Abastro

Theoretical optimum of cost efficiency to orbit (1.2)

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What is the current theoretical limit of the cost efficiency to orbit? For stock 1.2 without cheats, in terms of cost per ton, for these cases:

1. Without any recovery

2. Including recovery, without airplane flight path

3. Including recovery, with airplane flight path

Practically, there was an orbiter capable of 600/t without any recovery a few versions ago (AFAIK). For the reusable case, I got 500/t with TSTO rocket in 1.1.3 and 1.2, and there should be better one.

 

Here's a challenge to find the practical limit of the cost efficiency to orbit.

Here's a spreadsheet with optimal cost efficiency for each engines

Edited by Abastro
Added the spreadsheet to the OP.

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I'm not sure about the exact figure, but I think my SSTO can do 350-400/t. Unfortunately, the payload needs to fit into the long mk2 cargo bay. 

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If nothing pops out of the woodwork, we might have to bring this question to the challenge forums. @tseitsei89 posed exactly your question as a challenge for version 1.1 about a year ago, and it feels like a fine time for a reboot for version 1.2.

In the challenge, the non-recoverable systems were typically dominated by Kick Backs and Twin Boars. As for the cost efficiency I usually get, it's in the in the 700/ton to LKO range.  In v1.2, :funds:700/ton mega lifters can be made without much fuss using Mamoths and bundles of SRBs.

Kerbal_Space_Program_2017_02_24_22_14_46

 

I am hugely curious about your 500/ton craft. Mind posting some pictures?

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2 hours ago, Cunjo Carl said:

If nothing pops out of the woodwork, we might have to bring this question to the challenge forums. @tseitsei89 posed exactly your question as a challenge for version 1.1 about a year ago, and it feels like a fine time for a reboot for version 1.2.

 

Wow, this one is exactly what I was thinking. I'll post a reboot of the challenge with my own entry. This thread will be edited to be on the theoretical limit of the cost efficiency.

2 hours ago, Cunjo Carl said:

I am hugely curious about your 500/ton craft. Mind posting some pictures?

It's fully reusable TSTO craft made for practical use. Thus not so competitive...

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2 hours ago, InterCity said:

I'm not sure about the exact figure, but I think my SSTO can do 350-400/t. Unfortunately, the payload needs to fit into the long mk2 cargo bay. 

Hmm, so SSTO spaceplane looks definitely better. (Form factor of the cargo bay seems fine)

There's one with 84/t on the extreme end, on 1.1

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Once there was someone that made a profit from a mision and still had some fuel left so i teoreticly could be minus

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21 minutes ago, rkarmark said:

Once there was someone that made a profit from a mision and still had some fuel left so i teoreticly could be minus

Profit doesn't count as reduction of cost.

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6 hours ago, Abastro said:

Wow, this one is exactly what I was thinking. I'll post a reboot of the challenge with my own entry. This thread will be edited to be on the theoretical limit of the cost efficiency.

Neat! I look forward to it.

 

6 hours ago, Abastro said:

It's fully reusable TSTO craft made for practical use. Thus not so competitive...

500/ton is still pretty good for a reusable TSTO- they're almost trickier to make work well than SSTOs in a lot of ways!

 

Also, for building optimal ascent rockets, I learned quite a bit by playing with Gary Court's optimal rocket calculator which has been updated for version 1.2! It doesn't work one-for-one with an actual ascent, because you can only set one TWR in this, and for ascent your optimum wanders up and down throughout the launch profile, but it definitely gives some food for thought! Just make sure to uncheck all the "gimballing, throttling, single stack, etc." options if you want to see SRBs appear.

https://garycourt.github.io/korc/

 

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14 hours ago, Cunjo Carl said:

500/ton is still pretty good for a reusable TSTO- they're almost trickier to make work well than SSTOs in a lot of ways!

I don't have the photo right now. I just strapped radial parachutes and did shallower gravity turn. It's just a matter of timing: Give enough kick on the second stage to push apoapsis further, land the first stage to the ocean before second stage reaching apoapsis. Here are those (suboptimal) crafts, heavier ones are better.

Besides, here's the rebooted challenge.

