In the previous explanation, we covered the Comet aircraft experiencing a series of crashes and the process of formulating hypotheses about the cause of the accidents.
The most plausible hypothesis that was derived was,The cause was described as "mid-air disintegration due to fatigue failure caused by repeated tensile and compressive loads resulting from fluctuations in the internal pressure of the pressurized chamber and atmospheric pressure," and further stated that "stress concentration occurred at the corners of the windows and the holes in the antenna."It became.
However, this is merely a hypothesis.
Past and presentIn engineering, hypotheses alone are meaningless; they must be proven to be the cause.
This time, we will focus on explaining the subjects and results used to verify the hypothesis.
Let's consider safe methods for recreating the Comet jet crash.
The easiest way to prove a hypothesis is to actually fly it in the same way.
However, it is too dangerous to actually fly because there is a risk of mid-air disintegration.
In such situations, there's no choice but to consider alternative solutions.
In considering alternative methods, our current hypothesis is that the factor causing fatigue failure is the atmospheric pressure difference due to the difference in flight altitude, so we first focus on the load generated by the difference in flight altitude.
Reproduction of atmospheric pressure changes due to differences in flight altitude
First, we consider that a difference in environmental conditions occurred within the aircraft, from 1 atm (atmospheric pressure) at an altitude of 0m during takeoff to 0.2 atm (external pressure) at a maximum altitude of 12000m.
In this case, the pressure inside the pressurized chamber is always kept constant at 0.6 atm, but since the atmospheric pressure at ground level (altitude 0m) is greater at 1 atm, a force of 0.4 atm acts on the pressurized chamber, trying to compress it.
On the other hand, at an altitude of 12000m, the atmospheric pressure is 0.2 atm, which is a smaller pressure than the 0.6 atm inside the pressurized chamber. Therefore, a force acts on the pressurized chamber in the direction of expansion (bursting) at 0.4 atm.
To put it in simple, familiar units, a pressurized chamber is subjected to a load of approximately 4000 kg (4 tons) per square meter.
We must devise a way to efficiently generate these conditions through some safe method other than flight.
Here, the RAE (Royal Aeronautical Institute) took action based on an idea that was unconventional at the time (and I think it would still be unthinkable today).
Method for reproducing atmospheric pressure fluctuations due to altitude differences
We decided to place the entire massive pressurized chamber of the Comet into a swimming pool and apply water pressure to conduct a fatigue test.
Simply filling it with water wouldn't create a repetitive load, so we repeatedly filled and drained the pool.
Furthermore, since the aircraft undergoes repeated compression and expansion due to the pressure difference from an altitude of 0m to 12000m, this cannot be replicated simply by adding and removing water from a pool. Therefore, water was added to the pressurized chamber while the water from the pool was being drained.
This is an incredibly big decision, and conducting this fatigue test presents several major challenges.
First, you need a large pool big enough to fit the entire pressurized chamber of the Comet helicopter.
In terms of size, it should be slightly larger than the Comet, so it would need to be approximately 30m long, 4.5m wide, and 5m deep (author's estimate).
In terms of length and width alone, there are 50-meter swimming pools available, so it's not a big deal, but a pool with a depth of 5 meters doesn't exist, so we'll just have to somehow make one.
In reality, it seems that RAE (Real Estate Aircraft Company) added cargo containers to create a pool large enough to fit the entire Comet aircraft.
Furthermore, there's the problem of how to manage the water supply and drainage.
The load (stress) at which a material fails due to fatigue is called the fatigue limit, and determining this requires at least 10^7 cycles of repeated loading.
To put it in easily understandable terms, it would take about 1000 million repetitions to calculate it.
This is unthinkable today, but it seems they managed to cope with it somehow using human power.
It truly lives up to its reputation as a national project.
The next thing to consider in the exam is the measurement problem.
Method for measuring loads and pressures applied to a pressurized chamber
Simply adding and removing water from the Comet to apply pressure isn't enough to determine if the intended load is actually being applied. Without knowing how much load is being applied to specific areas, the test is meaningless.
It's exactly the same now as it was in the past.Just as hypothesis and verification go hand in hand, testing and measurement must always be considered together; otherwise, it's meaningless.
