Attempt towards an amateur orbital rocket.

[RGClark]

I see this is a minimum diameter rocket with no recovery systems or electronics. How will you recover the lower stages safely* and ignite the upper stages? How will you maintain trajectory once the atmosphere is no longer effective? I don't see any provision for steering nozzles or the like. If you have steering nozzles, why not just dump the fins and their drag/weight?

Rather than trying to force OpenRocket to do this, you could calculate the mass of motor, airframe, and associated systems needed to achieve orbital velocity from an apogee at orbital altitude. Then determine the rocket necessary to loft that mass to orbital altitude. Sure, it's a little bit of a hack since you'll start turning a real orbital rocket horizontal well before orbital altitude, but you'll be using roughly the same total amount of energy. It'll at least get you within an order of magnitude.

Alternatively, you could use another hobby program better suited to calculating orbital mechanics: Kerbal.

* At a bare minimum, the first and likely the second stages will need some kind of recovery. The third stage might be going fast enough to burn up on re-entry.

Yes. I am looking at other sim programs, and I have done a calculation in the thread "Orbital space is 25 times harder than suborbital" in the same vein you suggest.

Still the sim can be helpful in showing both the needed velocity for orbit and the needed altitude can be reached at the same time. Running this OpenRocket sim gives the result below.

Bob Clark

 

[boatgeek]

Yes. I am looking at other sim programs, and I have done a calculation in the thread "Orbital space is 25 times harder than suborbital" in the same vein you suggest.

Still the sim can be helpful in showing both the needed velocity for orbit and the needed altitude can be reached at the same time. Running this OpenRocket sim gives the result below.View attachment 550617

Bob Clark

The max velocity you cite above is the maximum upward velocity. You haven't even gotten to horizontal velocity (see next post for that).

 

[boatgeek]

In which I attempt to show through math that the proposed rocket in #1 doesn't do the job of getting to orbit. This was mainly for my own interest--I don't really expect it to change the OP's mind. But hey, math and spreadsheets--it's like candy for an engineer.
Starting with some extremely rash assumptions (never make assumptions about rashes!):
0.5 kg payload
0.5 kg nose cone, roll control system, and guidance computer
0.8 mass fraction for motors
Thrust vector control mass 0.5kg for Stage 4, 1 kg for Stage 3, 2 kg for Stages 1 & 2
ISP ~225s (matches the CTI O8000)
Thrust is constant, propellant mass burn rate is constant (this mainly just makes the math easier)

Note that these assumptions are extremely optimistic. I would be absolutely shocked if they are possible except possibly increasing the specific impulse.

My process was to work backwards. When Stage 4 burns out, you want to have reached 7800 m/s. You enter the propellant mass and the impulse (plus an assumed time, which doesn't really matter), you get starting and ending acceleration based on your loaded and burned out mass, you integrate the acceleration, and you get delta V. That gets you your desired starting velocity to reach that ending velocity. Then you wash, rinse, repeat with each stage below. The end result is the rocket you would have to loft to ~200 km, turn horizontal, and start firing to make it to orbit.

So here's how that shakes out:
Stage 4: Full O motor, 41000 N-s, delta V 1850 m/s
Stage 3: Full Q motor, 160000 N-s, delta V 2500 m/s
Stage 2: Full S motor, 640000 N-s, delta V 2300 m/s
Stage 1: 50% V motor, 890000 N-s, delta V 1150 m/s

The astute reader will notice that you need to loft 1730 kN-s worth of impulse to orbital altitude just to get from "standstill at that altitude" to "orbit at that altitude". That whole stack weighs just a hair over 1000 kg, so it seems fairly plausible given the mass and payload capacity of the Lambda 4S. Also note that this is far, far beyond the capabilities of any amateur rocket builder.

QED.

