For Questions That Don't Merit Their Own Thread

[Arco123]

Yeah, that's one thing. It doesn't have to be people. I knew I pulled that number out of somewhere. Anyways, there's two possible answers. One with tech which does everything for you. Low number. Or you have to do it yourself. High number. 

[tater]

 

[HaplessBystander]

I have an inquiry regarding how to find the theoretical maximum exhaust velocity of a relativistic rocket. I was able to find a document that provides an equation at the very bottom to do just that, but stops short of explaining the logic behind the equation:

http://www.relativitycalculator.com/images/rocket_equations/AIAA.pdf

Someone else had the same question:

https://physics.stackexchange.com/questions/514616/maximum-exhaust-speed-of-relativistic-rocket?answertab=votes#tab-top

The provided answer is very helpful! But, there's still, owing to my lacking some of the mathematical knowledge assumed on the part of the answer provider, a gap I was hoping you all of the fine Kerbal Space Program Forums would be able to fill in for me. 

So, two questions:

1) Why is the velocity of the rocket post-burn a derivative " dv' "? Isn't the derivative of a velocity with respect to time an acceleration? 

2) What, exactly, are the steps taken to get from the first equation to the second? I know that it states two of the steps, but the major tripping point is I've no idea what's being referred to by "O(dx^2) terms." 

Thanks for the help y'all. 

 

Edited January 12, 2020 by HaplessBystander

[razark]

5 hours ago, linuxgurugamer said:

...the best way to find out any realistic number would be to look ar real world examples of isolated populations.  Not something I’m going to do, but the data is there; there have been enough isolated populations that a reasonable answer could be found.

Just a quick check: https://en.wikipedia.org/wiki/Sentinalese#Population

50 - 200 seems to be possible.

 

This is for a very low-tech civilization, though.  More specialized division of labor might raise those numbers a bit.

Edited January 11, 2020 by razark

[kerbiloid]

2.
And a snake.
But they must have concrete names.

***

Afaik, the original population of proto-human apes is estimated as "probably ~10k".

Afaik, when ~70 ky ago the humanity has been (un)successfully vulcanized by Toba, there were ~10k of survivors, resolving into the genetic bottleneck.

Afaik, when the first generation of the civilization had appeared (~9 ky ago, Fertile Crescent), their culture and technologies made a qualitative leap once their largest settlements reached the 10k treshold.
(Because the diversity of production and interactions reached the point when you can make pots or boots and don't spend your tme on agriculture, so you can become a professional harry potter or a shoemaker.
On the other hand if you are a peasant you don't need to make all your goods yourself, because there is a person who makes them faster and better for a handful of food.
When you live in a small village, there is not enough buyers to live by pure shoemaking.
So, the 10k resulted into division of labour and faster technological progress.)

Afaik,if have a look at various recessive genetic diseases, they have ~1/(1..10k) probability to present in a random human.
So, afaik, ~10k is an estimated safe population size to prevent the inbreeding problems.

Also we should remember that there are technologically expensive technical solutions (like transport, nuclear plants and greenhouses) which make sense only from some amount of customers.

So, 10 k looks an absolute reasonable minimum for a colony, unless it's fully automated and consists of specially filtered and genetically optimized people (but then why do you need them there at all?)

[tater]

https://www.behance.net/gallery/34692063/Morgan-Silk-Rockets

Amazing images:

[magnemoe]

15 hours ago, kerbiloid said:

2.
And a snake.
But they must have concrete names.

***

Afaik, the original population of proto-human apes is estimated as "probably ~10k".

Afaik, when ~70 ky ago the humanity has been (un)successfully vulcanized by Toba, there were ~10k of survivors, resolving into the genetic bottleneck.

