Amateur solid-fueled rockets to *orbital* space?

GW Johnson · 2017-06-23 12:38:07

Getting good thrust coefficient CF at low Pc in vacuum is why the vacuum Isp data in my old Pratt & Whitney handbook are for Pc = 100 psia, while the sea level data are for 1000 psia. Thrusters in vacuum are usually quite low chamber pressure, so that the hardware is thinner and lighter.

Same could be true of upper stage engines, but that choice depends more on where that engine design came from: Spacex's second stage Merlin is just the first stage Merlin fitted with a much longer nozzle. They both use the same chamber design.

That low-pressure lightening-of-weight proves to be more significant than low pressure c* losses, at least for the kind of equipment specifically designed to take advantage of the effect.

Thruster expansion ratio is usually limited by packaging/installation issues than anything else, and the nozzles are quite often scarf-cut reflecting the outer mold line of the vehicle. This applies to mono- or bi-propellant thrusters. Basic CF applies to liquids and solids and hybrids.

I ran my spreadsheet version of thrust coefficient at a fixed Pc = 200 psia, and reset Pe iteratively until I got Ae/At = 750.9 at Pe = 0.0108 psia. The CF for Pe = Pamb at that expansion is 1.98047. CF vac is 2.0226. These were figured for specific heat ratio 1.20 and a 15 degree effective conical half angle to the nozzle, pretty "typical" values.

Thrust per unit throat area is Pc CF = 404.52 psi, using the vacuum CF.

Can't tell you what the thrust is, without some way to set throat area. Normally that is sized to get the thrust you want out of the stage, or else it comes from an existing design. Cannot tell you what Isp is until I know something about a 200 psia chamber c*.

If for an aluminized solid based on AP-HTPB the 200 psia c* is near 4800 ft/sec, then Isp = CF c* / gc ~ 302 sec. If instead it was 4900 fps, then Isp ~ 308 sec. If it is nearer 5000 fps, then Isp ~ 314 sec.

Chamber c* is a power function of Pc of the form c* = k Pc^m, where for solids m ~ .01, although the variation of m from propellant to propellant is significant. At 200 vs 1000 psia, for m = 0.01, we lose about 2% of our c*.

If c* were known, then you could figure the propellant flow through the throat per unit throat area: w/At = Pc gc / c*.

Hope that helps.

GW

Last edited by GW Johnson (2017-06-23 16:02:17)

RGClark · 2017-06-24 07:31:53

GW Johnson wrote:

Getting good thrust coefficient CF at low Pc in vacuum is why the vacuum Isp data in my old Pratt & Whitney handbook are for Pc = 100 psia, while the sea level data are for 1000 psia. Thrusters in vacuum are usually quite low chamber pressure, so that the hardware is thinner and lighter.
Same could be true of upper stage engines, but that choice depends more on where that engine design came from: Spacex's second stage Merlin is just the first stage Merlin fitted with a much longer nozzle. They both use the same chamber design.
...
GW

Do you know of examples of those low chamber pressure solid thrusters at Pc = 100 psia? For my upper stage of the all-solid launcher, I want to use one of the size of the Cesaroni motor used on the Up Aerospace suborbital rocket I mentioned in post #13 with a 412 pound fueled weight and 0.8 propellant fraction. This puts is it at about 80 pound empty weight and 320 pound propellant weight. If I got the chamber pressure smaller by a factor of 10, then I could reduce that empty weight to only 8 pounds, and the payload would increase by 72 pounds.

But this means I want to keep the same propellant weight, and use the same size case but only thinner wall thickness by a factor of 10. But I don't know if this is possible for a solid-fueled motor. For a liquid I could just reduce the propellant burn rate to reduce the chamber pressure, i.e., less propellant burn at any time, less pressurized gases produced at any time, therefore lower chamber pressure.

But decreasing the chamber pressure is not so easy to do with a solid. It won't work to just increase the case volume because that eliminates the advantage you wanted to get of having a smaller empty, i.e., case weight. You can't reduce the propellant amount either to get a larger volume for the central open section because you want the same size stage.