14 hours ago, Cunjo Carl said:

Also, for building optimal ascent rockets, I learned quite a bit by playing with Gary Court's optimal rocket calculator which has been updated for version 1.2! It doesn't work one-for-one with an actual ascent, because you can only set one TWR in this, and for ascent your optimum wanders up and down throughout the launch profile, but it definitely gives some food for thought! Just make sure to uncheck all the "gimballing, throttling, single stack, etc." options if you want to see SRBs appear.

https://garycourt.github.io/korc/

Thanks for the great resource!

Edited by Abastro

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So I played with formulas to find the theoretical bound for LF/Ox rockets.

There are 4(or 5) types of mass regarding rocket type propulsion: Payload, Fuel&Fuel Tank, Engine and Utilities(Probe/SAS, Aerodynamics and such).

(WARNING: Wall of Formulae)

There are certain requirements for a stage: It should have enough initial TWR and Δv budget.

These constraints can be expressed with the formulas:

yFmhfJR.png

Mass of each part has corresponding relations:

Pp61ASx.png

NOTE: The propellant fraction used here is wrong; It's propellant mass per dry weight.

(I think it's reasonable assumption that utility cost is proportional to dry mass, regarding the structural costs)

Putting these together, upper bound of payload mass to total (wet) mass is given by this formula:

eaqFaJ2.png

(Apparently, payload mass is the remnant mass without Fuel&Fuel Tank, Engine and Utilities)

Let's just deal with LF/O tanks, since Nerv has totally different profile. (Dawn? No)

Then the formula becomes:

OSMgXOc.png(Actually, the last term should be α/(ζ_tot+1))

Now, let's calculate price.

Usually, price of utilities can be ignored. For disposal lifters they are tiny fraction of the mass, and they just got recovered for reusable lifters.

    (There's one counterexample: Cheap solid fuel engines. I'll deal with them later)

And, it's generally acceptable to say that dry price of fuel tank is same with the fuel cost for big enough tanks. (Look at the numbers!)

Thus,

BrdHKq0.png(Inequality is inverted here)

(φ is price per mass of each part; T is for fuel tank, F is for fuel itself, eng is for engine

  φ_F = 91.8/t for LF/O Tanks)

For disposable lifters, lower bound of the price per single ton of payload is given by

0Whdpzk.png

For reusable lifters, the lower bound is

SxvRuna.png(Again, the last term should be α/(ζ_tot+1))

(Formulae end here)

Here's a spreadsheet with these information for some engines:

KSP Engine Specifications

(Twin-Boar is regarded as engine + Rockomax Jumbo-64 fuel tank)

These information is given for single stage rocket. This could be used to determine performance limit of simple multiple stage rocket.

This wouldn't work for asparagus staging / drop tanks, though. I'll take care of it next time.

PS. Twin-Boar seems to be OP for these purpose.

Edited by Abastro
Errors in equations...
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10 hours ago, Abastro said:

*Mathmathmath*

PS. Twin-Boar seems to be OP for these purpose.

It's definitely a favorite! The twinboar even got a small boost of fuel in v1.2 to make it slightly better, too. That having been said, every engine in this game has a place where it seriously shines*, and this is the Twin-Boar's. That balance is a big part of what makes the game compelling- it's very fun to discover new combinations of parts/rockets that feel OP. To balance it, the twinboar has a couple downsides, the largest for launching being its 2.5m diameter, which is traditionally quite draggy for a given fuel storage. Also in the past they've historically been quite difficult to use in numbers greater than one, but it's much easier in v1.2 thanks to automatic fuel transfer between radially attached tanks... It's the best!

A couple other fun discoveries: Because you're wasting fuel like crazy while accelerating off the launch pad (up to your optimal freefall velocity), thrust is actually more important than Isp in the first moments. The best cost/thrust by far is the flea, of all things! And now we have autostruts and rigid joints, we may even be able to take advantage of this. Also, the best Isp + thrust/cost for the low and middle altitudes is actually the whiplash + subsonic radial intake, even for disposable rockets. They're draggy and quite hard to work with in practice, but undoubtedly worth it. A practical disposable whiplash launcher has been a white whale of mine over the years.