Afaik, when the first generation of the civilization had appeared (~9 ky ago, Fertile Crescent), their culture and technologies made a qualitative leap once their largest settlements reached the 10k treshold.
(Because the diversity of production and interactions reached the point when you can make pots or boots and don't spend your tme on agriculture, so you can become a professional harry potter or a shoemaker.
On the other hand if you are a peasant you don't need to make all your goods yourself, because there is a person who makes them faster and better for a handful of food.
When you live in a small village, there is not enough buyers to live by pure shoemaking.
So, the 10k resulted into division of labour and faster technological progress.)

Afaik,if have a look at various recessive genetic diseases, they have ~1/(1..10k) probability to present in a random human.
So, afaik, ~10k is an estimated safe population size to prevent the inbreeding problems.

Also we should remember that there are technologically expensive technical solutions (like transport, nuclear plants and greenhouses) which make sense only from some amount of customers.

So, 10 k looks an absolute reasonable minimum for a colony, unless it's fully automated and consists of specially filtered and genetically optimized people (but then why do you need them there at all?)

Loads of technology who only makes sense if you population is far more than 10K, this probably includes any sort of mass production including stuff like textile mills outside of special settings like you need lots of sailcloth. 
Note that if you expect an very rapid population growth like more than an doubling every generation and have stockpiles of advanced technology you probably want to keep lots alive even if not practical as your population in 100 year will be above 100K. 

The general problem is that lots of industrial age technology require an mass marked to work out, or an large tax base to finance as they was very expensive or labor intensive. 
This issue has grown exponential, modern semiconductor plants or car factories cost many billions and has an large group of suppliers providing very specialized products who also require their specialized supply chain. 
Yes you can simplify stuff but don't think 3d printing help much.

You are basically making an von-newman machine, its simplified because humans is part of the system, or rather its simplifying on an terrestrial body there humans just need something to eat add some clothing and housing at worst.
Now try making an self supplied Mars base and you need to be able space suits life support systems and solar panels.
This will be very hard and need lots of major breakthroughs. Most likely we make universal replicators or teraform the place as both would be overall useful.

[kerbiloid]

5 hours ago, magnemoe said:

an very rapid population growth

would require same rapid growth of stable agricultural production.
So, would be more a problem than a requirement.

Imho, actually no colony would get self-sustainable in terms of food until it gets megalopolis-sized, i.e. reaches ~1 mln of people.
First of all because the Martian agriculture is a by-product of Martian iindustry.

Secondly, what if a Martian greenhouse suddenly cracks or weevils eat all potato? They need redundancy and/or a food reserve for years.
So they either have to transport it from the Earth (then why bother with greenhouses), or make that reserve from the uneaten part of previous harvests.
Also they can't produce just one species of crops, they need either grow algae and cultured meat, or a large set of greenhouses not to be scaled down.

So, while to survive they need ~10 k, actually they could become self-sustainable after their extraterrestrial industry first allows to grow just their own strawberries an tomatos, then the greenhouses get so numerous that they produce more edible organics than can eat. Also, there should be several separated farms for quarantine reasons.

[magnemoe]

13 hours ago, kerbiloid said:

would require same rapid growth of stable agricultural production.
So, would be more a problem than a requirement.

Imho, actually no colony would get self-sustainable in terms of food until it gets megalopolis-sized, i.e. reaches ~1 mln of people.
First of all because the Martian agriculture is a by-product of Martian iindustry.

Secondly, what if a Martian greenhouse suddenly cracks or weevils eat all potato? They need redundancy and/or a food reserve for years.
So they either have to transport it from the Earth (then why bother with greenhouses), or make that reserve from the uneaten part of previous harvests.
Also they can't produce just one species of crops, they need either grow algae and cultured meat, or a large set of greenhouses not to be scaled down.

So, while to survive they need ~10 k, actually they could become self-sustainable after their extraterrestrial industry first allows to grow just their own strawberries an tomatos, then the greenhouses get so numerous that they produce more edible organics than can eat. Also, there should be several separated farms for quarantine reasons.

In rapid population growth I assumed an earth like environment and you wanted to keep skills you would need later even if not needed now.
The US is producing M1 tanks even if they have more than they needs. The reason is that shutting down tank production today and restarting it in say 2030 will be much more expensive as all the people working at building tanks has moved on. 
And yes growing food is easy, we did that during the stone age after all. 

