Cheap Access to Space

There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

Back in 1972, it was estimated that the Space Shuttle would cost as
little as $455 per kg. In 2007 dollars, this works out to $2,188.05
per kg. And that was considered good. Below, I outline my theory as to
how we can achieve $600 per kg today, which would work out to $125 in
2007 dollars or better than the space shuttle was supposed to be.

If you can get costs below $600 per kg in today's dollars, you can
launch 25,000 kg of payload for $15 million and thus sell 20 tickets
to space for $15 million, or tickets are for sale at $750,000 per
ticket. That seems reasonable. (The Space Shuttle has a payload of
approximately 25,000 kg).

I will assume the first stage goes straight up and has an imparted
acceleration of 3 g's, e.g. an actual acceleration of 2 g's. I will
also assume it takes 9700 m/s to reach orbit from the ground (orbital
velocity is somewhat less but we must contribute both kinetic and
potential energy to achieve a circular orbit). I will also assume we
have a payload of 25,000 kg and the fuels used are liquid hydrogen
(LH2) and liquid oxygen (LOX). I assume hydrogen costs $3.00 per kg
and oxygen costs $0.20 per kg. These seem reasonable.

Finally I make one small blunder: the cost of the vehicle without fuel
is just $100 times the weight in kilograms. This seems reasonable if
it is made of aluminum alloy, but in practice it takes a lot of energy
to machine rocket parts from raw materials, and all this energy costs
money. Nevertheless $100/kg is a ball-park figure (note this low cost
precludes the use of titanium, baring any new technologies. Also we
might need to circulate a fluid throughout the skin of the first stage
to keep it from melting).

First, let's look at a 3-stage throw-away system for comparison with
my proposal.

A typical rocket is 71% propellant and has 15% payload, e.g. is 14%
empty weight. This corresponds with a mass ratio of 3.45 which seems
reasonable.

Stage 1 : 71% propellant, 15% payload, 14% empty. Imparted delta V is
4330 m/s but only 2881.2 m/s is realized due to gravity losses (we're
flying straight up). We assumed an exaust velocity of 3500 m/s which
is reasonable for LH2-LOX at sea level.

Stage 2 : 71% propellant, 15% payload, 14% empty. A delta-V of 5447 m/
s is realized. We assume an exaust velocity of 4400 m/s which is
reasonable for LH2-LOX in vacuum.

Stage 3 :1373 m/s is needed to reach our 9700 m/s figure. This leads
to a needed mass ratio of 1.366 e.g. 26.8% propellant, 14% empty,
59.2% payload.

Now using this figure as a baseline, we will see how my proposal
stands. The payload is
0.15 * 0.15 * 0.592 = 1.332%. Since we state that we have a payload of
25,000 kg, we deduce the vehicle must have a mass of 1,876,877 kg at
liftoff.

Let's get a minimum estimate of how much it costs, though. To do this,
we take the liftoff mass of 1,876,877 kg and multiply by 14% to get
the empty weight of just the first stage. At $100 / kg, just the first
stage costs $26,276,276.

Using this method, we can get to space, but it costs over $25 million
to reach orbit. That is, it costs over $1000 per kg to reach orbit.

Now for my proposal.

I propose, -decrease- the payload fraction, thus increasing the mass
of the vehicle, on purpose. Why you might ask? Because the first stage
is not reusable in the above system. But if the first stage is a
rocket-plane that flies to above 40 km and then deploys a 2-stage
rocket system that boosts to orbit, instead of a throw-away system,
then it is true the weight of the wings -adds- to the total weight of
the system, but the first stage, which is the most massive part of the
vehicle, becomes reusable.

I assume the first stage is a rocket-plane with an empty mass of 42%
(including wings, ball-park what the Concord's empty weight is). We
still want the rocket-plane to have 15% payload, and this leaves us
with only 43% rocket propellant. Using an exaust velocity of 3500 m/s
again, we see the first stage can impart only a delta-V of 1967 m/s.

