Amateur solid-fueled rockets to *orbital* space?

RGClark · 2017-06-06 19:09:02

I was impressed by this university teams launch to 144,000 feet of a solid fuel rocket:

USC Rocket Propulsion Laboratory Breaks Record.
Amy Blumenthal | March 16, 2017
Student-run RPL launches rocket of own design to 144,000 feet.
https://viterbischool.usc.edu/news/2017 … ks-record/

I did a rocket equation calculation that showed a 3-stage rocket of solid-fuel stages with altitude compensating nozzles could reach orbit. Based on the USC experience this should be something within the capabilities of most universities.

But how difficult is it to fuel a solid fuel rocket of say a few hundred kilos size?

Bob Clark

Last edited by RGClark (2017-06-12 09:41:09)

GW Johnson · 2017-06-07 07:28:48

The only problems are(1) what kind of propellant, and (2) who makes that propellant. Designing the rocket stages themselves is no real problem, especially if you can cartridge-load pre-made propellant grains in sleeves. Those sleeves can double as your case insulation. The biggest design problem to overcome is adequate vehicle attitude control, same as von Braun faced at Peenemunde long ago.

As for what propellant, something primitive like fireworks propellants or sugar nitrate has too low an Isp to be useful: something in the range 80 to 180 sec Isp. It takes a "real" propellant to do a launch job. Even the AN composites and the plain double base propellants are too limited at 200-220 sec Isp. It really takes either a composite-modified double base that uses AP not AN, or an AP-composite to get enough Isp to serve. These fall in the range of 240-260 sec sea level Isp.

Propellants like that are very dangerous to make, especially the double base, because you have to handle raw nitroglycerin. Even the AP is quite dangerous, because all by itself it is a class 1.1 mass detonable material. The folks who do this for a business do this with remote operated equipment. The danger is just too great. It is not a job for amateurs.

But, there are folks who make such propellants for the amateur rocketry folks. Some of it is AP-composite, too. High dollar stuff, but that's what you need.

A part of the design is chamber pressure: both thrust coefficient and Isp are greatly improved at higher chamber pressures. I'm unsure what pressures the amateur rocketry propellants are used at, but it's likely under 1000 psia. Most of the real tactical size rockets run in the 2000-4000 psia range. It was only square-cube law effects (steel is only so strong) at giant sizes that reduced the shuttle SRB's to 900 psia. A 20-inch diameter case made of D6ac will hold 2400 psig at a wall thickness of about 0.12 inches and 10% below ultimate tensile in hoop stress. It'll do that maybe once to 5 times. Smaller, and wall thickness is thinner.

That kind of thing isn't simple roll and weld stuff, it's thick wall seamless tube in the annealed state cold-rolled to shape and then very carefully heat treated to strength. According to Mil Handbook 5, the ultimate tensile strength (if everything is done to spec) can be 220 ksi, with 190 ksi yield. D6ac is a semi-austenitic martensitic high-alloy stainless. Fairly easy to form, machine, and weld.

GW

elderflower · 2017-06-07 09:58:12

The old Scout rocket was a solid, wasn't it?

RGClark · 2017-06-07 13:50:49

elderflower wrote:

The old Scout rocket was a solid, wasn't it?

Yes, it was. There have been several all-solid orbital rockets over the years:

http://www.astronautix.com/s/scouta.html

Bob Clark

SpaceNut · 2017-06-07 16:23:52

Plus there is still others..

Brings to mind childhood days of fly the Este's rockets.... Build the tube and shovel the engine in the end, setup the launch pad with the igniter in the chamber nozzle and connect power to the leads and puch the button and off you go until the engine quit burning....

GW Johnson · 2017-06-07 18:37:38

I worked on Scout at LTV in 1974. It wasn't the "A" model, but after all these decades, I don't remember what model it was. My job was customer support with achieved orbit analysis, and trajectory simulations of potential advanced models. One really oddball variant was used in an ICBM chase mission about a year after I showed it was possible.

Scout used "off the shelf" motors from the solid propellant companies (in those days there were many). None of these had any "trick" nozzles, just plain ablative convergent-divergent designs. It had small fins to enhance aerostability while the first stage was burning. The control system fired hydrogen peroxide thrusters to correct an attitude angle if it drifted out of an acceptable deadband. Very simple, but worked like a charm.

Memory fails, but I think I remember we were putting 200-pound-class payloads into geosynch transfer trajectories in 1974.

