Object moving thru a fluid medium

That looks like a very interesting title but I'm not sure I'm going to have the time to read it. I did download it though. While I was at work today I did a little simple layman's calculation. If I wanted to move 100,000 cubic feet down a track, what would be the shape with the least surface area? I figured the more it was shaped like an arrow, long and thin, the less energy it would take to move. And so I started with a shape that was 1'x1'x100,000'. But then I ended up with a surface area just over 400,000 square feet. And so I moved to the common way of doing things which is a boxcar with an approximate dimension of 10x10 in cross section. With a 10x10 cross section I ended up with about 40,000 square feet in total surface area. However, when I moved up to a 20'x30' cross section, I was able to put that 100,000 cubic feet into 17,000 square feet of surface area and so I cut my surface area by more than half over standard. The best that I could feasibly have done, I am guessing, would have been a perfect cube with about 12,000 square feet of surface area. However, I would have been up against a wall of diminishing returns the closer that I got to that shape and besides, I'm close enough as it is and it doesn't really need to be any size or shape other than what I already have it at. From what I have read about high speed rail, and I could certainly by wrong about this, but what I read was that above a certain speed the greatest drag is caused by skin friction. From my understanding the atmosphere only has to conform to the shape of the vessel at the very front end of the vessel where the front end is piercing the atmosphere. From that point, the air has already been moved out of the way and so for the rest of the vessel only skin friction is coming into play. I could be wrong about this and there could very well be other forces that I'm not considering.

Also, you make mention of the shape of the object as being necessary to calculate the surface drag. As it is for a train, the profile will most likely be that of a rectangle with rounded corners. Perhaps slightly bulging sides and with a pronounced bulge on top. That said, the exterior of the vehicle is within someone else's purview. I don't care how its designed, I just care about what I can do with it and at what cost.

Thank you for trying to answer my question though.

 

That said, I already know what the answer to my question is. I'm only here to confirm the answer. It takes less energy to move a given volume on a vehicle with a greater cross section as long as that cross section is on a vehicle that is very long in proportion to its cross section. That may not sound science-y but I'm pretty sure its the truth. As far as the cost to build such a thing? Astronomical. It would be the most expensive single thing every built by mankind. By an order of magnitude. Its not a cheap thing to build. Its not a cheap thing to run either. However, it can also fit about 150 passengers per car in very comfortable third class. If it was all third class, it could fit over 2000 passengers in a single load. I've got a whole book on it and its not all third class. Like to get it published. There are just a few things I need to get confirmed before I do that and this would be one of those things. And if there is something I am getting wrong about what I am saying, please do not let me make a fool out of myself anyplace other than here.

OK......lets try it this way. Lets assume that the shape of the two trains, both the large and the small were exactly the same and it was only the scale we were talking about. Same cross section and with a length of at least....oh say.........10 times its width. Which would cost less energy per unit volume to move any given distance? Thats really the only question that I'm asking. I'm not asking you come up with any specific numbers. I just want to know which costs less energy to move per unit volume. The large or the small.

 

You're making several fundamental errors. The first is that all the surface area has the same drag, which isn't true. The additional drag of an additional square foot of surface area lessens the area is added further downstream, in a logarithmic manner. Here's a plot of the skin friction coefficient (which is a nondimensional measure of the skin friction that takes account of the velocity-squared, air density and area scaling of the drag) versus Reynolds number (which is a nondimensional measure of length that takes account of the velocity, air density, and air viscosity). If all the area had the same drag, then the skin friction coefficient would be constant. But you can see that it drops by the approximately the 1/5 power of the length.


Your second fundamental error is thinking that the pressure drag is all due to the nose of the body. In fact, the pressure drag depends more on the flow at the tail of the body. If there were no skin friction, the air would not only be pushed aside at the nose, but would come together at the tail, with both processes producing an increase in pressure that would result in no net drag on the body at all, regardless of its shape. But real flows are more complicated than this. Especially when the flow at the tail trails back without closing in, leaving a turbulent wake, there is low pressure at the tail that causes considerable drag. For a train, it's true that this base drag is a small proportion of the total drag compared to the skin friction over the entire train. But that doesn't mean the train has the minimum drag for the volume of the train.