Now we are taking off vertically (the first-stage lands horizontally).
1967 m/s is the vertical velocity we'd achieve if there were no
gravity losses. It's mach 5.73 at sea level, but we'll be over 40 km
in altitude by this point, so "hypersonic" stage separation is a non-
issue. Again we assume an imparted acceleration of 3 g's (29.4 m/s^2).
The first stage boost thus lasts only 66.9 seconds.

Actual velocity achieved will be 1311.24 m/s (2 g's times 66.9
seconds). We achieve an altitude of 0.5 * 2g * t * t = 43861 m or just
over 40 km.

We are cruising upwords at 1311.24 m/s -- say 1300 m/s -- at 43,861 m
altitude. That is 143,901 ft. Way high up.

Now to achieve orbit, we need a delta-V of 9700 m/s. 9700 - 1300 =
8400 m/s.

That's where the space plane deploys its 2-stage rocket system. In 2
stages we must achieve a delta-V of 8400 m/s.

Stage 2 : 71% propellant, 15% payload, 14% empty weight. Using an
exaust velocity of 4400 m/s (in vacuum), we can achieve a delta-V 5447
m/s via Stage 2..

Stage 3 : to reach 9700 m/s we need a delta-V of 2953 m/s. That is, a
mass ratio of 1.96 or 49%. If it's 14% empty weight, we can have a
payload of 37%.

Putting it all together: 0.37 * 0.15 * 0.15 = 0.008325. That is to
say, we now have a payload fraction that has been reduced, to only
0.8325%. That sounds low, it's certainly lower than the payload
fraction of the disposable 3-stage rocket described above.

3,003,003 kg is the take-off weight needed for 25,000 kg to reach
orbit. It's considerably more than the weight of the 3-stage throw-
away (disposable) rocket system, but, let's see how the cost compares!

3.003003e6 * 0.42 = 1261261.26 x $100/kg = $126,126,126 (Not bad!
E.g. $ 504,505 / flight at 250 flights)

That is to say, the first stage "reusable" space plane costs $126
million. We amortize it over 250 flights, assuming it is good for that
many flights. Dividing $126 million by 250, we find the cost of the
first stage is only about $500,000 per flight. Compare that to the $25
million cost of the disposable first stage!

3.003003e6 * 0.15 * 0.14 = 63063.063 x $100/kg = $ 6,306,306.3
3.003003e6 * 0.15 * 0.15 * 0.14 = 9459.45945 x $100/kg = $
945,945.945
Total SHIP cost per flight: 504505 + 6306306.3 + 945945.945 =
$7,756,757.245
Dividing by 25,000 kg we find the ship cost is $310/kg

Propellant cost.
3.003003e6 * 0.43 = 1 291 291.29 kg
3.003003e6 * 0.15 * 0.71 = 319 819.8195 kg
3.003003e6 * 0.15 * 0.15 * 0.49 = 33 108.108075 kg

Total propellant: 1291291.29 + 319819.8195 + 33108.108075 = 1 644 219
kg
LH2 : 1644219 * 11800 / 81614 = 237726 * 3.00 USD = $ 713178.0
LOX : 1644219 * 69814 / 81614 = 1406493 * 0.20 USD = $ 281298.6

Total propellant cost: $994476.6

Total mission cost: 994476.6 + 7756757.245 = $ 8 751 233.845
E.g. $350 / kg

Thus, if amortizing over 250 flights is reasonable, e.g. if we can
actually find 250 customers that need to launch 25,000 kg into space
for a mission cost of $15,000,000 (e.g. ticket price of $750,000 for
20 tourists on a 3-day mission to space), then including fuel -and-
the cost of the disposable vehicle, we arrive at a total mission cost
of around $9.0 million.

But there are other costs like human salaries and so on, and providing
the payload itself, and profit, so we will round this figure up to
$15.0 million per mission.

Compare this cost to the first-stage cost of $25.0 million for a throw-
away system. Thus, I have shown that a reusable first-stage, despite
having a heavy wing weight, can substantially reduce the per-mission
and per-kg payload cost.