GW

RGClark · 2017-06-07 23:23:32

GW Johnson wrote:

The only problems are(1) what kind of propellant, and (2) who makes that propellant. Designing the rocket stages themselves is no real problem, especially if you can cartridge-load pre-made propellant grains in sleeves. Those sleeves can double as your case insulation. The biggest design problem to overcome is adequate vehicle attitude control, same as von Braun faced at Peenemunde long ago.
As for what propellant, something primitive like fireworks propellants or sugar nitrate has too low an Isp to be useful: something in the range 80 to 180 sec Isp. It takes a "real" propellant to do a launch job. Even the AN composites and the plain double base propellants are too limited at 200-220 sec Isp. It really takes either a composite-modified double base that uses AP not AN, or an AP-composite to get enough Isp to serve. These fall in the range of 240-260 sec sea level Isp.
Propellants like that are very dangerous to make, especially the double base, because you have to handle raw nitroglycerin. Even the AP is quite dangerous, because all by itself it is a class 1.1 mass detonable material. The folks who do this for a business do this with remote operated equipment. The danger is just too great. It is not a job for amateurs.
But, there are folks who make such propellants for the amateur rocketry folks. Some of it is AP-composite, too. High dollar stuff, but that's what you need.
A part of the design is chamber pressure: both thrust coefficient and Isp are greatly improved at higher chamber pressures. I'm unsure what pressures the amateur rocketry propellants are used at, but it's likely under 1000 psia. Most of the real tactical size rockets run in the 2000-4000 psia range. It was only square-cube law effects (steel is only so strong) at giant sizes that reduced the shuttle SRB's to 900 psia. A 20-inch diameter case made of D6ac will hold 2400 psig at a wall thickness of about 0.12 inches and 10% below ultimate tensile in hoop stress. It'll do that maybe once to 5 times. Smaller, and wall thickness is thinner.
That kind of thing isn't simple roll and weld stuff, it's thick wall seamless tube in the annealed state cold-rolled to shape and then very carefully heat treated to strength. According to Mil Handbook 5, the ultimate tensile strength (if everything is done to spec) can be 220 ksi, with 190 ksi yield. D6ac is a semi-austenitic martensitic high-alloy stainless. Fairly easy to form, machine, and weld.
GW

Thanks for that info. My calculation was assuming I could get vacuum Isp's in the 285 s range, like the Star solid rocket motors made by ATK.

I found a company that makes solid rocket motors for amateurs called Cesaroni that offers motors that can get 224 s sea level Isp.

http://www.pro38.com/products/pro150/motor.php

Could you get 285 s vacuum Isp by using long, vacuum optimized nozzles?

These motor use an aluminum case. I was thinking of using fiber wound casings to save on the empty weight. This can save 50% on the casing weight over aluminum. Amateurs have used fiber wound casings for their solids such as the USC team:

1000w

However, I don't know if the Cesaroni motors use the dangerous propellants you mentioned. After the high energy solid propellants are made, can they be safely handled by amateurs who want to fill their own casings?

Bob Clark

GW Johnson · 2017-06-08 08:42:28

Bob:

I haven't played with model rockets since I was an undergraduate student. In those days, a class C motor was about as big as was legal. The propellants were about one step away from fireworks black powder stuff, although they were castable. ~100 sec Isp stuff.

224.4 s Isp sort-of sounds like an AN-oxidized composite, although I found nothing on the Cesaroni site to indicate that. AN is a little safer to handle than AP, but it performs less. If I am right guessing an AN composite, then a high-expansion motor intended for vacuum service might top out around 260 sec Isp. Your exit diameter cannot be any bigger than the stage diameter, that's your real limitation.

The legalities of commercial rocket motor sales to the model rocket-flying public would limit their sales of reloads to some sort of pre-made grain assembly that only fits reloadable cases they sell separately. I noticed there was no indication of chamber pressures. If you can get specs for pressure and dimensions (including closures), you could replace the aluminum case with a graphite composite. One thing you might consider is machining-down the OD to a thinner wall, then over-wrapping it with your composite. That's just a mod to a store-bought case.

A typical AN composite as they were manufactured long ago would have a burn rate somewhere near .05 in/sec at 500 psia and .09 in/sec at 1000 psia. In a 6-inch diameter internal burning motor, I doubt the propellant web fraction would exceed roughly 30% in a commercial product, and that goes on a grain diameter reduced by case and grain sleeve thickness. Call it 25% of the radius on a 5 inch diameter propellant charge, for about 0.62 inches of web to burn. That would be a 13 sec burn at average 500 psia, or about a 6.9 sec burn at 1000 psia. That latter puts me in the ballpark of the thrust-time curve you posted.

