Almost
two weeks ago, I linked to the
Blog of Bernd Leitenberger, a german SpaceX Critic and author of
several books about Rockets and Space Travel.
Yesterday, He posted a new blog post, summing up again how the company is lying about the Falcon Rocket Data, simply by using math.
https://www.bernd-leitenberger.de/blog/2019/02/05/spacex-im-technikfaktencheck/
Once again, I'm allowing myself to translate this.
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SpaceX Technology Fact Check Posted on February 5, 2019 by Bernd Leitenberger Today's blog is not new in principle. The facts can be found in older articles. Unfortunately, it's in the nature of the blog that this, because it's in the past, likes to spill because you can't easily get to the articles. It is again about the bubble company SpassX.
(Translation Note: "SpassX" means "FunX", and is his nick for the company.) As at least those who deal more with it know, it shines above all by statements, which then prove to be wrong.
With the many project announcements this is easy to check by everyone. Just take one of the SpaceX projects, type in the name plus "SpaceX" in Google and read through some search results from different years. If you do this with the keyword "Red Dragon", you will get the following headlines:
28.4.2016: The unmanned Red Dragon landing on Mars is
announced.19.2.2017: The launch is
postponed by two years.19.7.2017: Red Dragon
won't land, but will rather be dropped1.10.2017: The mission is discontinued
In
my system, that's 1.8 Musk and 5.6 Elon.
(Translation Note: He made a Formula for "Elon Time" in an older blog post.) You'll find this in almost all of SpaceX's projects. They will be announced big. Then first shifted, then substantially modified and finally adjusted. Be it Falcon 1e, Falcon 5, Falcon 9 Block II, Falcon 9 Heavy or Gray Dragon. The BFR is just in the state of substantial modification, Starlink in the phase of rescheduling.
Technical facts are different. These are more persistent and are denied only after years and are also usually not falsifiable by outstanding directly. At least one needs space travel knowledge, in order to evaluate them as wrong or untrustworthy. In this blog I will illuminate some of the wrong technical details. They all revolve around the Falcon 9.
If you take the information on the SpaceX website and other information from tweets, as given by Wikipedia, the Falcon 9 is a marvel of technology with an enormous payload for the technology used. If the information is correct, it can also be accessed, I have calculated it myself. The stupid thing: I think they are wrong.
Record-breaking vacuum impulse
Let's start with the second stage record impulse. It is given as 348 s. The value in imperial units is in seconds, because a velocity (m/s) is divided by the acceleration due to gravity (m/s²). If you take the factor 9.81 m/s² for the acceleration due to gravity as multiplier, you get the SI unit in m/s for a velocity, namely that of the gas, when it leaves the nozzle. (If you are still used to calculating in kilopond instead of Newton, you will get the same numerical value without any problems).
The specific impulse is coupled as a quantity to two other quantities: the thrust and the fuel throughput.
Since the Merlin 1D vacuum of the second stage is a variant of the first stage engine, the fuel throughput is the same. But the thrust is not. It is more powerful: 987 instead of 914 kN. (According to the current user manual from January 2019). This is due to the only change there is: an extended nozzle. It has an area ratio of 165 instead of 16. But the specific impulse is 348 instead of 311 or 363 m/s more. Anyone who knows a lot about engines will be amazed - 363 m/s more just by a longer nozzle? This is not the case with other engines. Typically you get 150 to 200 m/s more.
It goes even further: The Merlin is a by-pass engine with an average combustion chamber pressure of 97 bar. Such an engine is comparable with other LOX/kerosene engines of the USA like the F-1 or RS-27. While the impulse of the first stage is in the same order of magnitude as this, the impulse of the second stage engine is much higher, higher than with mainstream engines. These engines have a higher combustion chamber pressure and make full use of the fuel. Bik bypass typically loses 2 to 5 percent in the gas generator, depending on the combustion chamber pressure. They must be subtracted from the total impulse. In short, anyone with technical expertise will doubt this value. But with the dependency
Specific impulse = thrust / fuel throughput
you can also write in first and second stage per engine with the same fuel throughput:
Specific impulse second stage engine = specific impulse first stage engine * thrust second stage engine / thrust first stage engine
and in values:
335.8 s = 311 s * 987 kN / 914 kN
So you get a specific impulse of 335.8 and not one of 348. 3294 m/s is an essentially credible value. You can also use the known data on combustion chamber pressure (97.2 bar), expansion ratios (16 and 165) and mixing ratio and the NASA FCEA program. This does not provide the real data of the Merlin, but only limits for idealized conditions, but one can take the difference there between vacuum value at 16 and 165 and comes also only to 278 m/s gain and not 446 m/s. That is a maximum of 3328 m/s, close to the value after the thrust calculation.