Main reason to grow food in space the next 25 years is salad, its taste good and is healthy so far (an generation old joke is eat lots of salad now while its still healthy) 
You can freeze meat and fish pretty well even most vegetables but not salad.  

And the business idea, GM an mix of an hen and an parrot, getting an social bird who lay your breakfast egg.

[Terwin]

On 1/11/2020 at 10:52 AM, HaplessBystander said:

So, two questions:

1) Why is the velocity of the rocket post-burn a derivative " dv' "? Isn't the derivative of a velocity with respect to time an acceleration? 

dv is short-hand for delta-v, or 'change in velocity'

The reason a rocket burn is always referred to by dv is because that is the only relevant value: how much does/did this burn change the velocity of the vessel?

(the number of newtons of force is useless without knowing the mass of the vessel, and even then you would need to calculate the acceleration based on the change of vessel mass as fuel is consumed; the rate of acceleration does not tell you much unless you also know the duration of that acceleration(and the rate of acceleration will generally change based on the change in vessel mass as fuel is consumed anyway)

Finally, the change in velocity is a single number which can tell you where you can go as well as how long it will take to get there:

 

 

[HaplessBystander]

3 hours ago, Terwin said:

dv is short-hand for delta-v, or 'change in velocity'

The reason a rocket burn is always referred to by dv is because that is the only relevant value: how much does/did this burn change the velocity of the vessel?

(the number of newtons of force is useless without knowing the mass of the vessel, and even then you would need to calculate the acceleration based on the change of vessel mass as fuel is consumed; the rate of acceleration does not tell you much unless you also know the duration of that acceleration(and the rate of acceleration will generally change based on the change in vessel mass as fuel is consumed anyway)

That's all very well but what I really need to know is just why that little prime symbol is there. It's specifically the calculus used in this math I don't understand

[tater]

https://www.eso.org/public/images/eso1242a/zoomable/

[kerbiloid]

The greatest optimists in the Solar System.

Spoiler

Floral camouflage for space troops!

At least somebody really believes in life beyond the Earth!

Upd.
The comments made my day, too, especially about Ewoks.

Edited January 19, 2020 by kerbiloid

[DDE]

3 hours ago, kerbiloid said:

The greatest optimists in the Solar System.

  Hide contents

Floral camouflage for space troops!

At least somebody really believes in life beyond the Earth!

Upd.
The comments made my day, too, especially about Ewoks.

Can we stop the repurposed bovine waste train, please?

We all know how the combat uniform will look like:

Spoiler

 

Edited January 19, 2020 by DDE

[K^2]

On 1/13/2020 at 2:37 PM, HaplessBystander said:

That's all very well but what I really need to know is just why that little prime symbol is there. It's specifically the calculus used in this math I don't understand

Prime doesn't always denote a derivative. In this case, it simply denotes velocity gained in the moving frame of reference. You'll still have to convert this to rest frame if you're interested in rocket's acceleration in rest frame. Further, in this case, all of the d-variables will be taken to zero in the limit as the final step so that you can get the actual acceleration - dv/dt.

It's a very ugly way of deriving the acceleration of the rocket, IMO, but it will give you correct answers if you take the limits properly and do all the cancellations. Wikipedia article gives a much cleaner derivation. Although, they skip a lot of intermediate steps. Nonetheless, if you want to understand a relativistic rocket, that's what I would recommend looking into. - Relativistic Rocket

[wumpus]

On 1/19/2020 at 8:04 AM, DDE said:

Can we stop the repurposed bovine waste train, please?

We all know how the combat uniform will look like:

  Hide contents

 

 

So all they really need are a lower visibility helmet (more places for cool logos) and that chest dohicky.  NASA already does orange:

[DDE]

3 hours ago, wumpus said:

So all they really need are a lower visibility helmet (more places for cool logos) and that chest dohicky.  NASA already does orange:

But do they do it better than muh boi?