Using the total impulse and propellant weight figures in the table, and a "reasonable" thrust coefficient for a sea level nozzle at 1000 psia, I get near 4900 ft/sec c* average. If it were AP, that ought to be significantly above 5000. Therefore, I think my assumption that this is an AN-oxidized composite propellant is fairly reliable.

I also calculate something on the order of 60% volumetric loading of propellant within the case, which is fairly good for an internal-burning grain design of some sort (the site mentioned something they called a "moon" grain design, but I have no clue what that really is). I can get a little more propellant loaded inside the case with a keyhole slot, but it will be slightly progressive at this L/D proportion, unless we cartridge-load two short assemblies inside the same case.

As for processing, the AN has to be ground to a controlled particle size distribution, which is 10's of microns powder range. You can handle that dry, but it is sensitive, and it is potentially mass detonable, given confinement. This gets added to some polymer binder, along with some fine-ground aluminum powder. That confers combustion stability as well as white smoke. Minor trace ingredients probably include single-digit percentages of opacifying carbon black, and yellow iron oxide burn rate-increasing catalyst.

This stuff is mixed under vacuum, with binder curative the last ingredient added. It is cast into sleeves fitted with the grain shape-forming tooling, and then cooked at about 200-250 F for a few days to both cure and "vulcanize" the rubber binder. All of this must be done with remote-operated equipment for safety. It's not something amateurs can do for themselves.

Buy the cases and grains ready-made, at most thinning wall and composite-overwrapping. Customize your upper stage nozzles for vacuum operation. Compensate the lower Isp range with another stage. That's what I would recommend.

Does that help?

GW

Last edited by GW Johnson (2017-06-08 09:08:40)

RGClark · 2017-06-08 16:48:16

I found this page after a web search that says the "White Thunder" propellant used by the Cesaroni P150 motor is Ammonium Perchlorate Composite:

FRIDAY, DECEMBER 4, 2009
APCP Chemistry
Happened across some information about Ammonium Perchlorate Composite Propellant that I think is pretty interesting.
The chemical formula is NH4ClO4. It burns with aluminum, the fuel of choice in white motors, like Aerotech's White Lightning, Cesaroni's White Thunder, and NASA's SRBs, with the equation 10Al + 6NH4ClO4 → 4Al2O3 + 2AlCl3 + 12H2O + 3N2. (source)
http://amateurgeek.blogspot.com/2009/12 … istry.html

The size of these motors isn't like an "Estes" model rocket engine, BTW. The P150 is 6 inches wide, 3 feet long, weighs 70 lbs with an aluminum casing, and puts out a max. 2,000 lbs of thrust. Some refs I've seen suggest their max combustion pressure is in the range of 1,000 psi.

For my vacuum optimized nozzles, I'm assuming an altitude compensation method that allows their effective area ratio to exceed that of a nozzle at the rockets diameter, such as by using an aerospike for example.

When these companies make their solid motors, do they bind the propellant to some lightweight casing then slide this into the aluminum casing, or do they bind the propellant to the aluminum casing directly? If it is the former then it would be easier for amateurs to just use the filled lightweight casing to slide into a filament wound casing they built themselves.

Bob Clark

GW Johnson · 2017-06-08 17:49:05

Bob:

If Cesaroni is really an AP-oxidized composite, their sea level Isp should be very much closer to 240-245 sec Isp at chamber pressures in the 1000-2000 psia range. In the defense business 3 decades ago (!!!!) we were getting 245-255 sec Isp at sea level, using AP-HTPB-Al or AP-CTPB-Al, at chamber pressures near 2000 psia.

If your numbers are right, they are doing a really bad job of ballistic design and propellant formulation. Which could easily be true! The chamber pressure has some influence over this, but it ought to be near 1000 psia for CF near 1.5, and down nearer 500 psia for CF nearer 1.4, given 14.7 psia for ambient backpressure. You get nearer 1.55 for chamber pressures nearer 2000 psia.

Almost all manufacturers for many decades have supplied grains in sleeves to be slid into uninsulated cases (but insulated closures). The grain sleeve literally IS the case insulation. Most are some sort of fiber-reinforced phenolic. Otherwise, you must cast into an insulated-and-primed case directly. There is NO WAY around that requirement.

Cast in the case insulations are usually Kevlar or asbestos fiber-reinforced rubbers of one sort or another, as long as they are compatible with the propellant binder system. For HTPB and CTPB propellant systems, that is usually an EPDM-based insulation.

As for aerospike (or other free-expansion design) nozzles, you get a little bit of benefit for a lot of design effort. Usually it is not very worthwhile, especially if the number of stages exceeds 2. This is because stage 2-on all fire in essentially vacuum conditions.

