Civilization Springs, 1/5
### Part 1. Golden Ku
At six, I fell into the hands of my grandfather’s handbook [50] on trucks of the mid-20th century. The sound quality, printed on smooth dense paper a rarity. The only thing left in general from the memory of his grandfather after the collapse of the country, wars and crossings.
The handbook contained many interesting TTH, so the word “carrying capacity” became familiar to me from early childhood. And when my father during a walk mentioned that any truck weighs as much as it takes itself, I remembered that. He remembered and, much later, became interested.
The father was right. For trucks of the 60s, this rule is carried out with rather surprising accuracy:
It is much more curious that this pattern is observed for vehicles completely different from trucks.
At first, for the sake of joke, I plotted cargo planes. And he was surprised. I began to add other vehicles. Riding, floating and flying, built in the centuries 19th, 20th, and 21st, working on thermal energy, nuclear, wind and even horse. Result? A weak power (value 1.125), if not just linear, dependence. On masses from one hundred kilogram to sixty thousand tons. With deviations, of course, wherever without them, up to 10 times sometimes, but on six orders of the masses, these are obviously trivialities.
Here it is, this dependence, pressing on to the diagonal of an immense empty field:
The graph indicated: cargo aircraft; transport helicopters; airships, modern and the beginning of the century; space launch vehicles (into low orbit); 60s Soviet trucks; modern mining trucks; modern trucks of Russia, USA, China and India; electric cars and scooters; trains (with rails); nuclear container ships; container ships and cargo ships (not tankers); sailing cargo ships of the 17th and 20th centuries; conveyor belts for the transfer of ore; nasovsky tractor for the removal of missiles at the start; and, finally, carts pulled by a horse.
If you enter the value of Q , defined as the mass of the transported cargo in relation to the dry weight of the vehicle, here’s how it looks for each of the groups:
In figures, the Q values are:
As can be seen, Q, although not everywhere strictly single, but within the framework of each group, to a general value close to unity.
It seemed to me ... mysterious. Why does a wooden sailboat, an aluminum electric car, and a nuclear container ship with a capacity of one hundred thousand electric cars, all raise more or less their weight? What makes us create vehicles with quality Q ≈ 1 on masses that differ thousands of times? Is it a manifestation of the properties of world physics, the terrestrial economy, is this a limitation of human intelligence? How universal is this law, will it be implemented for civilizations from other stars? Global issues. It is unlikely that they will be able to resolve here and now. But consider and take a glimpse of how much it will turn out, can and should be. This is what we will do.
The world record [ 180 ] of lifting a barbell is a man of average weight exceeding 200 kg. Theoretically, this means that our body has a margin of safety for jerk loads at least up to Q = 2.5. However, this requires such exorbitant strengths and training that it is never used in daily activities. It is more expedient to pack sugar into bags of 50 kilograms, although this requires four times more loaders or a walker. Note that this situation is the result of biological evolution, in which the human intellect has (almost) not participated, and therefore has an “alibi” in it.
Physics and engineering in themselves high Q is also not prohibited. Vaughn, the hydrogen turbopump assembly for the shuttle's main engine, that little thing on the right in the picture, develops power of 54 megawatts [ 60 ] with a car mass of 350 kg:
[Image credit: [ 10 ]]
If, simplifying, to assess Q by power per kilogram of mass, then it is 100 times higher than that of a decent car. Only after all, this thing is almost like a rocket! It is cheaper to make 100 cars with Q = 1 and transport the goods by them, rather than trying to “harness” this unit in a wheeled cart.
Such considerations suggest: the reasons are economic. And not in the narrow sense of specific economies and countries (for our devices are generated by very different peoples and systems), but rather in the sense of “expediency of efforts”. The feasibility is universal enough to, apparently, extend to very different products and somewhere even to animals.
Article written for the site https://habr.com . When copying please refer to the source. The author of the article is Evgeny Bobukh .
Let's try to explore the limits of this expediency quantitatively. We pose the question: how does the cost of a device with a fixed mass depend on Q ? Here, for example, there is a dump truck weighing 10 tons, taking away 10 tons of cargo. We also want to make 10 tons, but carrying 20 tons ( Q = 2) or even 50 tons ( Q = 5). At the same level of technology development, the same volume of release. It is clear that greater loads will increase the requirements for materials (steel -> titanium?), And for engines (other temperatures, pressures), and for engineering (less tolerances for errors, more cunning designs). It is clear that with increasing Q everything will be more expensive. But how many times, compared with ten-ton?
This task, of course, is not trivial. Nevertheless, some estimates for it can be obtained from the most general considerations. What we are doing now.
We introduce the function C ( Q ). It describes the lowest possible cost of a device with an efficiency Q , expressed in the costs of a similar device of the same mass with Q = 1. What is known about it?
1. C (1) = 1, by definition.
2. C ( Q ) is a continuous function, at least until the difference in mass is measured by unit atoms. Intuitively, it seems smooth enough to have the first few derivatives. I think it can be assumed (as with most physical functions) that it is generally analytical.
3. C ( Q ) is a strictly increasing function. The higher the quality Q , the harder it is to make the structure, and the more expensive it is. Those. dC ( Q ) / dQ > 0 at least for Q > 0.