 

[aerostadt]

I remember the Project Prometheus from 12 years ago stating on TRF that an amateur satellite rocket was feasible. Twelve years have passed and there has been no announcement of success.
https://www.rocketryforum.com/threads/team-prometheus-n-prize-mission.2744/

 

[rocket_troy]

Note that these assumptions are extremely optimistic. I would be absolutely shocked if they are possible except possibly increasing the specific impulse

The thing with upper stages (assuming solid here) is that it's "theoretically" possible to both dramatically increase specific impulse and reduce engine mass fraction increase propellant mass fraction.
Of course, you need high nozzle expansion ratios to achieve the former which might not be practically achievable in a small form factor multi-stage solid.
Achieving the latter would involve running the chamber at significantly lower pressures - we primarily run high chamber pressures for sea level ops - and reducing the structural retention of the chamber to accommodate.
Of course, there's first-order theoryland and there's practical realities where dry mass tends to continually creep up unexpectedly with vehicle development as things like control systems are developed and integrated.

TP

 

[boatgeek]

The thing with upper stages (assuming solid here) is that it's "theoretically" possible to both dramatically increase specific impulse and reduce engine mass fraction.
Of course, you need high nozzle expansion ratios to achieve the former which might not be practically achievable in a small form factor multi-stage solid.
Achieving the latter would involve running the chamber at significantly lower pressures - we primarily run high chamber pressures for sea level ops - and reducing the structural retention of the chamber to accommodate.
Of course, there's first-order theoryland and there's practical realities where dry mass tends to continually creep up unexpectedly with vehicle development as things like control systems are developed and integrated.

TP

On the issue of pressure, does the difference between sea level and vacuum really make that much difference? My understanding is that hobby solids are normally run around 500 psi-1000 psi chamber pressure. At that rate, the difference between 0 psi and 14.7 psi external pressure seems pretty small. I'm sure I'm missing something here...

 

[AlexBruccoleri]

On the issue of pressure, does the difference between sea level and vacuum really make that much difference? My understanding is that hobby solids are normally run around 500 psi-1000 psi chamber pressure. At that rate, the difference between 0 psi and 14.7 psi external pressure seems pretty small. I'm sure I'm missing something here...

It has to do with expansion ratio. At sea level you cannot over expand too much without the flow separating in the nozzle. In vacuum the ration can be quite high.

 

[RGClark]

No trick to that at all. It's called a burst disk.

Certainly it’s within the capabilities of most advanced amateurs.



Bob Clark

 

[plugger]

The conclusion you draw is any L3-level amateur can do a flight to suborbital space.

No, ffs no. How you went to 'a handful of people have come close and a university team with a near decade of incremental gains reached the goal = any amateur can do it' shows just how ignorant you are of the complexities of flights like these.

 

[rocket_troy]

Is the general equation for thrust coefficient (Sutton) ie. the contribution the nozzle provides to thrust.

So specific impulse is essentially the effective exhaust velocity ie. isp = c/g
the effective exhaust velocity is essentially the product of characteristic velocity (c*) and the nozzle contribution cf
c* is essentially the chamber impetus only (no nozzle contribution) from the propellant combustion and it doesn't *theoretically* change much with variations in chamber pressure.
What *can* change significantly with variations in chamber pressure is the thrust coefficient cf if all other conditions and geometries are equal.

If we focus in on the equation above and make the following assumptions for this example:

Area ratio (A2/At) remains constant ie. expansion ratio is constant
ratio of specific heats (k) is constant - typically 1.2 - 1.4 for most chamber and exhaust combinations
P1 (chamber pressure) is 1000 psi for case 1
P2 = P3 (exit pressure = ambient pressure) for both examples ie. the nozzle is ideally expanded for ambient conditions
Because P2 = P3 we can discard the 2nd part of the equation and only use the part under the square root

Case 1 (sea level): P1 = 1000 psi and P2 = 14.7 Psi and k = 1.3
plugging into excel:
Cf = 1.54969

now let's keep the same expansion ratio but operate at 100,000 ft and *reduce* our chamber pressure by the same ratio as we reduced P2

P2 (@100kft) = 0.145 (abouts)
The ratio to SL = 0.145/14.7 = 0.009863946
Now reduce our chamber pressure by that ratio = 1000 * 0.009863946 = 9.863946 psi (!)