The sensors used in this process are still exactly the same today: strain gauges and load cells.
A strain gauge is a special electrical resistance metal; when strain occurs in that metal, its electrical resistance changes.
In other words, by continuously passing an electric current through a strain gauge and reading the resulting voltage, you can determine how much strain there is.
If you know the strain, you can multiply that strain by the elastic modulus of the material to find the resulting stress (load, load).
For a detailed explanation of the relationship between stress and strain, please click here.
On the other hand, a load cell is simply like a weighing scale.
It's a sensor that measures weight, just like the bathroom scales you're all familiar with.
Instead of displaying numbers like a weighing scale, the voltage changes depending on the load.
The tests are primarily conducted by attaching these two sensors to the pressurized chamber.
The problem here is determining where and how many sensors to place in the pressurized chamber to verify the hypothesis.
Naturally, our hypothesis was that stress concentration occurred at the corners of windows and antenna holes, so it's obvious that we should attach sensors to those locations. However, since this is a large-scale test, we want to measure the load at as many locations as possible to increase the amount of data.
However, the number of sensors is finite, and recording and analyzing the measurement results is done by humans, so there are inherent limitations.
Moreover, recording those measurement results was quite difficult. Nowadays, it can be recorded in real time using a computer, but back then, practical computers didn't exist, so they had no choice but to rely on human effort.
The strain gauges and load cells I explained earlier simply change voltage in response to the applied load.
The changing voltage is displayed on a monitor via a device called an oscilloscope.
Each voltage displayed on the oscilloscope needs to be manually recorded by a human.
Moreover, at that time, basically one oscilloscope was required for each sensor.
Even if it's not just one oscilloscope assigned to each person, it still requires a considerable number of people and effort.
HypothesisEven just for the corners of the windows, you need at least four sensors per window, and if there are 20 windows, that already amounts to 80 sensors.
Since we'll be measuring other things as well, the total number will definitely exceed 100.
In my opinion, something of this scale might require around 1000 units.
Reading and recording sensor data in this way requires considerable effort, so there is naturally a limit to the number of sensors that can be installed.
In other words, The number of sensors to place and where to attach them depends on the engineer's skill and judgment (a huge responsibility).
Of course, if sensors are placed in meaningless locations, the test will be wasted.
This is still pretty much the same today.The difference in expertise regarding these testing and measurement methods is a measure of a company's true capabilities that cannot be measured solely by economics.
To top it all off, this test isn't something you can do just once; you need to do it multiple times to get reliable data.
Since the possibility of randomness (variability) cannot be ruled out from a single result, such tests are still conducted multiple times.
Therefore, the load generated in the test and the number of recordings would be an astronomical number: X × 1000 million.
Even from my own perspective, there were this many challenges, so in reality, there were probably many more.
RAE overcame these challenges through ingenuity, resourcefulness, effort, and cost to conduct the tests.
This type of test is called a reproduction test.
The reliability and concentration of reproduction tests
The repeated loading described so far, X × 1000 million times, is not realistic, and given the circumstances at the time, a quick conclusion was needed, so they devised a test that would be as accurate and quick as possible using statistics.
Furthermore, it's pointless to conduct reproduction tests without verifying whether they match the actual events that are occurring.
So how do we verify the accuracy of the test and complete it quickly (concentrate it)? We use a field of study called reliability engineering.
The basics of reliability engineering
In reliability engineering, there is a function called the Weibull curve that represents the probability density distribution, and this curve is used to determine the likelihood and concentration of a test.
In other words, the load is adjusted within a range that mimics the actual events occurring, allowing the test to finish sooner.
Simply doubling the load on an actual aircraft doesn't mean the test will finish twice as quickly.
I'll only give an overview, as going into too much detail would take us too far off-topic.
Simply put, it involves calculating the probability of an accident occurring at different distances based on actual accident data and then using a special function to create a graph (statistical processing).
From that graph, you can calculate MTBF (Mean Life Expectancy).
In reproduction tests, the test results are compared with graphs created using the same processing (statistical processing) as the actual accidents and malfunctions that occurred.