4. When Q is greater than about 3, C ( Q ) begins to grow faster than linearly. Why? Because we see that it is cheaper for people to make three trucks per ten tons with Q = 1 than one at thirty c Q = 3. To summarize, we write: k * C (1) < C ( k ) for k > ≈3 - other In other words, C ( k ) grows faster than k , with k > ≈ 3.
5. Similarly, since ten aircraft with Q = 0.1 are clearly uneconomical than one with Q = 1 (because they build the second, not the first), then for k > ≈3 we have: k * C (1 / k )> C (1), or C (1 / k )> 1 / k .
6. The cost of the pump from the Shuttle hints that at least up to Q ~ 100 the value of C ( Q ) does not increase as an exhibitor with a significant figure. Otherwise this THA would cost not millions of dollars, but some $ 10 20 commercial, and it is unlikely that we would have made it at all. Those. C (100) is somewhere 10 3 - 10 8 , but not 10 15 .
7. What is C (0)? This is the cost of a device that can still move itself, but is unable to take away any cargo. Obviously, such a "truck" cheaper full. But how many times? History shows that it is rather several times more than tens or hundreds. Some 15 years passed from the first aircraft, capable of moving only itself ( Q = 0), to transportation of goods by air. From the first gasoline vehicles to quite decent trucks with Q = 1.5 ([ 120 ] + [ 130 ]) there is not much more. If this development were an incredible complexity, it would hardly have ended so quickly. Consequently, the difficulty of manufacture and the cost of a vehicle with Q = 0 should not be quite radically different from it at Q = 1. Hence, we expect that C ( 0 ) is somewhere between 0.1 and 0.5.
8. Does this feature make sense with negative Q ? Completely! A truck with Q = -0.5 is one that will budge only if the tower crane is to “lift” half of its weight from it. And Q = -1 is a wagon developing zero thrust. Able to transport cargo only if you take it in tow. That is, generally without an engine. Obviously, its value, if not equal to zero, is very small. Therefore, we set C (-1) ≈ 0.
9. What is C (-2)? This is the cost of a device that needs to be pulled up with at least twice its weight in order to move! Yes, Q <-1 areas are anchors, foundations, piles, brakes. Devices preventing movement. There, of course, there is a completely different dynamic and its own laws, but at least we see that C ( Q ) does not terminate with a feature when Q <-1, and that in the region Q = -1 it has a minimum, which means that at least a small neighborhood of this point C ( Q ) should behave like a parabola.
Thus, the outline of C ( Q ) looks something like this:
We decompose C ( Q ) into a Taylor series at the point Q = -1:
From property (8) it follows that a 0 = 0. Properties (4), (5) and in part (9) hint that a 1 is close to zero, or in any case that its contribution does not dominate the range 0 .. .3.
And then it turns out that the first nonzero term in the decomposition of C ( Q ) is parabolic, and that when Q in the area of units of C ( Q ), it behaves approximately like a quadratic function or slightly more rapidly increasing:
C ( Q ) ≈ a 2 * ( Q +1) 2/2 + O (( Q + 1 ) 3 )
And from [1] it follows that a 2 ≈ 1/2.
Finally, since at least up to Q ~ 100 the function C ( Q ) is still not exponential (property (6)), then we can set it equal to Q p with the exponent p somewhere in the region of 2 ... 4. Hardly anymore.
Conclusion: With a fixed mass, the cost of a C (Q) device increases not less than (Q + 1) 2/4, but not faster than about O (Q 4 ) [1]
Is it possible to look at the real C ( Q ) dependency in order to understand how correct this conclusion is? Difficult. Most of the mechanisms manufactured by man are different masses, but fixed Q in the region of one. We also need the opposite: about the same mass, but different Q. At first I was hoping for data on aircraft engines ... but the work [ 70 ] [ 80 ] on their pricing is very funny. Engine prices are classified there, and only prediction formulas and average errors are published.
Fortunately, help came from the passenger cars [ 150 ] . It is with them, at approximately the same mass, there are engines of various capacities. And although power is not yet transported cargo, but with some engineering effort it is roughly proportional to it. What allows us to estimate whether our formula is close to reality.
It looks like yes:
[Source: [ 150 ]]
Blue dots - real cars. In the first approximation, their price increases as the power density to a power of 2.3.
Red dots - the price calculated by the formula [1], based on the assumption that Q = 1 corresponds to the cheapest cars per kilogram in the range of $ 20-30 thousand. It can be seen that the formula really gives a good estimate of C ( Q ) below (where we were aiming).
When looking at the mass of these tasty points, a strong temptation arises: to lead C ( Q ) through them and, thus, to investigate the dependence directly. You can not do this. Mainly because the price of a car is determined not only by its traction characteristics. It is difficult to imagine a car for a hundred kilobaksov, in which there is no very good conditioner, the most comfortable seats and a “platinum ashtray with rhodium trim”. And all this costs money that has no relation to our C ( Q ). However, the lower “branch” of cars, passing almost exactly according to the calculated C ( Q ), looks interesting. I dare to admit that this is just a car without frills. Where "not checkered, but to go." But about $ 100K more expensive for a car is no longer there.
Article written for the site https://habr.com . When copying please refer to the source. The author of the article is Evgeny Bobukh .
