And a newly developed ceramic is half that weight:
Thermal Protection System.
Benefits.
Low density (0.07 g/cm3 or 4.4 lb/ft3)
High temperature capability (4000°F [2204°C])
Low thermal conductivity (<1 W/m·K at 3600°F)
Ability to combine with ceramic matrix composite or coated carbon/carbon structural shells to produce an integrated airframe/insulator thermal protection system
Imperviousness to chemical attack below 302°F (150°C)
http://www.ultramet.com/thermalprotectionsystem.html
GW, has also discussed a lightweight ceramic that may be even lighter still:
Reusable Ceramic Heat Shields - GW Johnson - 16th Mars Society Convention.
http://www.youtube.com/watch?v=3MXYY3jnNr0
Bob Clark
]]>Bob Clark
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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
Thanks for that. Some of the Star series solid motors get remarkably high mass ratios considering the entire casing has to contain the high pressures of a solid motor combustion. See for example the Star 48B:
Spacecraft Propulsion, p. 163
https://books.google.com/books?id=P5dBC … e&q&f=true
It has a approx. 20 to 1 mass ratio, using titanium casing at an approx. 600 psi operating pressure. Suppose we could get a ca. 200 psi operating pressure. Then with proportionally thinner casing walls we might be able to get a 60 to 1 mass ratio(!) Clearly there never has been before a rocket stage with this high a mass ratio. But the prospect is tantalizing.
If the vacuum isp is then also 305s with a 750 to 1 nozzle area ratio, the vacuum delta-v could be 3050ln(60) = 12,500 m/s, well above that needed for an SSTO. There would need to be some modifications made though. According to the specs on the star 48B, the expansion ratio on the nozzle is in the range of 55 to 1. Then to get a 750 to 1 nozzle area ratio while maintaining the lightweight, it would require new, design and/or materials for the nozzle. Perhaps, the altitude compensation aerospike would work. Some other possibilities for getting altitude compensation at lightweight are discussed on my blog.
Imagine also the delta-v possible if the operating pressure could be brought down to only 100 psi.
Bob Clark
]]>GW
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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
]]>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.
]]>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
]]>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
]]>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
]]>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
]]>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
]]>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
]]>See here:
http://www.the-motorman.net/6452.html
Bob Clark
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