Even though the payload fraction is substantially reduced, and -
without- using single-stage-to-orbit or scramjets, we have found a way
to lower the cost of access to space, within the model used (e.g. $100/
kg empty cost etc.), to just $600 / kg which is marketable.

Anyone care to comment or check my numbers? Your feedback is
appreciated!

On Fri, 14 Dec 2007 23:23:55 -0800 (PST), in a place far, far away,
made the phosphor on my monitor glow in such a
way as to indicate that:

There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

Yes, a lot of mistaken interest in them. Scramjets, or any other
airbreather, are unlikely to be the solution to low-cost launch.

On 15 Dec, 07:23, wrote:
There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

Back in 1972, it was estimated that the Space Shuttle would cost as
little as $455 per kg. In 2007 dollars, this works out to $2,188.05
per kg. And that was considered good. Below, I outline my theory as to
how we can achieve $600 per kg today, which would work out to $125 in
2007 dollars or better than the space shuttle was supposed to be.

If you can get costs below $600 per kg in today's dollars, you can
launch 25,000 kg of payload for $15 million and thus sell 20 tickets
to space for $15 million, or tickets are for sale at $750,000 per
ticket. That seems reasonable. (The Space Shuttle has a payload of
approximately 25,000 kg).

I will assume the first stage goes straight up and has an imparted
acceleration of 3 g's, e.g. an actual acceleration of 2 g's. I will
also assume it takes 9700 m/s to reach orbit from the ground (orbital
velocity is somewhat less but we must contribute both kinetic and
potential energy to achieve a circular orbit). I will also assume we
have a payload of 25,000 kg and the fuels used are liquid hydrogen
(LH2) and liquid oxygen (LOX). I assume hydrogen costs $3.00 per kg
and oxygen costs $0.20 per kg. These seem reasonable.

Finally I make one small blunder: the cost of the vehicle without fuel
is just $100 times the weight in kilograms. This seems reasonable if
it is made of aluminum alloy, but in practice it takes a lot of energy
to machine rocket parts from raw materials, and all this energy costs
money. Nevertheless $100/kg is a ball-park figure (note this low cost
precludes the use of titanium, baring any new technologies. Also we
might need to circulate a fluid throughout the skin of the first stage
to keep it from melting).

First, let's look at a 3-stage throw-away system for comparison with
my proposal.

A typical rocket is 71% propellant and has 15% payload, e.g. is 14%
empty weight. This corresponds with a mass ratio of 3.45 which seems
reasonable.

Stage 1 : 71% propellant, 15% payload, 14% empty. Imparted delta V is
4330 m/s but only 2881.2 m/s is realized due to gravity losses (we're
flying straight up). We assumed an exaust velocity of 3500 m/s which
is reasonable for LH2-LOX at sea level.

Stage 2 : 71% propellant, 15% payload, 14% empty. A delta-V of 5447 m/
s is realized. We assume an exaust velocity of 4400 m/s which is
reasonable for LH2-LOX in vacuum.

Stage 3 :1373 m/s is needed to reach our 9700 m/s figure. This leads
to a needed mass ratio of 1.366 e.g. 26.8% propellant, 14% empty,
59.2% payload.

Now using this figure as a baseline, we will see how my proposal
stands. The payload is
0.15 * 0.15 * 0.592 = 1.332%. Since we state that we have a payload of
25,000 kg, we deduce the vehicle must have a mass of 1,876,877 kg at
liftoff.

Let's get a minimum estimate of how much it costs, though. To do this,
we take the liftoff mass of 1,876,877 kg and multiply by 14% to get
the empty weight of just the first stage. At $100 / kg, just the first
stage costs $26,276,276.

Using this method, we can get to space, but it costs over $25 million
to reach orbit. That is, it costs over $1000 per kg to reach orbit.

Now for my proposal.