So, we are able to estimate the cost of devices with high Q , at least in order of magnitude. Why was this necessary?
But why? Let's look at the first stage of the space carrier. Well, at least Proton-M [ 110 ] , for concreteness. It is almost a full-fledged vehicle, with engines, a control system, a decent safety margin and a dry weight of 31 tons. At the same time at the start of the rocket, it drags on its back not only the payload, but all the fuel, all the upper stages, and, of course, itself. In total - 683 tons. Plus starting overload, total (effectively) 1068 tons of load! From the point of view of the first stage, it works in a creepy mode Q = (1068/31) = 34.4! This is the equivalent of 50 tons of cargo piled on the car.
And we know that the cost of a high Q device is at least (Q + 1) 2/4 times higher than something similar with Q ≈ 1. For Proton, this amounts to ... 313 times.
That is, “Proton” should cost 300 times more than a similar device with Q = 1. And this figure does not depend much on progress and technology. For as soon as the "British scientists" invent a super-alloy that makes a rocket cheaper, then ground-based engines also become cheaper. Therefore, a chemical rocket, even a reusable one, will always be very expensive. Anyway.
Good. Let's say 300 times. But compared with what ? It would be nice to check our calculations with some objectively existing devices, to avoid gross errors?
Unfortunately, there are no thirty-rockets with Q = 1. But there are approximate analogues suitable for comparison:
It seems that we are not completely divorced from reality.
Let's sum up. Since rockets, even reusable ones, cost 2–3 orders of magnitude more expensive than trucks, any space settlement made of ground-based materials will also cost 100–1,000 times more than a land-based counterpart. This is a very high barrier to development.
Rockets, on the other hand, are expensive because they are very heavy and have to work with ungrounded about high Q. But why are rockets heavy? The answer (which is somewhat deeper than the Tsiolkovsky formula) will be considered in the second part.
Continued .
Update: several people tried to point out the ambiguities with regard to fuel when considering rockets. I thought about it. And I realized that the article does have some inaccuracy. Reviewed in the comments here .
At six, I fell into the hands of my grandfather’s handbook [50] on trucks of the mid-20th century. The sound quality, printed on smooth dense paper a rarity. The only thing left in general from the memory of his grandfather after the collapse of the country, wars and crossings.
The handbook contained many interesting TTH, so the word “carrying capacity” became familiar to me from early childhood. And when my father during a walk mentioned that any truck weighs as much as it takes itself, I remembered that. He remembered and, much later, became interested.
The father was right. For trucks of the 60s, this rule is carried out with rather surprising accuracy:
It is much more curious that this pattern is observed for vehicles completely different from trucks.
At first, for the sake of joke, I plotted cargo planes. And he was surprised. I began to add other vehicles. Riding, floating and flying, built in the centuries 19th, 20th, and 21st, working on thermal energy, nuclear, wind and even horse. Result? A weak power (value 1.125), if not just linear, dependence. On masses from one hundred kilogram to sixty thousand tons. With deviations, of course, wherever without them, up to 10 times sometimes, but on six orders of the masses, these are obviously trivialities.
Here it is, this dependence, pressing on to the diagonal of an immense empty field:
The graph indicated: cargo aircraft; transport helicopters; airships, modern and the beginning of the century; space launch vehicles (into low orbit); 60s Soviet trucks; modern mining trucks; modern trucks of Russia, USA, China and India; electric cars and scooters; trains (with rails); nuclear container ships; container ships and cargo ships (not tankers); sailing cargo ships of the 17th and 20th centuries; conveyor belts for the transfer of ore; nasovsky tractor for the removal of missiles at the start; and, finally, carts pulled by a horse.
If you enter the value of Q , defined as the mass of the transported cargo in relation to the dry weight of the vehicle, here’s how it looks for each of the groups:
In figures, the Q values are:
| Class of funds | Average Q | Standard deviation q |
| Cargo planes | 0.667091 | ± 0.206162 |
| Transport helicopters | 0.681605 | ± 0.225062 |
| Airships, modern and early century | 0.842673 | ± 0.374622 |
| Space launch vehicles (low orbit) | 0.372446 | ± 0.155810 |
| Soviet trucks of the 60s | 0.777435 | ± 0.232425 |
| Modern Mining Trucks | 1.349610 | ± 0.136840 |
| Modern trucks of Russia, USA, India, China | 1.293679 | ± 0.604313 |
| Electric cards and cargo scooters | 1.098433 | ± 0.343791 |
| Train (with rails) | 2.275989 | ± 0.205999 |
| Nuclear container ships | 1.035233 | ± NA |
| Sea container ships and cargo ships (not tankers) | 2.556004 | ± 0.378040 |
| Sailing cargo ships 17-20 centuries | 2.488461 | ± 0.671785 |
| Cargo conveyor belts | 3.703704 | ± NA |
| Nasovskiy tractor for the launch of rockets | 2.355919 | ± 0.525174 |
| Horse drawn carts | 1.203061 | ± 0.389183 |
As can be seen, Q, although not everywhere strictly single, but within the framework of each group, to a general value close to unity.
How to unit?