Is there some method to get the same amount of propellant to just burn at a slower rate? Another possible way it could work would be by having the propellant compressed to an extreme degree to only 1/10th it's usually volume. Don't know if that is technically feasible.

Bob Clark

GW Johnson · 2017-06-24 12:41:41

You have to design the motor specifically to be a low-pressure motor. Usually, that will be a different grain design as well as a lower burn rate. It is not possible to compress solid propellant; it simply is what it is.

Most of the propellants historically have not exhibited stable burn rate behavior under about 300 psia. There are many different failure modes. I have seen that limit go lower with AP-HTPB-type composites: around 100 psia. Very few work well below that, but I have actually seen a few very fuel-rich formulations (very low Isp) work at 30-50 psia.

Burn rates with AP composites more-or-less fall in the 0.2 to 0.3 in/sec range at about 400 psia. Ordinary ones have burn rates in the 0.3 to 0.4 in/sec range at 2000 psia (low exponent). The "high rate" composites can have burn rates in the 0.8 to 1.0 in/sec range at 2000 psia (high burn rate exponent). So there's room for a lot of burn rate tailorability by adjusting particle size distributions for the solids, and in using iron-bearing burn rate catalysts. Most of these propellants fall in the vicinity of 0.06-something lb/cu.in density.

Sorry, there's no simple "low pressure retrofit" to an existing motor design, other than just making throat area bigger. Each application is its own custom internal ballistic design. That's just the nature of solids. Grain design surface history is only part of that.

There are limits on the web/motor radius ratio associated with grain thermal-structural, limits on grain port to nozzle throat area ratio, limits on allowable pressure drop down the bore, etc. There are also limits on the burn rates, temperature sensitivity of that burn rate, and thermal-structural properties (including very serious visco-elastic effects hot, and glassy-transition brittleness cold).

The low pressure motor you would like probably does not exist within that set of case dimensions, but also probably could. It would have to be specifically designed, and its propellant specifically tailored to low burn rate in the lab, so that it could use similar nozzle throat dimensions and expansion proportions. Otherwise, your exit is limited to the stage diameter, period (excepting some sort of aerospike, perhaps, but I haven't seen much benefit to them in vacuum conditions over a physical bell). Whether this low pressure design would have exactly the same case/propellant ratios is problematical, but they probably could be made similar.

As for low-pressure thrusters, I have no specific example systems to name. Such data could be searched-for.

GW

Last edited by GW Johnson (2017-06-24 12:44:27)

RGClark · 2017-08-16 19:11:37

GW Johnson wrote:

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.
...
GW

I found this commercial solid motor with a similar sea level Isp as the Cesaroni solid rocket motors Pro150 I mentioned earlier:

Star 37.
Thiokol solid rocket engine. Total impulse 161,512 kgf-sec. Motor propellant mass fraction 0.899. First flight 1963. Solid propellant rocket stage. Burner II was a launch vehicle upper stage developed by Boeing for the Air Force Space Systems Division. It was the first solid-fuel upper stage with full control and guidance capability developed for general space applications.
AKA: Burner 2;TE-M-364-1. Status: First flight 1963. Number: 180 . Thrust: 43.50 kN (9,779 lbf). Gross mass: 621 kg (1,369 lb). Unfuelled mass: 63 kg (138 lb). Specific impulse: 260 s. Specific impulse sea level: 220 s. Burn time: 42 s. Height: 0.84 m (2.75 ft). Diameter: 0.66 m (2.16 ft).

Thrust (sl): 33.600 kN (7,554 lbf). Thrust (sl): 3,428 kgf.
http://www.astronautix.com/s/star37.html

So we might estimate the vacuum Isp of the Cesaroni to be in the Star 37's range of 260 s.

Using this as a vacuum Isp of a first stage and a 285 s vacuum Isp of second and third stage I get a three-stage solid rocket able to reach orbit, with not even particular high mass ratios of 5 to 1 for the stages:

With a payload of 7 kg:

And this with standard nozzles, no altitude compensation required.