The shape for minimum drag for a given volume depends on the Reynolds number (speed compared to the length), and is way shorter than a train. Here is one reference - if you do any research at all you can come up with others that are more relevant to your interests:
Parsons, Jerome S., Goodsont, Raymond E., and Goldschmied, Fabio R., "Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow," Journal of Hydronautics, VOL.8, NO. 3, AIAA, JULY 1974.

You'll notice that the shape of the body looks nothing like the proportions of a train. The Parsons body assumed a significant amount of laminar flow in the boundary layer next to the surface. If you assume fully turbulent flow in the boundary layer, the maximum thickness for the minimum drag body is positioned much further forward and the body has a more blunt tail. Instead of looking at trains as an example of the minimum drag shapes for a given volume, you would do much better to look at the shapes of dirigibles.

 

The large.

 

Google "loading gauge". Trains are more limited in cross sectional dimensions than most forms of transport. How is an oversized, but more efficient train, going to line up with the 'standard' platform ?

 

That is the most detailed answer I have ever received for any question I have ever asked and I would like to thank you for writing that. Honestly, that was way more than I was expecting. You have very precise diction. I also note that you make mention of the tail of the train. The tail would probably be shaped something like a tear drop. I was thinking an all plexiglass exterior on the tail section. Maybe stadium seating.
That said, its still not answering my question. What I really need to know is whether or not the size of the vehicle affects how much energy it uses per unit volume. You could use even the words "in general" several times in each sentence and I would not fault you for your diction or lack of precision. You could say, "in general, more" or "in general, less" or "in general, right about the same amount". I'm not asking you to put your name on anything next to an engineers stamp. I'm not going to go out in my backyard and start building this thing tomorrow. I will probably be dead before the first one even begins construction. I just want to know if I can keep writing on without having some energy hungry boogeyman waiting in the corner that is going to make my project untenable after many years of writing and thinking about it. I can justify the size without the energy savings. I am currently having no problem doing that. However, if the amount of power required to move the vehicle per unit volume was more than twice as much as the old way, then it becomes a lot harder to justify. If it was near the same amount though, then I could justify it.
I just want a quick professional opinion bordering on a guess. It could literally be one sentence, if you wanted, and without any evidence to back it up other than what your gut says. Everything depends on everything and devils are always in details, but if you were just to give it a quick guess, without any detailed study, what do you think the energy bill is going to be per unit volume? Will it cost more energy to move a train larger in cross section per unit volume or will it cost more energy to move a train smaller in cross section per unit volume?

 

Two completely different gauges. This train would not run in any shape or form on Common Gauge or any other gauge of rail or maglev, other than its own. It is an entirely unique entity. It would probably have a few Common Gauge rails that would come into its port. I can't imagine freight would be a large component of this train. Also the train has a name. I keep calling it "train" but I'm not really doing it justice. Ladies and Gentlemen. The IC. (Intercontinental.) The IC wasn't really designed to handle freight. That said, it would be a shame to waste the platform. Obviously roads would go to the port, not so obvious, canals.

It is more limited by its cross section than a smaller train would be. It cannot make as tight of curves. However, and this is something I may be wrong about, but......if it was wider it would be more stable. Standard rail uses cars that look like a fat woman in stilleto heels. If I made a piece of furniture to that shape in shop class, my shop teacher would give me a quick lesson on the necessity of safely built furniture in the home. I mean, it works, not saying it doesn't. It just seems like.........after two thousand years, we could come up with a gauge that wasn't based on the width of the axle of a horse cart.

 

Tom Speer has already answered this for you by saying "The shape for minimum drag for a given volume depends on the Reynolds number (speed compared to the length), and is way shorter than a train".

