Big dumb rockets vs. small dumb rockets

Big dumb rockets (also known as big dumb boosters)
are big, simple, pressure fed rockets. The most
popular implementation of this idea is a liquid
propellant, pressure-fed, regeneratively cooled
(plumbing circulating cold propellant), reusable,
first stage of a rocket launcher. The big dumb
rockets are unpopular because their mass ratio is
very low. (The mass ratio is the ratio of the mass
of a rocket filled with propellant to the mass of
empty rocket.) For example, if the pressure-fed
rocket has cylindrical shape and the height of
50 meters, its mass ratio is about 1.5.

According to the cubed-squared law, when scale is
reduced, properties which are a function of volume
(mass) will decrease faster than those which are
a function of area (thrust and strength). This
means that a small animal, e.g., ant can lift
more than its own weight, but a big animal, e.g.,
elephant cannot. It also means that reducing the
height of the big dumb rocket from 50 meters to
5 meters improves its mass ratio ten times. The
five meter high rocket would have the mass ratio
of 15 -- as good as the mass ratio of the expensive
turbopump-fed rockets. Another implication of the
cubed-squared law is that the gas pressure in
the tank and the combustion chamber of the small
dumb rocket is ten times lower -- on the order
of 1 MPa. Small size of the engine and its low
gas pressure mean that the Reynolds number is
low, which means low turbulence and high durability.
The fact that dumb rockets have two orders of
magnitude fewer moving parts than the conventional
pump-fed rockets also improves their durability.

The low gas pressure also means low heat flux
(which is good) and possibility of bubbles appearing
in the regenerative cooling channels (which is bad).
The bubbles may appear because the pressure is about 5
times lower than the critical pressure. (Boiling is
impossible above the critical pressure.) The cooling
aspect of the low pressure is a mixed blessing -- it
seems that the small engines are as easy to cool as
the big ones.

The small dumb rocket experiences relatively large
aerodynamic drag when it flies fast through the
troposphere, which is the most dense part of the
atmosphere. (At the elevation of 30 km density of the
atmosphere is about 50 times lower than its density at
the sea level.) There are two solutions of this problem:

The first solution is to lift the small dumb rocket
above the troposphere by other means, for example
airplane, balloon, or helicopter powered by hydrogen
peroxide monopropellant. It seems that the most
practicable solution is making a custom airplane which
drops the rocket through its aft end at the altitude
of 30 km. The small rocket can launch small payloads
only, but these small payloads can be assembled in
orbit by a telerobot (e.g., Dextre of Robonaut) into
structures or arbitrary size.

The second solution is to stack 20 or more small dumb
rockets sideways to make a large rocket launcher.
Image: http://www.islandone.org/LEOBiblio/SPBI1010.JPG
The stack is slender and streamlined, but all its
engines are oriented sideways, so they cannot
generate thrust in the troposphere, and some other
means must lift the launcher above the troposphere.
A large airplane can lift the rocket launcher, but it
would be difficult to separate the launcher from the
airplane safely. It seems that a reusable hydrogen
peroxide monopropellant rocket is the most practicable
means of lifting the large rocket launcher above the
troposphere.

The most important yardstick describing performance
of a rocket launcher is the payload fraction, which
is the ratio of the payload mass to the total mass of
the launcher. The conventional, pump-fed rocket
launchers have very high expansion ratio, which improves
the payload fraction, but they often incorporate
low-performance solid propellant motors in the first
stage, which lower the payload fraction. The stack of
small dumb rockets can be easily divided into four
stages which gives it performance advantage over
three-stage conventional launcher. The combined
effect of all these aspects of rocket performance is
the same payload fraction of the conventional, pump-fed
rocket launchers and the small dumb rocket launchers.

CONCLUSION

Small dumb rocket launchers have the same payload
fraction as the expensive turbopump-fed rocket
launchers, but they have the advantage of lower cost
and greater reusability.

February 1, 2005

Andrew Nowicki wrote:

Big dumb rockets (also known as big dumb boosters)
are big, simple, pressure fed rockets.