Update. Here in the comments a few people expressed bewilderment: what about the unit, when we have a three and 0.37 there? The general idea is this: if the carrying capacity and mass were absolutely unrelated, then, dividing the first into the second, we would get a spread of Q values from 10-5 to 10 5 on the available data. Obviously, plus or minus three times on the background of this is negligible, and it makes sense to talk about the “unit” and the strong connection of the parameters. The second question: what difference would it make no sense at all? The short answer is: the lower the spread of the Q values, the lower the probability that the linear dependence formed on the load-mass curve is just an accident. Depending on what probability of this randomness you consider negligible, you will receive different “acceptable” values of the deviation of Q from one. So (I counted), with a probability of 10 -11, this is ± 3 times. At 10 -9 this is ± 10 times. At 10 -8 ± 30. With 10 -5 ± 100 times. And so on. For me personally, the probability of an error of 1 to billion seems still acceptable, so I’m ready to call any Q from 0.1 to 10 “close to one”.
It seemed to me ... mysterious. Why does a wooden sailboat, an aluminum electric car, and a nuclear container ship with a capacity of one hundred thousand electric cars, all raise more or less their weight? What makes us create vehicles with quality Q ≈ 1 on masses that differ thousands of times? Is it a manifestation of the properties of world physics, the terrestrial economy, is this a limitation of human intelligence? How universal is this law, will it be implemented for civilizations from other stars? Global issues. It is unlikely that they will be able to resolve here and now. But consider and take a glimpse of how much it will turn out, can and should be. This is what we will do.
The world record [ 180 ] of lifting a barbell is a man of average weight exceeding 200 kg. Theoretically, this means that our body has a margin of safety for jerk loads at least up to Q = 2.5. However, this requires such exorbitant strengths and training that it is never used in daily activities. It is more expedient to pack sugar into bags of 50 kilograms, although this requires four times more loaders or a walker. Note that this situation is the result of biological evolution, in which the human intellect has (almost) not participated, and therefore has an “alibi” in it.
Physics and engineering in themselves high Q is also not prohibited. Vaughn, the hydrogen turbopump assembly for the shuttle's main engine, that little thing on the right in the picture, develops power of 54 megawatts [ 60 ] with a car mass of 350 kg:
[Image credit: [ 10 ]]
If, simplifying, to assess Q by power per kilogram of mass, then it is 100 times higher than that of a decent car. Only after all, this thing is almost like a rocket! It is cheaper to make 100 cars with Q = 1 and transport the goods by them, rather than trying to “harness” this unit in a wheeled cart.
Such considerations suggest: the reasons are economic. And not in the narrow sense of specific economies and countries (for our devices are generated by very different peoples and systems), but rather in the sense of “expediency of efforts”. The feasibility is universal enough to, apparently, extend to very different products and somewhere even to animals.
Article written for the site https://habr.com . When copying please refer to the source. The author of the article is Evgeny Bobukh .
Let's try to explore the limits of this expediency quantitatively. We pose the question: how does the cost of a device with a fixed mass depend on Q ? Here, for example, there is a dump truck weighing 10 tons, taking away 10 tons of cargo. We also want to make 10 tons, but carrying 20 tons ( Q = 2) or even 50 tons ( Q = 5). At the same level of technology development, the same volume of release. It is clear that greater loads will increase the requirements for materials (steel -> titanium?), And for engines (other temperatures, pressures), and for engineering (less tolerances for errors, more cunning designs). It is clear that with increasing Q everything will be more expensive. But how many times, compared with ten-ton?
This task, of course, is not trivial. Nevertheless, some estimates for it can be obtained from the most general considerations. What we are doing now.
We introduce the function C ( Q ). It describes the lowest possible cost of a device with an efficiency Q , expressed in the costs of a similar device of the same mass with Q = 1. What is known about it?
1. C (1) = 1, by definition.
2. C ( Q ) is a continuous function, at least until the difference in mass is measured by unit atoms. Intuitively, it seems smooth enough to have the first few derivatives. I think it can be assumed (as with most physical functions) that it is generally analytical.
3. C ( Q ) is a strictly increasing function. The higher the quality Q , the harder it is to make the structure, and the more expensive it is. Those. dC ( Q ) / dQ > 0 at least for Q > 0.
4. When Q is greater than about 3, C ( Q ) begins to grow faster than linearly. Why? Because we see that it is cheaper for people to make three trucks per ten tons with Q = 1 than one at thirty c Q = 3. To summarize, we write: k * C (1) < C ( k ) for k > ≈3 - other In other words, C ( k ) grows faster than k , with k > ≈ 3.
5. Similarly, since ten aircraft with Q = 0.1 are clearly uneconomical than one with Q = 1 (because they build the second, not the first), then for k > ≈3 we have: k * C (1 / k )> C (1), or C (1 / k )> 1 / k .
6. The cost of the pump from the Shuttle hints that at least up to Q ~ 100 the value of C ( Q ) does not increase as an exhibitor with a significant figure. Otherwise this THA would cost not millions of dollars, but some $ 10 20 commercial, and it is unlikely that we would have made it at all. Those. C (100) is somewhere 10 3 - 10 8 , but not 10 15 .