GraphUnless the test is designed so that the characteristics (such as the slope) and MTBF (Mean Time Between Failures) are the same as those of a graph created from an actual accident, it will not be a reproduction of the data.
In shortIt's not enough to simply apply flight loads; statistically processing the results and ensuring the same phenomena occur in both the actual aircraft and the test models is completely meaningless.
Furthermore, by utilizing the characteristics of this graph, it is possible to adjust the load of the reproduction test and determine the MTBF (Mean Time Between Failures) with a small amount of repeated load.
thisThis is called a concentrated reproduction test.
The RAE likely also performed this statistical processing during its Comet crash simulation tests, adjusting the accuracy of the simulations and the load to create concentrated simulation tests (reducing the number of load repetitions). However, it remains an extremely difficult test.
Incidentally, while MTBF (Mean Time Between Failures) might be an unfamiliar term, it's an important number that's very closely related to your daily life.
Examples of reliability engineering in everyday life
A clear example is the military, where the maintenance cycle for deployed weapons is determined by MTBF (Mean Time Between Failures), and this is strictly adhered to during operation (this applies to all industrial products, regardless of whether they are military or commercial).
A typical example that's familiar to most people is a private car.
The MTBF (Mean Time Between Failures) for each component is precisely defined, and dealers always replace any parts that need replacing according to these specifications.
Well, the lifespan of a machine is entirely determined by this statistical calculation of MTBF (Mean Time Between Failures).
Next, I will give an example of a concentration test.
For example, the approximate lifespan of a car is said to be 10 years or 10 km, but if you were to simply replicate the same test, it would take 10 years. Even if you matched the distance, driving 10 km would require an enormous amount of time and effort.
Therefore, in order to develop industrial products efficiently, this concentration test becomes essential.
Industrial products, including automobiles, should generally undergo similar durability tests to ensure their quality.
HoweverThe accuracy and reliability of the conditions for that concentrated test depend on the data, know-how, and quality of the engineers that the company possesses (the same applies to computer simulations).
ProbablyThe details of each automobile company's durability tests are top-secret information (a treasure trove of history and know-how, a valuable asset).
Yes, you can enjoy Okesa Persimmons in the form ofThisThis is what reveals a company's true capabilities, which cannot be measured solely by economics (second time saying this).
Simply put, if you have insufficient data and perform excessive testing, you'll end up with over-engineered products that are expensive and lose competitiveness. Conversely, if you can't perform enough testing, the quality will be poor and the product will be unacceptable.
A prime example in modern times is that electric vehicles developed solely by electronics companies often remain at the prototype stage. This is because they lack the necessary data and know-how to determine what kind of testing is required to ensure the vehicle can be sold without problems.
However, in recent times, the pursuit of short-term profits has led to a significant loss of opportunities to try new things, and consequently, opportunities to create new tests like these have decreased considerably.
In other words, Opportunities to pass on data, know-how, and technology are decreasing.
In my own short 15-year tenure, the development of new engines and parts drastically decreased. Under the guise of profit-seeking and efficiency, the standardization of engines and parts progressed significantly, and opportunities for true design and testing were greatly reduced.
Originally, the purpose was to use the increased profits and time gained from sharing parts to develop new machines, but blinded by short-term profits, the number of models that simply served to fill out the lineup like interchangeable dolls increased.
EitherAs time passes, data, know-how, and technology are lost, making it impossible to conduct new tests or even do anything at all.
What's worse is that sometimes the management gets angry and says, "Why can't we do it now when we used to be able to?"
They snap without realizing the situation they brought upon themselves.
in this wayIt is extremely difficult for a country, company, or organization to undertake something new.
At the same time, we must not forget the importance of passing on our skills.
Anyway, let's get back to Comet.
Preparations for a reenactment test of the Comet plane crash and public opinion at the time
No matter how much adjustments are made, the exam remains difficult, but the RAE (Royal Aeronautical Institute, similar to NASA in the US) did a good job.
However, it seems a little strange that such a difficult test could begin as early as the start of June 1954.
The third accident occurred in April 1954, and they managed to move from investigation to the start of testing in just two months.
