Lecture 2: Presentation Materials February 8, 2010
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Space Show Classroom Lesson 2: The Rocket Equation. Tuesday, February 9, 2010.
I. Presentation Material From Guest Panelist: Paul Breed of Unreasonable Rockets (http://unreasonablerocket.blogspot.com/).
Getting to Space is relatively easy, getting to orbit is hard.
The difference between Virgin and XCOR, etc… and Shuttle/SpaceX, etc…
Orbit means falling toward the earth, but going so fast you continually miss.
To get to orbit you to must go very very fast, the energy in orbit is 25x the energy on 100km suborbital hop.
You can almost think of it like the game tetherball, (http://en.wikipedia.org/wiki/File:Tetherball_flickr.jpg) A suborbital hop just pushes the ball straight out from the pole, it then falls back to the poll. If you really hit the ball it goes around the pole.
The absolute minimal possible orbital velocity is 7500 m/sec. (17000 mph)
This means your rocket must impart 7500 m/sec of horizontal velocity.
Any real world vehicle with drag will have higher requirements.
A very very large rocket could get close to 7500 m/sec but a very small rocket could easily require 10000 m/sec DV to counter the air drag.(1)
To go that fast a rocket needs to be mostly fuel.
It will also stage as this lets it drop the empty tank stage and big motors.
The Sci fi rockets like the Star Wars fighters, Star Trek shuttle, comic book rockets etc.. are not possible with chemical propulsion. We will never ever have a chemical powered orbital rocket that looks like a commercial air plane.
All orbital chemical rockets will look like a flimsy flying gas tank.
The very best commercial plane carries 1/2 its weight in fuel.
An orbital SSTO rocket needs to be more than 95% fuel mass. The other % must include structure, motors, and payload.
And its even worse than it seems for every pound of fuel a jet burns it uses 10 lbs of “free” air. A Rocket needs to bring along its own “air/oxidizer” and that is the definition difference between rockets and jet.
A rocket is not like a car where it pushes on the immoveable road to make it go forward. A rocket is like sitting on a row boat in the middle of the lake and throwing baseballs out the back to make it go forward. Probably works better if Roger Clemons is throwing.
Works really well if the baseball was shot out of cannon….. (cannons are heavy so there is a point of no return.)
In a rocket the baseballs are gas molecules and they are thrown very fast. The speed the balls are thrown are usually called ISP. higher pressures more complex motors can throw faster, but just like a cannon. If they get too heavy there is a point of diminishing returns.
The actual equation : delta V = Ve * ln (Mi/Mf)
Delta V = The change in velocity.
Ve = The exhaust velocity of the propellant leaving the rocket.
Mi = The initial Mass of the vehicle. (The empty wt + payload + propellant)
Mf = the final Mass of the vehicle. (The empty wt+ payload + reserves)
ISP (in seconds) = Ve/acceleration due to gravity
The 180 second LLC vehicles had an achieved delta V of 9.8m/sec * 180 = 1764 m/sec
(Minimal orbital is 7500 m/sec) 4.5 times as much dv, and it is logarithmic relation ship at least 20 times harder.
Using same level of performance as Masten’s LLLC vehicle carrying a 55lb payload (Assume 55lbs payload GLOW of 855lbs and hover of 195 seconds)
would require 4 stages and stages with equal DV per stage 1st stage would weigh more than 3M pounds. So the performance of a real useful orbital rocket needs to be much higher than the LLC vehicles.
Its not really quite that bad as when you gain altitude and don’t have to throttle the ISP performance improves significantly. But for the same level of technology that answer is within an order of magnitude.
This is why SSTO is almost impossible.
| Performance/Vehicle Class | ISP | Dry Mass to reach orbit |
| Improved LLC class | 250 | 3.9% |
| SpaceX Merlin | 310 | 7.4% |
| SSME* | 450 | 16% |
| NERVA* | 825 | 37% |
*Both SSME and NERVA used Liquid Hydrogen, hard to get good mass ratio with LH2 as it has the density of an empty Styrofoam cup Hydrocarbon Fuels require a higher mass fraction, but are much denser actually making the mass fraction easier to achieve.
Chemical rockets will remain expensive until you can reuse them, and the rocket equation makes that very hard.