I have some equations for doing the same manipulations on a stenopad around here somewhere. I'll have to compare notes later today! ... If I can find the darn thing....
Neat use of scripty little-phi and normal little-zeta. I'll admit though, seeing them together again is giving me (jokingly) anxiety attacks thinking back to physical chemistry. Oh gosh: P, M and little alpha are all there too! It's a very uncanny reunion. Undoubtedly, I like their use for cheaply flinging Kerbals to orbit much better than calculating corrected energy balances on open systems of multi-phase chemicals.

I'm glad you made a challenge and look forward to giving it a go after I get some other irons out of the fire!

* Except the Thud**- :D shots fired!
** Sorry thud fans, mostly joking.

Edited by Cunjo Carl
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9 hours ago, Cunjo Carl said:

It's definitely a favorite! The twinboar even got a small boost of fuel in v1.2 to make it slightly better, too. That having been said, every engine in this game has a place where it seriously shines*, and this is the Twin-Boar's. That balance is a big part of what makes the game compelling- it's very fun to discover new combinations of parts/rockets that feel OP. To balance it, the twinboar has a couple downsides, the largest for launching being its 2.5m diameter, which is traditionally quite draggy for a given fuel storage. Also in the past they've historically been quite difficult to use in numbers greater than one, but it's much easier in v1.2 thanks to automatic fuel transfer between radially attached tanks... It's the best!

Yeah, Twinboar is definitely one of the best. Besides, I discovered that Reliant could be reasonable choice for low dv. I couldn't ever expect this... this means they are great for application on small rockets!

9 hours ago, Cunjo Carl said:

A couple other fun discoveries: Because you're wasting fuel like crazy while accelerating off the launch pad (up to your optimal freefall velocity), thrust is actually more important than Isp in the first moments. The best cost/thrust by far is the flea, of all things! And now we have autostruts and rigid joints, we may even be able to take advantage of this. Also, the best Isp + thrust/cost for the low and middle altitudes is actually the whiplash + subsonic radial intake, even for disposable rockets. They're draggy and quite hard to work with in practice, but undoubtedly worth it. A practical disposable whiplash launcher has been a white whale of mine over the years.

Wow, flea? Hmm, I should analyze efficiency of the solid boosters.

And there goes airbreathers. I think they are too OP. Does they have high ISP IRL?

9 hours ago, Cunjo Carl said:

I have some equations for doing the same manipulations on a stenopad around here somewhere. I'll have to compare notes later today! ... If I can find the darn thing....
Neat use of scripty little-phi and normal little-zeta. I'll admit though, seeing them together again is giving me (jokingly) anxiety attacks thinking back to physical chemistry. Oh gosh: P, M and little alpha are all there too! It's a very uncanny reunion. Undoubtedly, I like their use for cheaply flinging Kerbals to orbit much better than calculating corrected energy balances on open systems of multi-phase chemicals.

Sorry for the messy and buggy formulae. I had hard time writing them here. I should fix those in some time...

9 hours ago, Cunjo Carl said:

I'm glad you made a challenge and look forward to giving it a go after I get some other irons out of the fire!

* Except the Thud**- :D shots fired!
** Sorry thud fans, mostly joking.

Thanks! And the Thud... i think some players might use them for side boosters. They are not that bad actually, as shown on the spreadsheet. (Better than Spark)

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1 hour ago, Abastro said:

Yeah, Twinboar is definitely one of the best. Besides, I discovered that Reliant could be reasonable choice for low dv. I couldn't ever expect this... this means they are great for application on small rockets!

Wow, flea? Hmm, I should analyze efficiency of the solid boosters.

And there goes airbreathers. I think they are too OP. Does they have high ISP IRL?

Sorry for the messy and buggy formulae. I had hard time writing them here. I should fix those in some time...