GW

Last edited by GW Johnson (2017-06-08 17:59:52)

RGClark · 2017-06-09 10:51:02

This page from the Cesaroni web page says their high power rocket motors use ammonium perchlorate composite propellant (APCP):

http://www.pro38.com/regulations.php

They sell mostly to amateurs so perhaps they don't make the propellant with the optimal requirements to optimize performance.

BTW, I was reading some articles of applications of nanotubes, among the now numerous applications of them I found some refs that found adding nanotubes to fuels speeds up the combustion speed to an extraordinary degree:

Highly energetic compositions based on functionalized carbon nanomaterials.
Qi-Long Yan a, Michael Gozin *a, Feng-Qi Zhao b, Adva Cohen a and Si-Ping Pang c
DOI: 10.1039/C5NR07855E (Review Article) Nanoscale, 2016, 8, 4799-4851
http://pubs.rsc.org/en/content/articleh … c5nr07855e [free full text]

Enhanced Energy Release from Homogeneous Carbon Nanotube-Energetic Material Composite.
Authors: Um, Jo-Eun; Yeo, Taehan; Choi, Wonjoon; Chae, Joo Seung; Kim, Hyoun Soo; Kim, Woo-Jae
Source: Science of Advanced Materials, Volume 8, Number 1, January 2016, pp. 164-170(7)
Publisher: American Scientific Publishers
http://www.ingentaconnect.com/content/a … cation/pdf [abstract only]

I wonder if this could increase the burn rate for the solid propellants even at relatively low pressures.

Bob Clark

Last edited by RGClark (2017-06-09 11:02:13)

GW Johnson · 2017-06-09 13:27:40

Lessee, a 5 sec burn at a nominal 0.3 in/sec for AP-composites yields a web burned of 1.5 inches, about 50% of the radius of a 6-inch motor. That's definitely in the ballpark for the thrust-time curves you posted. I cannot pin down a pressure from this, as burn rates are tailorable from 0.2 to 1+ in/sec at 1000, and pressure exponents are typically quite low (near 0.3).

Reducing motor pressure from 1000 psia to around 500 psia, with a 14.7 psia backpressure, reduces pressure ratio from 60-ish to 30-ish, which reduces CF from near 1.5 to nearer 1.4. That reduces c* from just over 5000 ft/sec to around 4800-4900 ft/sec, which is just about what I computed from the tabular thrust and impulse data from their propellant weight.

I would hazard the guess their average chamber pressure is nearer 400-500 psia, which brings down Isp into the range they quote. Most of the military hardware I worked on had chamber pressures above 1500 psia, and we typically got the higher Isp values.

With AP-composites, somewhere down around 50-100 psia is where you hit unstable burning or erratic burning. The exponents can shift to quite large values, even unstable ones at 1 or higher. Motors either won't burn, or explode on ignition, or else they "chuff" unsteadily. Too low a chamber pressure is bad. There's a whole lot of poorly-understood phenomena in the low pressure range. That happens around 300 psia with AN composites and some of the double base materials. AP goes lower successfully.

As for nanotube stuff, those are interesting lab results. Typically, it takes 10-20 years for a lab result to become a real technology or material we can apply. Most lab results never get that far. We'll see, but I don't recommend holding your breath for it.

Has anyone yet figured out how to spin nanotubes together to make a twine yet? As last I understood, that was the weak point: twines hold together by friction between fibers, such that the actual individual fiber strength has little to do with the finished product strength.

GW

Last edited by GW Johnson (2017-06-09 18:42:18)

RGClark · 2017-06-13 18:39:17

GW, I found this after a web search:

CTI rocket motor successfully powers the launch carrying the ashes of astronaut and James Doohan - April 30, 2007.
On April 28th, a Spaceloft™XL rocket successfully completed a round-trip space flight launched from Spaceport America. This rocket was developed by UP Aerospace Inc. of Hartford, Conn. The rocket carried a wide variety of experiments and payloads, which included the cremated remains of Star Trek's "Scotty", James Doohan and NASA astronaut and pioneer Gordon Cooper. In addition, the cremated remains of more than 200 people from all walks of life were onboard. Also flown into space on the SL-2 Mission were dozens of student experiments from elementary schools to high schools to universities - from across America and worldwide - as well as innovative commercial payloads.

The flight was a successful demonstration of the rocket motor developed and built by Cesaroni Technology Incoporated (CTI). CTI started the design process in September of 2005. CTI specializes in low cost propulsion systems for military and space applications and used its experience to develop an affordable, reliable propulsion system for the rocket. The motor has a carbon fiber composite case and a monolithic solid propellant grain that is bonded to the casing.

