Sunday, October 30, 2011

The Vanguard Satellite Launch Vehicle

So much has been written about the Vanguard launchers that research on them
was pretty easy. Nonetheless, it is worth putting the stage information in
a format that can make comparisons easier with other similar launchers.
However, it looks like we can safely say that the Vanguard is the second
smallest land-based launcher (by mass).

In summary, the Vanguard was a small three stage rocket launcher able to
place 22 lbs payloads into orbit. The first stage used liquid oxygen (LOX)
with kerosene as the fuel. The second stage used nitric acid with UDMH
as the fuel. The third stage was a solid rocket motor without guidance.
The second stage was responsible for orienting the third stage prior to
its ignition to ensure a proper orbit. As the Engineering Summary document
states:
    "A three stage vehicle, with two guided stages and an
    unguided but spin-stabilized third stage, fired at
    second stage apogee, represented the most efficient
    vehicle combination consistent with rocket technology
    at that time."
One of the most obvious things about the Vanguard versus a solid launcher
like the Lambda 4S is that it has substantially lower mass ratios. Even
though the Vanguard is only a 3 stage vehicle, doesn't have substantially
higher Isp, it outperforms the Lambda 4S in delta V despite a larger effective payload.


THE STATISTICS
Here's the statistics table for Vanguard SLV-1. The SLV-1 was preceded by
six test vehicles, TV-0 through TV-5, and was the first operational version
of the design series. Later versions had numerous improvements over this
basic design. Although SLV-1 failed to place a payload in orbit, it represents
the basic Vanguard design and is the one that I used for my analysis. The
reason for SLV-1's failure likely was a control system problem which resulted
in stage 3 having an improper trajectory.


It should be pointed out that the calculated Gross Liftoff Weight (GLOW) is
different than that in the Engineering Summary document. This is because
they use a weight which includes ice on the Lox tank and aerodynamic
surfaces used on the ground to minimize wind shaking of the vehicle.
Therefore, the GLOW used in the analysis subtracts out the ice and
aerodynamic wind breaks.

One other significant issue is that the nosecone is properly part of stage 2
but its weight is included in stage 1. The reason for this is that the nose cone
is ejected from stage 2 shortly after separation and therefore, its effects
are not felt by stage 2 but mostly by stage 1.


STAGE 1
Although the Engineering Summary document is authoritative, making sense
of the effects of various weights on stage 1 requires careful attribution
of various weights to the overall stage performance. In the Rocket Equation,
it is important to get the weight at liftoff (GLOW) and the weight at stage
burn out correct as well as the effective specific impulse (Isp). These weights
have to be factored properly into the analysis or the results will not be
as accurate as one might desire.

In the case of stage 1, it is necessary to figure in the weights of the
Hydrogen Peroxide and the Helium used in the propulsion system and account
for their effect on both the weight and the effective propulsion system
efficiency as expressed by the average Isp. This means that the weights
of these fluids must be included into the weight of the "propellants"
which includes the oxidizer and the fuel. Doing so, gives the stage
weights below:
Fuel and Oxidizer:      15952 lbs
Helium:                    13 lbs
Hydrogen Peroxide:        315 lbs
---------------------------------
Propellant Weight:      16280 lbs
It should be noted that the total Hydrogen Peroxide weight was given
as 340 lbs, but only 315 lbs is reported as having been used. Therefore,
the additional 25 lbs was assigned to the burnout weight of stage 1.

Reported Emtpy Wt:       1587 lbs
Unused Peroxide:           25 lbs
---------------------------------
Burnout Weight:          1612 lbs
The first stage engine used a turbopump to raise the propellant feed pressure
to 616 PSI. The exhaust gas of the turbopump was directed to roll control
nozzles to provide attitude control beyond the stage 1 motor gimballing.

STAGE 2
Stage 2 used pressure fed nitric acid and Unsymmetrical DiMethyl Hydrazine (UDMH)
as propellants. The motor used was an Aerojet AJ10-37. The AJ10 motor, with
improvements, has continued to be used to this day in the Delta II upper stage.
With variations, this motor has also been used on the Apollo Service Module and
on the Shuttle's Orbital Maneuvering System. This motor has a long history from
the first American orbital attempts to this day.