Even by modern standards, it's far too fast. In my opinion, even with a frantic effort, it would take at least four months.
Upon investigation, it appears that the RAE had long considered the possibility of fatigue failure based on their experience with high-altitude flight in military aircraft during the war. While the internal pressure of other pressurized cabins at the time was at most 0.4 atm, the Comet's was as high as 0.6 atm, suggesting they were concerned.
Therefore, I think it would be extremely difficult time-wise to assume that preparations for the test began before this fatigue failure hypothesis was made public.
I suspect that someone within the government (probably Churchill) was behind it.
On the other hand, the Comet's development and manufacturing company (the prestigious de Havilland) also developed and produced military aircraft, including the Mosquito, though not to the same extent as the RAE, so they likely had confidence in their own aircraft.
Whether it's true or false is impossible to verify, but it seems the development and manufacturing companies believed that the RAE fatigue tests would only serve to prove their own technological prowess and the high reliability of the Comet.
Naturally, at that time, we were considering various causes, such as pilot error, terrorism, or a collision with some object.
Results of the Comet crash reconstruction test
Regardless of all the hype surrounding it, RAE calmly proceeded with preparations for the test, and the fatigue test began.
The construction schedule for the swimming pool was as follows: construction began in April 1954 and was completed on May 29, 1954.
Fatigue testing began in June 1954.
Naturally, since this was a fatigue test, RAE, as well as many other people involved, must have been prepared for it to be a long and arduous process.
It seems they estimated it would take about five months after investigating.
From a modern perspective, it seems like it took a little too long, but considering the facilities at the time, it must have been a very demanding fatigue test that required that much time.
Incredibly, during a pressurization test on June 24, 1954, a crack appeared in the corner of a window in the pressurized cabin and grew, eventually slicing the fuselage into sections.
In just over two weeks, the repeated load application was only 1830 times.
Even though it's a concentrated test, fatigue tests are basically designed for cycle counts of around 1000 million, so 1830 cycles is within the margin of error.
Given the sheer scale of the aircraft and the need to quickly determine the cause, the aircraft used in the fatigue test was a used one that had flown 1230 times (it would probably take more than three months to manufacture a new one). However, even with this test, the aircraft failed after a total of only 3060 flights, which is an impossibly short lifespan for any machine (ideally, it would be best to randomly select an aircraft from mass-produced models).
Based on design estimates from the development and manufacturing companies, and fatigue test results, it was thought that the device would last at least 54,000 cycles (which, in my opinion, is extremely low and worrying). However, RAE's fatigue tests showed that it failed at a number of cycles that was nowhere near $ \frac{1}{10}$.
Upon further investigation, it was found that the aircraft involved in the second accident had completed 1290 flights, while the aircraft involved in the third accident had completed 900 flights.
In the first placeThe fatigue test assumed 10 million cycles of repeated loading, and the development and manufacturing companies estimated 54,000 cycles. However, the actual accident and the RAE fatigue test results were less than 3000 cycles, which is orders of magnitude different from failure. This shows just how dangerous it is, and anything could happen.
moreoverThe fact became undeniable when a beach mark indicating fatigue failure was found in the corner of the antenna mounting hole on the top of the aircraft, which was recovered on August 12, 1954.
Faced with such blatant evidence, both government officials and private companies (development and manufacturing companies) had no choice but to admit the truth.
So the cause is,"Stress concentration occurred at the corners of the pressurized chamber windows and the mounting holes for the antenna, leading to progressive failure, fatigue failure, and ultimately, the aircraft disintegrating in mid-air."This was the conclusion reached.
Next time, we'll explain the detailed fracture mechanism. Let's clarify what the engineering issues are.
To those who found this article helpful in understanding design:
Since we're on the subject, I'd like to recommend a book that's essential for mechanical design.
To be honest, the content is extremely unhelpful, but it can be used like a dictionary when you forget the details. If you read this article, you should be able to understand the content and use it effectively. It also includes commonly used standards, making it quite useful.
If you don't already own one, I highly recommend getting one, even though it's a bit pricey. However, new ones are expensive, so if you're considering buying a used one, I strongly recommend checking that the surface roughness conforms to the new JIS standard.
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