Watch the post-launch coverage as carried by local television station KRQE here (9 Mb)
Watch the launch as carried by the BBC here (1 Mb)
Watch pre-launch coverage as carried by CTV Toronto here (9 Mb)
Watch pre-launch coverage as carried by CBC Toronto here (9 Mb)

Technical data for the UPA-264-C rocket motor

http://www.cesaroni.net/news.php

So Cesaroni also makes solid motors for professional aerospace companies. A few interesting facts in the table. First, this motor is quite large at nearly 10 feet long and at 412 pounds. Second, by using carbon composite casings we can get the propellant fraction in the .8 range. This corresponds to a saving in the dry mass of about half over the aluminum casings. Having a propellant fraction in this range was important for my calculation. Third, the sea-level Isp is in the 240 s range. This is in the range you suggested should be achievable for APCP propellant, so then we should be able to achieve 285 s in the vacuum Isp.

Also, interesting is amateurs do make the APCP propellant themselves:

How to Make Amateur Rockets
(2nd Edition)
Book, Video & Software Set
http://www.space-rockets.com/newbook.html

Bob Clark

GW Johnson · 2017-06-13 23:33:00

Bob:

You are definitely better at finding stuff on the internet than I am. It would appear that Cesaroni is an industry supplier of rocket motors who also serves the hobby public. It appears they are running in the vicinity of 400-500 psia chamber pressures with their AP composites, based on the published figures. I would guess that such motors might get much higher Isp given a good vacuum nozzle. Whether 285 is possible below 1200 psia chamber, well, I dunno.

I am surprised to see amateurs mixing and casting their own AN and AP propellants. Decades ago, even sugar nitrate was infamous and discouraged, because its processing temperature was so close to its thermal cookoff temperature. I couldn't really tell from the book table of contents whether its recommended formulations were gravity/sleeve castable, or the higher-solids, thixotropic pressure castable. Such processing is even more dangerous, but offers a single-handful of seconds higher Isp. However, given high chamber pressures in the 1000-2000 psia range, AP composite Isp near 250-255 sec at sea level is easily feasible.

Carbon composite cases do save weight, but add costs because of the extra effort to do all the winding. Long ago, one we made was 4 or 5 inches diameter and about a yard long. It had a non-aluminized AP composite propellant at about 4000 psia. We had a thin liner, but no external insulation, just extra case thickness to ablate away on its way to the target. This was an anti-tank round that flew at Mach 5 right on the deck. Nearly everything was case bonded. Cartridge-load disappeared from military products long ago.

The cheapest mass production rounds had martensitic stainless cases, cold-formed to shape and properties, then heat treated to final strength. We replaced asbestos rubber case liners with kevlar rubber liners. Nearly all propellants were AP oxididized, HTPB or CTPB binders, some aluminized, others not. The plant where I worked uniquely knew how to process impossibly-high solids loadings for higher performance, and do it with reliable grain quality. We also did solid propellant gas generator-fed ramjets; that was my main specialty (among several diverse roles). We did eject-nozzle boosters and nozzle-less boosters for liquid and solid ramjets. The nozzle-less form works best as a dual cast overcast grain, using two different burn rates. That's how you keep the pressure high enough to only lose 25% performance, not 50+%.

GW

Antius · 2017-06-14 15:50:44

Why not use a LOX-rubber hybrid? Solid propellants sound downright dangerous. The sort of hobby that could end up depriving a man of his arms.

Last edited by Antius (2017-06-14 15:58:58)

elderflower · 2017-06-14 16:03:06

LOX is quite hazardous too. See what will happen if it is spilled on organic material such as a human.

RGClark · 2017-06-15 06:25:40

Antius wrote:

Why not use a LOX-rubber hybrid? Solid propellants sound downright dangerous. The sort of hobby that could end up depriving a man of his arms.

Some amateur groups are working on hybrid engines. However, they are not as safe as portrayed, as the accident at Scaled Composites shows. Also they are not as well understood as solids and liquids, as the 10 year development cycle to get the hybrid engine on SpaceShipTwo to work properly shows.

Bob Clark

Last edited by RGClark (2017-08-15 01:29:46)

RGClark · 2017-06-15 06:45:31

GW, I assume you have some engine performance programs available such as RPA, http://propulsion-analysis.com/index.htm. I was surprised when I tried it that for an extra large, vacuum optimized nozzle, expansion ratio of several hundred, that you can get the vacuum Isp to be in the 325 s range. This would result in a significant increase in payload over the 285 s Isp common with APCP solid rockets.