I propose, -decrease- the payload fraction, thus increasing the mass
of the vehicle, on purpose. Why you might ask? Because the first stage
is not reusable in the above system. But if the first stage is a
rocket-plane that flies to above 40 km and then deploys a 2-stage
rocket system that boosts to orbit, instead of a throw-away system,
then it is true the weight of the wings -adds- to the total weight of
the system, but the first stage, which is the most massive part of the
vehicle, becomes reusable.

I assume the first stage is a rocket-plane with an empty mass of 42%
(including wings, ball-park what the Concord's empty weight is). We
still want the rocket-plane to have 15% payload, and this leaves us
with only 43% rocket propellant. Using an exaust velocity of 3500 m/s
again, we see the first stage can impart only a delta-V of 1967 m/s.

Now we are taking off vertically (the first-stage lands horizontally).
1967 m/s is the vertical velocity we'd achieve if there were no
gravity losses. It's mach 5.73 at sea level, but we'll be over 40 km
in altitude by this point, so "hypersonic" stage separation is a non-
issue. Again we assume an imparted acceleration of 3 g's (29.4 m/s^2).
The first stage boost thus lasts only 66.9 seconds.

Actual velocity achieved will be 1311.24 m/s (2 g's times 66.9
seconds). We achieve an altitude of 0.5 * 2g * t * t = 43861 m or just
over 40 km.

We are cruising upwords at 1311.24 m/s -- say 1300 m/s -- at 43,861 m
altitude. That is 143,901 ft. Way high up.

Now to achieve orbit, we need a delta-V of 9700 m/s. 9700 - 1300 =
8400 m/s.

That's where the space plane deploys its 2-stage rocket system. In 2
stages we must achieve a delta-V of 8400 m/s.

Stage 2 : 71% propellant, 15% payload, 14% empty weight. Using an
exaust velocity of 4400 m/s (in vacuum), we can achieve a delta-V 5447
m/s via Stage 2..

Stage 3 : to reach 9700 m/s we need a delta-V of 2953 m/s. That is, a
mass ratio of 1.96 or 49%. If it's 14% empty weight, we can have a
payload of 37%.

Putting it all together: 0.37 * 0.15 * 0.15 = 0.008325. That is to
say, we now have a payload fraction that has been reduced, to only
0.8325%. That sounds low, it's certainly lower than the payload
fraction of the disposable 3-stage rocket described above.

3,003,003 kg is the take-off weight needed for 25,000 kg to reach
orbit. It's considerably more than the weight of the 3-stage throw-
away (disposable) rocket system, but, let's see how the cost compares!

3.003003e6 * 0.42 = 1261261.26 x $100/kg = $126,126,126 (Not bad!
E.g. $ 504,505 / flight at 250 flights)

That is to say, the first stage "reusable" space plane costs $126
million. We amortize it over 250 flights, assuming it is good for that
many flights. Dividing $126 million by 250, we find the cost of the
first stage is only about $500,000 per flight. Compare that to the $25
million cost of the disposable first stage!

3.003003e6 * 0.15 * 0.14 = 63063.063 x $100/kg = $ 6,306,306.3
3.003003e6 * 0.15 * 0.15 * 0.14 = 9459.45945 x $100/kg = $
945,945.945
Total SHIP cost per flight: 504505 + 6306306.3 + 945945.945 =
$7,756,757.245
Dividing by 25,000 kg we find the ship cost is $310/kg

Propellant cost.
3.003003e6 * 0.43 = 1 291 291.29 kg
3.003003e6 * 0.15 * 0.71 = 319 819.8195 kg
3.003003e6 * 0.15 * 0.15 * 0.49 = 33 108.108075 kg

Total propellant: 1291291.29 + 319819.8195 + 33108.108075 = 1 644 219
kg
LH2 : 1644219 * 11800 / 81614 = 237726 * 3.00 USD = $ 713178.0
LOX : 1644219 * 69814 / 81614 = 1406493 * 0.20 USD = $ 281298.6

Total propellant cost: $994476.6

Total mission cost: 994476.6 + 7756757.245 = $ 8 751 233.845
E.g. $350 / kg

Thus, if amortizing over 250 flights is reasonable, e.g. if we can
actually find 250 customers that need to launch 25,000 kg into space
for a mission cost of $15,000,000 (e.g. ticket price of $750,000 for
20 tourists on a 3-day mission to space), then including fuel -and-
the cost of the disposable vehicle, we arrive at a total mission cost
of around $9.0 million.