The Cesaroni Pro150 retails for about $3,000 and in general the Cesaroni solids cost in the range of $100 per kg of the motor mass:

Cesaroni O8000 White Thunder Rocket Motor.
$3,099.95
Product Information
Specification
Brandname: Pro150 40960O8000-P Manufacturer: Cesaroni Technology
Man. Designation: 40960O8000-P CAR Designation: 40960 O8000-P
Test Date: 4/10/2008
Single-Use/Reload/Hybrid: Reloadable Motor Dimensions mm: 161.00 x 957.00 mm (6.34 x 37.68 in)
Loaded Weight: 32672.00 g (1143.52 oz) Total Impulse: 40960.00 Ns (9216.00 lb/s)
Propellant Weight: 18610.00 g (651.35 oz) Maximum Thrust: 8605.10 N (1936.15 lb)
Burnout Weight: 13478.00 g (471.73 oz) Avg Thrust: 8034.50 N (1807.76 lb)
Delays Tested: Plugged ISP: 224.40 s
Samples per second: 1000 Burntime: 5.12 s
https://www.csrocketry.com/rocket-motor … motor.html

So take the cost of the third stage, derived from the Cesaroni Pro1050, as $3,000, and the second stage 4 times larger as $12,000, and the first stage larger by an additional factor of 4 as $48,000. So $63,000 for a small sat launcher with a 7 kg payload to orbit.

Bob Clark

Last edited by RGClark (2017-08-17 02:44:14)

louis · 2017-08-16 19:23:03

I've looked into this before...can't remember any real details but I think you could get one or two people off the surface of Mars with a few tonnes (maybe 5-8 tonnes) of fuel/propellant. Think it was 3 tonnes for the Moon...but technology moves on.

RGClark · 2017-08-17 02:42:21

louis wrote:

I've looked into this before...can't remember any real details but I think you could get one or two people off the surface of Mars with a few tonnes (maybe 5-8 tonnes) of fuel/propellant. Think it was 3 tonnes for the Moon...but technology moves on.

I thought of using small solid motors to do a Mars sample return mission. It would seem to cost a small fraction of NASA's $10 billion estimate for such a mission.

But the calculation in that last post was to suggest any university would have the capability of conducting their own smallsat launch to LEO.

Bob Clark

Last edited by RGClark (2017-08-17 02:46:20)

SpaceNut · 2017-08-17 16:41:40

http://nasawatch.com/archives/2017/08/g … -on-i.html

GAO: Surplus Missile Motors: Sale Price Drives Potential Effects on DOD and Commercial Launch Providers

GAO estimated that DOD could sell three Peacekeeper motors—the number required for one launch, or, a "motor set"—at a breakeven price of about $8.36 million and two Minuteman II motors for about $3.96 million, as shown below. Other methods for determining motor prices, such as fair market value as described in the Federal Accounting Standards Advisory Board Handbook, resulted in stakeholder estimates ranging from $1.3 million per motor set to $11.2 million for a first stage Peacekeeper motor.

RGClark · 2017-08-18 01:47:12

SpaceNut wrote:

http://nasawatch.com/archives/2017/08/g … -on-i.html
GAO: Surplus Missile Motors: Sale Price Drives Potential Effects on DOD and Commercial Launch Providers
GAO estimated that DOD could sell three Peacekeeper motors—the number required for one launch, or, a "motor set"—at a breakeven price of about $8.36 million and two Minuteman II motors for about $3.96 million, as shown below. Other methods for determining motor prices, such as fair market value as described in the Federal Accounting Standards Advisory Board Handbook, resulted in stakeholder estimates ranging from $1.3 million per motor set to $11.2 million for a first stage Peacekeeper motor.

Article doesn't say how much these motors repurposed as orbital launchers could loft to orbit. Anyone know that?