Another reason why I am a big proponent of altitude compensation methods such as the aerospike.

Bob Clark

Last edited by RGClark (2017-06-15 06:46:19)

GW Johnson · 2017-06-15 09:05:32

Hi Bob:

No, I don't have any programs for anything like that. I have always (for 4 decades now) just done it pencil-and-paper with the thrust coefficient equation, or (for rougher estimates) with charts drawn long ago using that equation and an input efficiency. I did recently put the CF equation into a spreadsheet, which makes iterating a little easier. Main thing was working the right definition of nozzle efficiency into the right places in the equation; this is not done correctly in some books (making inappropriate modeling assumptions for the sake of unwarranted mathematical simplification).

There are very small differences in results using this or that value of specific heat ratio for the gas, but basically you won't be significantly wrong using 1.20 across the board. How delivered c* varies with chamber pressure is a noticeably bigger effect. And of course chamber pressure affects CF directly - that's the first order effect along with expansion ratio.

The thing about vacuum expansion is that the larger you make your expansion area ratio, the higher the Isp performance you get. But such high numbers, while quite real, are often deceptive: there are usually physical real-world limitations on how big you can make your area ratio.

One is the diameter(s) of your nozzle exit(s) exceeding your stage diameter - that simply won't work in any practical vehicle design. Another is the length of such an extremized expansion bell - there is usually no room for super-long nozzles in practical designs, and even if there were, the surrounding adapter shroud connecting the stages gets to be an excessive inert weight.

The vacuum expansion data reported in my ancient Pratt & Whitney handbook were limited to Ae/At = 40 for exactly those same reasons. It is possible in some designs to go larger, but not a whole lot larger. Every design is unique in that respect. The handbook writers used that ratio as a "typical" figure for "representative" data. I see in the much more modern AIAA handbook that they pretty well report vacuum Isp data to the same expansion convention.

The other disparity between handbook Isp data and real-world performance is that in most of the handbooks, the reported vacuum expansion Isp data are for low chamber pressures like in thrusters, down near 100 psia. The sea level data are for a nominal 1000 psia chamber pressure; most modern engines run higher than that, some a lot higher.

You are better off running CF from Pc/Pa and Ae/At for yourself, and using the handbook data to model delivered c* = k Pc^m for your ballistics. Bear in mind that mix ratio r usually varies with Pc as well. Be sure that your nozzle kinetic energy efficiency gets applied to the momentum term but not the exit pressure-difference term in your CF equation.

For simple conical nozzles, there is a constant conical half-angle "a". The dominant influence in supersonic expansion is streamline divergence off axial, so the nozzle efficiency models really well as KE efficiency = 0.5*(1 + cos a). For curved bells, there are two easily-measured half angles: one at the exit lip, the other right up near the throat. Arithmetically-average them, and use that as "a". You won't get any better estimate than that, and it matches up very well with real nozzle calibration tests.

Beware of the simplification Isp = CF c* / gc. That assumes that 100% of the propellant flow to the engine goes through the propulsion nozzle. For a lot of liquid engine cycle designs, this is not true. The gas stream powering the turbopump machinery gets instead dumped overboard, in more than one such cycle. Your best, most reliable approach to a representative Isp for the rocket equation is to compute the nozzle thrust force and divide it by the total propellant flow, not just the propulsive flow.

GW

RGClark · 2017-06-18 10:39:07

GW Johnson wrote:

Hi Bob:
...
The thing about vacuum expansion is that the larger you make your expansion area ratio, the higher the Isp performance you get. But such high numbers, while quite real, are often deceptive: there are usually physical real-world limitations on how big you can make your area ratio.
One is the diameter(s) of your nozzle exit(s) exceeding your stage diameter - that simply won't work in any practical vehicle design. Another is the length of such an extremized expansion bell - there is usually no room for super-long nozzles in practical designs, and even if there were, the surrounding adapter shroud connecting the stages gets to be an excessive inert weight.
The vacuum expansion data reported in my ancient Pratt & Whitney handbook were limited to Ae/At = 40 for exactly those same reasons. It is possible in some designs to go larger, but not a whole lot larger. Every design is unique in that respect. The handbook writers used that ratio as a "typical" figure for "representative" data. I see in the much more modern AIAA handbook that they pretty well report vacuum Isp data to the same expansion convention.
The other disparity between handbook Isp data and real-world performance is that in most of the handbooks, the reported vacuum expansion Isp data are for low chamber pressures like in thrusters, down near 100 psia. The sea level data are for a nominal 1000 psia chamber pressure; most modern engines run higher than that, some a lot higher.
...

