That doesn’t mean it’s wrong.
Bob Clark
You are wrong. People have been telling you this on here, on reddit, and on the arocket email list every single time you show up with these proposals.
Why don’t we go through this article line by line, and see what there is to see.
Making a good composite case is hard. You not only need to contain the pressure of the motor, you also need to keep the heat from getting the casing too hot. This is a tricky problem, and while it is solvable, it isn’t trivial. You have a habit of assuming many things that are very difficult are in fact easy, and then ignoring them.
Let’s get into the meat of the article now. You chose the Cesaroni O8000 as the basis for your analysis. This is actually a suboptimal motor for high performance flights, due to several factors, including relatively low isp, poor mass ratio because of the overly thick casing, and a large frontal area for the amount of impulse it has. I’ll include it in this analysis, but I’ll also throw in a few motors which I think would be superior options. The Aerotech O5280 is a 98mm motor in a composite casing that uses a high isp propellant. The Cesaroni N5800 is another 98mm motor with a high performance propellant, although it uses aluminum hardware. The Cesaroni O3400 fits more impulse into the same casing as the N5800, it uses a high density propellant that gives a high mass ratio, but relatively low isp. Finally the Aerotech M2050 is a 75mm diameter motor that uses the same propellant as the O5280, it has the highest isp of any commercially available amateur motor.
You decided that a carbon fiber casing could achieve a mass ratio of 0.8. I talked with some people I know who are developing carbon fiber motor casings, and they said that a carbon case could reduce the dry mass of some commercial solid motors by around 50%. While I doubt that a mass ratio of 0.8 is possible at amateur sizes and budgets, I ran the numbers for all of the motors at that mass ratio as well.
Next, you chose a vacuum isp of 285s for your motors. This is an unreasonable assumption. As stated previously, the O8000 doesn’t use a high isp propellant. I ran some simulations in Openmotor with a motor similar to the ones I was evaluating, and when changing the exit pressure to a vacuum, and enlarging the nozzle exit, I saw about a 20% increase in isp. This seems to match what I’ve been able to find for performance on motors used in industry. Here is the first part of my spreadsheet, with the isp and delta V calculated for each motor, at the stock hardware mass, half hardware mass, and a 0.8 mass fraction.
Note that while most of the motors aren’t matching your 285s estimate, the M2050 is actually significantly above it, at 296s.
Now we get to the fun part. You didn’t calculate the delta V of any of your proposals. You came up with your numbers, and then plugged them into a
launch performance calculator. A launch performance calculator that according to
it’s own documentation does not properly consider aerodynamic drag losses from a high thrust to weight ratio rocket. This
has been pointed out to you before, and yet you keep on showing off this flawed analysis. For a math professor, you seem to be allergic to running the actual calculations yourself. So let’s calculate the Delta V of each of the motors, at each of the different mass ratios (stock, half casing mass, and 0.8) for both the single motors, and your proposed launch vehicle and see what we get.
Conventional wisdom is that LEO has a delta V requirement of about 9.4 km/s. I followed the article and made each stage four times the mass of the one above it. I used the vacuum isp for the upper two stages, and the sea level isp for the first stage. The first three rows of the results show the delta V contribution of each stage to the total stack, and the final row is the total delta V of the stack.
First here are the results for a vehicle with unmodified casing masses. The O5280 is the clear winner here, with a calculated delta V of just over 6 km/s. The N5800 and O3400 come a little ways behind, followed by the O8000 and the M2050. The M2050 suffers from a comparatively poor mass ratio, due to a rather thick casing, and the square cube law. Smaller motors will tend to have worse mass ratios, since they have more surface area for their propellant volume.
Moving on to calculating delta V for motors with the dry mass halved. The O5280 is the clear leader at almost 8.6 km/s. It’s already a composite cased motor with a relatively high mass fraction, so I doubt that you can cut the casing mass in half by replacing fiberglass with carbon fiber.
Finally we have the numbers for when the motors are set to the 0.8 mass ratio specified in the article. Since we’re disregarding the initial hardware masses, this ends up just being an isp contest that the M2050 handily wins. It’s also the only configuration to break 9.4 km/s.
Now comes the elephant in the room. These mass ratios are impossible. You have a habit of disregarding all component masses besides the motor mass. This is wrong. An orbital rocket will require many more systems beyond just the motors. It will need control systems, whether those take the form of a gimbaled nozzle, RCS thrusters, or actuated fins on the first stage. It will need avionics to control those systems to keep it on course. It will need a structure to hold all of these things, and to couple the stages together. It will need a fairing to protect the payload from the atmosphere on the way up. Hell, I didn't even include a gram of payload mass. These calculations are for an unguided stack of motors, not a launch vehicle. A single solid rocket motor with a mass ratio of 0.8 might be possible for a very experienced amateur motor maker really pushing the limits of what’s possible in the hobby. A mass ratio of 0.8 for an entire vehicle is impossible to do at the amateur scale. You have neglected to consider any factors at all besides raw propulsion numbers. There is far more to building an orbital launch vehicle than building something that meets the theoretical delta V requirements.
There’s also the fact that the 9.4 km/s delta V requirement that I’ve been using is likely to be a major underestimate. Accelerating to high speeds within the lower atmosphere will send your drag losses through the roof. You have been told this multiple times before, and yet you keep on trotting out this article as proof that orbital rockets are easy.
Next, let’s look at the proposed vehicle design. You suggest clustering the motors in the first and second stage. This runs into a square cube law problem, where a cluster of smaller motors will have a worse mass ratio and performance than a single large motor of the same impulse.
Then we have the part that shows your ignorance about solid rocket motor design. You correctly identify that ignition of 16 motors in the first stage is difficult. The proposed solution of combining four motors into one long motor is patently absurd. While I haven’t made any motors yet, I have spent a fair amount of time talking with people and running simulations in Openmotor. Long motors are hard. Making a motor twice as long as the O8000 or M2050 might be possible, because they are relatively short. It would probably require increasing the core diameter of the bottom grains, which would reduce propellant mass. But extending that to triple or quadruple the length of the initial motor is frankly impossible for amateur motor makers.
And then at last we have the costs. Your entire budget for a launch in the article is $63,000, which solely comes from the O8000 motors. The budget does not include the carbon fiber casings. It does not include any of the other subsystems I mentioned earlier. It does not include the cost of the tools and machinery to build the rocket. It does not include the cost of building a launcher. It does not include the cost of using the launch site. It does not include the cost of labor. In the end the $63,000 cost of propellant is going to be a relatively small proportion of the cost of an orbital launch.
Finally, let’s take a look at what it takes to launch a cubesat into orbit with solid rocket motors. The Japanese SS-520 sounding rocket with a third stage placed a cubesat into orbit in 2018. The SS-520 rocket weighs 2,600 kg, and at 0.52m in diameter is significantly larger than any amateur rocket I’ve ever heard of. The SS-520 is tiny in comparison to other orbital rockets, but it is well outside the realm of what’s possible for an amateur group.