But there are other costs like human salaries and so on, and providing
the payload itself, and profit, so we will round this figure up to
$15.0 million per mission.

Compare this cost to the first-stage cost of $25.0 million for a throw-
away system. Thus, I have shown that a reusable first-stage, despite
having a heavy wing weight, can substantially reduce the per-mission
and per-kg payload cost.

Even though the payload fraction is substantially reduced, and -
without- using single-stage-to-orbit or scramjets, we have found a way
to lower the cost of access to space, within the model used (e.g. $100/
kg empty cost etc.), to just $600 / kg which is marketable.

Anyone care to comment or check my numbers? Your feedback is
appreciated!

The number of flights you amorize something over depends on the demand
there is in the system.

We have two possibilities :- Hypersonic aircraft or 2STO. Neither is
proven as an answer to low cost access.

Costs for anything are a function of supply and demand. Put the demand
up and unit costs tend to fall. Henry Ford proved this with car
construction.

It could well be that the answer to low cost space access is simply to
mass produce expendables - in short make them as cheap Kg for Kg as
cars and not worry about any alternative technology. It is not
intuitively obvious that either route (hypersonics or reusable
rockets) will produce a lower cost than the "Ford" route.

In point of fact the energy cost of fabricating rockets is small ,as
is the fuel cost. The main cost is in the highly skilled precision
engineering required + checking and testing. The fundamental reason
why costs are high is that demand is low. Costs will therefore be high
regardless of the technology.

Rand does not seem to appreciate this. I would still like to ask him
what technology he would prefer, but all I get is abuse.


- Ian Parker

On Fri, 14 Dec 2007 23:23:55 -0800 (PST), wrote:

There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

"Has been", past tense. That interest went away when everyone
realized that the hypersonics people didn't have a clue how to
build a scramjet that would be useful for space launch. As John
Hare put it, there's an extra "r" in scramjet.


Anyone care to comment or check my numbers? Your feedback is
appreciated!

I didn't see anything wrong with them on a quick look, but your
numbers are based on the assumption that someone comes up with a
useful scramjet.

Since we can build even niftier imaginary spaceships if someone
comes up with Cavorite, I don't think it's really worth considering
in such detail.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-718-0955 or 661-275-6795 * -58th Rule of Acquisition *

On Sat, 15 Dec 2007 09:00:37 -0800, in a place far, far away, John
Schilling made the phosphor on my monitor
glow in such a way as to indicate that:

On Fri, 14 Dec 2007 23:23:55 -0800 (PST), wrote:

There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

"Has been", past tense. That interest went away when everyone
realized that the hypersonics people didn't have a clue how to
build a scramjet that would be useful for space launch. As John
Hare put it, there's an extra "r" in scramjet.


Anyone care to comment or check my numbers? Your feedback is
appreciated!

I didn't see anything wrong with them on a quick look, but your
numbers are based on the assumption that someone comes up with a
useful scramjet.

Actually, it looked to me like he was proposing an all-rocket system.

Your numbers are good enough, but China already offers "Cheap Access
to Space", and at not costing ten cents on our badly inflated dollar,
especially CATS worthy if China is officially in charge of doing our
moon and of controlling the moon's L1 usage.

Of course we could always use those fully proof-tested and 100%
reliable methods of using our extremely LEO efficient Saturn, such as
for otherwise having gotten nearly 50 tonnes into a close orbit of our
moon within 3 days, and all of such accomplished with a mere 60:1
ratio of rocket per payload, as well as for having to deal with a
nearly 30% inert GLOW at that. As far as we know, there's still
nothing of such fly-by-rocket capability available that's hardly half
as good.
- Brad Guth


wrote:
There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

Back in 1972, it was estimated that the Space Shuttle would cost as
little as $455 per kg. In 2007 dollars, this works out to $2,188.05
per kg. And that was considered good. Below, I outline my theory as to
how we can achieve $600 per kg today, which would work out to $125 in
2007 dollars or better than the space shuttle was supposed to be.

