Reusables

Hmm, it could be the case. I think mk1 pod + crew cabin topped by a parachute won't have heating problem, though.

Let me test again. Probably I recall it wrong.. Will post the result in a day.

That can happen if the craft has bad glide ratio. Reentry has changed recently(1.2), probably you were playing on 1.0.5 or 1.1 back then?

Usually there's no need of headshield on the top of typical command pod, because those parachutes have great heat tolerance.

Strap 2 'Elevon 1' on the craft in mirror symmetry. Deploy them before reentry, and you won't hit the ground before parachute gets deployed. They are basically early-game heat-tolerant airbrakes. Also, it might be better to set parachutes to deploy when risky.

Besides, if you unlocked aerodynamics, 2 deployed eleven 1 works really well with reentry issues. It lets the craft decelerate quite fast, and prevent it from getting in streamlined attitude.

I found that Pe of 38km~42km generally works well. Provides enough deceleration while not giving too much heat burning up. Heat tolerant parts(2000K) can definitely handle the reentry even when they are placed directly to the airstream. Also entering parachute-first is helpful as the parachute have excellent heat tolerance. (2600K, it's next to the best) Besides, does it slow down well under 10km? If it don't want to decelerate on transonic speed, then you're definitely in trouble. The spaceship won't land safely, if you don't have drogue parachutes. (i.e. try drogue parachutes if this is the case)

Calculating optimal first stage? I'm looking forward to it!

It's atmospheric ISP of Reliant, which means it only applies on surface level. Isp of the engine will increase quite fast during the ascent, so the final altitude will be higher. Also drag is relatively small effect for an aerodynamic rocket.

I tried to find the optimum for the general case, but I got kinda lost with what kind of restriction I should put on. Should I restrict engines by mass? Also should I optimize mass ratio for dv, or dv for mass ratio? What kind of conditions users would need? This is hard..

This one is old for now, but anyway: I made electricprop-rocket spaceplane SSTO. Developed this rocket while trying to design even SSTO. No single airbreathers included! With better propeller engines out there nowadays, propeller-nuke SSTO is quite feasible. Though Eve sea-level SSTO is definitely out of reach.

EVT is trivial as Well, given that one know relevant concepts pretty well. I think understanding these concepts is hard. I posted the theorem without thinking. Btw, local non-global maxima sounds like 'a local maximum which is not global maximum'.

It's one of the fundamental theorem in real analysis. https://en.m.wikipedia.org/wiki/Extreme_value_theorem The generalized version. This is actually quite hard to prove...

Usually, it doesn't matter in atmosphere. Aerodynamically stable craft can hold itself on prograde.

I think I can easily derive the optimal case if continuous number of stage was a thing. (In the case putting the best engine is optimal) But as stage number is quite restricted, I can't just say that way.

Really? I'm sure that I can rewrite the equation above into polynomial equation. So analytic solution does exist for number of stage less than 5, isn't it? Besides, great work! Now it's much more clear.

I've played around with the math with the simple multi-engine case, ignoring those decouplers. I think I got something here. 1. Optimum on Fixed number of stage & Fixed engine properties for each stage I'll deal with variable number of stage later.

The math involved here is similar with generic case. Though disposable tank should be different, as TWR will keep increase. (In the case you should get used to the low initial TWR)

@Spricigo, I think the scope of this article does not cover the general case yet.

Then what about moving this thread to the Tutorials section?

I can't find any error on your math. On the problem of the 4th part: The graph might look a bit off, but the relative dv for stage-to-stage ratio of 50 is only 1200m/s. So it's not that much. This result is also consistent with the last part. Besides, I found this online plotter which has grid to make things clear. It seems that we like to enlarge small things in our brain. EDIT: Even NERVs doesn't seem to bother staging on low TWR. (TWR 0.6 is high for nukes, isn't it?) EDIT2: Also, even though the graph doesn't seem to converge to 0, math says that it should converge to zero. ln(x) is one of the most slowly increasing graph which in turn diverges to infinity.

If you consider roving mun, this is enough. It is even fully reusable. Nervs will shave the mass further. (If I recall correctly, this is before I got Nerv tech)

I don't like the blunt edge of the hatch. It's the problem That's one of the most useless node for me.. I just don't want to unlock the node. It has the same amount of fuel with the shortest 2.5m tank, while being more heavy. Also I want to haul less fuel, about 600 units of LF+Ox for 4 crewed one.

I don't care much about using mk1 command module, but it does look too heavy. I use 1 spark and up to 2 ants for the propulsion, or it ends up cost more fuel than 12 passenger shuttle.

It highly depends on your TWR. If you have sufficient TWR(over 4 relative to the planet), you would get the dv written on the dv map. So what's your TWR? I usually add 100m/s~200m/s or so for safety margin. This helps in case of accident. How did you perform the transfer burn? Did you get the periapsis down to Kerbin? After reaching Eve, you can get to Jool with several gravity assists. I think this approach will get you to Jool in 1.2km/s of dv with several gravity assist, which should save good amount of fuel. (Also chemical engines take over nukes with the dv) There is one disadvantage with this approach: takes too much time, both in-game one and real one.