Name one functioning orbital Big Dumb Rocket.

You are talking about something that not only
does not exist, but has never existed.

Usually, that's referred to as 'psychosis'.
Thomas Lee Elifritz
http://elifritz.members.atlantic.net

"Andrew Nowicki" wrote in message
...
For example, if the pressure-fed
rocket has cylindrical shape and the height of
50 meters, its mass ratio is about 1.5.

How did you arrive at this number? You simply cannot determine the mass
ratio of a rocket based on its height, so where is the rest of your math?

According to the cubed-squared law, when scale is
reduced, properties which are a function of volume
(mass) will decrease faster than those which are
a function of area (thrust and strength). This
means that a small animal, e.g., ant can lift
more than its own weight, but a big animal, e.g.,
elephant cannot. It also means that reducing the
height of the big dumb rocket from 50 meters to
5 meters improves its mass ratio ten times. The
five meter high rocket would have the mass ratio
of 15 -- as good as the mass ratio of the expensive
turbopump-fed rockets.

Again, you're leaving out the math. Where is it?

Another implication of the
cubed-squared law is that the gas pressure in
the tank and the combustion chamber of the small
dumb rocket is ten times lower -- on the order
of 1 MPa. Small size of the engine and its low
gas pressure mean that the Reynolds number is
low, which means low turbulence and high durability.
The fact that dumb rockets have two orders of
magnitude fewer moving parts than the conventional
pump-fed rockets also improves their durability.

I have no idea how you arrive at this conclusion. Again, where's the math?

The second solution is to stack 20 or more small dumb
rockets sideways to make a large rocket launcher.
Image: http://www.islandone.org/LEOBiblio/SPBI1010.JPG
The stack is slender and streamlined, but all its
engines are oriented sideways, so they cannot
generate thrust in the troposphere, and some other
means must lift the launcher above the troposphere.
A large airplane can lift the rocket launcher, but it
would be difficult to separate the launcher from the
airplane safely. It seems that a reusable hydrogen
peroxide monopropellant rocket is the most practicable
means of lifting the large rocket launcher above the
troposphere.

Now you're really smoking your hair. From a mass ratio standpoint, it would
be far more mass efficient to build a single stage that's 20 times larger
than your small dumb rocket than to cluster 20 of them together.

CONCLUSION

Small dumb rocket launchers have the same payload
fraction as the expensive turbopump-fed rocket
launchers, but they have the advantage of lower cost
and greater reusability.

I think this conclusion is completely bogus. Prove us wrong by showing the
math. We can take it.

Jeff
--
Remove icky phrase from email address to get a valid address.

wrote in message
oups.com...
February 1, 2005

Andrew Nowicki wrote:

Big dumb rockets (also known as big dumb boosters)
are big, simple, pressure fed rockets.

Name one functioning orbital Big Dumb Rocket.

You are talking about something that not only
does not exist, but has never existed.

Usually, that's referred to as 'psychosis'.

By your logic engineers working on new vehicles must all be psychotic, since
they design, build, and fly vehicles that have never flown before.

Andrew's real problem is that he's arguing using lots of hand waving and not
showing his work for his math. If he showed us the equations he's using,
we'd be better able to show him where he's right and wrong with his hand
waving arguments.

Jeff
--
Remove icky phrase from email address to get a valid address.

Andrew Nowicki wrote:

For example, if the pressure-fed rocket
has cylindrical shape and the height of
50 meters, its mass ratio is about 1.5.

Jeff Findley wrote:

How did you arrive at this number? You simply cannot
determine the mass ratio of a rocket based on its height,
so where is the rest of your math?