The only way to get both high thrust and high ISP is either some form of external power like the Laser Launch scheme, or some form of nuclear power, fission, fusion etc…
Some electric propulsion system have very high ISP’s but they have very low thrust to weight, i.e. 1/1000th or less. So they can not climb out of the gravity well to LEO.
Long term LEO access can be somewhat solved with very large engineering projects, like the space elevator, Loftsrom loop (http://en.wikipedia.org/wiki/Launch_loop) to get to low earth orbit and nuclear propulsion, preferably fusion for going from LEO onward.
In the short term one might see some benefit from rotavators or other tether schemes. Based on what I know, the space elevator has big material and stability issues. The loop has a physically larger footprint on the ground but requires no new materials.
If one could generate a machine with 50% energy efficiency getting a human to orbit would require less than $200 of energy at current electrical energy rates.
90Kg * 8000 m/sec^2 * 50% = 2880 MJoules = 800 Kilo watt hours
At 10c a kwa = $80.00
I really like the Orion concept, but humans have become very risk adverse, the open air atomic bombs would be unpopular. ;-(
(1) https://e-reports-ext.llnl.gov/pdf/321763.pdf How Small can a Launch Vehicle Be AIAA 2005-4506.
______________________________________________________________________________________________________________________
II. Presentation Material from Co-Host Dr. John Jurist:
The Rocket Equation: Delta-V = Ve * ln (Mi / Mf)
Delta-V = The change in velocity of the rocket in absence of gravitational and aerodynamic losses.
Ve = The exhaust velocity of the propellant leaving the rocket.
ln = Natural logarithm = loge
Mi = The initial mass of the vehicle. (empty wt + payload + propellant)
Mf = The final mass of the vehicle. (empty wt + payload + reserves)
Isp = Specific Impulse (in seconds) is Ve /acceleration due to gravity. In English units, it is the pounds of thrust generated by a specific propellant combination at a burn rate of one pound per second.
Some implications of the rocket equation are considered below:
One reason an orbital launcher will not look like a commercial airplane is wings and landing gear – used mostly for landing but very heavy to carry up to orbit. If the vehicle takes off from the ground, the landing gear must be sized for the takeoff weight. The Shuttle gear is sized for the landing weight because the STS launches vertically. Also, loads on an airplane are mostly transverse. If an aerospace plane launches horizontally, the loads will switch from transverse during takeoff and initial climb out to mostly longitudinal during the higher altitude and orbital insertion portions of the flight. The loading then switches back to mostly transverse for re-entry and landing. In contrast, vertical takeoff rockets have mostly longitudinal loads and can be built lighter. That improves the potential payload fraction.
Horizontal air launch potentially adds drag losses during the initial flight envelope and also the vehicle requires more robust structure relative to a conventional vertical takeoff rocket in order to tolerate the pitch up maneuver as it starts the atmospheric climb out.
Because air has oxygen, many people suggest a combined jet/rocket engine (or separate jet and rocket motors) to reduce the quantity of oxidizer to be carried on board an orbital launcher. One of several problems with this approach is that the thrust to mass ratio of a rocket motor is much greater than that of a jet engine. The mass penalty for an air breathing launch vehicle ends up very severe and in practice exceeds the advantage of using ambient oxygen.
Examination of the rocket equation shows that increasing exhaust velocity improves things. Liquid fluorine-liquid hydrogen has better exhaust velocity than liquid oxygen-liquid hydrogen, but is too toxic to be feasible. Liquid oxygen-liquid hydrogen is the best we have in terms of exhaust velocity, but hydrogen’s low density and insulation requirements are both issues.
In a two stage launcher, first stage performance isn’t quite as critical as is second stage performance. This drives the use of liquid hydrogen in second stages with hydrocarbon fuel in the first stage.
When considering the payload fraction of a launch vehicle, there are some scaling problems that come into play as vehicle size changes. For smaller vehicles, the surface to mass ratio is increased and aerodynamic losses become relatively more significant. The propellant fraction of the vehicle tends to be reduced because of tank volume/area considerations and relatively fixed masses associated with motors, pumps, plumbing, etc.