7. What is C (0)? This is the cost of a device that can still move itself, but is unable to take away any cargo. Obviously, such a "truck" cheaper full. But how many times? History shows that it is rather several times more than tens or hundreds. Some 15 years passed from the first aircraft, capable of moving only itself ( Q = 0), to transportation of goods by air. From the first gasoline vehicles to quite decent trucks with Q = 1.5 ([ 120 ] + [ 130 ]) there is not much more. If this development were an incredible complexity, it would hardly have ended so quickly. Consequently, the difficulty of manufacture and the cost of a vehicle with Q = 0 should not be quite radically different from it at Q = 1. Hence, we expect that C ( 0 ) is somewhere between 0.1 and 0.5.
8. Does this feature make sense with negative Q ? Completely! A truck with Q = -0.5 is one that will budge only if the tower crane is to “lift” half of its weight from it. And Q = -1 is a wagon developing zero thrust. Able to transport cargo only if you take it in tow. That is, generally without an engine. Obviously, its value, if not equal to zero, is very small. Therefore, we set C (-1) ≈ 0.
9. What is C (-2)? This is the cost of a device that needs to be pulled up with at least twice its weight in order to move! Yes, Q <-1 areas are anchors, foundations, piles, brakes. Devices preventing movement. There, of course, there is a completely different dynamic and its own laws, but at least we see that C ( Q ) does not terminate with a feature when Q <-1, and that in the region Q = -1 it has a minimum, which means that at least a small neighborhood of this point C ( Q ) should behave like a parabola.
Thus, the outline of C ( Q ) looks something like this:
We decompose C ( Q ) into a Taylor series at the point Q = -1:
From property (8) it follows that a 0 = 0. Properties (4), (5) and in part (9) hint that a 1 is close to zero, or in any case that its contribution does not dominate the range 0 .. .3.
And then it turns out that the first nonzero term in the decomposition of C ( Q ) is parabolic, and that when Q in the area of units of C ( Q ), it behaves approximately like a quadratic function or slightly more rapidly increasing:
C ( Q ) ≈ a 2 * ( Q +1) 2/2 + O (( Q + 1 ) 3 )
And from [1] it follows that a 2 ≈ 1/2.
Finally, since at least up to Q ~ 100 the function C ( Q ) is still not exponential (property (6)), then we can set it equal to Q p with the exponent p somewhere in the region of 2 ... 4. Hardly anymore.
Conclusion: With a fixed mass, the cost of a C (Q) device increases not less than (Q + 1) 2/4, but not faster than about O (Q 4 ) [1]
Is it possible to look at the real C ( Q ) dependency in order to understand how correct this conclusion is? Difficult. Most of the mechanisms manufactured by man are different masses, but fixed Q in the region of one. We also need the opposite: about the same mass, but different Q. At first I was hoping for data on aircraft engines ... but the work [ 70 ] [ 80 ] on their pricing is very funny. Engine prices are classified there, and only prediction formulas and average errors are published.
Fortunately, help came from the passenger cars [ 150 ] . It is with them, at approximately the same mass, there are engines of various capacities. And although power is not yet transported cargo, but with some engineering effort it is roughly proportional to it. What allows us to estimate whether our formula is close to reality.
It looks like yes:
[Source: [ 150 ]]
Blue dots - real cars. In the first approximation, their price increases as the power density to a power of 2.3.
Red dots - the price calculated by the formula [1], based on the assumption that Q = 1 corresponds to the cheapest cars per kilogram in the range of $ 20-30 thousand. It can be seen that the formula really gives a good estimate of C ( Q ) below (where we were aiming).
When looking at the mass of these tasty points, a strong temptation arises: to lead C ( Q ) through them and, thus, to investigate the dependence directly. You can not do this. Mainly because the price of a car is determined not only by its traction characteristics. It is difficult to imagine a car for a hundred kilobaksov, in which there is no very good conditioner, the most comfortable seats and a “platinum ashtray with rhodium trim”. And all this costs money that has no relation to our C ( Q ). However, the lower “branch” of cars, passing almost exactly according to the calculated C ( Q ), looks interesting. I dare to admit that this is just a car without frills. Where "not checkered, but to go." But about $ 100K more expensive for a car is no longer there.
Article written for the site https://habr.com . When copying please refer to the source. The author of the article is Evgeny Bobukh .
So, we are able to estimate the cost of devices with high Q , at least in order of magnitude. Why was this necessary?
But why? Let's look at the first stage of the space carrier. Well, at least Proton-M [ 110 ] , for concreteness. It is almost a full-fledged vehicle, with engines, a control system, a decent safety margin and a dry weight of 31 tons. At the same time at the start of the rocket, it drags on its back not only the payload, but all the fuel, all the upper stages, and, of course, itself. In total - 683 tons. Plus starting overload, total (effectively) 1068 tons of load! From the point of view of the first stage, it works in a creepy mode Q = (1068/31) = 34.4! This is the equivalent of 50 tons of cargo piled on the car.
And we know that the cost of a high Q device is at least (Q + 1) 2/4 times higher than something similar with Q ≈ 1. For Proton, this amounts to ... 313 times.
That is, “Proton” should cost 300 times more than a similar device with Q = 1. And this figure does not depend much on progress and technology. For as soon as the "British scientists" invent a super-alloy that makes a rocket cheaper, then ground-based engines also become cheaper. Therefore, a chemical rocket, even a reusable one, will always be very expensive. Anyway.