Thanks! And the Thud... i think some players might use them for side boosters. They are not that bad actually, as shown on the spreadsheet. (Better than Spark)

I suspect what you discovered for the Reliant is the reason why they just pushed it behind the Swivel in the tech tree (plus swivel is more user friendly). A lot of folk were just forgoing Swivel for Reliant's cheaper, higher TWR push. And the thud... Hmm. You know, you're right. I hadn't considered how cheap it is relative to the other radials. I'm actually building a reliant+thud Kerbin-ascent stage right now that needs to stay low-mass & low-cost, and a couple thuds are keeping me surprisingly stable during ascent without breaking the budget. Maybe I'll warm up to that brick of an engine in the end.

Yeah, in practice the Flea is hypothetically good en mass at hurling an otherwise low TWR rocket off the pad, the hammer makes a surprisingly nice middle stage because of its low drymass, and the kickback has unparalleled cost/impulse performance (good for initial stages). I'm a big SRB proponent, maybe it shows :)

Plane ISPs can be quite high because they're able to push off the air. You can imagine the engine as creating a certain amount of power, which means a certain amount of energy per time. In chemical rockets, all of that energy needs to be focused into the tiny amount of exhaust products. But planes can put that energy into exhaust and extra air (called 'bypass'). For a given energy, if you push 4 times the mass, it'll only come out half as fast, but will still give you twice the momentum because energy is mv^2 while specific impulse (momentum) is mv. Those huge fuel-efficient turbofans on airliners can push a lot of air so they can get very efficient! As for its practicality for space travel, the only company I know of trying to make an airbreathing spaceplane is REL with The Skylon and they still haven't flown anything yet, but their static tests have been pretty exciting.

Specific_impulse_kk_20090105.png

Image courtesy of wikipedia.

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Well in practice, with a spaceplane, under 200 per ton is easily achievable, even using disposable fairings to protect the payload (obviously not needed for an inline payload of kerbodyne tanks for example).

For theory, lets start by assuming infinite TWR engines and infinite mass ratio tanks, no drag.

Assuming 100% re-usability... You'll get to a maximum of about 1600 airbreathing speed, so 1,800 orbital. You'll need another ~550 m/s to get to orbit.

I'm going to assume Rapiers only at 3200 Isp, and a payload of 1 ton.

Rocket fuel costs:

550= 305*9.81*ln mass ratio : ln mass ratio = 0.184 : mass ratio = 1.2. For every 1 ton of payload, you must buy 0.2 tons of LF+O. That is 18 units of LF and 22 of O. 

This comes out to less than 18.36 funds per ton

Airbreathing fuel costs

1600 = 3200 * 9.81 * ln (mass ratio) :  0.051 = ln (mass ratio): mass ratio = 1.05. For one ton of fuel, you need 50 kg.. but you'll also need another 0.2 tons of rocket fuel per 1 ton of payload... 60 kgs of LF... 12 units : 9.6 funds.

27.96 funds per ton would be an absolute limit with rapiers... and that would assume no drag, and a payload fraction of ~74%. In reality, maximum payload fractions for SSTO spaceplanes gets to 50% . You can figure on doubling the airbreathing costs because of drag, - 37.56 funds per ton, but only ~10% of total mass. These 50% designs are still going to roughly 25% LFO. So with 10% going to fuel for airbreathers, 25% going to fuel for rockets,50% for payload, that leaves 15% for non payload dry mass. (50+15)/50 = 1.3x... so now figure you spend at least 1.3*18.36 = 23.9 funds on rocket fuel per ton, and another 19.2 *1.3 = 25 funds on jet fuel.

49 funds per ton would then be the limit.

I've heard claims of lower than 80 funds/ton, but I rarely saw the payload fraction winners calculating fund per ton - but in these cases the payloads are special, normally chosen for an aerodynamic protfile and high density (veyr high ballistic coefficient).

Similar calculations cna be done for SSTO rockets assuming no better than a 15% payload fraction (if I remember correctly) and 3,400 dV needed to get to orbit.

Edited by KerikBalm
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In all conventional rocket design I managed a ~275/t for a 4½ ton payload.

20770 spacebucks / 75 tons. = 276,93/t

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19 hours ago, Cunjo Carl said:

 A practical disposable whiplash launcher has been a white whale of mine over the years.