If you can get costs below $600 per kg in today's dollars, you can
launch 25,000 kg of payload for $15 million and thus sell 20 tickets
to space for $15 million, or tickets are for sale at $750,000 per
ticket. That seems reasonable. (The Space Shuttle has a payload of
approximately 25,000 kg).

I will assume the first stage goes straight up and has an imparted
acceleration of 3 g's, e.g. an actual acceleration of 2 g's. I will
also assume it takes 9700 m/s to reach orbit from the ground (orbital
velocity is somewhat less but we must contribute both kinetic and
potential energy to achieve a circular orbit). I will also assume we
have a payload of 25,000 kg and the fuels used are liquid hydrogen
(LH2) and liquid oxygen (LOX). I assume hydrogen costs $3.00 per kg
and oxygen costs $0.20 per kg. These seem reasonable.

Finally I make one small blunder: the cost of the vehicle without fuel
is just $100 times the weight in kilograms. This seems reasonable if
it is made of aluminum alloy, but in practice it takes a lot of energy
to machine rocket parts from raw materials, and all this energy costs
money. Nevertheless $100/kg is a ball-park figure (note this low cost
precludes the use of titanium, baring any new technologies. Also we
might need to circulate a fluid throughout the skin of the first stage
to keep it from melting).

First, let's look at a 3-stage throw-away system for comparison with
my proposal.

A typical rocket is 71% propellant and has 15% payload, e.g. is 14%
empty weight. This corresponds with a mass ratio of 3.45 which seems
reasonable.

Stage 1 : 71% propellant, 15% payload, 14% empty. Imparted delta V is
4330 m/s but only 2881.2 m/s is realized due to gravity losses (we're
flying straight up). We assumed an exaust velocity of 3500 m/s which
is reasonable for LH2-LOX at sea level.

Stage 2 : 71% propellant, 15% payload, 14% empty. A delta-V of 5447 m/
s is realized. We assume an exaust velocity of 4400 m/s which is
reasonable for LH2-LOX in vacuum.

Stage 3 :1373 m/s is needed to reach our 9700 m/s figure. This leads
to a needed mass ratio of 1.366 e.g. 26.8% propellant, 14% empty,
59.2% payload.

Now using this figure as a baseline, we will see how my proposal
stands. The payload is
0.15 * 0.15 * 0.592 = 1.332%. Since we state that we have a payload of
25,000 kg, we deduce the vehicle must have a mass of 1,876,877 kg at
liftoff.

Let's get a minimum estimate of how much it costs, though. To do this,
we take the liftoff mass of 1,876,877 kg and multiply by 14% to get
the empty weight of just the first stage. At $100 / kg, just the first
stage costs $26,276,276.

Using this method, we can get to space, but it costs over $25 million
to reach orbit. That is, it costs over $1000 per kg to reach orbit.

Now for my proposal.

I propose, -decrease- the payload fraction, thus increasing the mass
of the vehicle, on purpose. Why you might ask? Because the first stage
is not reusable in the above system. But if the first stage is a
rocket-plane that flies to above 40 km and then deploys a 2-stage
rocket system that boosts to orbit, instead of a throw-away system,
then it is true the weight of the wings -adds- to the total weight of
the system, but the first stage, which is the most massive part of the
vehicle, becomes reusable.

I assume the first stage is a rocket-plane with an empty mass of 42%
(including wings, ball-park what the Concord's empty weight is). We
still want the rocket-plane to have 15% payload, and this leaves us
with only 43% rocket propellant. Using an exaust velocity of 3500 m/s
again, we see the first stage can impart only a delta-V of 1967 m/s.