One surprising aspect of stage 2 is its use of liquified propane as the attitude
control gas for roll control. A blanket heater was used to keep the propane
vapor pressure at 240 PSI. Again, the propane's weight has to be taken into
account for the stage performance
Fuel and Oxidizer:      3372 lbs
Propane:                  13 lbs
Helium:                   17 lbs
--------------------------------
Propellant Weight:      3402 lbs
STAGE 3
Stage three used a solid rocket motor which was spun along its axis to
maintain orientation. The second stage essentially used "point and
shoot" with the third stage and it contained the guidance system.

A spring-loaded separation device separated the payload from the third
stage motor at the appropriate time.


PERFORMANCE SUMMARY
Based on the vehicle defined in the performance table, above, an
aerodynamic model and an Isp vs altitude model, a simulation was
performed to identify various performance characteristics. The
trajectory was made to match the published values in the Engineering
Summary. From this, we can estimate gravity and aerodynamic losses
of the first stage.

Designed delta V:       10594.742 fps
Observed delta V:        6399.13  fps
Aerodynamic Losses:       440.31  fps
Gravity Loss:            3755.302 fps
Additionally, we can observe the apparent allocation of delta velocity (delta V)
to each stage:

Stage 3:                14072.890 fps
Stage 2:                10410.299 fps
Stage 1:                10594.742 fps
-------------------------------------
Total:                  35077.931 fps
SUMMARY
The Vanguard satellite launcher provides an interesting example for those
interested in small launch vehicles. The idea of a small launch vehicle
with an unguided final stage provides one way to simplify the design
and development task. It drops the weight of the guidance system from
the final stage where it will have the greatest impact on launch vehicle
weight, down to the second stage where it will have less effect.

The Vanguard satellite launch vehicle is a fascinating example of a
small orbital launcher.

REFERENCE
The Vanguard Satellite Launching Vehicle - An Engineering Summary
http://hdl.handle.net/2060/19740072500

Friday, October 28, 2011

News: NASA Robotic Lander Test Flight Nov. 4

NASA Robotic Lander Test Flight Nov. 4
SpaceRef, 28 October 2011
http://www.spaceref.com/news/viewpr.html?pid=35088

NASA will conduct a 100-foot robotic lander altitude test flight Friday, Nov. 4, to mature the technology needed to develop a new generation of small, smart, versatile robotic landers capable of achieving scientific and exploration goals on the surface of the moon, asteroids or other airless bodies.

Thursday, October 27, 2011

Reports on Wiki-Launcher

Here are various reports by various people working on ideas related to the
N-Prize [http://www.n-prize.com/]. There might be something of interest
for you in these.

Study of a nozzle vector control for a low cost mini-launcher
http://upcommons.upc.edu/pfc/bitstream/2099.1/12521/1/memoria.pdf

Study and Implementation of the stability and control system of a mini-launcher
http://upcommons.upc.edu/pfc/bitstream/2099.1/12940/1/memoria.pdf

Design and Implementation of a Second Stage Nozzle for a Low Cost Mini-Launcher
http://upcommons.upc.edu/pfc/bitstream/2099.1/11742/1/memoria.pdf

Implementation of a femto-satellite and a mini-launcher
http://upcommons.upc.edu/pfc/bitstream/2099.1/9652/1/memoria.pdf

Use of Hardware-on-the-loop to test missions for a low cost mini-launcher
http://upcommons.upc.edu/pfc/bitstream/2099.1/11754/7/TFC_LaiaNavarro_memoria_v2.0.pdf

Design and Implementation of a Synthetic Aperture Antenna for a Femto-Satellite
https://upcommons.upc.edu/pfc/bitstream/2099.1/11686/1/memoria.pdf

Study of a Low Cost Inertial Platform for a Femto-Satellite Deployed by a Mini-Launcher
http://upcommons.upc.edu/pfc/bitstream/2099.1/9668/7/TFC_EsteveBardolet_memoria_V2.pdf

There's also a bit more information here:

Wikilauncher
Google Code
http://code.google.com/p/moon-20/wiki/WikiLauncher

Wednesday, October 26, 2011

News: Generation Orbit Vies for Small Satellite Air Launch

Generation Orbit Vies for Small Satellite Air Launch
Generation Orbit, 26 October 2011
http://www.generationorbit.com/

Generation Orbit Launch Services, Inc. (or GO) presents a fast, flexible, and dedicated nanosatellite (1-30 kg) orbital payload delivery service called GO Launcher, utilizing existing high speed jet aircraft and mostly existing rockets.