Now let's calculate the cf again but with P1 (chamber pressure) of 9.863946 psi and P2 = 0.145 psi

Cf = 1.54969 ie. it's *theoretically* the same!
ie. it's primarily determined by our P2 : P1 *pressure ratio*, so as we decrease P2 and P3, there's plenty of room to also decrease P1 respectively.

Of course there's limits to this (practically) - especially with highly aluminised propellant that will suffer combustion efficiency issues, agglomeration and residence time effects, but there is significant theoretical scope for dramatic decreases in Pc with altitude ops.

TP

 

[rocket_troy]

On the issue of pressure, does the difference between sea level and vacuum really make that much difference? My understanding is that hobby solids are normally run around 500 psi-1000 psi chamber pressure. At that rate, the difference between 0 psi and 14.7 psi external pressure seems pretty small. I'm sure I'm missing something here...

Also, I've developed a nice little interactive PEP tool as part of my GrainsCAD software to held illustrate this with sliders to vary Pc, Pa and expansion ratio for any chosen propellant simulation:

https://www.propulsionlabs.com.au/Software/GrainsCAD_Test.zip
TP

 

[RGClark]

No, ffs no. How you went to 'a handful of people have come close and a university team with a near decade of incremental gains reached the goal = any amateur can do it' shows just how ignorant you are of the complexities of flights like these.

It wouldn’t be instant. And there would be false starts and failures, but flight to von Karman line is within the capability of most advanced amateurs:

The experiences of the USC RPL student team that reached it, the Princeton University student team that would have succeeded if their sustainer ignited, Project Mesos that essentially reached it at 90 km, and the project by member Andrej Vrbec and Denis Banovic that likely reached it by a P to O motor rocket, as well as the FourCarbYen 2-stage rocket of Jim Jarvis, which simulations show without airframes also could reach it, prove commercial-off-the-shelf high power motors O, N, and even M with staging can reach the von Karman line if they don’t use airframes.

Here‘s a challenge: for advanced amateurs who have done O, N, and M motor flights, what altitude would a staged rocket using such high power motors sim to without airframes?

Bob Clark

 

[RGClark]

In which I attempt to show through math that the proposed rocket in #1 doesn't do the job of getting to orbit. This was mainly for my own interest--I don't really expect it to change the OP's mind. But hey, math and spreadsheets--it's like candy for an engineer.
Starting with some extremely rash assumptions (never make assumptions about rashes!):
0.5 kg payload
0.5 kg nose cone, roll control system, and guidance computer
0.8 mass fraction for motors
Thrust vector control mass 0.5kg for Stage 4, 1 kg for Stage 3, 2 kg for Stages 1 & 2
ISP ~225s (matches the CTI O8000)
Thrust is constant, propellant mass burn rate is constant (this mainly just makes the math easier)

Note that these assumptions are extremely optimistic. I would be absolutely shocked if they are possible except possibly increasing the specific impulse.

My process was to work backwards. When Stage 4 burns out, you want to have reached 7800 m/s. You enter the propellant mass and the impulse (plus an assumed time, which doesn't really matter), you get starting and ending acceleration based on your loaded and burned out mass, you integrate the acceleration, and you get delta V. That gets you your desired starting velocity to reach that ending velocity. Then you wash, rinse, repeat with each stage below. The end result is the rocket you would have to loft to ~200 km, turn horizontal, and start firing to make it to orbit.

So here's how that shakes out:
Stage 4: Full O motor, 41000 N-s, delta V 1850 m/s
Stage 3: Full Q motor, 160000 N-s, delta V 2500 m/s
Stage 2: Full S motor, 640000 N-s, delta V 2300 m/s
Stage 1: 50% V motor, 890000 N-s, delta V 1150 m/s

The astute reader will notice that you need to loft 1730 kN-s worth of impulse to orbital altitude just to get from "standstill at that altitude" to "orbit at that altitude". That whole stack weighs just a hair over 1000 kg, so it seems fairly plausible given the mass and payload capacity of the Lambda 4S. Also note that this is far, far beyond the capabilities of any amateur rocket builder.

QED.