Now we are taking off vertically (the first-stage lands horizontally).
1967 m/s is the vertical velocity we'd achieve if there were no
gravity losses. It's mach 5.73 at sea level, but we'll be over 40 km
in altitude by this point, so "hypersonic" stage separation is a non-
issue. Again we assume an imparted acceleration of 3 g's (29.4 m/s^2).
The first stage boost thus lasts only 66.9 seconds.

Actual velocity achieved will be 1311.24 m/s (2 g's times 66.9
seconds). We achieve an altitude of 0.5 * 2g * t * t = 43861 m or just
over 40 km.

We are cruising upwords at 1311.24 m/s -- say 1300 m/s -- at 43,861 m
altitude. That is 143,901 ft. Way high up.

Now to achieve orbit, we need a delta-V of 9700 m/s. 9700 - 1300 =
8400 m/s.

That's where the space plane deploys its 2-stage rocket system. In 2
stages we must achieve a delta-V of 8400 m/s.

Stage 2 : 71% propellant, 15% payload, 14% empty weight. Using an
exaust velocity of 4400 m/s (in vacuum), we can achieve a delta-V 5447
m/s via Stage 2..

Stage 3 : to reach 9700 m/s we need a delta-V of 2953 m/s. That is, a
mass ratio of 1.96 or 49%. If it's 14% empty weight, we can have a
payload of 37%.

Putting it all together: 0.37 * 0.15 * 0.15 = 0.008325. That is to
say, we now have a payload fraction that has been reduced, to only
0.8325%. That sounds low, it's certainly lower than the payload
fraction of the disposable 3-stage rocket described above.

3,003,003 kg is the take-off weight needed for 25,000 kg to reach
orbit. It's considerably more than the weight of the 3-stage throw-
away (disposable) rocket system, but, let's see how the cost compares!

3.003003e6 * 0.42 = 1261261.26 x $100/kg = $126,126,126 (Not bad!
E.g. $ 504,505 / flight at 250 flights)

That is to say, the first stage "reusable" space plane costs $126
million. We amortize it over 250 flights, assuming it is good for that
many flights. Dividing $126 million by 250, we find the cost of the
first stage is only about $500,000 per flight. Compare that to the $25
million cost of the disposable first stage!

3.003003e6 * 0.15 * 0.14 = 63063.063 x $100/kg = $ 6,306,306.3
3.003003e6 * 0.15 * 0.15 * 0.14 = 9459.45945 x $100/kg = $
945,945.945
Total SHIP cost per flight: 504505 + 6306306.3 + 945945.945 =
$7,756,757.245
Dividing by 25,000 kg we find the ship cost is $310/kg

Propellant cost.
3.003003e6 * 0.43 = 1 291 291.29 kg
3.003003e6 * 0.15 * 0.71 = 319 819.8195 kg
3.003003e6 * 0.15 * 0.15 * 0.49 = 33 108.108075 kg

Total propellant: 1291291.29 + 319819.8195 + 33108.108075 = 1 644 219
kg
LH2 : 1644219 * 11800 / 81614 = 237726 * 3.00 USD = $ 713178.0
LOX : 1644219 * 69814 / 81614 = 1406493 * 0.20 USD = $ 281298.6

Total propellant cost: $994476.6

Total mission cost: 994476.6 + 7756757.245 = $ 8 751 233.845
E.g. $350 / kg

Thus, if amortizing over 250 flights is reasonable, e.g. if we can
actually find 250 customers that need to launch 25,000 kg into space
for a mission cost of $15,000,000 (e.g. ticket price of $750,000 for
20 tourists on a 3-day mission to space), then including fuel -and-
the cost of the disposable vehicle, we arrive at a total mission cost
of around $9.0 million.

But there are other costs like human salaries and so on, and providing
the payload itself, and profit, so we will round this figure up to
$15.0 million per mission.

Compare this cost to the first-stage cost of $25.0 million for a throw-
away system. Thus, I have shown that a reusable first-stage, despite
having a heavy wing weight, can substantially reduce the per-mission
and per-kg payload cost.