GO1 = 1 to 10 kg to Low Earth Orbit
GO1 would be an initial demonstrator utilizing mostly existing solid rockets, essentially a minimum viable launch system. GO1 could mature into an operational capability in the 1-10 kg class (LEO payload delivery capability, 250 km circular orbit). The GO1 system may include international participation.

GO2 = 20 to 30 kg to Low Earth Orbit
GO2 would be a larger operational system than GO1 that offers a minimum payload delivery service in the 20-30 kg class (LEO payload delivery capability, 450 km circular orbit) with the potential for future growth. GO2 would use the experience gained from GO1 to reduce overall risk and prove the "Your Orbit, On Time" operations model. GO2 would also include options for inclusion of new technologies.

Tuesday, October 25, 2011

News: Rumor of Nanosat Challenge Allied Partner

Rumor of Nanosat Challenge Allied Partner
Team Phoenicia, 24 October 2011
http://teamphoenicia.blogspot.com/2011/10/regarding-team-phoeniciatechshop.html

"Delightfully, we were just updated that the agreement has been signed between NASA and the allied org. HOWEVER! We were told to hang on for the official PR mill to get set to grind. This was not NASA's choice, fwiw. They want to get this out as fast as possible, too. They have been directed to hold off as well."

News: Welcome to Copenhagen Suborbitals

Welcome to Copenhagen Suborbitals
Wired, 24 October 2011
http://www.wired.com/wiredscience/2011/10/welcome-to-copenhagen-suborbitals/

"We design and build everything from scratch using ordinary materials. We try to overcome the complex process of making a suborbital space rocket by letting the ordinary and plain be our guide, instead of letting the complex and extreme become our obstacles."

Monday, October 24, 2011

News: Replicators Have Arrived

Replicators Have Arrived
The Once and Future Moon, 24 October 2011
http://blogs.airspacemag.com/moon/2011/10/replicators-have-arrived/

"We’re not quite there yet but crude versions of such imagined machines already exist. These machines are called “rapid prototype” generators or three-dimensional printers. They take digitized information about the dimensions and shape of an object and use that data to control a fabricator that re-creates the object using a variety of different materials. Typically, these machines use easy to mold plastics and epoxy resins but in principle, any material could be used to create virtually any object."

Sunday, October 23, 2011

The Japanese Lambda 4S Launcher

NOTE: It was kindly pointed out by Stephen Pietrobon that I had made an error in my interpretation of the mass table. The following is the corrected version of the analysis. (CORRECTED 12 August 2012)

Is it possible to put a payload into orbit on a multistage rocket without a guidance system? The answer is "yes." In 1970, Japan launched its Lambda 4-S (or L4-S) launcher with the Osumi satellite and placed its payload into orbit. This vehicle had no on board guidance system and is, to date, the smallest ground based launch vehicle to place a satellite into orbit. This vehicle provides some interesting lessons to those with small launch vehicle orbital aspirations.

The history of the Lambda L4-S is in solid propellant sounding rockets where most of the four stages were developed. The first stage was composed of the L735 sounding rocket motor with 2 SB-310 strap on booster motors. The second stage was a shortened version of the first stage known as the L735-1/3 (it was about 1/3 the length of the first stage). The third stage was a sounding rocket motor known as the L500. The fourth stage was a small spherical solid motor known as the L480S.

The payload placed into orbit was the Osumi satellite which was composed of the fourth stage motor plus the satellite instrumentation. It was placed into an orbit with a perigee of 200 miles and an apogee of 1500 miles. Launched in 1970, its orbit finally decayed in 2003 and it entered the atmosphere.



THE ANALYSIS
Information on this rocket is scarce but, piecing together a cryptic table of masses and performances from the Japan Aerospace Exploration Agency (JAXA), finding some other documentation at the NASA Technical Report Server (NTRS), and fitting everything into the rocket equation, I was able to get a reasonable model of the stages, their weights and performances.