Good. Let's say 300 times. But compared with what ? It would be nice to check our calculations with some objectively existing devices, to avoid gross errors?
Unfortunately, there are no thirty-rockets with Q = 1. But there are approximate analogues suitable for comparison:
- The very first is a mining truck. Yes, not a rocket. But still, too, the heat engine, not quite a trivial engineering, and one of the cheapest means for the transport of goods. And if we are talking about space exploration, shouldn't a truck be a prototype for the business model of the space cab? So we will try, at least for the general estimation. Here is a 30-ton BelAZ-7540. The market price [ 140 ] is 3.7 million rubles, i.e. $ 62K. For the Proton, this is converted into the cost of the first stage in the region of $ 19 million. Wikipedia stands for [ 100 ] launch costs as $ 65 million. Pretty close, considering that this amount includes a lot more, except for the price of the very first step.
- An experimental rocket platform on rails is described in [ 160 ]. Mass under 10 tons, five steps, accelerates to 4 km / s. Price 750 kilobaksov. Judging by the published pictures and parameters, this device works somewhere at Q = 10. Not one, but still not 34. If we start from these numbers, the first step of Proton should cost about $ 23 million.
- Generally, when I try to imagine a rocket with Q = 1, in front of my mind there is such a hefty disc with a small hollow filled with gunpowder. Gunpowder burns out and pushes the pig forward. Quite a bit, so much you will not overclock. I spent two days redeeming this picture until I realized what it reminds me of. This is ... a pneumatic hammer! Where gas expands and pushes the disc. Ultimate bastardization of the idea of a jet engine, still retaining some kind of kinship. Well, we are looking for. Yeah, here is [ 170 ] the Stanko M212 air hammer. The weight of the blank is 2 tons, the whole structure is 58.3 tons. The Q system, therefore, is a modest 0.034. Sold for 40 thousand euros. If you extrapolate the value of this joke to Q = 34.4 according to the formula [1], then you get ... 47 million euros. Or 24 million in a proportion of 30 tons.
It seems that we are not completely divorced from reality.
Let's sum up. Since rockets, even reusable ones, cost 2–3 orders of magnitude more expensive than trucks, any space settlement made of ground-based materials will also cost 100–1,000 times more than a land-based counterpart. This is a very high barrier to development.
Rockets, on the other hand, are expensive because they are very heavy and have to work with ungrounded about high Q. But why are rockets heavy? The answer (which is somewhat deeper than the Tsiolkovsky formula) will be considered in the second part.
Continued .
Update: several people tried to point out the ambiguities with regard to fuel when considering rockets. I thought about it. And I realized that the article does have some inaccuracy. Reviewed in the comments here .
About data
Those who wish to independently analyze the data can find them (together with the sources) here in CSV format. (By the way, what are the best options on Habré, apart from uploading a file to a third-party hosting?) When working with them, consider the following.
1. Only freight vehicles were considered. Tesla passenger with a trunk capacity of 70 kg - not a truck. Cargo vans are also (almost) excluded - their cargo protection means introduce significant distortions.
2. It was a pleasure to work with Soviet trucks. Here is the weight, here is the permissible load, everything is clear. With modern, especially American - trouble. Few people publish their maximum payload. Instead, there are laws that allow a particular load for each type of business and roads. Plus the addition to the truck: "meets the standard number such and such, § such and such." A complete, devastating victory for the bureaucracy over physical reality. In cases where the capacity is still published, it is very often takenfrom the baldies for marketing reasons. You build a graph - and there is an obvious “Christmas tree”, sorry, product line. For this reason, alas, the data of modern trucks are more noisy (± 0.60) than the old ones (± 0.23). The situation was partly saved by China, Russia and India: their truck performance characteristics are still readily available.
3. The lightest electric cars and motorcycles often weigh 30–70 kg, carrying 200–400 kg of cargo. At first glance, it looks like Q in the region of the ten. But I thought and realized something. All these vehicles do not drive without a person. Moreover, a person in them also performs a structural-power and balancing role. It is in them - not the payload, without which you can and go, but an integral part. Therefore, the mass of them must be considered with the driver (+80 kg). And this is 100-150 kg. A similar amendment was made to the characteristics of horse-drawn carriages, with a horse mass adopted for 500 kg.
4. I counted the mass of the train with a mass of rails lying on it. For, unlike other vehicles, the train can move only along the rails, and they weigh significantly and hold the transport load. Like a caterpillar in a bulldozer. Only not carried with them. At the same time, there are a lot of intricate specifications on the rails, wagons and electric locomotives, in which I am not the fact that I understood correctly.
5. There is one atomic cargo icebreaker in the world: the Russian Northern Sea Route [ 600 ] , so there is only one point in this group.
6. With cargo shipping vessels is not all that simple either. For most of them, neither the maximum mass of the load nor the empty mass of the structure is published. For the second, however, there is still a term: LWT - Light Weight Tonnage, and its values are occasionally found on the ship auctions (such as [ 610 ] and [ 620 ]). By a long manual subtraction of these sites I hid the numbers on the LWT, but what about the cargo being transported? Instead, the DWT (Deadweight Tonnage) value is usually used, which is the total maximum weight of the ship. Which includes not only the weight of the load, but also the design, fuel, auxiliary liquids, and even some trifles. Rummaging through different sites, I found that in practice, the maximum load weight is usually 85% of (DWT - LWT), with a range of 65-90%. This had to be satisfied. So the load capacity was considered as G = 0.85 * ( DWT - LWT ). That, perhaps, brought an error to 30%.