Even though the payload fraction is substantially reduced, and -
without- using single-stage-to-orbit or scramjets, we have found a way
to lower the cost of access to space, within the model used (e.g. $100/
kg empty cost etc.), to just $600 / kg which is marketable.

Anyone care to comment or check my numbers? Your feedback is
appreciated!

CATS

http://commonsensecentral.net/how_to_achieve_cats.htm

Bob...

wrote:

That is to say, the first stage "reusable" space plane costs $126
million. We amortize it over 250 flights, assuming it is good for that
many flights. Dividing $126 million by 250, we find the cost of the
first stage is only about $500,000 per flight. Compare that to the $25
million cost of the disposable first stage!

What's the minimum time to perform those 250 missions using a single
reusable launcher? You cannot just divide the initial capital cost by
the number of flights to get the cost per flight, because you're
incurring an opportunity cost on the capital tied up in the launcher.

The cost per flight also has to include a component that reflects the
risk that the launcher will be lost before completing its 250 missions.
This might be covered by insurance, but either way it's a cost that has
to be included.

Sylvia.

On Dec 15, 12:14 pm, (Rand Simberg)
wrote:
On Sat, 15 Dec 2007 09:00:37 -0800, in a place far, far away, John
Schilling made the phosphor on my monitor
glow in such a way as to indicate that:



On Fri, 14 Dec 2007 23:23:55 -0800 (PST), wrote:

There has been lots of interest in Scramjets because of their
potential to lower the cost of access to space, or Single Stage to
Orbit as a means of lowering cost of access to space.

"Has been", past tense. That interest went away when everyone
realized that the hypersonics people didn't have a clue how to
build a scramjet that would be useful for space launch. As John
Hare put it, there's an extra "r" in scramjet.

Anyone care to comment or check my numbers? Your feedback is
appreciated!

I didn't see anything wrong with them on a quick look, but your
numbers are based on the assumption that someone comes up with a
useful scramjet.

Actually, it looked to me like he was proposing an all-rocket system.

Yes, it does look like an all-rocket system.
However, I saw the word scramjet and didn't
bother reading further until your post.

There is a lot of potential range for the numbers
within the context of an all-rocket system--some
better and some worse, IMO. Our approach "wastes"
a lot more delta vee, but much more than makes up
for this waste in other structural, performance and cost
improvements. As a net result of our particular
approach, II think the bottom-line, overall goal
is actually quite modest and achievable, including
the "forgotten" factors pointed out by Sylvia.

Nothing makes much sense at low traffic levels
below 200 flight per year. At higher traffic levels,
I think that $500/kg is a quite achievable price,
not cost, goal. I think failure to take proper account
of traffic level is probably the main factor between
the "pessimistic" and "optimistic" posters on this
news group. And, as Fred points out, the chicken-and-
egg nature has to be addressed. However, this just
makes this problem a problem, not an un-surmountable
barrier.

Len

On Dec 15, 8:34 pm, Sylvia Else wrote:
wrote:
That is to say, the first stage "reusable" space plane costs $126
million. We amortize it over 250 flights, assuming it is good for that
many flights. Dividing $126 million by 250, we find the cost of the
first stage is only about $500,000 per flight. Compare that to the $25
million cost of the disposable first stage!

What's the minimum time to perform those 250 missions using a single
reusable launcher? You cannot just divide the initial capital cost by
the number of flights to get the cost per flight, because you're
incurring an opportunity cost on the capital tied up in the launcher.

The cost per flight also has to include a component that reflects the
risk that the launcher will be lost before completing its 250 missions.
This might be covered by insurance, but either way it's a cost that has
to be included.

Sylvia.

Yes these are important cost factors not to be
overlooked--and we have not overlooked them.

As I indicate in my reply to Rand's post elsewhere
in this thread, I think the bottom-line, overall goal
of $500 to $600/kg to LEO in 2007 dolllars is quite
modest and achievable--including your "forgotten"
factors. There may be several approaches
capable of achieving this goal with an all-rocket
system; we know of one, at least.

Len