Thanks for the calculation. A quite key factor is that the vacuum Isp and vacuum thrust is significantly higher than the sea level Isp and thrust. If anyone is familiar with using OpenMotor or Burnsim, I’d like to see what is the vacuum Isp of the Cesaroni motor this 4-stager is based on:



Bob Clark

 

[plugger]

I'm not sure when you switched from composite casings to submin vehicles as your special sauce to get performance gains but it's not the silver bullet you think it is Bob.

 

[boatgeek]

Is the general equation for thrust coefficient (Sutton) ie. the contribution the nozzle provides to thrust.

So specific impulse is essentially the effective exhaust velocity ie. isp = c/g
the effective exhaust velocity is essentially the product of characteristic velocity (c*) and the nozzle contribution cf
c* is essentially the chamber impetus only (no nozzle contribution) from the propellant combustion and it doesn't *theoretically* change much with variations in chamber pressure.
What *can* change significantly with variations in chamber pressure is the thrust coefficient cf if all other conditions and geometries are equal.

If we focus in on the equation above and make the following assumptions for this example:

Area ratio (A2/At) remains constant ie. expansion ratio is constant
ratio of specific heats (k) is constant - typically 1.2 - 1.4 for most chamber and exhaust combinations
P1 (chamber pressure) is 1000 psi for case 1
P2 = P3 (exit pressure = ambient pressure) for both examples ie. the nozzle is ideally expanded for ambient conditions
Because P2 = P3 we can discard the 2nd part of the equation and only use the part under the square root

Case 1 (sea level): P1 = 1000 psi and P2 = 14.7 Psi and k = 1.3
plugging into excel:
Cf = 1.54969

now let's keep the same expansion ratio but operate at 100,000 ft and *reduce* our chamber pressure by the same ratio as we reduced P2

P2 (@100kft) = 0.145 (abouts)
The ratio to SL = 0.145/14.7 = 0.009863946
Now reduce our chamber pressure by that ratio = 1000 * 0.009863946 = 9.863946 psi (!)

Now let's calculate the cf again but with P1 (chamber pressure) of 9.863946 psi and P2 = 0.145 psi

Cf = 1.54969 ie. it's *theoretically* the same!
ie. it's primarily determined by our P2 : P1 *pressure ratio*, so as we decrease P2 and P3, there's plenty of room to also decrease P1 respectively.

Of course there's limits to this (practically) - especially with highly aluminised propellant that will suffer combustion efficiency issues, agglomeration and residence time effects, but there is significant theoretical scope for dramatic decreases in Pc with altitude ops.

TP

Ah, I see now. I was thinking of the pressure as a difference when it's a ratio. That makes all the sense in the world. When you get out into a hard vacuum, does the assumption that P2 = P3 still hold? It seems like it ought to, but I've already been wrong once here.

And now I've learned something, which makes this thread worthwhile!

 

[boatgeek]

I'm not sure when you switched from composite casings to submin vehicles as your special sauce to get performance gains but it's not the silver bullet you think it is Bob.

Step 1: composite casings
Step 2: submin vehicles
Step 3: ?????
Step 4: Profit!

 

[rocket_troy]

Thanks for the calculation. A quite key factor is that the vacuum Isp and vacuum thrust is significantly higher than the sea level Isp and thrust. If anyone is familiar with using OpenMotor or Burnsim, I’d like to see what is the vacuum Isp of the Cesaroni motor this 4-stager is based on:

View attachment 550643

Bob Clark

Vacuum Isp will *always* be higher than SL, BUT, it will only be "significantly" higher with the utilisation of a high expansion ratio. As I mentioned earlier, fitting one of those in might be tricky depending on desirable peak thrust levels and vehicle width.

TP

 

[rocket_troy]

When you get out into a hard vacuum, does the assumption that P2 = P3 still hold? It seems like it ought to, but I've already been wrong once here.

*Practically* no, not really. Only because the optimal expansion ratio for a vacuum or near vac is insanely large ie. totally impractical to achieve especially with the diminishing returns as you chase harder and harder.