Thrust-To-Weight Factor
For each engine you can specify an additional characteristic value, the TW or Thrust to Weight Ratio. It indicates how many times the engine weight the engine can hold in suspension due to its own thrust and is calculated after:
TW = thrust / g / weight
with g as acceleration due to gravity (9.81 m/s²) and is dimensionless if the units are considered:
TW = thrust [N = kg*m/s²] / [m/s²] / [kg]
The TW depends on the size of the engine - as with most machines, it becomes more efficient when it gets bigger - a gasoline engine in a passenger car also delivers more horsepower per kilogram of mass than a lawnmower engine. The choice of fuel also plays a role. LOX/LH2 engines have a different factor than LOX/kerosene because temperatures and mean molar mass of the gas and thus combustion chamber pressure are different and last but not least the pressure also plays a role: the higher it is, the higher the TW factor.
From 1000 kN thrust, the TW hardly rises and LOX/kerosene engines in the bypass process reach a TW of about 90 to 100. The Merlin 1C was also in the range: 483 kN vacuum thrust at 522 kgh mass, giving a TW of 92.5.
A TW of 180 is now given for the
Merlin 1D: This corresponds to a weight of 468 kg and a thrust of 914 kN. The question is, is this credible? One can of course believe the SpaceX specification, which implies that all other companies that have developed rocket engines for 60 years are unable to build a lightweight engine. Not only in the USA, but also in Russia, China, Europe, India and Japan. This is particularly piquant to ensure that all Russian engines are also beaten. From the mid-sixties onwards, the USA hardly developed any new engines: the existing ones were sufficient for the launch vehicles and military missiles were only powered by solid matter. Russia continued to develop engines powered by liquid fuels and used the mainstream process at high pressure. The record of TW I know so far was held by the NK-33 with 125:1. (There are still some Russian engines with higher TW factors, but the facts are relatively imprecise, and none reaches a TW of 180).
But there are some reasons to doubt it. The main reason is that the Merlin 1D was developed from the Merlin 1C. This worked at 58 bar. But the Merlin 1D with 97 bar and a bigger nozzle. Even if I assume that the SpaceX on the Merlin 1C used a combustion chamber that can withstand much too high a combustion chamber pressure and has already designed it for 97 bar, the Merlin 1D has to be heavier than the Merlin 1C due to the longer nozzle (area ratio 16 instead of 14.5 to 1) and the more powerful fuel delivery system that has to inject more fuel at higher pressure and the actuators that move the engine. According to SpaceX, however, it is lighter! That's like when Porsche develops a 600 hp engine from a 300 hp engine and then weighs even less, a physical contradiction.
In addition, the combustion chamber pressure is high above a bypass engine, but not at the level of the NK-33 of 146 bar. The higher the pressure, the better the TW can become, because the combustion chamber becomes smaller and so does the nozzle. I suppose the value only refers to the combustion chamber, which weighs about half of the engine. Then the total TW would come into a range of 90 to 100 and thus into a range that is plausible.
Structural Factors
The structural factors of the Falcon 9 are also suspect records. Musk names 30 for the first stage and "nearly 25" for the upper stage. The structural factor is defined as:
Structure factor=full mass of a stage/empty mass of a stage
Very large LOX/Kerosin stages (it depends on the fuel because of the tank size) come to 17 to 18. So the Thor and the S-IC but also the Atlas D-F as carrier rocket. Early ICBM first stages of Atlas and Titan were higher, but they were not designed to transport heavy upper stages and aerodynamically unfavourable payloads. The Atlas collapsed at
MA-1, the first use of the Atlas for the Mercury program, because the aerodynamic load by the Mercury was too high. Later versions of the first stages, which had larger upper stages, also had 17 to 18 take-off masses/dry masses. A structure factor of 30 means that SpaceX can produce the stages with half the dry mass that is usual elsewhere. Today, the trend is towards poorer structural factors and less expensive production.