[Jestersage]

Would you consider "surface redezvous" actually rendezvous, or just using such term for the purpose of stating mission profile?

For context: Surface rendezvous, specifically that of Lunar Suface Rendezvous, is what used to describe the ILREC 1990s plan, in which a lander with lander with ISRU land first to deliver oxygen to the subsequence lander for the return trip.

Another I can think of that is similar is the Mars Direct, where a lander land on Mars with ISRU to refuel, then once done, another craft will land; then crew depart on the first lander.

[AngrybobH]

Because of Oberth, burning at pe is more efficient but what about capture burns like you would need to do around an airless body?

[Terwin]

11 hours ago, AngrybobH said:

Because of Oberth, burning at pe is more efficient but what about capture burns like you would need to do around an airless body?

You still have a point of closest approach, even if you are not in orbit.  The pe is just used as short-hand for 'point of trajectory that is deepest inside the gravity well', with regards to Oberth, and any time you pass a body you will still have that, even if it has a different name.(and with a wonky-enough gravity map, it might not even be the pe in all cases)

[mikegarrison]

[AngrybobH]

2 hours ago, Terwin said:

You still have a point of closest approach, even if you are not in orbit.  The pe is just used as short-hand for 'point of trajectory that is deepest inside the gravity well', with regards to Oberth, and any time you pass a body you will still have that, even if it has a different name.(and with a wonky-enough gravity map, it might not even be the pe in all cases)

ok. i get all that with respect to leaving an orbit. Are you saying the same point is also the best for slowing down enough to achieve orbit? It makes sense that at pe (or near it) is the best place to affect your ap directly. I just always wondered if there was a better place in a flyby to do a capture burn with respect to dV spent.

[StrandedonEarth]

23 hours ago, AngrybobH said:

ok. i get all that with respect to leaving an orbit. Are you saying the same point is also the best for slowing down enough to achieve orbit? It makes sense that at pe (or near it) is the best place to affect your ap directly. I just always wondered if there was a better place in a flyby to do a capture burn with respect to dV spent.

Well, that depends on your TWR and how much dv is needed. In theory the lower your pe the less dv is needed, but I don’t know if it’s a linear Relationship or what. In practice, I’ve had a several minute long Moho capture burn lower my already low pe into the regolith   So surface skimming can be dangerous when starting a burn well before pe. Extra-Careful planning is required 

Edited January 25, 2020 by StrandedonEarth

[mikegarrison]

1 hour ago, StrandedonEarth said:

Well, that depends on your TWR and how much dv is needed. In theory the lower your pe the less dv is needed, but I don’t know if it’s a linear Relationship or what. In practice, I’ve had a several minute long Moho capture burn lower my already low pe into the regolith   So surface skimming can be dangerous when starting a burn well before pe. Extra-Careful planning is required 

1) For an instantaneous delta-v change, (whether speeding up or slowing down), it is most efficient when you are moving the fastest. You move the fastest when you are deepest in the gravity well. That's why you burn at pe.

2) The point you raise here is important, namely that for low-TWR engines the actual delta-v change is far from instantaneous. I suppose the most efficient burn would be whatever involved the highest integrated total of exhaust velocity * ship velocity (just guessing on that, I didn't do the math). It's also important (as you say) to consider that you don't want to smash into the planet. And also, when you end your burn you will necessarily be in your final orbit. so if you wanted to end your burn in a perfectly circular orbit at a certain altitude, for instance, you would have to plan your burn very carefully to make sure you ended it in this exact situation. (In practice it's probably better and certainly easier to make a "capture burn" and then follow this up with other burns to correct the orbit to what you want as the final orbit.)

[ARS]

Does the mass of the vehicle affect the G-force strain inflicted on the human body? For example, let's take a 2-ton car and 60-ton tank going at 200km/h (don't ask how the tank got that fast in the first place). If both vehicles suddenly pulled a sharp turn (without flipping over), does the bulk of tank's mass causing more strain on human body compared to the car?