I have two TSTO disposable whiplash launchers! One of them (J.A.M.S - Jet Assisted Micro Shuttle) is a drone... I wouldn't really call it practical tbh.. it can take a tiny payload to LEO, but I've never actually used it on preference to my 1.25m rockets which can lift more for less. The other design is a crew transport which is insanely fun to fly! Take it up to a space station, change crew and then return, much more fun than a rocket! This second design (J.A.R.O.D.S - Jet Assisted Rapid Orbital Deployment Shuttle) is one that I actually use, though launch timing is pretty essential.

As far as I can tell both designs have 3 flaws:

1) "disposable" whiplash systems are less cost effective than traditional rockets (though I guess this only matters in Career mode)

2) I use ram intakes rather than shockcones, so that sees a reduction in performance. Cost trade off (see above)

3) both are fairly small designs and end up with not a lot of fuel to play with once in orbit
 

On the other hand they are SOOO0o0o0o cool.

I'll upload some photos tonight if I remember

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9 hours ago, Cunjo Carl said:

snip

Wow, bypass? I couldn't think of that.

BTW, is it possible to make efficient orbiter soly out of the solid boosters?

6 hours ago, KerikBalm said:

Well in practice, with a spaceplane, under 200 per ton is easily achievable, even using disposable fairings to protect the payload (obviously not needed for an inline payload of kerbodyne tanks for example).

For theory, lets start by assuming infinite TWR engines and infinite mass ratio tanks, no drag.

Assuming 100% re-usability... You'll get to a maximum of about 1600 airbreathing speed, so 1,800 orbital. You'll need another ~550 m/s to get to orbit.

I'm going to assume Rapiers only at 3200 Isp, and a payload of 1 ton.

Rocket fuel costs:

550= 305*9.81*ln mass ratio : ln mass ratio = 0.184 : mass ratio = 1.2. For every 1 ton of payload, you must buy 0.2 tons of LF+O. That is 18 units of LF and 22 of O. 

This comes out to less than 18.36 funds per ton

Airbreathing fuel costs

1600 = 3200 * 9.81 * ln (mass ratio) :  0.051 = ln (mass ratio): mass ratio = 1.05. For one ton of fuel, you need 50 kg.. but you'll also need another 0.2 tons of rocket fuel per 1 ton of payload... 60 kgs of LF... 12 units : 9.6 funds.

27.96 funds per ton would be an absolute limit with rapiers... and that would assume no drag, and a payload fraction of ~74%. In reality, maximum payload fractions for SSTO spaceplanes gets to 50% . You can figure on doubling the airbreathing costs because of drag, - 37.56 funds per ton, but only ~10% of total mass. These 50% designs are still going to roughly 25% LFO. So with 10% going to fuel for airbreathers, 25% going to fuel for rockets,50% for payload, that leaves 15% for non payload dry mass. (50+15)/50 = 1.3x... so now figure you spend at least 1.3*18.36 = 23.9 funds on rocket fuel per ton, and another 19.2 *1.3 = 25 funds on jet fuel.

49 funds per ton would then be the limit.

I've heard claims of lower than 80 funds/ton, but I rarely saw the payload fraction winners calculating fund per ton - but in these cases the payloads are special, normally chosen for an aerodynamic protfile and high density (veyr high ballistic coefficient).

Similar calculations cna be done for SSTO rockets assuming no better than a 15% payload fraction (if I remember correctly) and 3,400 dV needed to get to orbit.

Great analysis! This would be good starting point to analyze efficiency of a spaceplane. Probably more thorough analysis regarding L/D will give tighter bounds. I'll try it.

3 hours ago, TimePeriod said:

In all conventional rocket design I managed a ~275/t for a 4½ ton payload.

20770 spacebucks / 75 tons. = 276,93/t

Wow, that's impressive. Did you use reusable rockets or airbreathers?

1 hour ago, MR L A said:

I have two TSTO disposable whiplash launchers! One of them (J.A.M.S - Jet Assisted Micro Shuttle) is a drone... I wouldn't really call it practical tbh.. it can take a tiny payload to LEO, but I've never actually used it on preference to my 1.25m rockets which can lift more for less. The other design is a crew transport which is insanely fun to fly! Take it up to a space station, change crew and then return, much more fun than a rocket! This second design (J.A.R.O.D.S - Jet Assisted Rapid Orbital Deployment Shuttle) is one that I actually use, though launch timing is pretty essential.

