3 ms·

Ahh, thanks for the tip, and the wonderful discussion! I agree, that would not work. I was suggesting that motorized rollers move the track longitudinally inst

Ahh, thanks for the tip, and the wonderful discussion! I agree, that would not work. I was suggesting that motorized rollers move the track longitudinally instead of sideways. Essentially they would take up the slack and actively push it to the end stations, counteracting the friction from the passive rollers. You could use thermometers and position sensors to model the stress on the tube.

sillysaurus3 12y ago
Whoops, I see. Sorry for the confusion! That's an interesting idea, but are you sure that thermal expansion imparts enough force against 175 miles of steel in order to push it all the way to the station? 175 miles of steel would be incredibly heavy. It seems like the heating/cooling might even cause the steel to weaken enough such that, rather than rolling the tube towards the station, it would start to scrunch like an accordion. But I wish a structural physicist would step in with some calculations to prove whether or not 175 miles of steel on rollers could be pushed by thermal expansion without compromising hyperloop's structural stability. Maybe we could ask /r/askscience? EDIT: After re-reading your comment, I think you're saying the rollers would actually provide the force necessary to move 175 miles of steel, rather than letting the expansion passively push it. But those rollers would have to grip onto something in order to do that. They wouldn't be rollers so much as tank treads. Hmm... Do you think that might work? Could 175 electric motors working in unison provide enough force to tank treads that bite into the concrete pillar below, and into the steel tube above, in order to successfully shift 175 miles of steel? And the system has to have temperature sensors every mile, and those sensors must not ever report incorrect readings or else the whole tube breaks. And those motors must never break down or run out of power... I'm sounding pessimistic, but honestly I have no idea whether that would work. EDIT 2: Ah, I think I've figured out why it can't work. It's not a straight tube. It bends all along the route. http://i.imgur.com/3TavjCY.png http://i.imgur.com/3TavjCY.png So motorized rollers would actually need to bend the tube in order to successfully transmit the thermal expansion. In other words, when a piece of steel tubing is initially created, it's bent with a certain curvature. But if rollers are to transmit the expansion all the way to the station, the exact location of where the steel is bent needs to be dynamically defined at runtime, rather than statically assigned at compile time. Did I phrase that very clearly? It would help to be in-person, or maybe I could draw a picture if needed. It doesn't seem like rollers could dynamically bend the steel all along the 175 mile track in order to carry the expansion.
- schiffern 12y ago
  >are you sure that thermal expansion imparts enough force against 175 miles of steel in order to push it all the way to the station? Nope. That's why you may need to push it! :) Assume the rollers have the Crr of a passenger train wheel (0.0020). If each section weighs 193 tonnes (23 mm thick by 2.23m diameter by 100' by 8 g/cm³), then each roller will provide ~400 N of friction. Over 175 miles (worst case) that works out to 3.56 meganewtons of resistance to motion. For a thin-walled cylinder, buckling stress is modeled using the large deflection approximation[1] as: σ_x = 0.238 Et/r Where σ_x is the bucling pressure, E is the material's Young's modulus, t is the wall thickness, and r is the radius. Plugging in 190 GPa, 20 mm, and 1.125 m yields… 58 meganewtons, or about 16 times as strong as the predicted frictional force I guess they may not need active control after all! But what about curves? Won't it result in a lot of sideways force? Needs more calculations… [1] The weaker of the two. http://www.dtic.mil/dtic/tr/fulltext/u2/a801283.pdf http://www.dtic.mil/dtic/tr/fulltext/u2/a801283.pdf
  - sillysaurus3 12y ago
    Sweet calculations! Thanks! Check out my above comment again, since I was apparently writing out an "EDIT 2" while you were doing these awesome calculations. Basically, what do you think about the fact that it's not a long, straight tube? The rollers would need to dynamically bend the steel tube in order to carry the expansion all the way to the station, wouldn't they? Is that possible? Even if there aren't any rollers, the tube still needs to re-bend itself somehow. But how? That would mean steel curves near the endpoints would move a whopping 150 meters in total. So it seems like part of the tube manufactured as a curve in summer would need to become a straight length of pipe by winter.
    - schiffern 12y ago
      Heh, I love that we thought of two different but related problems simultaneously! First yours, since it's much cooler. The minimum curve radius is 3.67 km, or a length difference of 18 mm between the left and right side over the length of one pylon. Assuming that all sections start as straight tubes, how much sideways force would that apply on the pylon? For that we need to calculate the "flexural stiffness"[1], which for a hollow cylinder is given as: EI = E pi/4 (D⁴ - d⁴) Where E is Young's modulus, and D and d are the outer and inner diameter. Therefore the bending moment[2] M is: M = EIκ = E pi/4 (D⁴ - d⁴)κ Where κ is the curvature, equal to 1/r. Finally, muddling through the equations on the bending moment article (and treating the tube as a 200' beam with a load in the center) yields: f = M / (100')²/(200') [not sure about this one] A whopping 300 tonnes•f of lateral force on the pylons! Probably doable, but it means if your tubes are constructed straight your pylons are going to be buttressed at a ~60° angle. Also, note that this only applies to the slip distance (~150m, or three pylons), since the tube sections well within the curve will never move enough to be in a non-curved section of track, so they can be built curved from the beginning. Also you can vary the curvature smoothly[3], which can substantially reduce the forces involved. For example, if you eased into the curve over 30 pylons and it only moved by 3, the sideways force would be reduced by 10x (since the curvature is always "about right"). Further calculations here are left as an exercise to the interested reader. :D As for my own objection… Even on the sharpest turns successive pylons will only vary from straight line by 0.15°, so the lateral forces caused by expansion and contraction shouldn't exceed 9 tonnes force. Piddly by comparison. [1] http://www.explorelifeonearth.org/cursos/CB-18%20simple%20structs%3B%20EI,%20Euler.pdf http://www.explorelifeonearth.org/cursos/CB-18%20simple%20st... [2] https://en.wikipedia.org/wiki/Bending_moment#Example https://en.wikipedia.org/wiki/Bending_moment#Example [3] i.e. the curve doesn't start suddenly, but gradually; this is how actual tracks/roads are laid out. https://en.wikipedia.org/wiki/Euler_spiral https://en.wikipedia.org/wiki/Euler_spiral TL;DR as long as you ease into the curves (which is good for comfort anyway), it looks totally doable even without motorized rollers.