To add a bit more detail:
Considering aerodynamic losses only, and considering a fixed shape of cross section (i.e. fixed height to width ratio), there will be a train length (and corresponding cross section dimensions) that gives the minimum energy loss for a given train volume. I dont know what that length is, but it will be shorter than most trains actually are. I am basing this on a quick web search that came up with this link: http://www.railway-energy.org/static/EnergyEfficiencyTech.pdf. Figure 2 of that article is a pie chart showing a breakdown of aerodynamic drag for a 14 coach high speed train, presumably of 'normal' cross section dimensions. It is notable that only 8% of the total drag is atributable to the nose and tail of the train. The bogies and wheels account for a very significant 45.5% and I would imagine that is going to reduce as you make the train shorter and fatter, at least as long as you dont make it ridiculously short - a shorter but fatter train would presumably have fewer bogies and wheels even though they may be a bit more bulky to carry more weight per length of train and have a bit longer axles because of the increased width. At 27% of total drag the sides and roof of the train are also very significant and a shorter train of the same volume will have less area in the sides and roof, so that drag goes down despite some increase in the skin friction coefficient as explained by Tom Speer. Incidentally, cross winds affect that skin friction quite a lot since, in crude terms, they 'blow away' the boundary layer so a vehicle (including a boat - note the mandatory nautical content!) running in a cross wind has to expend energy by constantly accelerating air to make new boundary layer.

So, purely from the point of view of aerodynamic drag for a given train volume, most trains are too long and thin. But that does not mean that you save energy if you cut them into separate coaches spaced out along the track - that way you just make more noses and tails adding about 8% of the drag of the 14 coach train for each cut.

Of course, train designers are not free to make a free choice of train cross section, so for any given volume of train both the length and the cross section are essentially fixed.

If you are writing a technical book on the design of railway vehicles I cant help thinking these considerations must have already been covered in great detail by authors specialising in the subject.

 

True but you have not addressed the increase in drag that the cross section will cause. It will change the drag factor significantly. Certainly for your example, the shape drag, nose, tail is 8% but with a train twice or more as wide the drag associated with this increased area will go up. If the area goes up say 3 times, the drag might go up more than 3 times for this aspect only.
Additionally, while the OP is on a tight focused venue, ie make it wider for more efficiency, and I am expecting that he is meaning less fuel to move a given amount of weight a certain difference, that is only one part of the COST to be concerned with.
Ie The goal of a train company is to reduce the overall cost of moving a certain weight over a given distance. NOT just the fuel saved to move the certain weight over a given distance. If the capital expense of wider bridges, more expensive train car components, more expensive maintenance to the train AND the bridges, road bed could become high which might very well negate any fuel saving saved.

Additionally, as so often is the case, unless I have missed something, the OP has not given us the most important parameter, being the speed at which he is going to target the train to move at. Ie if skin friction only increases as the square of the velocity, then the obvious point is that if the train moves slower, this skin drag component (as well as shape drag) reduces dramatically. This is an easy fix if only fuel savings is a concern, ie slow down. use the current capitalized infrastructure.

Your example of a high speed train at 27% is for exactly that, a high speed train. Perhaps at freight train speed, skin friction is not relevant.

The number of bogeys might not be able to be reduced as the contact stresses between the wheels and the rails are extremely high and due to the large Hertzian contact stresses imposed by a round wheel running on a flat surface.
Currently, wheel/axle assemblies after a certain period of time have to be built up to diameter specifications due to wear.

Additionally, I would wonder how, if the number of bogeys would be reduced, could you build a ballast system, ie the rock under the ties, strong enough to carry the more point load. I believe that the load bearing analysis is covered under Statically Indeterminate Beams, ie all of us have seen a bogey from a train running over a crossing and you can see each tie being loaded so that the entire load is transferred at various rates to the ties with ties ahead of the wheel and behind the wheel taking a share of the load. With less bogeys a new type of rail would have to be developed to transfer high wheel loading (due to the higher weight of the train per 50 feet due to its weight) to the ties.

It would have been better had the OP taken a look at the overall picture, ie reducing the total cost of operating the train with a certain weight over a certain distance, including all the expenses, the effect of saving a small amount of fuel by minimizing skin drag, would have been put into perspective

 

First off, I'm not married to a 28 foot width. It would accomplish 80% of what it needed to accomplish at 16 foot. Its just that it would accomplish more at 28. I'm not pretending to be an engineer. I don't have the qualification.