The reason for the Falcon 9's structural factors, apart from the Merlin 1D with the TW factor of 180, is said to be light aluminum-lithium alloys. Now SpaceX is inventing nothing new. The alloy really does exist, it is AL 2195. As the number reveals, it belongs to the group of aluminium-copper alloys but also contains some lithium and is therefore wrongly called Al-Li alloy. As with many alloys, the weight advantage of the 2219 and 2014 depends on the application and thus on the type of forces acting. SpaceX uses them for tanks. NASA did the same when it switched from the LWT of the
Space Shuttle to the SWLT in 1998. In the LH2 tank, the alloy reduced the mass from 13,155 to 11,340 kg, 16%. This does not mean the structural factor of 30, especially since the first stage is equipped with a very long stage adapter due to the large nozzle of the second stage engine. In a LOX/kerosene rocket, the tanks make up about half of the mass. Thus, if you save 16% there, you can achieve a total of 8%.
There are some indications that the values are not correct. The best is provided by SpaceX itself. When the Falcon 9 was still flying in the first version, it was said that the engine block weighed 7756 kg, half the total mass of the stage, which NASA says weighed 17,726 kg. Now the current Falcon weighs 550 tons at launch, compared to 333 tons for the first version. The tanks are identical in diameter, only longer. Nevertheless, the current Falcon first stage would have to be lighter than its predecessor with 60 % fuel mass if the fuel quantity was calculated on the basis of thrust, burn time and specific momentum. This is only possible with materials that have a negative weight.
This is even more fun if you take the current data from SpaceX. From the SpaceX website of the Falcon 9:
- GLOW mass: 549.054 kg
- Thrust vacuum first stage: 8227 kN
- Firing time first stage: 162 s
- Specific pulse Vacuum 303 s
- Thrust vacuum second stage: 934 kN
- Firing time first stage: 369 s
- Specific pulse Vacuum 348 s
If g = 9.81 m/s² is added to convert the US impulses into the metric system, the fuel quantity can be calculated as follows:
Fuel quantity = thrust * burning time / specific impulse / g
You get 448378.6 and 100954.3 kg. If you subtract this from the GLOW, you get -279 kg for the residual mass, i.e. the dry weight! Yes, you have read correctly, the Falcon 9 has negative structure mass! And this, although the GLOW (Gross-Liftoff-Wetmass) still contains the payload fairing and payload itself. A real marvel of technology!
With other suppliers of launch vehicles one could now look into the
Users Guide for potential customers. There you can find the essential data of the rocket like structural mass, fuel and specific impulse. Not so with SpaceX. There you will find - this is absolutely unique - as a launch service provider who wants to launch satellites - not even a single specification for typical payloads for certain orbits.
Last but not least, SpaceX disproves the information itself. In
this statement, SpaceX's carrier rocket payload manager writes that the maximum GTO payload (without recovery) is 6500 kg, not 8300 kg as stated on the website. If you take a look at the list of launches, you will also discover several launches where there was no landing and still only a sub-synchronous GTO was reached, even though the satellite was far below 8.3 tons.
In my opinion the website is also completely useless as an information medium, because SpaceX doesn't have something like a media department. It has people responsible for it, but they are not allowed to give out any information. So it only keeps the information that Musk himself has already tweeted. But Musk probably doesn't talk about real data, but about his specifications, no matter if they are reached or not. Much of what he decides makes no sense on closer inspection. So he
fired the managers of his Starlink project. The satellites are too heavy and expensive. Since SpaceX has a deadline of the FAA to launch half of the more than 4400 planned satellites within six years, this is sometimes suboptimal, because there are delays in any case. The weight (the two prototypes weighed 500 kg each) should not be a problem. Because now you can reuse the Falcon 9 first stage
100 times. Then you only have to re-produce 1/5 of the rocket per launch - the upper stage and without the many Starlink launches a first stage wouldn't even have 100 missions due to the lack of other launches. In addition, you now have the Falcon Heavy, which could launch 100 to 120 satellites at once. With 20 Falcon Heavy in six years the constellation would be possible. So not logical.
Also not logical is the transition from CFRP to steel at the BFR. Clearly CFK is much more expensive - Musk talks of a price drop from
$135 per kilogram to $3. But the vehicle is supposed to be 100% reusable and even regularly flights to airports for passenger transport from continent to continent. So it is logical that the one-off manufacturing costs, even if they are higher, can be quickly recovered through more payload. The CFRP weighs at least 50% less than steel with the same load, so more payload or passengers can be transported. I suppose Musk thinks about what's cool and others have to do that and if it's not possible, then there are such twists.
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Notes:
- Once again, I hope the translation is correct, since DeepL is not 100% perfect with german grammar. (And Leitenberger has a tendency for typos.)
- If you look into the comments of the original blog post, you can see that it alsmost immediatly got attacked my a Musk Cultist, who, as you might have gussed, instead of trying to debunk Leitenberg's post, just attacks him personally.