You can determine the mass ratio if you know
both the height and the shape. Suppose that
we are talking about a single stage rocket
which has cylindrical shape and the height
of 50 meters. You can easily calculate the
volume and mass of propellant enclosed by
the cylinder. The structural mass is made
up of the tanks and the engine. I assumed
that the entire rocket is made of aluminum
alloy having yield tensile strength of 690 MPa.
The mass ratio is independent of rocket
diameter for slender rocket shapes. Suppose
that rocket diameter is 10 meters, tank
pressure is 15 MPa, and combustion chamber
pressure is 10 MPa. You can quickly estimate
how thick the cylindrical tank wall must be
to withstand the 15 MPa pressure. Knowing
the wall thickness you can quickly estimate
the mass of the tank and you can guess the
mass of its engine. (Engine diameter is also
10 meters.) Now you have to determine the
expansion ratio (the ratio of the exhaust
nozzle exit area to the throat area). Since
the exhaust nozzle exit area is fixed
(= 10 meters = diameter of the rocket),
you adjust the expansion ratio by adjusting
the throat area. If you increase the throat
area, you get bigger thrust, but lower exhaust
gas velocity. You need enough thrust to lift
the rocket against the force of gravity. This
thrust corresponds with the expansion ratio
of 10-15 and the exhaust gas velocity of
about 3 km/s.

You can get the exhaust gas velocity from
charts posted at:
http://www.dunnspace.com/performance.htm

All these rough estimates are simple enough
for a high school student.

If you divide your 50 meter high, cylindrical
rocket into 3 cylindrical stages, the total
mass of the rocket will be slightly smaller
because the upper stages do not need the
high tank pressure and thick tank walls.
The change of the total mass is not significant
because nearly all the mass of the divided
rocket is in the first stage.

Andrew Nowicki wrote:

According to the cubed-squared law, when scale is
reduced, properties which are a function of volume
(mass) will decrease faster than those which are
a function of area (thrust and strength). This
means that a small animal, e.g., ant can lift
more than its own weight, but a big animal, e.g.,
elephant cannot. It also means that reducing the
height of the big dumb rocket from 50 meters to
5 meters improves its mass ratio ten times. The
five meter high rocket would have the mass ratio
of 15 -- as good as the mass ratio of the expensive
turbopump-fed rockets.

Jeff Findley wrote:

Again, you're leaving out the math. Where is it?

Every engineer knows the cubed-squared law, and
nearly every 12 year old kid knows enough geometry
to prove this law. If you are mathematically
challenged person, just pull out a calculator,
a formula for volume of a cylinder, and test the
the cubed-squared law on a few examples.

I used to be a structural engineer, but this estimate
does not call for the skills of a structural engineer.
It is just rough, back of the envelope estimate. Here
is a hint how to estimate strength of the cylinder:
- cut the cylinder with a plane
- the plane will cut the gas inside the cylinder
and its material (aluminum alloy)
- knowing the gas pressure inside the cylinder,
and its area cut by the plane, you will figure
out the force that pulls the cylinder apart
- knowing the area of aluminum alloy cut by the plane
and the gas pressure force, you can calculate
the stress in the aluminum alloy; it must not
exceed 690 MPa

February 1, 2005

Jeff Findley wrote:

wrote in message
oups.com...
February 1, 2005

Andrew Nowicki wrote:

Big dumb rockets (also known as big dumb boosters)
are big, simple, pressure fed rockets.

Name one functioning orbital Big Dumb Rocket.

You are talking about something that not only
does not exist, but has never existed.

Usually, that's referred to as 'psychosis'.

By your logic engineers working on new vehicles must all be psychotic, since
they design, build, and fly vehicles that have never flown before.

It must be an english tense problem, then, apparently.

http://www.optipoint.com/far/far8.htm

http://www.smad.com/scorpius/AIAA_paper_JPC04CHAK1.pdf

Thomas Lee Elifritz
http://elifritz.members.atlantic.net

"Andrew Nowicki" wrote in message
...
Andrew Nowicki wrote:

For example, if the pressure-fed rocket
has cylindrical shape and the height of
50 meters, its mass ratio is about 1.5.

Jeff Findley wrote:

How did you arrive at this number? You simply cannot
determine the mass ratio of a rocket based on its height,
so where is the rest of your math?