What I will say is that rail inside of the United States has never really taken off. Once we found airplanes, that was it. All of a sudden it was all about the airplanes and there was never anything that could compete. We have Greyhound but usually the first time you ride Greyhound is your last. But we don't have a middle ground and we don't have that middle ground because we haven't fallen in love with the idea of high speed rail. It just hasn't captured the imagination inside of the United States and so we suffer thru high ticket prices for airlines and consequently we don't travel enough. But if you gave them something they could fall in love with and something that resounded inside of their imaginations then you might get something closer to a closed deal on high speed rail. High speed rail is moving in the direction of about 60 years worth of entrenched interests in the airline industry. If high speed rail doesn't have enough inertia to overcome those entrenched interests then it will just be set back to right where it started except with everybody older.

I will say that I am married to a two level car. We got engaged right at the beginning and we won't be breaking up. Its necessary to move inter-car traffic on at least one level. However, if there are two levels then we don't have to worry about intercar traffic on one of them. As long as we design in stairs and wheelchair access elevators into each car. (A wider car does give you more space to put those kinds of things in.) If there is a level with no thru traffic then that level could be used as a restaurant, cafeteria, or really, anything that would make enough money to justify its inclusion.

It costs more money to build a wider track and there is greater upkeep to consider as well. You will never hear me say that it would be cheaper to build a wider track.

As far as the track itself is concerned. In my head its a little bit like a fancy roller coaster track with floating bogeys. There would probably be either four or five rails. The point load would obviously be less under five rails than under two. That said, the weight spreads out over a wider area. Also, fully loaded coal cars weigh more than passenger trains and there are no fully loaded coal cars on this track. That said, I'm not an engineer. If everything was free it would probably be maglev. Shame about everything not being free. That said, the expense is actually a good thing if looked at from the right perspective. It puts engineers to work and it puts construction crews to work and it throws the money straight back into the economy. It only has to be built once. After that it just has to be maintained.

The OP has not given the most important parameter. My apologies. 160mph is what I base everything on. All inter-country travel would be accomplished in less than 24 hours. The system I designed doesn't have layovers. There is no hub and spoke model and there is also no need for one. The speed does not need to be higher and it could be slightly lower.

As I have said previously, the name of the company is The InterContinental or "IC" for short. The IC is the company that prototypes the train and the track. After prototyping, the IC manages the standards of the system. What is the minimum passenger space allowance, What is the minimum bathroom space allowance, How many cars are allowed to run on a load......those sorts of things. The IC also owns and manages the locomotive and/or front end as well as the caboose. The IC does not own or manage any of the cars between the locomotive and caboose but it does charge a per ton mile fee to those companies, portions of which are split between the IC and the country that owns and manages the rail within that country. The IC is entirely electrically powered. The IC owns all of its own electrical generation facilities with a combined nameplate rating of approximately 100 gigawatts. About half nuclear and with the balance split between natural gas and renewables. The IC sells its excess electrical generation capacity back to the grid to further reduce the cost of travel. The IC is a not for profit company. We are not here to make money, however, we are here to allow money to be made.

The IC could only begin its existence with vast and almost unheard of amounts of angel money. I do not have that money. However, I am writing a book that may or........most likely......may not be paid attention to by people that do.

Are there any wild guesses as to how much greater energy usage per unit volume would be necessary for a train of a wider dimension? 28'x20' is the wide cross section. 16'x20' is the narrower cross section. The last cross section would be how we are doing it right now.

 

Ohh, also. I forgot to say thank you for giving me such a great reply. Also for the link to that website. That website was exactly what I was looking for. I didn't think there would be a website like that and so I didn't just google it. I think this conversation will probably be moved over there as that seems like a much more appropriate venue for it. Its just that I like boats and I respect you guys for what you do. If I had it to do all over again I might have been a Naval Architect.

 

Cavitation occurs when the pressure lowers enough to make water or other liquid boil. For example, when a propeller turns too fast. It has absolutely nothing to do with oxygen in the water.

 

Has this thread "derailed"? The " submarine train " as I recall, was great entertainment. For the information of the OP, a limiting factor in trains is axle load, so super-sized trains would run into this, conventional trains seem not to operate with loads much over 4o tons/axle, for various reasons.

 

Amazing. (Does the water boil in the vacuum?)
I'll listen to Mr Efficiency and let this thread remain as interesting as it was a few posts ago.

 

Any liquid will boil in a vacuum