sillysaurus3 12y ago

Whoops, I see. Sorry for the confusion! That's an interesting idea, but are you sure that thermal expansion imparts enough force against 175 miles of steel in order to push it all the way to the station? 175 miles of steel would be incredibly heavy. It seems like the heating/cooling might even cause the steel to weaken enough such that, rather than rolling the tube towards the station, it would start to scrunch like an accordion. But I wish a structural physicist would step in with some calculations to prove whether or not 175 miles of steel on rollers could be pushed by thermal expansion without compromising hyperloop's structural stability. Maybe we could ask /r/askscience? EDIT: After re-reading your comment, I think you're saying the rollers would actually provide the force necessary to move 175 miles of steel, rather than letting the expansion passively push it. But those rollers would have to grip onto something in order to do that. They wouldn't be rollers so much as tank treads. Hmm... Do you think that might work? Could 175 electric motors working in unison provide enough force to tank treads that bite into the concrete pillar below, and into the steel tube above, in order to successfully shift 175 miles of steel? And the system has to have temperature sensors every mile, and those sensors must not ever report incorrect readings or else the whole tube breaks. And those motors must never break down or run out of power... I'm sounding pessimistic, but honestly I have no idea whether that would work. EDIT 2: Ah, I think I've figured out why it can't work. It's not a straight tube. It bends all along the route. http://i.imgur.com/3TavjCY.png http://i.imgur.com/3TavjCY.png So motorized rollers would actually need to bend the tube in order to successfully transmit the thermal expansion. In other words, when a piece of steel tubing is initially created, it's bent with a certain curvature. But if rollers are to transmit the expansion all the way to the station, the exact location of where the steel is bent needs to be dynamically defined at runtime, rather than statically assigned at compile time. Did I phrase that very clearly? It would help to be in-person, or maybe I could draw a picture if needed. It doesn't seem like rollers could dynamically bend the steel all along the 175 mile track in order to carry the expansion.