TP

 

[StreuB1]

Read these words carefully


MASS

FRACTION

DOES

NOT

SCALE

Stop talking about no airframes on rockets in the realm that any of us here play with. It does not scale to our realm of the universe.

 

[RGClark]

I'm not sure when you switched from composite casings to submin vehicles as your special sauce to get performance gains but it's not the silver bullet you think it is Bob.

I’m discussing both rockets to the von Karman line and orbital rockets. Rockets just to the von Karman line can be done with literally straight off the shelf commercial motors by using staging. No carbon fiber casings required, no special vacuum optimized nozzles required. But you do have to construct the rockets without using airframes, i. e., no body tubes, since they add excessive weight. This requires skill at the advanced amateur level since you would need to use a fin can or directly attach the fins to the motor casing.
Amateurs at the advanced level can confirm with sims that high power motors with staging and without airframes can get well-beyond the von Karman line. Using sims, you can simulate no body tubes by assigning 0 weight and 0 wall thickness to the body tubes in the sim.

For orbital rockets, though minimizing weight needs to be taken to another level. I advise carbon fiber casings, though specialty high strength, and high cost, aluminum, steel or titanium can get as good or better performance than carbon fiber.

Bob Clark

 

[StreuB1]

I surmise that it would take...hmmmm......

Mark 57 to a Mark 57 to a Talos to a Talos to a Taurus to an Apache to have enough snort to get to "orbital velocity" and that is assuming the stack could handle the g-forces in the arc up to orbital tanget......it won't, not even close.

Those motors are the most easily obtainable motors in the US stockpile that could be used. Notice how Wallops is not dragging out old HoJo booster motors from their magazines and chaining them together to give Antares a run for its money?? It's not due to lack of supply.

 

[boatgeek]

I surmise that it would take...hmmmm......

Mark 57 to a Mark 57 to a Talos to a Talos to a Taurus to an Apache to have enough snort to get to "orbital velocity" and that is assuming the stack could handle the g-forces in the arc up to orbital tanget......it won't, not even close.

Those motors are the most easily obtainable motors in the US stockpile that could be used. Notice how Wallops is not dragging out old HoJo booster motors from their magazines and chaining them together to give Antares a run for its money?? It's not due to lack of supply.

You could connect up 7 Mk 57 motors with ratchet straps, baling wire, and chewing gum and then maybe just need 2-3 extra stages.

 

[wclaybaugh2]

PLEASE do not use the Lambda 4S as existence proof that an amateur can make a small orbital solid motor launch system. The Japanese government spent years and a huge budget to prove it could be done. Once out of 5 attempts. It's just an outlier. It's not a road map to success for regular folks (or corporations, or governments). Just the opposite: almost 3 tons on the pad, millions of $$$, international regulatory cooperation, and never considered as an operational launcher. In other words, a barely successful demonstration flight which failed to prove a practicable system. After almost 50 years, almost no one has wasted time attempting all-solids to orbit.

For an example of a successful operational all-solids launch system, look at Scout. 25 tons on the pad, and the full efforts of the US military-industrial complex. Retired in 1994 and never replaced with an all-solids launch system.

Modeling a minimum all-solids to orbit vehicle is an interesting academic past-time. The closer one gets to considering all the physical (and regulatory) limitations, the more it becomes only academic.

Now back to souping up my gocart to run it in the Indianapolis 500.

John:

I'm pretty sure the decision to kill Scout was based on the availability of Pegasus...which was all solids (except for the insertion stage). I much later was part of discussions to kill Pegasus because Minotaur was much lower cost (to government users)...and it too was all solid save for an insertion stage.

As a pointless aside: if I were looking at this with OR I'd just look for 25,000 ft/sec straight up. Any vehicle that can do that should be able--with guidance--to reach orbit assuming the mass of the guidance is included in the "straight up" model since vertical ascent will require more energy than a gravity turn.

