# Object moving thru a fluid medium

Discussion in 'Hydrodynamics and Aerodynamics' started by Patrick Hickey, Jun 8, 2017.

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### Patrick HickeyJunior Member

Hello. I am stupid. But I am writing a book and trying to at least sound smart. What I am trying to figure out is if the part I have written below is correct.

"That said, once the track is built, it is cheaper to move people over a larger train with a greater cross section. Any moving object has to take into account any counter-forces that are trying to impede its movement. If there was no gravity and we were in space then the only counter force would be resistance to acceleration. But we are on a planet and we are on a planet with an atmosphere and that atmosphere is 14lb per cubic foot at sea level. You don't really notice it much when you are standing still but it will rip your clothes straight off of you at 160 mph. This train will have to contend with surface drag and surface drag will be its greatest impedance to movement at that speed. The surface drag of an object increases with the cube of its velocity. The faster the train, or any object goes, the more resistance to movement there is and that resistance does not increase in a linear manner, it increases in an exponential manner, so whatever we can do to reduce that drag gives us a more efficiently moving train. Lets take a look at a simplified cross sectional analysis.

(This website is not allowing me to upload images so you'll just have to use your imagination. Its four separate boxes of the same size spaced apart in two rows of two columns and each side of each of the four boxes has a 1 next to it.)

Here we have four boxes. Each box has four surface units. One, two, three and four. There are four boxes (squares actually and not boxes, if we are looking at it in cross section.) with four surface units for a total of 16 surface units.

But now look what happens when we move those boxes together.

(Imagination time again. Now the boxes have been combined into one box and the 1 text has been removed from all of the sides of the boxes that are now touching each other and only the only "ones" that are left are the ones around the surface of the combined squares.)

All of the surface units that were in the middle are now magically gone. And now we only have 8 surface units. Same amount of area inside of the larger box that was inside of the smaller boxes but now with only 8 surface units instead of 16.
In other words, from a standpoint of surface area, it is cheaper to run one 4 unit train than it is to run 4 one unit trains. This the reason why there are such things as gigantic container ships. Because its just cheaper to do it that way. It cost less in fuel to use a vessel with a lower surface area to usable volume ratio. Its cheaper to run one big ship than it is to run four smaller ships with the same total volume as the larger ship."

So, my question for this forum is, am I correct about this? From the standpoint of surface drag, does it make more sense to use a larger vessel to overcome it or is there something that I am missing here?

Patrick Hickey

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### David CooperSenior Member

Surely the best way to do long-distance high-speed train stuff is the hyperloop where you remove most of the air drag. The track for levitating trains is expensive, so you want to make it narrow rather than wide and reduce the amount of material it needs to lift at any point. In situations where the distances aren't so great, high speed travel from station to station is much less important - what really matters is the time taken for travellers to get to their end destination, so breaking trains up into individual pods that can switch line individually (and take to the road when the track runs out) could enable a system with relatively slow moving pods to beat high-speed trains in terms of total journey time while using a fraction of the amount of energy per journey. I think we should get rid of conventional trains altogether.

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### tom28571Senior Member

I got lost at 14lb per cu ft.

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### TANSLSenior Member

I have also been surprised by the 14lb per cu ft. but, forgetting that, I was able to continue. Then :
While this assumption may be correct, there may be many other motives that make several boats preferable to one larger.

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### tspeerSenior Member

If you want to see empirical data on the resistance of various shapes, and the effect of multiple shapes in tandem, a good reference is Hoerner's Fluid Dynamic Drag.

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### Mr EfficiencySenior Member

You meant square rather than cube ?
There are a host of considerations when running any kind of transport service, and whilst limiting the drag of the conveyance where possible is no doubt part of the picture, it is just one of a complex of many factors to be considered. Cars would probably be shaped like tear-drops if getting air drag down was job #1, but it would be a handicap in other ways.

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### Patrick HickeyJunior Member

My apologies, but this is a very early draft and has not yet been proofed by persons of greater intelligence than myself which is exactly what I am doing right now. Yep, its not 14lb per cubic foot, its 14lb per square inch. Thank you for noting that. I was half awake when I wrote that line.

In regards hyperloop: so far its just an idea in some guys head. There is quite a bit of money behind it, but, from what I understand, no demonstratable model. My guess would be that the tolerances would be very tight and the cost per person per mile traveled would be exorbitantly high. Also, there's no room for a bathroom and the comfort level is non-existent.

But really I just need to know whether my surface drag is cut in half from the example that I posted.

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### Patrick HickeyJunior Member

My thoughts were that if I wanted to know about surface drag or skin friction I would speak with the guys that knew the subject best, and that would be boat designers. If I am wrong in that regard then please feel free to correct me.

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### Patrick HickeyJunior Member

I like the Hyperloop and I try to keep up with it but there's only so much you can do with it. The track for maglev is expensive. From memory it seems like the Shanghai Maglev was about 500 million per mile. It was, however, a demonstration project and there was technology that needed proving out. As far as making it narrower rather than wide, I would have to disagree. The amount of weight at any given point shouldn't be too very much greater. Sure, the pylons will be thicker and the beams as well but probably not by too much as the weight is being spread out over a wider area. One way or another, however, it is much more expensive to build wide than long. No question of that. Its just a question of what you get out of a wider train. In my design concept I can put a 28 foot wide, 78 foot long super-luxury yacht onboard and then I can move that yacht from east coast to west coast inside of a single day. Might cost a hundred grand to get it done, but it could be done.

You might be able to get rid of passenger train altogether, short of commuter rail. I'm not too sure you could get rid of freight trains anytime in the near future. They are elegant in their brutal simplicity and freight doesn't care how long it takes to get to where-ever.

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### Patrick HickeyJunior Member

I pulled this quote directly from wikipedia. "Note that the power needed to push an object through a fluid increases as the cube of the velocity". Is wikipedia incorrect?

My goal in running a transport service is to run the greatest volume at the lowest cost and that is what I am making an effort to do by making the vehicle larger in cross section. I am here to find out if I am incorrect in my assumptions regarding surface drag to volume ratios. I do not have the education necessary to know this information on my own.

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### latestarterSenior Member

No, it is correct.
Power = work done in a unit of time.
Work = force x distance moved
Therefore power = force x distance moved in a unit of time. As distance moved in a unit of time is velocity; so power = force x velocity
The force varies as the square of velocity.
So the equation for power includes velocity 3 times.

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### TANSLSenior Member

Just for the purpose of verifying sources other than Wikipedia, I have consulted the studies of people who have addressed these issues, such as Morton and Getler, Guldhamer and Harvald, Holtrop and Mennen. I have seen few references in them to the third power of speed. As an example, Holtrop-Mennen make the following decomposition of the power necessary to tow a ship : (How to move from V ^ 2 to V ^ 3 is something I do not know)

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### gonzoSenior Member

Pressure is in force x surface area not volume. Also, friction is related to viscosity of a fluid. Pressure will increase viscosity on a gas though, so it is a secondary factor. Also, a larger cross section will increase, not decrease, drag.

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### TANSLSenior Member

Pressure is in force/surface area not force x surface area.

Last edited: Jun 9, 2017

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