You can determine the mass ratio if you know
both the height and the shape. Suppose that
we are talking about a single stage rocket
which has cylindrical shape and the height
of 50 meters. You can easily calculate the
volume and mass of propellant enclosed by
the cylinder. The structural mass is made
up of the tanks and the engine. I assumed
that the entire rocket is made of aluminum
alloy having yield tensile strength of 690 MPa.
The mass ratio is independent of rocket
diameter for slender rocket shapes. Suppose
that rocket diameter is 10 meters, tank
pressure is 15 MPa, and combustion chamber
pressure is 10 MPa. You can quickly estimate
how thick the cylindrical tank wall must be
to withstand the 15 MPa pressure.

This is all true. For the below first order approximaion, I'll only concern
myself with the mass of the cylindrical portion of the tanks (ignoring the
tank end caps, engine, plumbing, and etc).

P = pressure
r = tank radius
t = tank thickness
h = height
vm = volume of tank material (ignoring the end caps)
m = mass of tank material
d = density of tank material

hoop stress = P*r/t

t = P*r/hoop stress

vm = 2*pi*r*h*t
vm = 2*pi*r^2*h*P/hoop

m = d*vm

m = d*2*pi*r^2*h*P/hoop

mp = mass of propellant
dp = density of propellant
vt = volume of tank

vt = pi*r^2*h
mp = vt*dp
mp = pi*r^2*h*dp

mass ratio = tank mass/propellant mass

mass ratio = (d*2*pi*r^2*h*P)/(hoop*pi*r^2*h*dp)
mass ratio = d*2*P/(hoop*dp)

According to this very rough approximation, mass ratio here depends on your
selection of materials (tank and propellant) and on your selection of the
tank pressure. It does not depend on any physical dimension (tank radius or
tank height).

Knowing
the wall thickness you can quickly estimate
the mass of the tank and you can guess the
mass of its engine. (Engine diameter is also
10 meters.) Now you have to determine the
expansion ratio (the ratio of the exhaust
nozzle exit area to the throat area). Since
the exhaust nozzle exit area is fixed
(= 10 meters = diameter of the rocket),
you adjust the expansion ratio by adjusting
the throat area. If you increase the throat
area, you get bigger thrust, but lower exhaust
gas velocity. You need enough thrust to lift
the rocket against the force of gravity. This
thrust corresponds with the expansion ratio
of 10-15 and the exhaust gas velocity of
about 3 km/s.

You can get the exhaust gas velocity from
charts posted at:
http://www.dunnspace.com/performance.htm

All these rough estimates are simple enough
for a high school student.

If you divide your 50 meter high, cylindrical
rocket into 3 cylindrical stages, the total
mass of the rocket will be slightly smaller
because the upper stages do not need the
high tank pressure and thick tank walls.
The change of the total mass is not significant
because nearly all the mass of the divided
rocket is in the first stage.

Andrew Nowicki wrote:

According to the cubed-squared law, when scale is
reduced, properties which are a function of volume
(mass) will decrease faster than those which are
a function of area (thrust and strength). This
means that a small animal, e.g., ant can lift
more than its own weight, but a big animal, e.g.,
elephant cannot. It also means that reducing the
height of the big dumb rocket from 50 meters to
5 meters improves its mass ratio ten times.


I fail to see how the square-cubed law impacts the mass ratio here as we've
already seen that the mass ratio (to a first order approximation) is
independant of height. If I've made a mistake in my first order
appoximation, please enlighten me. Perhaps I've not had enough caffeine
today.

Jeff
--
Remove icky phrase from email address to get a valid address.

This is sort of moot, but in your case the cube-square law goes the
other way. For a simple illustration:

Let's say we have a rocket in the shape of a cube 10 m on a side (makes
math simpler - but the shape doesn't matter...).

The volume is 10*10*10=1000 m^3
The surface area is 10*10 * 6 = 600 m^2

The surface to area ratio is 600/1000, or 0.6. The mass ratio is
vaguely inversely proportional to that.

Now we shrink the rocket to 1 m on a side:

The volume is 1*1*1=1 m^3
The surface area is 1*1 * 6 = 6 m^2

Now the surface to area ratio is 6/1, or 6. The mass ratio is vaguely
inversely proportional to that. So as we shrank the rocket, the mass
ratio gets worse.