7. For space carriers, I relied mainly on [ 110 ]. There is a breakdown of many rockets by steps and their masses. Unfortunately, sometimes with the notation that the mass of the step includes residues of unburned fuel, which are not really known. For this reason, the Q value for rockets may have been underestimated by 10 percent.
8. Were there vehicles that didn't fit into this picture? Of course. First, non-freight . Tanks. Passenger cars, cruise ships. They have Q significantly less than one. Everything is clear with the latter: their goal is not to take away the load, but people, and even with comfort. The weight of comfort means it spoils the picture. Secondly, tankers do not fit here, in which Q often reaches 3-8 units. But tankers have a special and very “convenient” load, allowing uniform load distribution across the hull and holding it not so much by its own strength as by external sea pressure. On land, an analogue of this would be a truck with “crutches”, but there are no such, there is nothing to compare with, and therefore I did not indicate tankers on the chart (although I mention here).
Those who wish to independently analyze the data can find them (together with the sources) here in CSV format. (By the way, what are the best options on Habré, apart from uploading a file to a third-party hosting?) When working with them, consider the following.
1. Only freight vehicles were considered. Tesla passenger with a trunk capacity of 70 kg - not a truck. Cargo vans are also (almost) excluded - their cargo protection means introduce significant distortions.
2. It was a pleasure to work with Soviet trucks. Here is the weight, here is the permissible load, everything is clear. With modern, especially American - trouble. Few people publish their maximum payload. Instead, there are laws that allow a particular load for each type of business and roads. Plus the addition to the truck: "meets the standard number such and such, § such and such." A complete, devastating victory for the bureaucracy over physical reality. In cases where the capacity is still published, it is very often taken
3. The lightest electric cars and motorcycles often weigh 30–70 kg, carrying 200–400 kg of cargo. At first glance, it looks like Q in the region of the ten. But I thought and realized something. All these vehicles do not drive without a person. Moreover, a person in them also performs a structural-power and balancing role. It is in them - not the payload, without which you can and go, but an integral part. Therefore, the mass of them must be considered with the driver (+80 kg). And this is 100-150 kg. A similar amendment was made to the characteristics of horse-drawn carriages, with a horse mass adopted for 500 kg.
4. I counted the mass of the train with a mass of rails lying on it. For, unlike other vehicles, the train can move only along the rails, and they weigh significantly and hold the transport load. Like a caterpillar in a bulldozer. Only not carried with them. At the same time, there are a lot of intricate specifications on the rails, wagons and electric locomotives, in which I am not the fact that I understood correctly.
5. There is one atomic cargo icebreaker in the world: the Russian Northern Sea Route [ 600 ] , so there is only one point in this group.
6. With cargo shipping vessels is not all that simple either. For most of them, neither the maximum mass of the load nor the empty mass of the structure is published. For the second, however, there is still a term: LWT - Light Weight Tonnage, and its values are occasionally found on the ship auctions (such as [ 610 ] and [ 620 ]). By a long manual subtraction of these sites I hid the numbers on the LWT, but what about the cargo being transported? Instead, the DWT (Deadweight Tonnage) value is usually used, which is the total maximum weight of the ship. Which includes not only the weight of the load, but also the design, fuel, auxiliary liquids, and even some trifles. Rummaging through different sites, I found that in practice, the maximum load weight is usually 85% of (DWT - LWT), with a range of 65-90%. This had to be satisfied. So the load capacity was considered as G = 0.85 * ( DWT - LWT ). That, perhaps, brought an error to 30%.
7. For space carriers, I relied mainly on [ 110 ]. There is a breakdown of many rockets by steps and their masses. Unfortunately, sometimes with the notation that the mass of the step includes residues of unburned fuel, which are not really known. For this reason, the Q value for rockets may have been underestimated by 10 percent.
8. Were there vehicles that didn't fit into this picture? Of course. First, non-freight . Tanks. Passenger cars, cruise ships. They have Q significantly less than one. Everything is clear with the latter: their goal is not to take away the load, but people, and even with comfort. The weight of comfort means it spoils the picture. Secondly, tankers do not fit here, in which Q often reaches 3-8 units. But tankers have a special and very “convenient” load, allowing uniform load distribution across the hull and holding it not so much by its own strength as by external sea pressure. On land, an analogue of this would be a truck with “crutches”, but there are no such, there is nothing to compare with, and therefore I did not indicate tankers on the chart (although I mention here).