Bill

 

[Adrian A]

I’m discussing both rockets to the von Karman line and orbital rockets. Rockets just to the von Karman line can be done with literally straight off the shelf commercial motors by using staging. No carbon fiber casings required, no special vacuum optimized nozzles required. But you do have to construct the rockets without using airframes, i. e., no body tubes, since they add excessive weight. This requires skill at the advanced amateur level since you would need to use a fin can or directly attach the fins to the motor casing.
Amateurs at the advanced level can confirm with sims that high power motors with staging and without airframes can get well-beyond the von Karman line. Using sims, you can simulate no body tubes by assigning 0 weight and 0 wall thickness to the body tubes in the sim.

For orbital rockets, though minimizing weight needs to be taken to another level. I advise carbon fiber casings, though specialty high strength, and high cost, aluminum, steel or titanium can get as good or better performance than carbon fiber.

Bob Clark

I sim a 3-stage rocket with an M an L and a K motor that can get to the Von Karman line with airframes that are basically lightweight fairings over the motor and thicker/stronger where they extend past the motor for staging and deployments.

I think a (relatively) compact, lightweight TVC is possible for a flight like this that could also work in a vacuum for a 4 or 5 stage orbital attempt. You would just need 2 small cold gas thrusters and a small tank for roll control. The sensing and computing power is already available for a few grams.

These aren’t trivial systems to implement but they are doable without breaking any laws of physics. They can be smaller and lighter than is generally assumed. Getting motors with high enough mass fraction and ISP is arguably harder.

 

[plugger]

But you do have to construct the rockets without using airframes, i. e., no body tubes, since they add excessive weight. This requires skill at the advanced amateur level since you would need to use a fin can or directly attach the fins to the motor casing.

Show me where or how you came to uncover this 'law of suborbital space flight' please.

 

[RGClark]

Show me where or how you came to uncover this 'law of suborbital space flight' please.

In the professional industry, for suborbital sounding rockets and for orbital rockets, airframes, i.e., body tubes, aren’t used because they add unneeded extra weight, where minimizing weight is paramount.

I think using body tubes is a holdover from the old Estes rockets days where you placed the little motors for the rockets inside the cardboard tubes that came with the kits.

Amateurs have constructed rockets without body tubes called “subminimum“ diameter rockets. I’m not a fan of the term since it seems to be contradicting itself.

Bob Clark

 

[RGClark]

I surmise that it would take...hmmmm......

Mark 57 to a Mark 57 to a Talos to a Talos to a Taurus to an Apache to have enough snort to get to "orbital velocity" and that is assuming the stack could handle the g-forces in the arc up to orbital tanget......it won't, not even close.

Those motors are the most easily obtainable motors in the US stockpile that could be used. Notice how Wallops is not dragging out old HoJo booster motors from their magazines and chaining them together to give Antares a run for its money?? It's not due to lack of supply.

SpaceX was able to show it is possible to literally cut 90% off the development cost of an orbital rocket. Now imagine a scenario where you literally have zero labor costs, using university students willing to work for pizza during lunch breaks and college credits?

Bob Clark

 

[StreuB1]

SpaceX was able to show it is possible to literally cut 90% off the development cost of an orbital rocket. Now imagine a scenario where you literally have zero labor costs, using university students willing to work for pizza during lunch breaks and college credits?

Bob Clark

Have you ever taken an ethics course?

 

[rfjustin]

SpaceX was able to show it is possible to literally cut 90% off the development cost of an orbital rocket. Now imagine a scenario where you literally have zero labor costs, using university students willing to work for pizza during lunch breaks and college credits?

Bob Clark

Are you an artificial intelligence based bot? Asking for a friend...

 

[kramer714]

So a challenge....
Lets assume you are right, but you need to build something to prove it out. Just build your first stage, full scale, truly representative. Use it to launch a weight equal to your proposed 'remainder of the rocket' .. Use a little of the weight for a recovery system.

Does it meet your Isp, total thrust, mass fraction, velocity (per your prediction), does it truly meet ALL of your assumptions. Does the motor case meet the burst pressure, do you fins stay on without flutter, does the trajaectory stay straight... If you cant make the first stage ACTUALLY meet your predictions, none of the rest matters right? Use college kids, for this - determine the calibrated capability and availability of college students.

Mike K

Bonus Challenge - RESPECTFULLY suggest what to use for the dummy weight.