What do you calculate the Isp would be for a 1,000 psi and 2,000 psi engine with an area ratio of, say, 500 to 1? As you say that would make a regular bell nozzle impractically large, well outside the motor's diameter. But with an aerospike it would stay inside the motors diameter. Surprisingly, after knowing about the aerospike for over 50 years there still have been no high altitude tests of the aerospike where the ambient pressure would be near vacuum. The only flight tests have only been at about 30,000 ft. where the pressure is still 1/3 sea level.

BTW, what do you use as the solid motors throat area when it is not circular but cross-shaped? Also it would seem to me the throat area should change as the solid fuel burns away.

Bob Clark

GW Johnson · 2017-06-18 11:43:48

OK, I ran my spreadsheet for nozzle CF at 1000 psia max = 1000 psia min, using sp.ht. ratio = 1.2, and got perfect expansion to 0.09 psia at Ae/At = 495.972. The vacuum thrust coefficient is 2.0053. I used a constant effective expansion bell half angle of 15 degrees for this.

Doing the same thing at 2000 max / 2000 min psa and 0.18 psia backpressure gives me exactly the same vacuum CF.

Note that there is no room to throttle down, only up, without disrupting things with overexpansion effects.

For a solid, Isp really is CF c* / gc, so for a nominal 4949 fps c* value, Isp should fall in the range of 315.7 sec using that 2.053 vacuum CF value.

To show that my c* is valid, I ran a 2000 max / 2000 min psia design at gamma=1.2 and 14.7 psia backpressure. That gave me a CF of 1.6512 on an expansion ratio of 15.02, for which Isp calculates as 254 sec, just about where a 2000 psia tactical motor would fall in a ground test when fueled with an AP-HTPB composite with around 20% aluminum, and about 86% total solids in the propellant mix.

That very same solid run in vacuum has a vacuum CF of 1.7616, and a vacuum Isp = 271.0 sec. So you can get high vacuum Isp without utterly extremizing your expansion. To get 285 sec out of this system, the nozzle design backpressure is near 4 psia with a CF = 1.8528. At 4 psia with 2000/2000 chamber, I got vacuum CF = 1.8563 at Ae/At = 41.370. That would be Isp = 285.5 sec at c*=4949 fps.

The exit/throat diameter ratio (assuming one single circular nozzle) is 6.43. That's actually sort of realistic for staying within the stage diameter. It is the ballistically-determined throat area that determines this, though.

Once again, this isn't a "real" motor design, but is does show you can get a lot of improvement out of an upper stage essentially flying in vacuum without a ridiculous nozzle exit size.

As for nozzle throats, the minimum geometric flow area is simply that, no matter what is shape is. The shape can seriously affect its discharge coefficient, though. It is the product of geometric throat and discharge coefficient that is the effective throat area one uses in the ballistics equation for nozzle massflow (the one where flow rate = chamber pressure * effective throat area * gc / c*).

That massflow much match the propellant grain massflow, which is density * burning surface area * burn rate * expulsion efficiency. Please note that expulsion efficiency is an experimentally determined factor, usually above 97% in a decent design. Burn rate and c* are both power functions of pressure. Burn surface area almost always varies during the course of the burn; that's part of grain design, to allow and account for that. Throat area is actually variable, conceptually described as follows:

In solids as I knew them with ablative nozzle liners and graphite throats, there were two competing effects upon geometric throat area during the course of a burn: erosion of the graphite, tending to make the hole larger, and slag deposition, tending to make the hole smaller. Only test data can determine how those two balance for net effect. They also alter shape and discharge coefficient. Our usual designs tended to minimize that last effect, what you are talking about does not.

GW

Last edited by GW Johnson (2017-06-18 12:01:14)

RGClark · 2017-06-19 08:40:00

Thanks for the info. The new start-up Arca Aerospace will test this year for the very first time, 50 years after the aerospike was developed, the high altitude performance of an aerospike on their liquid-fueled demonstrator for their planned SSTO:

Flight of the Aerospike: Episode 1.

https://www.youtube.com/watch?v=L1hnImvI2gw

Bob Clark

Last edited by RGClark (2017-06-19 17:01:00)

RGClark · 2017-06-19 10:32:25

Speaking of SSTO's, there are some solid stage motors with high mass ratio, in the range of 20 to 1. If this was kerolox or hydrolox with their high maximum vacuum Isp's this would be enough for a SSTO. Unfortunately, for solids their vacuum Isp's are typically only in the range of 285 s.