Over the years, aerospace engineers have developed numerous parametric relationships to estimate the inter-relationships of masses of different components as a function of overall size. These relationships not only relate structural mass to propellant mass, for example, but relate many of these parameters to development cost and to production cost. A good source for those who wish to dig into this pragmatic aspect of rocket engineering in more detail is a book by Dietrich Koelle: Handbook of Cost Engineering for Space Transportation Systems. It is published and sold by Microcosm.
The bottom line is that a developed launch vehicle is the result of countless technical tradeoffs and compromises. A few of the variables that are involved include:
- Delta-V budget between stages,
- Propellant combination, boil off rate for cryogenic propellants, etc.
- Launch trajectory (tradeoffs of gravity and aerodynamic losses versus burn time and vehicle acceleration),
- Propellant pumps versus pressure-fed propellants,
- Ablatively cooled versus regeneratively cooled motors,
- Composite versus metal tanks,
- Multiple small motors versus few larger motors,
- Structural issues related to steady state wind shears and gust loading, and
- Tolerance of payload for acceleration profile, vibration and noise environment.
All of these variables and more must be considered in light of the vehicle or program lifecycle (spreading development costs over the number of anticipated launches). In addition, risk analyses must be done that determine insurance costs for general liability and for potential payload losses.
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The Space Show Classroom Blog 
Before tonight’s class I received a question about why this rocket equation makes things so expensive.
It all has to do with margins. If I build a concrete structure with a factor of 10 safety factor, its easy, if my concrete has a bit to much sand in it and looses 30% of its strength and I under estimate the loads by 50% I still have plenty of safety factor. With a rocket I can’t handle the mass necessary to make things 10x to strong. Some rockets have flown with safety factors of 1.2 this means one has to REALLY understand your loads and really control your process and materials so so you get the desired strength. If one little spot of metal gets a slight scratch and has a tress concentration of 10% and I get 10% more vibration then expected my safety factor goes below 1 and I have a failure. Useful orbital rockets have low safety factors, they are also disposable. The holy grail is a reusable rocket, but reuse means things like the tank might get a scratch, or a micromeeorite or….. so for real reuse one needs higher margins than for a perfectly controlled one time expendable. Reducing the usefulness ..
Your assumption seems to be that the rocket equation forces you to spend much more to develop a spacecraft that carries a given tonnage, then a aircraft with similar “energy distance” abilities. It doesn’t. The development costs of the craft, engines, production costs of RLV craft and engines – all per cargo tonnage – show minor differences. Totally unrelated to the thousand fold cost differences.
Really the big difference is flight rate. The craft, even to total cost of actually launching, gets lost in the fixed and overhead costs.
I commented about your comment that
> Long term LEO access can be somewhat solved with very
> large engineering projects, like the space elevator, Loftsrom loop..
If anything, these seem unable to ever compete with Rockets. Current Launch costs are dominated by overhead and fixed costs (R&D, facilities construction, fleet construction) exacerbated by low flight rates. space elevator and Loftsrom loop have staggering construction costs and low carrying capacity. Essentially making the biggest current launch cost issues far worse, while lessening the minor fuel costs.
Specifically in one space elevator project I calculated that the given volume and mass of Nano cable composite they stated they’ld need, would if it cost as much as the wholesale costs of Kevlar and Carbon-fiber composite -cost $100-$200 billion; but only carry a max of 2000 tons a year. It would be hard pressed to compete with a current Falcon launcher in price per pound.
It does seem that the rocket equation constrains our efforts to counter act Earths gravity well (the beast!) with current chemical rocket technology, unless there is a new propulsion method is found. Paul Breed raised a very interesting point towards the end of the class. Should we be looking at astroids which have a very small gravity well, as initially being a better destination for humans to explore and attempt to settle, rather than a destination such as Mars which poses the same problems regarding a substantial gravity well as here on Earth! This was a outstanding show from a non-scencist or engineers perspective (me!) where the guest speakers made this complex topic understandable. Thank you!
Hey All:
This is a little document I put together for the SEDS folks here in Tucson. Maybe it will contribute to the discussion.
Andrew’s Rocket Equation Writeup.
To Dave, John, Paul Breed, and Dr. Jim Logan
I think you guys did a very pretty good job explaining the rocket equation, but did so in a way that kind of got lost in the weeds and became badly misleading for the big launch cost question. Yes, the mass ratio of a RLV sucks, so does the mass ratio of a UPS truck delivering your envelop. What matters is what is the COST to deliver the pound/ton/etc of cargo. How do you get the cost down? What impact, if any, does the rocket equation have to the cost per pound/ton/etc of cargo mass to orbit.