STRAP ON BOOSTERS
The first stage to consider is the strap-on boosters and their involvement in launching the rocket onto its trajectory. Two SB-310 motors were strapped on to enhance the boost rate and delta V of the vehicle. These motors are each 12.2 inches (310 mm) in diameter, 19 feet (5772 mm) long, weighed about 1100 pounds and produced about 21,000 lbs ( 1824 N) of thrust each, burning for 7.1 seconds with an Isp of 220 seconds. These motors continued seeing use in the later Mu family launchers.

STAGE 1
The first solid stage motor, designated L735, was about 2.4 feet (735 mm) in diameter, and 27 feet (8280 mm) long. It had four fins to stabilize it and weighed about 20721.22 lbs (9399 kg). It produced 92170 lbs (410 kN) of thrust, burned for about 29 seconds and had a sea level Isp of about 215 seconds.

STAGE 2
Stage 2 was a shortened version of the Stage 1 motor and was called the L735-1/3 because it was 1/3 of a first stage solid motor. It was 2.4 feet (735 mm) in diameter, about 12 3/4 feet (3900 mm) in length and weighed about 5400 lbs (2450 kg). It produced about 26,527 lbs ( 118.00 kN ) of thrust burning for about 38 seconds with an Isp of 242.9 seconds.

STAGE 3
Stage 3 was a solid rocket motor designated L-500. It was about 1.64 feet in diameter (500 mm), 8.2 feet (2500 mm) in length, weighed about 1700 lbs (800 kg) and had an Isp of 249.3 seconds. It weighed about 1760 lbs ( 800 kg ). Stage 3 also had spin up motors to cause gyroscopic stabilization.

STAGE 4
Stage 4 was a spherical solid rocket which stayed in orbit with the satellite; it was designated the L-480. It had a diameter of 1.3 ft (480 mm), weighed about 220 lbs ( 100 kg ) full and had a vacuum Isp of 254 seconds. Stage 4 also included spin up and spin down motors which were used in preparation for the horizon sensing and azimuth setting activity.

PERFORMANCE TABLE SUMMARY
Because of the strap-on boosters, we must break down the time when both the boosters and the first stage are firing and treat this as one "stage" after the strap on boosters are ejected, what's left of the first stage is another "stage." I therefore include the thrust of the boosters plus that of the first stage during their coincident burn duration. This is designated in the performance table as "Stage 0." After the strap-on boosters burn out and are ejected, the stage 1 rocket tube plus the remaining propellant in the first stage motor constitutes "Stage 1." The upper stages require no other coincidence considerations and follow the published stage figures from JAXA.

GUIDANCE AND TRAJECTORY
Although details are sketchy and hard to come by, the best available details suggest that stages 1 and 2 used fixed aerodynamic surfaces and a gravity turn to direct the vehicle trajectory. Then the third stage used spin motors to gyroscopically stabilize itself. The fourth stage despun itself, pointed in the correct orientation and then fired its motors to set itself on the desired trajectory and respin itself for stabilization. Apparently the reason for this approach to "guidance" was that Japan's constitution forbade technology that could have military purposes so the guidance system had to avoid military applications. This system wasn’t properly a “guidance system,” but more of a one-shot pointing system.

AERODYNAMIC AND GRAVITY LOSSES
My simulation shows about 218 fps of aerodynamic losses. But, this number is hard to establish with certainty because I don't have a good way of calculating coefficients of drag for shapes which are not bodies of revolution.

The simulation also showed about 870 feet per second for gravity losses through the 1st stage burnout.

LESSONS LEARNED
Some of the most obvious things that can be learned from this launcher are the kinds of weight ratios that each of the stages had. This can be useful in estimating weight ratios for our own rocket designs (or at least suggesting reasonable ranges for similar rockets).

Another lesson that can be learned is that the launch vehicle total delta V had a small margin above what was required for orbit (about 20%). Looking at the number in the analysis table, we see that this launcher had a total delta V of about 29526 fps.

Another thing worth pointing out is that it is possible to orbit a satellite with only a final stage orientation mechanism, leaving the other stages only to follow gravity turn trajectories.

