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Re: Train Physics Problem

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On 11/3/2015 12:41 PM, benj wrote:
> On 11/03/2015 09:38 AM, Odd Bodkin wrote:
>> On 11/2/2015 8:05 PM, Fabian Russell wrote:
>>> Attention physics enthusiasts:
>>>
>>> In all of the information that I have encountered about train
>>> physics -- and there is not a lot of material available -- the
>>> energy required to move a train is calculated by considering
>>> factors such a inertia (train mass), mechanical resistance (friction),
>>> and air resistance (drag).
>>>
>>> However, one significant factor is always ignored, and that is
>>> the rotational energy of the wheel sets.
>>>
>>> Why?  What is the reason for omitting the rotational energy?
>>>
>>> In the US, a train wheel is very nearly 1 meter in diameter and
>>> has a mass of 1000 kg.  The rotational energy for one wheel is
>>> then 1/2 * I * w^2.  At 60 mph (27 m/s) speed, the energy is 179862
>>> Joules.
>>>
>>> At 4 wheel sets per car (8 wheels) with an average train containing
>>> 100 cars, the total rotational energy of the wheels is a whopping
>>> 143889600 Joules = 144 megajoules.
>>>
>>> Yet this energy is ignored.
>>
>> I don't know that it's ignored, but let's put those large numbers in
>> perspective.
>>
>> Let's compare the rotational kinetic energy of the wheels to the
>> translational kinetic energy of the wheels.
>> w = v/r, and for a disk wheel, I = (1/2)m*r^2.
>> So the rotational KE = (1/2)(1/2)m*r^2 * (v/r)^2 = (1/4)mv^2. The
>> rotational KE of the wheels is thus half the translational KE of the
>> wheels.
>>
>> Now we can compare the translational kinetic energy of the wheels to the
>> translational kinetic energy of the train as a whole.
>>
>> As you say, 800 wheels on a 100-car train has a mass of about 800 metric
>> tons. But the mass of a fully loaded train is about 10,000 metric tons.
>> So the translational kinetic energy of the wheels is about 8% of the
>> train's translational kinetic energy, and the rotational kinetic energy
>> of the wheels is then about 4% of the train's total kinetic energy.
>>
>> Not insignificant, but not huge either.
>
> Except that train wheels are closer to hoops than disks which could
> increase the value by a factor of almost two.

Could, if they were in fact closer to hoops than disks. But in reality 
they're not: 
http://patentimages.storage.googleapis.com/US20030079328A1/US20030079328A1-20030501-D00004.png

> Plus, trains also travel
> unloaded at which time the wheel inertia could become very significant.

But then again, so is friction in the axles and so on.

>
> OF course all you need to do is install titanium wheels and you much
> reduce the problem. (Talking like a Lib "idea man" now) I'll let
> "railroad men" work out how to pay for them.
>


-- 
Odd Bodkin --- maker of fine toys, tools, tables

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Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 02:05 +0000
  Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 02:31 +0000
    Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 02:38 +0000
    Re: Train Physics Problem gillyshin <spectrum8@sincity.info> - 2015-11-03 04:38 +0000
      Re: Train Physics Problem gilber34 <fafa@invalid.com> - 2015-11-02 22:58 -0600
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 05:22 +0000
  Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 08:38 -0600
    Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 18:19 +0000
      Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 15:00 -0600
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 21:22 +0000
          Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 16:55 -0600
            Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 23:19 +0000
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 21:31 +0000
          Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 17:17 -0600
    Re: Train Physics Problem benj <none@gmail.com> - 2015-11-03 13:41 -0500
      Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 18:53 +0000
        Re: Train Physics Problem benj <none@gmail.com> - 2015-11-04 18:08 -0500
          Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-04 23:33 +0000
      Re: Train Physics Problem Odd Bodkin <bodkinodd@gmail.com> - 2015-11-03 15:10 -0600
        Re: Train Physics Problem Fabian Russell <root@localhost.localdomain> - 2015-11-03 21:48 +0000
          Re: Train Physics Problem benj <nobody@gmail.com> - 2015-11-04 02:45 -0500
  Re: Train Physics Problem "reber g=emc^2" <herbertglazier0@gmail.com> - 2015-11-03 09:19 -0800
    Re: Train Physics Problem "reber g=emc^2" <herbertglazier0@gmail.com> - 2015-11-04 15:15 -0800

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