For example. You at one point mentioned the ELVs big mass ratio advantages over a RLV, and implied this was an important factor. But didn’t mention the RLV’s cost per pound to orbit is generally less. For example a shuttle can lift 25-30 tons to LEO (a number of 30,000lb to ISS was given, but that’s due to the ISS’ hard to get to orbit) vs. 100+ tons for a Saturn-V as you stated. I know shuttle would cost much less per cargo ton to orbit then a Ares-V, even though the A-5 would lift several times as much tonnage. (I think the same for Sat-V, but not sure what its cost per ton was back then.) Shuttle cost less to deliver 7-8 folks to the ISS then Ares-1 / Orion could have hoped to. (One factor for that though is the Ares-1/Orion cost almost 50% more in now year dollars to develop, and obviously the per flight servicing costs for a fully expendable system sucks.)
The Rocket equation says current launch vehicles need about $8 worth of LOx and Fuel per pound of cargo to orbit. You could halve or double that with various engineering changes – or different cost rates for LOx & fuel. That’s bad compared to $1-$2 for a air freighter going the same “energy distance”; but negligible to the launch costs of thousands to tens of thousands of dollars per pound to orbit of most current launchers.
You were right when you (John Jurist I believe) mentioned that the development cost, and other upfront costs your trying to amortorize over x number launches, is dominant in launch costs. But given those costs for RLV or ELV are similar on a per pound of cargo basis to that in an airliner. It’s only a driver now because of the dramatically lower flight rates of launchers. Get the flight rate up so the overhead and fixed costs divided by flight drop down, and like now the margin costs (fuel, servicing, etc) dominate.
Servicing and margin costs even on a shuttle only come to about $1100 a pound (and its explicitly NOT designed for ease of servicing – nor was it to be so modified). Build a easier to service craft (quite doable now, but not worth bothering with currently) you could drop costs down to the tens of dollars a pound level. That’s close to 3 orders of magnitude lower then say shuttle now. The rocket equation supports this; historic patterns for aerospace craft would then suggest a low tens of dollars per pound to orbit cost is achievable given current mass ratios, chemical rockets, and technology.
On a related issue, this is by the way why (In case I wasn’t clear on the blog post) things like space elevator can’t really hope to compete on a cost per cargo pound basis with even current launchers. The huge capital costs of building the elevator cable compared to developing and fielding a fleet of current launchers or RLV’s, and the cables low carrying capacity, means the current gen launchers can easily beat them on a cost per pound to GEO, much less LEO basis..
Also your assumption that all the space craft need to get staggeringly delicate care to work is untrue. Certainly when I toured factories making Helicopters, boosters, fighters, etc I didn’t see any dramatic difference in cleanliness etc concern. Given the kicking around the shuttles took in servicing, and junk seen floating out of the bays in orbit, they were not getting clean room treatment on the ground. And again, this isn’t translating into big differences in manufacturing costs.
Nits,
As to jet engines not working above 6,000 mph, and that’s only 16% of orbital velocity.
Your overlooking the fact the rocket equation also shows that you burn half your reaction mass getting to Mach 6 (4500 (ish) mph). Turbo ramjets with t/w of over 16 are capable of more than that. Rocket ramjets are even lighter. A rocket ramjet roughly doubles the average ISP from ground to orbit, Turbo ramjets are obviously higher given ISP of the turbojet of something over 5,000 before you start getting to high supersonic, and use the ramjet.
So you lose half you’re tank weight. The remaining tanks can act as the lifting surface, etc. You have a smaller craft, which could have lower per flight servicing etc costs. (I was working up numbers on this for a suborbital commercial transport craft I was trying to get off the ground – pun not intended.)
Oh. Your comment that if the delta-V to orbit was %5 more we couldn’t get into space. If that was true we couldn’t launch east to west to LEO, a delta v of 17,000 mph (east) vs. 19,000 mph (west) is over 10%.
The gravity well isn’t that big a problem. Cost wise it means air fright costs to orbit with Chemical rockets can’t get below $20-$40 a pound regardless of the market size.