A final thing to notice is that the length to diameter ratio (fineness ratio) is about 22. As rockets get smaller, it is more beneficial to go with larger fineness ratios to counteract the increased effects of aerodynamics which don't scale equivalently with the mass.

REFERENCES
Jaxa Website
http://www.isas.jaxa.jp/e/enterp/rockets/vehicles/l-4s/index.shtml

Encyclopedia Astronautica Website
http://www.astronautix.com/

“Survey of Japanese Space Program With Emphasis on Kappa and Lambda Type Observation Rockets”
NASA NTRS, http://ntrs.nasa.gov/search.jsp

Thursday, October 20, 2011

News: Book Review: The Apollo Guidance Computer

Book Review: The Apollo Guidance Computer
Universe Today, 21 October 2011
http://www.universetoday.com/90128/book-review-the-apollo-guidance-computer/#more-90128

"Written by Frank O’Brien, The Apollo Guidance Computer is a thorough review of the computer system used during the Apollo missions. The Apollo Guidance Computer rings in at a whopping 430 pages – most readers will likely only pick out certain parts of the book to read." ...

Wednesday, October 19, 2011

News: NACA Five-Stage Solid Rocket

NACA Five-Stage Solid Rocket
YouTube, 6 April 2011
http://www.youtube.com/watch?v=ucCieq5p95M&feature=youtu.be

Research by the NACA Pilotless Aircraft Research Division on the 5-stage solid rocket. Tests appear to have taken place at Wallops Flight Facility, originally part of Langley Research Center.

News: Russians see room for moonbase in lunar lava caves

Russians see room for moonbase in lunar lava caves
Reuters, 18 October 2011
http://www.reuters.com/article/2011/10/18/us-russia-moon-idUSTRE79H69P20111018

The United States may have put the first man on the moon, but Russian scientists and space explorers are now gazing at a new goal -- setting up a colony on the moon.

Tuesday, October 18, 2011

A More-Realistic Weight Analysis

In the last analysis, I did a simplified analysis using off-the-shelf commercial motors from ATK [http://orbitalaspirations.blogspot.com/2011/10/looking-at-solid-first-stage-booster.html]. In that earlier analysis, I used the weights of the motors without any additional weight considerations for control systems, guidance or aeroshells. I’d like to go to the next level of design detail and make a first-step attempt at including those weights.

First Stage

Starting at the first stage, although I showed an aeroshell around the upper stages, I didn’t actually include any weight for it. Therefore, I want to include that into my estimates. Without having a particular design, it’s hard to know what to put, but I’m going to make an assumption that the upper aeroshell, fins and control systems are equivalent in weight to the structure of the motor. This is obviously going to be wrong by some amount but this will give us a first-order approximation. Therefore, whatever mass I allocate for the motor casing, I will allocate equal weight for the additional components of the first stage.

Second Stage

For the second stage, I need to consider the fact that it must be mounted to the first stage and that the motor nozzle needs gimbal control. No guidance is needed since that is provided by the fourth stage. There are no aerodynamic loads that have to be figured in because it is presumed to be operating only in a vacuum. On that basis, I added a few percent (5%) of the propellant weight to account for the stage control, coupling and ejection.

Third Stage

Like the second stage, I added a small percentage (5%) for stage control, coupling and ejection.

Fourth Stage

Like the previous two space stages, I added weight (5%) to account for stage control, coupling and ejection, but I also added additional weight to account for a guidance system (0.5%).

Analysis Results

Now that I added the additional weights, the delta V available from the stages changed. Each stage weighed a bit more and its delta V was less. To account for this, I had to re-design the second stage to provide more delta V for the in-space stages. Because I am limiting myself in this experiment to considering off-the-shelf ATK motors, I had to change the motor from a Star 15G to a Star 17A. This motor has a bit more propellant and compensates for the lost delta V. However, it actually provides appreciably more delta V and is a bit larger.

Because of the weight increases of the in-space stages (stages 2 through 4), as well as the aerodynamic loss which wasn’t adequately considered in the earlier design, the first stage was no longer able to provide sufficient delta V. I had to increase the first stage motor to a larger one, from the ASAS 21-85V to an ASAS 28-185. This is a much larger motor, with a diameter of 28.5 inches.