Bob Clark

SpaceNut · 2017-08-18 16:51:02

you are in luck as these are already being used for the https://en.wikipedia.org/wiki/Minotaur_(rocket_family) derived from converted Minuteman and Peacekeeper intercontinental ballistic missiles.

https://en.wikipedia.org/wiki/LGM-118_Peacekeeper

Engine Three-stage solid-fuel rocket.
First stage: 500,000 lbf (2.2 MN thrust) Thiokol SR118 solid-fuel rocket motor
Second stage: Aerojet General SR119 solid-fuel rocket motor
Third stage: Hercules SR120 solid-fuel rocket motor

https://en.wikipedia.org/wiki/LGM-30_Minuteman

Engine Three-stage solid-fuel rocket engines
First stage: Thiokol TU-122 (M-55);
second stage: Aerojet-General SR-19-AJ-1;
third stage: Aerojet/Thiokol SR73-AJ/TC-1

Current https://en.wikipedia.org/wiki/Minotaur_V

The Minotaur V is a five-stage vehicle, and is designed to place up to 630 kilograms (1,390 lb) of payload into a geosynchronous transfer orbit, or 342 kilograms (754 lb) on a trans-lunar trajectory. It consists of a Minotaur IV+, with a Star-37 as a fifth stage.
Two variants are available, one with a spin-stabilized Star-37FM upper stage, and the other with a Star-37FMV capable of three-axis stabilization. The Star-37FMV upper stage is heavier, reducing payload capacity, but is more maneuverable.

First stage – SR-118 Engines
Thrust 1,607 kilonewtons (361,000 lbf)
Burn time 83 seconds
Second stage – SR-119 Engines
Thrust 1,365 kilonewtons (307,000 lbf)
Burn time 54 seconds
Third stage – SR-120 Engines
Thrust 329 kilonewtons (74,000 lbf)
Burn time 62 seconds
Fourth stage – Star-48BV Engines
Thrust 64 kilonewtons (14,000 lbf)
Burn time 84 seconds
Fifth stage (Baseline) – Star-37FM Engines
Thrust 47.26 kilonewtons (10,620 lbf)
Burn time 63 seconds

RGClark · 2017-08-20 02:59:03

GW Johnson wrote:

...
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

I'll need some type of attitude control for the upper stages operating in little atmosphere, as fins would be ineffective. How did the hydrogen peroxide thrusters work?

Bob Clark

elderflower · 2017-08-20 15:46:12

High test peroxide is passed through a catalyst bearing mesh. It breaks down to steam and oxygen. For use with a cheap silvered mesh the peroxide concentration is limited to about 85% to restrict the temperature of the breakdown products. For higher concentrations the catalyst needs to be more robust and platinum coated mesh has been used.
High test peroxide can breakdown in the tank or pipework if it isn't scrupulously clean and correctly designed and fabricated, causing an explosion as the reaction runs away. Submarines have been destroyed due to runaway peroxide used as torpedo propellant, with loss of many lives. Stabilisers are available which help with it's stability, but it has still gone out of fashion as rocket propellant or oxidiser and for torpedoes.
If you only want attitude thrusters it can be used as a monopropellant. For main motors a fuel can be burned in the oxygen/steam stream which gives greater Isp than the peroxide monopropellant.

SpaceNut · 2017-08-20 17:58:58

Basically getting a better buy than the maker of the Minotaur from the same source could mean a new industry could be born as they are reclaimed and repurposed.

RGClark · 2017-08-20 18:54:31

RGClark wrote:

...
So take the cost of the third stage, derived from the Cesaroni Pro1050, as $3,000, and the second stage 4 times larger as $12,000, and the first stage larger by an additional factor of 4 as $48,000. So $63,000 for a small sat launcher with a 7 kg payload to orbit.
Bob Clark

To save, costs I'm envisioning making the components as much "off-the-shelf" as possible. But among its standard products Cesaroni offers the Pro150 as the largest motor. So to get the larger second and first stages, I would have to combine multiple copies of this motor.

I could cluster them in parallel, but for the first stage that would be 16 of them, and you would have the problem of simultaneous ignition with that many motors.

So what I'm envisioning is take 4 copies of the Pro150 stacked vertically one on top of the other for the second stage, then cluster 4 of these second stage motors in parallel for the first stage.

The question I have about the vertical stacking though is how much the thrust scales in this case. If for the solid motors the propellant burned from the bottom upwards, then the thrust would be the same as for a single motor, you would just get 4 times longer burn time.

But that's not how solid motors work. Actually, they have a hollow region in the center so the propellant burns from the inside surface, proceeding outwards.

In this case, this would seem to mean you have a greater amount of propellant being burned per second because of the larger vertical area with the stacked segments. In fact the thrust should scale linearly with the number of segments. Is this correct?