A bigger problem is just planets don’t offer much. They are a lot harder to get to and from, to export things back to markets back on Earth, and good ores and such are buried and mixed up with a lot of rock. Also, none have the necessary gravity and radiation shielding that humans require.
So yeah floating shielded colonies consuming the high quality ores and such in deep space (even near Earth) that are far better places to build colonies, and are far more accessible.
Lets face it – we already are settled on a planet. Earth is richer in the resources planets can give then any other one we can get to. So if we go into space it will need to be for things floating in space.
David, this is a test to see if the new option worked regarding post authorship.
Kelly, with respect to airbreathing, turboramjets have higher Isp with lower T/W ratio than rocket motors. Ramjets operate only within a relatively narrow Mach number window. Carrying multiple motor types with additional plumbing, etc. drives up structural mass and obviates the advantage of airbreathing. In addition, airbreathing increases atmospheric dwell time during the launch and increases aerodynamic losses enormously compared to a typical rocket launch trajectory. Structural masses increase because of load shifting during different parts of the launch trajectory. Look at LTC (now Col) Gary Henry’s 2003 Air War College master’s thesis for a thorough discussion of this topic.
I said that many experienced people had opined that if Earth were 5-10 percent “bigger,” we would be stuck. This does not mean we can’t get 5% more delta-V. A larger Earth implies a bit more gravity field but a significantly denser atmosphere with concomitantly higher aerodynamic losses and the mission delta-V goes up much more than 5%. With the initial jump so much more difficult, early attempts to build orbital vehicles would have not been feasible. These opinions took a lot more into consideration than just simplistically increasing delta-V by 5%. You jump to your conclusion based on a misinterpretation.
For all the reasons Dr Jurist pointed out air breathing become a liability. Why do designers dream of them? Reason 1 your point, high Isp. However if you look at a performance chart you’ll see that the highest Isp devices known to man today are all subsonic engines. I believe turbo fans operate in the 10,000 sec range. Try taking a huge turbofan to supersonic let alone hypersonic speeds. The killer ap for having a turbo fan or jet is the much longed for flyback first stage. The idea is to take all the performance hits of wings, and air breathing, in exchange for getting your hardware back after boost and having the ability to land on a runway like a civilized member of the industrial world. Thank you. For some insight into the ‘inefficiencies’ of such an approach, compare the Russian Soyuz (R-7 based booster NATO designation Sapwood) vs the McDonnell (Don’t let anyone fool you into thinking it’s a Boeing product) Delta II. They are quite close in performance but the Russian booster is much more massive and almost twice as large. They also launch in all weather, on time, and almost never fail. Americans consider the Russian booster to be inferior to the Delta as it is much less efficient. Which strictly it is, however economically the Russian product is superior in every measure, and I’d gladly steal, and copy the Russian system over the Delta system any old day. But the kind of price you can expect to pay for a turbo-machine flyback system would give you a vehicle that compares to an expendable system the way the Soyuz compares to the Delta II. It’ll be bigger, heaver, and the performance for a like sized expendable will be less. However, you get your hardware back.
> Ramjets operate only within a relatively narrow Mach number window. ==
No you can get ramjets that adjust over a wide speed range. NASA was projecting the RBCC would work from 0-over Mach 6 in ramjet mode, and potentially up to Mach-10 in scramjet mode (the same engine can also switch from ramjet/to scramjet modes
>Carrying multiple motor types with additional plumbing,
> etc. drives up structural mass and obviates the advantage
> of airbreathing.
Does it? Need to do a detailed trade study.
As to mass, the engines could well weigh less then the tanks it replaces. And make a tougher ship.
> In addition, airbreathing increases atmospheric dwell
> time during the launch and increases aerodynamic losses
> enormously compared to a typical rocket launch trajectory. ==
Again, I’ve seen enough AIAA papers disagreeing on the point.
=
>==I said that many experienced people had opined
> that if Earth were 5-10 percent “bigger,” we would be stuck.
Oh, miss heard.
Though really you can bost out of any planet. But you may need a hell of a lot of stages to do it.
😉
>==
> With the initial jump so much more difficult, early
> attempts to build orbital vehicles would have not been
> feasible.