schiffern 12y ago
>are you sure that thermal expansion imparts enough force against 175 miles of steel in order to push it all the way to the station? Nope. That's why you may need to push it! :) Assume the rollers have the Crr of a passenger train wheel (0.0020). If each section weighs 193 tonnes (23 mm thick by 2.23m diameter by 100' by 8 g/cm³), then each roller will provide ~400 N of friction. Over 175 miles (worst case) that works out to 3.56 meganewtons of resistance to motion. For a thin-walled cylinder, buckling stress is modeled using the large deflection approximation[1] as: σ_x = 0.238 Et/r Where σ_x is the bucling pressure, E is the material's Young's modulus, t is the wall thickness, and r is the radius. Plugging in 190 GPa, 20 mm, and 1.125 m yields… 58 meganewtons, or about 16 times as strong as the predicted frictional force I guess they may not need active control after all! But what about curves? Won't it result in a lot of sideways force? Needs more calculations… [1] The weaker of the two. http://www.dtic.mil/dtic/tr/fulltext/u2/a801283.pdf http://www.dtic.mil/dtic/tr/fulltext/u2/a801283.pdf
- sillysaurus3 12y ago
  Sweet calculations! Thanks! Check out my above comment again, since I was apparently writing out an "EDIT 2" while you were doing these awesome calculations. Basically, what do you think about the fact that it's not a long, straight tube? The rollers would need to dynamically bend the steel tube in order to carry the expansion all the way to the station, wouldn't they? Is that possible? Even if there aren't any rollers, the tube still needs to re-bend itself somehow. But how? That would mean steel curves near the endpoints would move a whopping 150 meters in total. So it seems like part of the tube manufactured as a curve in summer would need to become a straight length of pipe by winter.
  - schiffern 12y ago
    Heh, I love that we thought of two different but related problems simultaneously! First yours, since it's much cooler. The minimum curve radius is 3.67 km, or a length difference of 18 mm between the left and right side over the length of one pylon. Assuming that all sections start as straight tubes, how much sideways force would that apply on the pylon? For that we need to calculate the "flexural stiffness"[1], which for a hollow cylinder is given as: EI = E pi/4 (D⁴ - d⁴) Where E is Young's modulus, and D and d are the outer and inner diameter. Therefore the bending moment[2] M is: M = EIκ = E pi/4 (D⁴ - d⁴)κ Where κ is the curvature, equal to 1/r. Finally, muddling through the equations on the bending moment article (and treating the tube as a 200' beam with a load in the center) yields: f = M / (100')²/(200') [not sure about this one] A whopping 300 tonnes•f of lateral force on the pylons! Probably doable, but it means if your tubes are constructed straight your pylons are going to be buttressed at a ~60° angle. Also, note that this only applies to the slip distance (~150m, or three pylons), since the tube sections well within the curve will never move enough to be in a non-curved section of track, so they can be built curved from the beginning. Also you can vary the curvature smoothly[3], which can substantially reduce the forces involved. For example, if you eased into the curve over 30 pylons and it only moved by 3, the sideways force would be reduced by 10x (since the curvature is always "about right"). Further calculations here are left as an exercise to the interested reader. :D As for my own objection… Even on the sharpest turns successive pylons will only vary from straight line by 0.15°, so the lateral forces caused by expansion and contraction shouldn't exceed 9 tonnes force. Piddly by comparison. [1] http://www.explorelifeonearth.org/cursos/CB-18%20simple%20structs%3B%20EI,%20Euler.pdf http://www.explorelifeonearth.org/cursos/CB-18%20simple%20st... [2] https://en.wikipedia.org/wiki/Bending_moment#Example https://en.wikipedia.org/wiki/Bending_moment#Example [3] i.e. the curve doesn't start suddenly, but gradually; this is how actual tracks/roads are laid out. https://en.wikipedia.org/wiki/Euler_spiral https://en.wikipedia.org/wiki/Euler_spiral TL;DR as long as you ease into the curves (which is good for comfort anyway), it looks totally doable even without motorized rollers.