In reality, though - you must alter the second case by increasing the
wall thickness. For the math to be easier, you should use a sphere -
but the basic result is that since the wall thickness scales up exactly
as fast as the surface area scales up, a smaller rocket is exactly the
same ratio.

Of course large engines are harder to debug, small engines are harder
to cool, electronics don't scale, and you could argue that safety
factors get better or worse with different sizes. But using just the
tanks and estimates for the engines (BTW, I recommend just using a
thrust to weight ratio of 50 to estimate engine weight), there is
pretty much no difference.

-David

Jeff Findley wrote:

mass ratio = tank mass/propellant mass

Actually, the mass ratio is defined as the
ratio of the total mass (rocket engine, structural
parts, propellant, and cargo) to dry mass
(everything except propellant).

mass ratio = (d*2*pi*r^2*h*P)/(hoop*pi*r^2*h*dp)
mass ratio = d*2*P/(hoop*dp)

According to this very rough approximation, mass ratio here depends on your
selection of materials (tank and propellant) and on your selection of the
tank pressure. It does not depend on any physical dimension (tank radius or
tank height).

You forgot one important detail: the rocket must
generate enough thrust to lift itself off the ground.
The pressure of propellant inside the tank cannot be
arbitrarily low. If we are comparing oranges with
oranges, the exhaust gas velocity of the big rocket
should be the same as the exhaust gas velocity of the
small rocket. If you double the rocket's height, you
must also double the tank pressure to keep the exhaust
gas velocity the same.

The thrust produced by a rocket equals F = P*A*Cf
whe
P = pressure inside the combustion chamber
A = throat area
Cf = thrust coefficient (which depends on the
expansion ratio)

If the expansion ratio, Cf, and exhaust gas
velocity are the same for the big rocket and the
small rocket, their thrust is proportional to the
exhaust nozzle exit area and to the tank pressure.
If you double the rocket dimensions, its weight
grows 8 times, but its exhaust nozzle exit area
grows only 4 times.

You can cheat a little on the cubed-squared law by
shaping the rocket like a cone (or Soyuz launcher).
If you go too far, your rocket will generate too
much aerodynamic drag.

David Summers wrote:

This is sort of moot, but in your case the cube-square law goes the
other way. For a simple illustration:

Let's say we have a rocket in the shape of a cube 10 m on a side (makes
math simpler - but the shape doesn't matter...).

The volume is 10*10*10=1000 m^3
The surface area is 10*10 * 6 = 600 m^2

The surface to area ratio is 600/1000, or 0.6. The mass ratio is
vaguely inversely proportional to that.

It is not.

Now we shrink the rocket to 1 m on a side:

The volume is 1*1*1=1 m^3
The surface area is 1*1 * 6 = 6 m^2

Now the surface to area ratio is 6/1, or 6. The mass ratio is vaguely
inversely proportional to that. So as we shrank the rocket, the mass
ratio gets worse.

You do not understand the definition of the
mass ratio, and you do not understand that
the mass ratio depends on the thrust produced
by the rocket.

A better illustration of the cubed-squared
law would be a cube-shaped ant and a cube-shaped
elephant. How much stress there is at the bottom
of the ant and at the bottom of the elephant?
If the elephant is bigger than the ant, the
stress at its bottom is bigger.

Of course large engines are harder to debug,

They are, in general, much more unstable than
small, low pressure engines because their Reynolds
number is much bigger. The intensity of turbulence
is determined by Reynolds number: R = VPD/N,
where V is gas flow velocity, P is gas density,
D is diameter of the engine, and N is gas
viscosity.

small engines are harder to cool

The opposite is true.

...and you could argue that safety factors
get better or worse with different sizes.

If your rocket launcher has 16 small engines,
and one of them fails, it still has enough
thrust to reach orbit.

If your rocket launcher has only one big engine,
and this engine fails, this is a catastrophic
failure.