Well – neither were ours. Course given the V-2 adn Nerva rocket were 20 years apart – it likely wouldn’t have made a lot of difference in history.
😉
> Andrew
>
> == Americans consider the Russian booster to be inferior to
> the Delta as it is much less efficient. Which strictly it is, however
> economically the Russian product is superior in every measure,
> and I’d gladly steal, and copy the Russian system over the
> Delta system any old day. ===
Big agree. One big problem folks interested in space often get into is they stress big time over marginal efficiency differences, but ignore cost differences. No “$” in the Rocket equation. Not even much cost impact from the rocket equation.
Its especially important since US launcher makes frequently do make ultra efficient, ultra light, improved cargo mass fraction craft – that cost a fortune to build and operate.
In the post to sci.space.policy copied below I show why an SSTO is easier with dense propellants than with hydrogen.
In fact I would go further than that: an SSTO is EASY with dense propellants rather than by using hydrogen.
Bob Clark
=======================================
Newsgroups: sci.space.policy, sci.astro, sci.physics, sci.space.history
From: Robert Clark
Date: Sun, 21 Mar 2010 07:17:58 -0700 (PDT)
Subject: Re: A kerosene-fueled X-33 as a single stage to orbit vehicle.
On Mar 15, 10:02 am, Me wrote:
> On Mar 14, 9:24 pm, Robert Clark wrote:
> > Then it is important that such a SSTO vehicle be produced even if
> > first expendable to remove the psychological barrier that it can not
> > be done. Once it is seen that it can be done, and in fact how easily
> > and cheaply it can be done, then there it will be seen that in fact
> > the production of SSTO vehicles are really no more difficult than
> > those of multistage vehicles.
> > Then will be opened the floodgates to reusable SSTO vehicles, and low
> > cost passenger space access as commonplace as trans-oceanic air
> > travel.
> More clueless BS. Clark thinks he is smarter than everyone else.
[re-posted to correct typos.]
No. I’m reporting what some experts in the field have said, that it
is easier to produce a SSTO vehicle with dense fuels rather than with
hydrogen.
Some examples:
Single Stage To Orbit Mass Budgets Derived From Propellant Density and
Specific Impulse.
John C. Whitehead, Lawrence Livermore National Laboratory.
32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference.
Lake Buena Vista, FL July 1-3, 1996
Abstract
“The trade between specific impulse and density is examined
in view of SSTO requirements. Mass allocations for
vehicle hardware are derived from these two properties, far
several propellant combinations and a dual-fuel case. This
comparative analysis, based on flight-proven hardware,
indicates that the higher density of several alternative
propellants compensates for reduced Isp, when compared
with cryogenic oxygen and hydrogen. Approximately half
the orbiting mass of a rocket-propelled SSTO vehicle must
be allocated to propulsion hardware and residuals. Using
hydrogen as the only fuel requires a slightly greater fraction
of orbiting mass for propulsion, because hydrogen engines
and tanks are heavier than those for denser fuels. The
advantage of burning both a dense fuel and hydrogen in
succession depends strongly on tripropellant engine weight.
The implications of the calculations for SSTO vehicle
design are discussed, especially with regard to the necessity
to minimize non-tankage structure.”
http://www.osti.gov/bridge/servlets/purl/379977-2LwFyZ/webviewable/37…
A Single Stage to Orbit Rocket with Non-Cryogenic Propellants.
Clapp, Mitchell B.; Hunter, Maxwell W.
AIAA, SAE, ASME, and ASEE, Joint Propulsion Conference and Exhibit,
29th, Monterey, CA, June 28-30, 1993.
Abstract
“Different propellant combinations for single-stage-to-orbit-rocket
applications were compared to oxygen/hydrogen, including nitrogen
tetroxide/hydrazine, oxygen/methane, oxygen/propane, oxygen/RP-1,
solid core nuclear/hydrogen, and hydrogen peroxide/JP-5. Results show
that hydrogen peroxide and JP-5, which have a specific impulse of 328
s in vacuum and a density of 1,330 kg/cu m. This high-density jet fuel
offers 1.79 times the payload specific energy of oxygen and hydrogen.