I really didn’t like having to make these adjustments to much larger motors, but the weight drove them up to provide the necessary performance. The ¼ pound to orbit rocket went from about 2000 pounds up over 8000 pounds. As such, these represent closer to reality for the weights and weight ratios.

Here are the new rocket specifications:


And here is a comparison between the design before and after:


Comparison of Sizes before and after more enhanced weight model

Summary

In this analysis, I used a more accurate weight model. As a result, the whole rocket grew appreciably. One reason I want to establish a more reasonable weight model is that I want to use these mass ratios in future rocket design analyses. These will provide a useful baseline for comparison of various performance improvements.

News: Why Not Space?

This author looks at some of the negative aspects of space travel and colonization. I think it is worth being a realist and considering both the benefits and problems in any proposition. This author has some cogent arguments. He could be right, he could be wrong but we should consider his ideas, I think.

Ed L

Why Not Space?
Do The Math, 12 October 2011
href="http://physics.ucsd.edu/do-the-math/2011/10/why-not-space

"In other words, I’m an insider—and a supporter. I whole-heartedly believe that space offers tremendous scientific promise." ...

"But I want to caution against harboring illusions of space as the answer to our collision course of growth on a finite planet. We live at a special time. We have enjoyed spending our inheritance of fossil fuels, and are feeling rather heady about our technological prowess. For many generations now, we have ridden an exponential growth track, conditioning ourselves to believe that our upward trajectory is an eternal constant of our existence."

Sunday, October 16, 2011

Looking at a Solid First Stage Booster


Just because I thought it might be worth considering what an all-solids launcher
might look like using high-performance commercial ATK motors, I found what was a
reasonable booster suitable for the first stage. The following diagram shows the
numeric specifications and compares the solid first stage with an equivalent liquid stage. I’ve darkened out the parameters of the upper stages because those things haven’t changed from my last post.


If you look at the image below, one thing that stands out is that the solid booster is physically shorter (for the same diameter) compared to the liquid booster.


This is due to the solid booster's higher average propellant density, which is almost double that of the liquids that I had selected. In actuality, the liquid booster is lighter by about 200 lbs, but it is physically larger because of the lower propellant density.

A summarization of this Comparison

Now, the main impetus of this design experiment was to look at reasonable performance
solids as examples of upper stage vehicles and, then finally, as a first stage booster.

For amateurs to develop these kinds of vehicles, they would have to try to duplicate
the performance factors of these commercial motors with their own designed and fabricated motors. One good thing from this is that they have a known working example and explicit specifications for trying to develop their own versions of the commercial motors. This will simplify the development task somewhat.

Because I went with off-the-shelf motors, their specifications dictated many of the
requirements for the vehicle (such as stage delta V, thrust and mass ratios). In many ways, I consider these designs to be an upper limit of reasonable size for launching a payload as small as a 1/4 pound (113 grams). Think about it: a payload of 1/4 pound required a launcher with a GLOW of 1914 lbs. This is an effective payload:glow ratio of 0.00013 or 0.013 %. This is pretty poor overall. Nonetheless, with smaller launchers we'll see these kinds of ratio values. But we can do better. To do better means that a fundamental ratio between payload and total rocket takeoff mass will be a higher number. Let's examine how to get to smaller, more manageable rockets in upcoming future posts.

Saturday, October 15, 2011

An All-Solid-Upper-Stages Booster



An All-Solid-Upper-Stages Booster
By Ed LeBouthillier

I don't want anyone to think that I'm picking on solids as being incapable for booster stages. To the contrary, they're very capable and offer many benefits of their own over liquid stages. To show their capability (and some aspects of their requirements), I'm going to do a quick analysis of an all-solid-upper-stages booster utilizing off-the-shelf solid rockets.

ATK [http://www.atk.com/corporateoverview/corpover_missiongroup.asp] produces some very high quality solid motors which are used in various military and space applications. Their 2008 catalog can be found online [
http://www.atk.com/capabilities_space/documents/atk_catalog_may_2008.pdf] so I thought I'd look at their offerings to look at what a solid-upper-stages booster might look like. Now, before you start saying "cool! let's do it," I should point out that these motors are what many of us would call "very expensive." But, they provide some ideas on what a small orbital launcher using solid upper stages might look like.