But I was surprised running the engine simulation program RPA, http://propulsion-analysis.com/index.htm, that the APCP solids could get vacuum Isp's in the range of 325 s and above by using nozzles with extremely high area ratios, in the range of hundreds to 1. Then running the launch performance calculator, http://silverbirdastronautics.com/LVperform.html, I found they could be SSTO.

Here's one solid motor with the high mass ratio:

Star 48
Thiokol solid rocket engine. Used in Delta 3900; Conestoga; PAM-S; PAM-D. Total flown included in total for Star-48-8. Total impulse 575,682 kgf-sec. Motor propellant mass fraction 0.946. First flight 1982.
AKA: PAM-D;PAM-S;TE-M-711-3. Status: Out of Production. Number: 125 . Thrust: 67.20 kN (15,107 lbf). Gross mass: 2,114 kg (4,660 lb). Unfuelled mass: 114 kg (251 lb). Specific impulse: 287 s. Burn time: 88 s. Height: 2.04 m (6.69 ft). Diameter: 1.24 m (4.06 ft).
Chamber Pressure: 40.00 bar. Area Ratio: 49.
http://www.astronautix.com/s/star48.html

Here's how the input screen looks on the launch performance estimator for this motor:

Note there some quirks of this program you need to be aware of if you use it. First, always use the vacuum values for the Isp's and thrust numbers, since the program already takes into account the diminution at sea level. Second, always set the "Restartable Upper Stage" option to "No", rather than the default "Yes", otherwise the payload will be reduced. This is true even for a supposed SSTO.
Third, always set the launch inclination to match the launch site latitude, otherwise the payload will be reduced. This is related to the fact that changing the orbital plane involves a delta-v cost. So for the Cape Canaveral launch site, the launch inclination should be set to 28.5 degrees.

Now, here's the result:

i.e., 0 payload is the estimation.

Now, for the case where the vacuum Isp can be raised to 325 s by using the aerospike or other altitude compensation methods the results are then:

i.e., 33 kg is the payload estimation.

Bob Clark

GW Johnson · 2017-06-20 09:04:07

Bob:

Be sure and double-check how the program figures its thrusts and impulses. Subtracting PaAe from a vacuum thrust works only up to the separation point, but no further. Pa is the ambient pressure and Ae the exit area.

For chamber pressure Pc and Ae/At expansion ratio, the ideally-expanded pressure at Ae is Pe. Let Psep be the backpressure that causes separation. The correlation I favor is Psep/Pc = (1.5 Pe/Pc)^0.8333.

This effect is why sea level nozzles have much smaller expansion ratio than altitude nozzles. Separation (or backpressure thrust loss) limits the expansion ratio down low in the atmosphere.

In vacuum, you can use much larger expansions, limited more by mechanical packaging, as I already indicated. There is also the effect that as Ae/At gets very large, you get less and less increase in exit Mach number. It's a diminishing-returns sort of thing.

There are no hard-and-fast estimates for separation risk, only approximate correlations. And then there's test data, which trumps everything.

As a rough-and-ready rule-of-thumb, I often recommend a limiting backpressure Plim that is the average of Psep and Pe. It lets you take the PaAe loss, but without letting it get too big, and keeps you very far from actual separation. Ae/At that fails a criterion like that is just too large to be practical.

For applications like launch, thrust off the pad is critical. You want no overexpansion losses at all. That means you do an ideal expansion to sea level air pressure Pa = Pe, period, end of issue. And that sets your Ae/At.

That's just the ways we usually do it, which have proven out rather well in the past.

GW

Last edited by GW Johnson (2017-06-20 09:06:48)

RGClark · 2017-06-23 10:08:39

Thanks for that. Another interesting fact I discovered using the RPA engine analysis program is that you can get high vacuum Isp by using high area ratio even with low chamber pressure. For instance, according to the program, I could let the chamber pressure be only 200 psi instead of 2,000 psi and get a 325 s Isp with a 750 to 1 area ratio.

This low pressure will reduce the thrust. But for an upper stage, where the high Isp is most important, thrust isn't as important. In fact, for upper stages the thrust is often only half the stage weight.

But if the chamber pressure only had to be 1/10th as high, you could reduce the empty weight also by a factor of 10. This would be important for an upper stage to maximize payload.

But I need to know what thrust you could get at this low a chamber pressure. Suppose you used a very high area ratio, say by an aerospike, of 750 to 1. But let the chamber pressure be only 200 psi. What would be the Isp and thrust then?

Bob Clark

Last edited by RGClark (2017-06-23 17:15:49)

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