By catalytically decomposing the hydrogen peroxide to steam and oxygen
before injection into the thrust chamber, the JP-5 can be injected as
a liquid into a high-temperature gas flow. This would yield superior
combustion stability and permit easy throttling of the engine by
adjusting the amount of JP-5 in the mixture. It is concluded that
development of modern hydrogen peroxide/JP-5 engines, combined with
modern structural technology, could lead to a simple, robust, and
versatile single-stage-to-orbit capability.”
Click to access SSTORwNCP.pdf
Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix, Arizona
April 25 =96 27, 1996
Introduction
“The most commonly proposed propellant combination for an SSTO
launcher is liquid oxygen and liquid hydrogen, at a mixture ratio of
approximately 6.0. There have been a number of studies of alternate
fuels for SSTO launchers, but they have been limited. To date, most
studies have concentrated on methane, propane and RP-1 burned with
liquid oxygen to the exclusion of other oxidizers and other fuels.
These studies have often, but not always shown lower vehicle dry
masses for hydrocarbon propellants (for the same payload size). The
lowest dry masses of all are found in dual-fuel vehicles, using dense
hydrocarbons early in the flight and hydrogen late in the ascent.
These vehicles however suffer from mechanical and structural
complexity over their single-fuel cousins, and are unlikely to
represent the least expensive way to get a defined payload to orbit.”
http://www.dunnspace.com/alternate_ssto_propellants.htm
This is certainly a minority opinion that dense fuels are better for a
SSTO than hydrogen, but it has occurred numerous times in science that
the minority opinion turns out to be the correct one.
The argument for why dense propellants are better for a SSTO is quite
simple and can be understood by anyone familiar with the “rocket
equation” that describes the relationship between the exhaust
velocity and the mass of propellant for a rocket. Indeed the argument
is as about as close to a mathematical proof as you can get in
engineering.
First two key facts have to be kept in mind: 1.) the tank mass scales
by volume, *NOT* by the mass of the fluid contained. This means that
the same size and *same mass* tanks can hold about 3 times as much
kero/LOX as LH2/LOX. This is extremely important because the
propellant tanks make up the single biggest component of the dry
weight of a rocket, typically 30% to 40%, even more than that of the
engines.
And 2.) dense propellant engines such as kerosene ones typically have
thrust/weight ratios twice as good as hydrogen ones. This is key
because switching to kerosene means your fuel load and therefore gross
mass will be greater. But because of the kerosene engines better T/W
ratio, the increase in engine weight will be relatively small.
Many people get the second of these points. It’s the reason why first
stages generally use kerosene or other dense propellant for example.
However, the first point most people are not as familiar with. But
it’s the more important of the two because the increase in propellant
being carried far exceeds the increase needed to overcome the lowered
Isp of the dense propellants.
To see why tank mass scales with volume, take a look at the equations
for tank mass here:
Pressure vessel.
http://en.wikipedia.org/wiki/Pressure_vessel#Scaling
Note it depends only on tank dimensions, internal pressure, and
strength and density of the tank material. Then because the internal
pressure of the tanks will be about the same for the hydrogen case as
for the kerosene case, for proper operation of the turbopumps, the
kerosene filled tanks will hold about 3 times more propellant at the
same size and weight of the tanks.
Now for the calculation that switching to kerosene can result in
multiple times greater payload. The vacuum Isp for good hydrogen
engines is about 450 s, and for good kerosene ones about 350 s. This
means the mass ratio for a hydrogen SSTO is about 10 and for a
kerosene one it’s about 20. These values are higher than what you
would expect based just on the vacuum Isp alone because you also have
to consider gravity and air drag, and the fact that the Isp is
decreased at sea level and low altitude.
Now suppose we switch our hydrogen-fueled SSTO for a kerosene-one
using the same sized tanks. The volume stays the same so the mass of
the tanks stays the same. But the amount of propellant is now about 3
times larger.
For the engines, since propellant mass makes up almost all the
vehicle gross weight, the gross weight will be about 3 times larger
too. So the engines will need about 3 times the thrust.
For the original hydrogen-engines the thrust/weight ratio was about
50 to 1. And since the gross mass was about 10 times the dry mass for
the hydrogen vehicle, this means the engine mass was about 1/5, or
20%, of the dry weight.