BTW, the reason why I don't just also stack the first stage vertically, is because of the thinness of the rocket that would result. The Pro150 is about 3 feet long and 1/2 foot wide. If you stacked vertically 16 for the first stage, 4 for the second, and 1 for the third, that would be a rocket 63 feet high but only 1/2 foot wide, for a ratio of length to width of over 120 to 1.

This ratio of length to width is called the "fineness ratio". Rocket engineers don't like for it to be higher than about 20 to 1 because of the severe bending loads that would result. The upgraded version of the Falcon 9 has been noted for its long, skinny profile, and has a fineness ratio of about 20 to 1. The Scout solid rocket had a fineness ratio of about 24 to 1. Solid rockets can support a higher fineness ratio because their thicker walls can withstand higher loads. Still, 120 to 1 would very likely be too high.

So to avoid this I decided to form the first stage by clustering in parallel 4 copies of the second stage.

Bob Clark

SpaceNut · 2017-08-20 19:12:12

The stacking of the solids do have another thing to consider in that there is a harmonic change due to length of the assembly and that is why the shuttles 5 segment versus the 4 had issues that required Orion to be made heavier that it needed to be as to dampen out the resonating vibration....

RGClark · 2017-08-22 19:28:28

Discussion of low cost orbital rockets for cubesats and smallsats that are within the capabilities of most university undergraduate labs:

Orbital rockets are now easy, page 2: solid-rockets for cube-sats.
http://exoscientist.blogspot.com/2017/0 … age-2.html

Feasibility comments encouraged.

Bob Clark

RGClark · 2017-08-24 19:51:40

GW, looking at some prices for these solid rockets, I saw the price depended on the "grain" size, with the grain listed from 1 to 6.
What is the "grain" size, and why do the higher grains cost more, perhaps by two to three times more for 6 grain over 1 grain?

See here:

http://www.the-motorman.net/6452.html

Bob Clark

Last edited by RGClark (2017-08-24 23:25:30)

GW Johnson · 2017-08-25 11:27:10

Hi Bob:

It was hard to tell for sure, but it looks like that outfit makes 1 single propellant grain, and sells various cases that hold anywhere from 1 to 6 of them. I could not identify what that grain design actually is, but clearly there is a port down the middle.

Obviously, they are not having the resonance instabilities that going from a 4-segment to a 5-segment SRB design encountered, but that's a function of absolute size, as well as shape proportions, and what species are in the 2-phase flow mix.

That being the case, perhaps they don't offer a 7 grain stack because the bore port would come too close to choking, which usually leads to sudden motor explosion. The port is pretty big to pass the massflow from 6 grains, which means web fraction and volumetric loading are fairly low, regardless of the design details.

GW

RGClark · 2017-08-26 11:23:54

GW Johnson wrote:

Hi Bob:
It was hard to tell for sure, but it looks like that outfit makes 1 single propellant grain, and sells various cases that hold anywhere from 1 to 6 of them. I could not identify what that grain design actually is, but clearly there is a port down the middle.
Obviously, they are not having the resonance instabilities that going from a 4-segment to a 5-segment SRB design encountered, but that's a function of absolute size, as well as shape proportions, and what species are in the 2-phase flow mix.
That being the case, perhaps they don't offer a 7 grain stack because the bore port would come too close to choking, which usually leads to sudden motor explosion. The port is pretty big to pass the massflow from 6 grains, which means web fraction and volumetric loading are fairly low, regardless of the design details.
GW

You mean the "grain" simply means the weight of propellant?

Bob Clark

GW Johnson · 2017-08-26 13:05:08

It means a chunk of propellant of an appropriate size and shape, and it usually also includes the lightweight sleeve into which the propellant is cast. This propellant-in-a-sleeve assembly is a stand-alone "propellant grain", and it can be cartridge-loaded into a motor case. The sleeve then becomes part of the case insulation scheme. Multiple sleeve grains can be loaded into a long single case. That seems to be what the supplier you found actually does.