I've selected 3 ATK solid motors for the upper stages: the Star 5C, the Star 9 and the Star 15g as being representative of good solid motors suitable for this task.

This analysis has a number of caveats worth considering:

1. DELTA-V - I've only allowed for about 24500 fps (7467.6 m/s) for upper stages
2. CONTROL - I haven't included any weight for control systems (i.e. TVC)
3. GUIDANCE - No weight has been included for a guidance system

The idea in this analysis is merely to show what a small orbital vehicle might look like in a rough way.

Here are the results that I get:


Stage 4
Stage 3
Stage 2
Stage 1

Oxidizer
AP
AP
AP
Lox

Fuel
HTPB/Al
HTPB/Al
HTPB/Al
Propane


Star 5C
Star 9
Star 15G


Payload
0.250
10.110
51.111
257.707
lbs
OF Ratio
6.400
6.400
6.400
2.200

Oxidizer Density
121.700
121.700
121.700
71.23
lbs/cuft
Fuel Density
68.498
68.498
68.498
33.36
lbs/cuft
Avg Density
114.511
114.511
114.511
59.396
lbs/cuft
Average Isp
268.1
289.1
281.8
250
Seconds
Desired DeltaV
4928.1
9102
10674
10409
FPS
Body:Fuel Mass
1.2409
0.2853
0.1587
0.2467

Thrust
450
1200
1000
6350
lb-f






Payload Ratio
0.025
0.247
0.247
0.105

Structural Coef
0.554
0.222
0.137
0.198

Propellant Ratio
0.446
0.778
0.863
0.802

Mf/Me Ratio
1.771
2.661
3.245
3.648







Propellant Mass
4.400
31.900
178.300
1967.312
lbs
Oxidizer Mass
3.805
27.589
154.205
1352.527
lbs
Fuel Mass
0.595
4.311
24.095
614.785
lbs
Oxidizer Volume
0.031
0.227
1.267
18.988
cuft
Fuel Volume
0.009
0.063
0.352
18.429
cuft
Stage Weight
9.860
41.001
206.596
2452.648
lbs
MT
5.460
9.101
28.296
485.336
lbs
Me
5.710
19.211
79.407
743.042
lbs
Mf
10.110
51.111
257.707
2710.354
lbs






Max G's
78.811
62.464
12.593
8.546
g's
Cum Delta V
4928.050
14029.800
24703.410
35112.410


So, the Gross Lift Off Weight (GLOW) is about 2710 lbs (1011 kg). The payload experiences upwards of 79 g’s as the final stage is nearing empty (presuming a fairly constant near-average thrust which is what the thrust curve does show).

But, as a feasibility or model of a possible launcher, it shows what is possible. The first stage is a scaled-up Aerobee 150 sustainer. The body diameter is 20 inches, the finspan is 3 feet 11 inches and the total height is about 24 feet 2 inches.



A Short Survey of Off-The-Shelf Solid Motors for Orbital Upper Stages


A Short Survey of Off-The-Shelf Solid Motors for Orbital Upper Stages
By Ed LeBouthillier

Many suggest using off-the-shelf solid motors (or similar custom motors) for upper stages of small orbital launchers. In this discussion, I review some of the requirements for upper stages and the possibility of using solids as upper stage motors. I will presume that a basic 1/4 pound (113 gram) payload is selected.

OFF THE SHELF MOTORS
High Power rocketry uses motors that provide many benefits for someone considering upper stages for orbital launchers. They are efficient, use modern propellants, come in a wide range of impulses and require little development.

The following table lists a few different solid motors that might be suitable for upper stages and their parameters:

Manuf.
Model
Total Impulse
(N-s)
Propellant Weight
(grams)
Loaded
Weight
(grams)
Empty Weight
(grams)
BP Ratio
(λ)
SL Isp
Vac Isp
Aerotech
I305
450
302.1
581
278.9
0.92
150 s
211 s
Cesaroni
I303
538
270.0
500
230.0
0.85
189 s
235 s
Aerotech
I350R
2500
1400.0
2294
894.0
0.64
189 s
235 s
( Note: BP Ratio = Empty Weight/Propellant Weight )

Let me explain how I estimated the specific impulses for sea level (SL) and vacuum (Vac) exhaust pressures.

