First I'd like to start by saying I'm not an engineer, so this post regarding the thermal expansion issues of the Hyperloop brought up by Drang are not meant to be a criticism of his analysis, but more a platform to ask and raise a number of question I personally have regarding the Hyperloop, that I don't feel Drang addresses, or for that fact have been fully addressed by Musk.
I will be using Drang's article as a springboard for my thoughts and comments.
While I agree that thermal expansion does pose a problem, one thing that I've not seen addressed by his article and anywhere else is the amount by which the total "POTENTIAL" expansion of the loop will be negated by the following points.
1) Type of steel. Different types of steel expand differently. I ploughed around the net and the library and found some references for common steel with a value as low as 5.5 for its linear temperature expansion coefficient, also some steels that were as high as 9.6.
1b) Also the rate of temperature change in steel will also dictate the rate of expansion. So, does that not mean that the mean temperature coefficient can change dependant on how fast the steel is heating up and or cooling down?
2) Overall temperature changes across a 300 mile length of pipe. This means different portions of the pipe will be cooling and heating at different rates. So while some areas will expand, some will in fact be contracting. Hint: sections tunnelled into the ground will generally be contracting. See more thoughts about tunnels in point 5.
3) The environment inside the tube. Would the pressurization and air flow inside the tube not affect the thermal expansion of the steel as well? Especially if the air is moving it would wick heat out of the steel reducing the thermal expansion.
4) All 11 of those curved portions of track seen in the image on page 44 of the pdf. (Ya, I know it's a proposed route. But having curves makes a difference over assuming it's one straight pipe as those curves will act in a similar fashion to the expansion loops Drang talks about in his post. Is there anything that one could read to get a better idea as to how much bend you need in a tube to compensate for a set amount of thermal expansion? I found nothing that was useful in that regard.
5) Tunnels. The potential to have some sections of the loop hard anchored, especially in locations where the loop needs to tunnel through something. Note: There is only minimal talk about tunnelling but apparently he has looked at something that makes him think tunnelling will be required as there is a $600-700 million dollar price tag added in for tunnelling operations. Also: is there a good reference out there regarding the cooling factor tunnelling underground has on things like steel tubes? I've been in a lot of tunnels and mines and even at the half a mile mark it can get rather cold down under the earth, especially in a straight tube that has a good amount of air flow.
3) Slip joints. Telescoping end points similar to the telescoping air plane ramp are noted in the pdf. This can be done much easier along the ground, and with the capsules already slowed right down even a 500foot long telescoping tube is feasible. Also if in the last couple miles the overall speed of the capsule is reduced enough multiple slip joins could be put in place to compensate for some of that expansion.
Anyway I could be completely off base here, but it seems that if as Drang states a 3/4" of expansion over 100' can add up to be a lot, a lot of the points I make above could add up to being a lot of reduction on his initial 1030' estimate...or they might make it even worse, but in either case, making a case for or against the Hyperloop based on 300miles of tube and the difference in temperature of Fresno seems, a bit off.
That stated, I get the impression from reading the Hyperloop pdf, that Musk has more information available to him that was not added into the initial brief, whether for brevity, for simplicity, or to hide pain points I do not know.
I will be using Drang's article as a springboard for my thoughts and comments.
While I agree that thermal expansion does pose a problem, one thing that I've not seen addressed by his article and anywhere else is the amount by which the total "POTENTIAL" expansion of the loop will be negated by the following points.
1) Type of steel. Different types of steel expand differently. I ploughed around the net and the library and found some references for common steel with a value as low as 5.5 for its linear temperature expansion coefficient, also some steels that were as high as 9.6. 1b) Also the rate of temperature change in steel will also dictate the rate of expansion. So, does that not mean that the mean temperature coefficient can change dependant on how fast the steel is heating up and or cooling down?
2) Overall temperature changes across a 300 mile length of pipe. This means different portions of the pipe will be cooling and heating at different rates. So while some areas will expand, some will in fact be contracting. Hint: sections tunnelled into the ground will generally be contracting. See more thoughts about tunnels in point 5.
3) The environment inside the tube. Would the pressurization and air flow inside the tube not affect the thermal expansion of the steel as well? Especially if the air is moving it would wick heat out of the steel reducing the thermal expansion.
4) All 11 of those curved portions of track seen in the image on page 44 of the pdf. (Ya, I know it's a proposed route. But having curves makes a difference over assuming it's one straight pipe as those curves will act in a similar fashion to the expansion loops Drang talks about in his post. Is there anything that one could read to get a better idea as to how much bend you need in a tube to compensate for a set amount of thermal expansion? I found nothing that was useful in that regard.
5) Tunnels. The potential to have some sections of the loop hard anchored, especially in locations where the loop needs to tunnel through something. Note: There is only minimal talk about tunnelling but apparently he has looked at something that makes him think tunnelling will be required as there is a $600-700 million dollar price tag added in for tunnelling operations. Also: is there a good reference out there regarding the cooling factor tunnelling underground has on things like steel tubes? I've been in a lot of tunnels and mines and even at the half a mile mark it can get rather cold down under the earth, especially in a straight tube that has a good amount of air flow.
3) Slip joints. Telescoping end points similar to the telescoping air plane ramp are noted in the pdf. This can be done much easier along the ground, and with the capsules already slowed right down even a 500foot long telescoping tube is feasible. Also if in the last couple miles the overall speed of the capsule is reduced enough multiple slip joins could be put in place to compensate for some of that expansion.
Anyway I could be completely off base here, but it seems that if as Drang states a 3/4" of expansion over 100' can add up to be a lot, a lot of the points I make above could add up to being a lot of reduction on his initial 1030' estimate...or they might make it even worse, but in either case, making a case for or against the Hyperloop based on 300miles of tube and the difference in temperature of Fresno seems, a bit off.
That stated, I get the impression from reading the Hyperloop pdf, that Musk has more information available to him that was not added into the initial brief, whether for brevity, for simplicity, or to hide pain points I do not know.