Links
[10] SSME scheme: http://www.jht.com/icuf/Space-Science/LiquidRockets/PT-04-125.htm
[50] A. P. Runova, A. A. Wagner. TRUCKS. CATALOG. Printing house TsINTIMASH, 1960
[60] Power-to-weight ratios: https://en.wikipedia.org/wiki/Power-to-weight_ratio#Heat_engines_and_heat_pumps
[70] Development and Production Cost Estimating Relationships for Aircraft Turbine Engines by John Birkler, Jeffrey B. Garfinkle, Kenneth E. Marks, https://www.rand.org/content/dam/rand/pubs/notes/2005/N1882.pdf
[80] Military Jet Engine Acquisition (Technology Basics and Cost-Estimating Methodology), Obaid Younossi, Mark V. Arena, Richard M. Moore
Mark Lorell, Joanna Mason, John C. Graser, https://www.rand.org/content/dam/rand/pubs/monograph_reports/2005/MR1596.pdf
[100] Стоимость пуска Протона-М: https://en.wikipedia.org/wiki/Proton-M
[110] Данные по ступеням «Протона»: http://www.spacelaunchreport.com/proton.html
[120] Ford TT curb weight: https://www.conceptcarz.com/s13963/ford-model-tt-type-c.aspx
[130] Ford TT load capacity: https://en.wikipedia.org/wiki/Ford_Model_TT
[140] Цена на Белаз-7540: http://www.raise.ru/market/mining/haul-trucks/id-market_43697/
[150] Подборка ста с лишним автомобилей с данными по мощности, весу, цене, и удельным параметрам: https://oppositelock.kinja.com/whats-the-best-power-weight-ratio-per-dollar-1699756090 (автор проделал нетривиальную работу, но почему-то гадает, нужны ли эти данные. Да ещё как нужны!)
[160] Ракетные сани: http://www.impactlab.net/2006/01/15/the-fastest-rocket-sled-on-earth/
[170] Пневматический молот https://www.machineseeker.com/Air-steam-Forging-Hammer-double-action-Stanko-M212-RAM-2000kg/i-3521173
[180] Мировые рекорды в тяжёлой атлетике: https://ru.wikipedia.org/wiki/%D0%9C%D0%B8%D1%80%D0%BE%D0%B2%D1%8B%D0%B5_%D1%80%D0%B5%D0%BA%D0%BE%D1%80%D0%B4%D1%8B_%D0%B2_%D1%82%D1%8F%D0%B6%D1%91%D0%BB%D0%BE%D0%B9_%D0%B0%D1%82%D0%BB%D0%B5%D1%82%D0%B8%D0%BA%D0%B5
[10] SSME scheme: http://www.jht.com/icuf/Space-Science/LiquidRockets/PT-04-125.htm
[50] A. P. Runova, A. A. Wagner. TRUCKS. CATALOG. Printing house TsINTIMASH, 1960
[60] Power-to-weight ratios: https://en.wikipedia.org/wiki/Power-to-weight_ratio#Heat_engines_and_heat_pumps
[70] Development and Production Cost Estimating Relationships for Aircraft Turbine Engines by John Birkler, Jeffrey B. Garfinkle, Kenneth E. Marks, https://www.rand.org/content/dam/rand/pubs/notes/2005/N1882.pdf
[80] Military Jet Engine Acquisition (Technology Basics and Cost-Estimating Methodology), Obaid Younossi, Mark V. Arena, Richard M. Moore
Mark Lorell, Joanna Mason, John C. Graser, https://www.rand.org/content/dam/rand/pubs/monograph_reports/2005/MR1596.pdf
[100] Стоимость пуска Протона-М: https://en.wikipedia.org/wiki/Proton-M
[110] Данные по ступеням «Протона»: http://www.spacelaunchreport.com/proton.html
[120] Ford TT curb weight: https://www.conceptcarz.com/s13963/ford-model-tt-type-c.aspx
[130] Ford TT load capacity: https://en.wikipedia.org/wiki/Ford_Model_TT
[140] Цена на Белаз-7540: http://www.raise.ru/market/mining/haul-trucks/id-market_43697/
[150] Подборка ста с лишним автомобилей с данными по мощности, весу, цене, и удельным параметрам: https://oppositelock.kinja.com/whats-the-best-power-weight-ratio-per-dollar-1699756090 (автор проделал нетривиальную работу, но почему-то гадает, нужны ли эти данные. Да ещё как нужны!)
[160] Ракетные сани: http://www.impactlab.net/2006/01/15/the-fastest-rocket-sled-on-earth/
[170] Пневматический молот https://www.machineseeker.com/Air-steam-Forging-Hammer-double-action-Stanko-M212-RAM-2000kg/i-3521173
[180] Мировые рекорды в тяжёлой атлетике: https://ru.wikipedia.org/wiki/%D0%9C%D0%B8%D1%80%D0%BE%D0%B2%D1%8B%D0%B5_%D1%80%D0%B5%D0%BA%D0%BE%D1%80%D0%B4%D1%8B_%D0%B2_%D1%82%D1%8F%D0%B6%D1%91%D0%BB%D0%BE%D0%B9_%D0%B0%D1%82%D0%BB%D0%B5%D1%82%D0%B8%D0%BA%D0%B5
[600] Севморпуть, советское ледокольно-транспортное судно (лихтеровоз) с атомной силовой установкой: https://ru.wikipedia.org/wiki/Севморпуть_(лихтеровоз)
[610] Доска объявлений по продаже кораблей: http://www.seaboats.net
[620] Доска объявлений по продаже кораблей: http://www.vedshipping.com
Source: https://habr.com/ru/post/437910/