Now switching to kerosene makes the gross weight about 3 times
larger. If the kerosene engines had only a 50 to 1 T/W ratio then you
would need 3 times heavier engines so they would be at 3/5 of the dry
weight. But since the thrust/weight of the kerosene engines is twice
that of the hydrogen ones, the engine weight is 1.5/5, 30%, of the dry
weight so the vehicle dry weight is increased only by 10%, due to the
heavier engines.
Now since the mass ratio is 10 for the hydrogen case but 20 for the
kerosene, you normally need about twice the kerosene propellant for
the same sized vehicle+payload total to reach orbit. But what we
actually have is about 3 times more propellant in our kerosene
vehicle, 1.5 times more than is necessary to get the same vehicle size
and payload to orbit. The vehicle does weigh about 10% more in dry
weight, so then the total vehicle+payload weight that can now
be lifted to orbit will be 1.5/1.1 = 1.364 times higher than for the
hydrogen case.
Now for the hydrogen powered SSTO vehicles that have been proposed
the payload is a fraction of the vehicle dry weight. The 100,000 kg
dry weight of the VentureStar compared to the 20,000 kg payload
capacity is typical. Then the kerosene version of such a vehicle could
loft (1.364)*(120,000 kg) = 164,000 kg to orbit. Or considering that
our vehicle is at a dry weight of 110,000 kg with the kerosene-engine
change, the payload would be 54,000 kg, 2.7 times the payload weight
of
the hydrogen case.
As I said this is an easy calculation to do. But many people simply
won’t do it. They have been so conditioned to think that Isp is the
most important thing that the assumption is hydrogen must be used for
an SSTO. It probably doesn’t help matters the fact that the gross mass
becomes about 3 times as great with the dense propellants. Gross mass
has been frequently used as the measure of the cost of a launch
vehicle, which I like to call “the hegemony of the GLOW weight”.
But this is actually a very poor measure to use. The reason is
propellant cost is a trivial component of the launch cost to orbit.
More important is the dry mass and complexity of the launch vehicle
for the payload that can be orbited. Then what’s important is
switching to a dense propellant allows multiple times greater payload
at the same sized and similarly dry-massed vehicle.
Bob Clark
=======================================
Nice post Bob!
I have to keep this one. I get asked to explain why lower ISP dense fueled SSTOs are easier to do, adn your explanations better written and documented then what I usually come up with.
😉
High test peroxide is 1.4 times as dense as LOX and the OF ratio is higher so you get significantly better density than RP/LOX
One minor nit to pick, is that denser fuels need heavyer thrust structure etc…. With hydrogen the acceleration head pressure will minor, maybe not minor for a dense fuel vehicle.
The rocket equation presented is correct; however, to actually get to space in a rocket, there are additional complications that come into play when computing the fuel needed to reach orbit. These complications cannot be ignored and have been identified and analyzed for most rockets that go to space. They are:
1) There is a Delta V associated with losses due to gravity. And gravity changes as a function of altitude and geodetic location over the Earth. This major complication requires much more fuel than the rocket equation needs by itself. That’s why we are contemplating using on-orbit fuel depots since once you are in orbit, the fuel you use from there on has less Delta-V losses due to gravity because gravity is much lower up there than on the ground. It can easily be accounted for by applying these losses in a rocket trajectory simulation from the ground to orbit to find out how much fuel and burn time you need to reach orbit. Imagine for an instant you drop a steel ball in a vacuum and it drops for the time of powered flight which is around 500 seconds. The initial velocity is zero and the final velocity is = G*Delta Time = 32.2 * 500 = 16,085 ft/sec. The Delta-V is the initial velocity (0) minus the final velocity (16,085) = -16,085 ft/sec. This equation is simplified to make a point.
2) Major changes in the rocket’s mass during the launch, especially at staging points. Easily programmed in a simulation.
3) Flying through the atmosphere with upper wind shears predicted pre-launch that creates a drag profile which can be broken down to Delta V losses due to drag.
4) Engine thrust and exhaust velocity changes constantly during a launch which directly affects the results from the rocket equation. Again, integrating the predicted thrust and exhaust velocity profile in a trajectory simulation accounts for these Delta-V losses.
5) Fuel slosh tends to sway the rocket around its desired trajectory path and can be modeled in the trajectory simulation. They are minor compared to the other contributors.
Sorry for the late entry.
Joe
Houston