toward Kerbin.

[hak8or]

This is the equation I came up with to help me find the number of tanks that need to be added to have a certain delta-v (if I know how much delta-v I want, then I can easily work out the mass ratio required to acheive said delta-v) . I just started off by describing what the mass ratio is equal to. So this is what I ended up with:

Mr=(a+n. / (a+n.c)

Where Mr=Mass ratio. (Initial mass/empty mass)

a=Mass you start off with (including mass of any stages above and mass of all engines in this stage)

b=Initial mass of one full fuel tank

c=dry mass of one fuel tank

n=number extra fuel tanks I need

So I have this equation where I know Mr, a, b, c, but not n. I tried and tried to rearrange it to get n on it\'s own, but with no luck. I asked many of my friends in school, but they couldnt find a way either. I would very much appreciate if someone can rearrange it, showing all of the steps. I actually have an equation with n on one side, which I got with help fom Wolfram alpha. I just typed in my mass ratio equation, and it gave me different forms of the equation, and it showed what n was equal to. I then ran some numbers through it for a rocket I was familiar with, and the result worked. So I have the equation, but I want to know how to rearrange my mass ratio equation to end up with the equation for n. I won\'t post the equation here yet, so that those trying to rearrange the equation start off with a blank sheet. Please give it a go if you think you can do it.

I think I got it, though I may be wrong.

1) Write equation

2) Get rid of the denominator by multiplying everything with the reciprocal of it.

3) Distribute the Mass Ratio (I changed Mr to M so it looks cleared)

4) Subtract the product of the mass Ratio and total Initial mass from the left

5) Subtract the product of the number of needed fuel tanks so you have N on just one side

6) Now you can take out N

7) Divide and viola, you get N

8) Rewrote it to make it clearer

[closette]

mknote has the equation for 'n' correct above.

It\'s reassuring when experience accords with simple model predictions!

1. You are correct that although TWR=2 is optimal in terms of fuel for ascending vertically in a constant-density atmosphere.

As I mentioned above I tried attaching SRBs to the EZ Minimum II, which help by getting up to speed faster and saving a bit of fuel, but did not seem to make a lot of difference to the fuel I had remaining after achieving orbit. So that tells me you are close to optimal in terms of fuel usage.

Looking back at earlier calculations, I now see that your launch TWR of 1.5 is still within 90% of optimal, as the graph below shows:

(The fuel efficiency is proportional to Sqrt(1-r) / r where r is the Thrust/Weight ratio, so this is what I plotted).

As you can see though, for a TWR below 1.5 the fuel efficiency drops off steeply as you spend more time hanging around fighting gravity and getting almost nowhere. So don\'t go much lower in your quest to save on engine mass!

2. As we found in the Goddard problem mini-challenge thread, for a changing atmospheric density, the optimal speed for a vertical climb is equal to the local terminal speed, which of course increases with altitude, and the resulting optimal TWR required to 'chase' the terminal speed turns out to be 2.0 + a/g, where a is the acceleration required to keep up with that increasing terminal speed.

Using the exponential atmosphere model and a 'typical' sea-level terminal speed of about 100 m/s (it depends on the rocket\'s maximum_drag factors a little bit), I found that the optimal TWR as a function of altitude should be approximately given by:

TWR_opt = 2 + 0.1*Exp[+altitude / 5000] where the altitude is measured in meters.

Below 10000m the second term is small, but above that it begins to increase quickly, so you are right that above that altitude you need a TWR bigger than 2 (in fact closer to 3) at least until pitchover.

I can provide the steps leading to this equation if anyone is interested - it just takes a little time to do the formatting.