First, the sea level Isp is derived from the published data (and verified as being reasonable). The equation is:

                                    Avg Thrust * Burn Duration
            Ideal Isp =        --------------------------
                                         Propellant Mass

These propellants are specified as being composite propellants. I used Propep as the
combustion code to estimate the Isp. I put Ammonium Perchlorate and HTPB into ProPep. I then set the mixture ratio similar to what is published as commonly used. I presumed that the published value represents 90% of the theoretical maximum Isp. Therefore, if 150 seconds is the value derived from published figures, then the theoretical ideal value of the Isp is 150 seconds / 0.90 = 166 seconds. I then adjusted the chamber pressure in Propep until I got a theoretical value equal to this Ideal Isp. I then calculated the Isp in a vacuum using Propep and then multiplied that value by 90% to get the vacuum Isp. It’s rough, but it gives meaningful statistics for comparison.

IMPLICATIONS
Based on the above figures, we can estimate the likely delta V from one of these motors.
If we presume no payload, and just the motor weight, then using the Aerotech I350R as an example we have:

            dv = g * Isp * ln( Mf / Me )

            dv = 9.8 * 235 * ln( 2294 g / 894 g )
            dv = 2303 * ln( 2.57 )
            dv = 2303 * 0.94
            dv = 2164.82 m/s (7102 fps)

Since we need to provide about 7467.6 m/s (24500 fps) to 7772.4 m/s (25500 fps) in the upper stages, we would need about 7772 / 2165 = 4 stages at this performance level (for a total of 5 stages with a first stage). Presuming a 113 gram payload, a 113 gram guidance and control system for the 5th stage, we have:


Stage 5
Stage 4
Stage 3
Stage 2
Stage 1

Oxidizer
AP
AP
AP
AP
Lox

Fuel
HTPB
HTPB
HTPB
HTPB
Propane








Payload
0.113
2.5
39.5
619.5
9704.6
kg
OF Ratio
2.333
2.333
2.333
2.333
2.200

Oxidizer Density
1.949
1.949
1.949
1.949
1.141
g/cc
Fuel Density
0.919
0.919
0.919
0.919
0.582
g/cc
Avg Density
1.640
1.640
1.640
1.640
0.966
g/cc
Average Isp
235
235
235
235
252
seconds
Desired DeltaV
1867.4
1968.3
1968.3
1968.3
3172.7
m/s
Body:Fuel Mass (λ)
0.72
0.63
0.63
0.63
0.197








Payload Ratio
0.047
0.068
0.068
0.068
0.155

Structural Coef
0.419
0.387
0.387
0.387
0.165

Propellant Ratio
0.581
0.613
0.613
0.613
0.835

Mf/Me Ratio
2.249
2.349
2.349
2.349
3.610








Propellant Mass
1.402
22.711
356
5574
52152
kg
Oxidizer Mass
0.981
15.897
249
3901
35854
kg
Fuel Mass
0.421
6.814
107
1672
16297
kg
Oxidizer Volume
503.2
8154.5
127748.1
2001297.1
31423640.1
cc
Fuel Volume
457.3
7410.7
116096.3
1818760.5
28004727.9
cc
Stage Weight
2.411
37.018
580
9085
62425
kg
MT
1.009
14.308
224
3511
10274
kg
Me
1.123
16.832
264
4131
19978
kg
Mf
2.524
39.542
619
9705
72130
kg







Stage Impulse
3230
52338
819926
12844938
128880945
N-s
Cum delta V
1867
3836
5804
7772
10945
m/s

The important thing to notice is that the size of the 3rd stage is quickly too large (close to 620 kg [1370 lbs]). By the time you get to the second stage, it is up to 9705 kg (21000 lbs). The reason is that the performance is too low and weight too high for these motors. For a tiny 113 gram payload, the exo-atmospheric stages are 9705 kg.

SUMMARY
Based on this quick survey of a few commercial rocket motors (yes, it’s a small sample but I think it’s representative), we can see that typical off-the-shelf motors are likely too low in performance and too heavy for orbital launchers. This is not to say that these motors are not of high reliability and capability: they are highly engineered and quality products developed for the commercial market. They are safe and reliable and often reusable. However, these design choices work against them being the lightest possible and what is needed for orbital vehicles.