The alternative is what most military rocket motor makers do: cast the propellant directly into an insulated case. There is no sleeve when done this way. But, it is one propellant grain in one case. The only way to use multiple grains is to join multiple case segments together. That was the shuttle SRB. Joints are a risk to be avoided, if possible. The propellant is case-bonded, so thermal shrinkage or expansion induces severe stresses in the propellant and in its bond to the case insulation. Great care must be taken to design this adequately. But once done "right", this is the cheapest and most effective approach for mass production.

That case-bonded mass production approach is not the business model of the hobby motor supplier. The stand-alone sleeve grain approach suits what he does better, and he gets to avoid the case-bond design stress-strain problem entirely.

GW

Last edited by GW Johnson (2017-08-26 13:11:31)

RGClark · 2017-09-15 10:34:50

I've gotten feedback about the proposed solid-rocket cube-sat launcher discussed in post #40. The main criticism is the high acceleration and therefore high drag associated with these stages which only have a burn time of about 5 seconds. So to remove this objection, could we lengthen the burn time?

If we kept the same propellant amount by shortening the length of the Pro150 segments by a factor of 4 but increasing the radius by a factor of 2, so the volume is the same, this would mean the internal burn surface area would decrease by a factor of 2.

This should mean the propellant burn rate should decrease by a factor of 2, right? Then IF the Isp remained the same, the thrust would be cut in half. At the same time, the burn time is determined by the thickness of the loaded propellant, so if this is doubled the burn time should be doubled, correct?

Would this be a way to reduce the thrust, thus reducing the T/W ratio, and increase the burn time, while keeping the Isp the same?

Bob Clark

Last edited by RGClark (2017-09-15 16:49:08)

GW Johnson · 2017-09-15 16:22:27

Propellant volume divided by the web (distance to be burned) is average burning surface. Massflow is burning surface multiplied by density, burn rate (a function of pressure), and expulsion efficiency (% of propellant cast that is actually expelled, usually around 98%).

CF increases at higher pressure, and decreases at lower pressure, for a variety of reasons. Thrust is CF x pressure x throat area, where massflow is pressure x throat area x gc / c*.

I think if you keep the volume and increase the radius, surface goes up. For the same burn rate, pressure goes up (probably to catastrophic values), so thrust and Isp go up. Burn time gets longer, so massflow is down. This adjusts throat area.

To keep the motor from exploding, you need a far lower burn rate, which lengthens burn time and lowers massflow even more. Throat area adjusts again.

Equilibrium motor pressure is the key: P = (rho Surf a k nexp /At gc) ^ exponent, where rho is density, Surf is burning surface, a is the constant in burn rate r = aP^n, k is the constant in c* = k P^m, At is throat area, and gc is the gravity constant to make the units work. The exponent is 1/(1-n-m), where n is usually near 0.4 and m is usually near 0.01. A small change in any of the factors is a huge change in P. Exceedingly nonlinear. The exponent is usually at least 1.6, and sometimes over 5.

You cannot guess solid ballistics. You literally have to do them right. There is no guessing.

GW

RGClark · 2017-09-16 07:35:55

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.

Based on this estimate of burn rate for APCP motors, we can get a longer burn rate by doubling the diameter. Such longer burn motors though won't be "off-the-shelf" for Cesaroni.

Could amateurs make their own APCP of this size? I did see on the net discussion of amateurs making their own APCP though not in the size range we require. You mentioned the dangers of making AN propellant, such as vacuum-curing. Is APCP simpler and/or safer than this?

The SS-520-4 is an example of a solid motor orbital rocket that had stages with short burn times in the 20 to 30 second range for the separate stages:

Experimental Launch of World’s Smallest Orbital Space Rocket ends in Failure.
January 14, 2017
http://spaceflight101.com/ss-520-4-rock … l-mission/

The first test flight wasn't successful for the SS-520-4 but this is believed to be due to an easily correctable electrical flaw in the first stage.

Bob Clark

GW Johnson · 2017-09-16 10:03:57

AP is definitely more hazardous to deal with than AN. It is more friction-sensitive, requires much smaller particle sizes (which makes every sensitivity worse), and is far more mass detonable with a greater yield than AN.