As far as I can tell both designs have 3 flaws:

1) "disposable" whiplash systems are less cost effective than traditional rockets (though I guess this only matters in Career mode)

2) I use ram intakes rather than shockcones, so that sees a reduction in performance. Cost trade off (see above)

3) both are fairly small designs and end up with not a lot of fuel to play with once in orbit
 

On the other hand they are SOOO0o0o0o cool.

I'll upload some photos tonight if I remember

I think you should be using cheaper air intake (like diverterless) and doing more aggressive gravity turn. Ram intakes are just too expensive for a disposable craft. Also you need less initial TWR for the airbreathers.

AFAIK whiplash has OP Isp (nearly no need to bother fuel usage) and decent TWR on supersonic speed..

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1 hour ago, Abastro said:

Wow, that's impressive. Did you use reusable rockets or airbreathers?

Its a disposable rocket, all you have to do is be very skeptic about what parts you really "need".

Edit: If I spent some more time tweaking the dV budget, looking for better part mixes and general optimization I could squeeze out 5-10% cost-reduction.  

20170227172012_1_zpsq7wl42ag.jpg

Edited by TimePeriod

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Just looking at that picture, it seems that your payload is 4.5 tons... as claimed.

Thus for 275/ton as claimed, you have a budget of 1,237.5 space bucks. I see 3 reliants... at 1,100 a piece... 3,300 already... nope, over budget already.

Also, 4 SRBs at 850/piece (3400) + 221 funds for the Fuel (883.2 for solid fuel), Then you've got roughly 1 orange tank's worth of fuel in other tanks - 1 orange tank's worth of fuel costs 2937.5 funds....

Nope, even if that was somehow a SSTO that gets 100% recovery, that is no where near 275 funds/ton

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Back when I ran a similar challenge in 1.0.5, it was a major accomplishment to get below 700 funds/ton, and only a few got below 600 funds/ton.  It might be a good idea to take a look at those previous entries for design ideas.

 

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I imagine the theoretical limit would be close to 0. if  you use a spaceplane with ISRU and had an asteroid in LKO. Once you reach space a release payload you could then restock on fuel from the asteroid and return to KSC as though you hadn't used any fuel at all, less the 30-40 m/s required to deorbit. 

Edited by Leafbaron

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2 hours ago, KerikBalm said:

Just looking at that picture, it seems that your payload is 4.5 tons... as claimed.

Thus for 275/ton as claimed, you have a budget of 1,237.5 space bucks. I see 3 reliants... at 1,100 a piece... 3,300 already... nope, over budget already.

Also, 4 SRBs at 850/piece (3400) + 221 funds for the Fuel (883.2 for solid fuel), Then you've got roughly 1 orange tank's worth of fuel in other tanks - 1 orange tank's worth of fuel costs 2937.5 funds....

Nope, even if that was somehow a SSTO that gets 100% recovery, that is no where near 275 funds/ton

I do not really understand what you are trying to get at? I already said it was a disposable rocket, nor an SSTO.

 I took the total cost of the entire craft+cargo and divided it by the total tonnage, is that not you are supposed to do when figuring out how much it would cost pr ton?

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25 minutes ago, TimePeriod said:

I took the total cost of the entire craft+cargo and divided it by the total tonnage, is that not you are supposed to do when figuring out how much it would cost pr ton?

I assume that a more relevant figure would be launcher cost divided by payload tonnage.

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3 minutes ago, Curveball Anders said:

I assume that a more relevant figure would be launcher cost divided by payload tonnage.

In that case, we get a lot higher number; 19345 / 4.5 = 4298/t (I think)

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4 minutes ago, Curveball Anders said:

I assume that a more relevant figure would be launcher cost divided by payload tonnage.

I would say an even more relevant figure would be the cost of the launch vehicle not including the cost of the payload then divide that figure by weight of the payload. 

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