Below about 1 micron particle size, it must be processed "wet" in Freon, or it will blow you up. That was known as "UFAP", for ultra-fine AP. It's getting fairly dangerous just to handle at 10 microns. Yet, 10 to 30 microns are very common particle sizes in AP composite propellants. Usually there are specified distributions of particle sizes, to get all the other ballistic properties needed, not just burn rate.

That being said, most any solid propellant is dangerous for real amateurs to make, because safety requires remotely-operated equipment, and a deluge system to save that equipment in the event of a mixer fire. That's a huge capital investment. Doing it manned in mix sizes over about half a coffee-cup's worth is a path to serious injury or death. Sooner or later, it WILL get you. And don't you dare store ingredients in the mix cell: any fire will set them off, because such fires usually start violently. This is NOT kitchen stove-top stuff to do!

I don't really see the objection to short burn times in your stages, unless your payloads are too fragile for the launch accelerations. Faster accelerations shorten the drag impulse integrals, leading to lower drag loss penalties going up. Shorter burn times also lower gravity loss penalties by the same shorter impulse integrals over time.

For most internal-burning grain designs, your web-to-burn should not exceed about 70-75% of the available insulated case radius, driven by case-bond and grain stress considerations when cold soaked. Cartridge-load of sleeve grains relieves some of that, but your bore area should still be at the very least twice the area of your throat, and preferably much larger. So more than about 80% of case radius is just impossible, for all practical purposes.

Web/burn rate-at-pressure = burn time. No way around that one. What you can tailor in the lab sets burn rates, and what you can tolerate with your case design sets the pressure. Burn rate-at-pressure and available web set burn time. Period. However long this grain design is, essentially sets your burning surfaces, and you set the throat area to match them, to maintain the desired pressures. That and the pressure level determines your thrust. Grain mass and burn time essentially set massflow. Thrust / massflow is Isp. You get what you get.

Grain length is not an independently-set variable. The surface vs web history is a very strong function of not only the shapes you choose to use, but also their L/D. This is a real 3-D geometry problem. Get it wrong, and you blow up your motor. If the burn rate exponent turns out to be nearer .7 than .4, that exponent in the pressure equilibrium equation is nearer 5 than 1.6. A 10% change in burn surface becomes factor 2 on pressure.

It's not an easy thing to balance-out in the design process. What's in the textbooks about interior solid ballistics is not enough to sit down and do this successfully. It's at least 50% engineering art. I haven't done it in 23 years. And those around me who supplied a lot of that art are long gone.

My mentor in ballistics was W. T. Brooks, who wrote the NASA monograph on it in 1976 (update: not 1976, 1972. NASA SP-8076, March 1972). Ted died many years ago. But while we worked together long ago, we did some very unique motor designs. None of those ever made it into the textbooks.

GW

Further update: By the way, I am just about ready to submit my ramjet book to AIAA for possible publication. I am suggesting to them that it be through their "continuing education" series. There are two chapters devoted to the how-to of solid propellant ballistics, one for boosters, the other for fuel-rich gas generators. In the fuel-rich solids, c* is not just a function of motor pressure, it can also be a function of varying motor free volume. Elementary grain design discussions and examples include both the cylindrical segment grains, and my favorite booster design: the keyhole slot.

Last edited by GW Johnson (2017-09-17 12:25:31)

RGClark · 2017-09-19 06:19:41

GW Johnson wrote:

...
Further update: By the way, I am just about ready to submit my ramjet book to AIAA for possible publication. I am suggesting to them that it be through their "continuing education" series. There are two chapters devoted to the how-to of solid propellant ballistics, one for boosters, the other for fuel-rich gas generators. In the fuel-rich solids, c* is not just a function of motor pressure, it can also be a function of varying motor free volume. Elementary grain design discussions and examples include both the cylindrical segment grains, and my favorite booster design: the keyhole slot.

Great. I'm looking forward to reading it. In aerospace engineering probably more than any other engineering field key facts are known by individuals in the field but not expressed in books or journals.

Thanks for revealing the "black arts" of ramjet design.

Bob Clark

elderflower · 2017-09-19 17:12:38

That should be very interesting GWJ. Post the book data for us when it comes out, please.

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