Re: [NSW] 'Errors' in the Central Coast Timetable (longish reply)

["Al" <alpout@optusnet.com.au>]

"Jonathan Boles" <jaboles@bigpond.com> wrote in message
sTuD6.6649$482.28857@newsfeeds.bigpond.com">news:sTuD6.6649$482.28857@newsfeeds.bigpond.com...
> > 2-car K sets are referred to by some in the rail system as "wheelbarrows",
> > ie. you really have to push them to get them moving. Bear in mind the V
> set
> > that you are referring to has 4 cars (2 motor cars) that are relatively
> more
> > powerful than any old suburban rollingstock, whilst the K set only has one
> > motor car.
>
> Yes but remember that the motor car to trailer car ratio is still 1:2 in
> both situations.
>
> Here are some figures:
> Mass of K set driver: 47t    From memory, power = approx 135kWx4 = 540kW
> Mass of K set trailer: 41t
> Mass of V set driver: 59t    Power: 4x160kW = 640kW
> Mass of V set trailer: 40t
>
> So 540kW has to accelerate 88t on a K set and 640kW has to accelerate 99t on
> a V set.
>
> Now for some equations. P=power (Wats), W=work, F=force, r=distance, t=time,
> v=speed (ms^-1 [=m / s]), m=mass (kg), a=acceleration(ms^-2 [=m / s / s]).
>
> Of course kg are used because these values are in the MKS system.
>
> v=r/t
> F=ma
> W=Fr
> P=W/t
> From these eq'ns, P=mav, or Power = Mass x Acceleration x Speed
>
> Lets say a K set and a V set both have to accerate to 60kmh^-1, which is
> equal to approximately 16.67ms^-1.
>
> Now
> P(K set)=540,000W,  m(K set)=88,000kg,  a(K set)=?,  v(K set)=16.67ms^-1
> P(V set)=640,000W,  m(V set)=99,000kg,  a(V set)=?,  v(V set)=16.67ms^-1
>
> By making a (Accelertion) the subject of the equation, a= P / mv
> so a(K set) = 540,000 / (88,000 x 16.67) = Approximately 0.3681 ms^-2
> and a(V set) = 640,000 / (99,000 x 16.67) = Approximately 0.3878 ms^-2
>
> Obviously the V set accelerates at only 0.0197ms^-2 faster than the K set,
> and the K set isn't as much of a 'wheelbarrow' as you might think.

Um, that is only the average acceleration from rest to that speed.  For a
higher speed it will show a lower acceleration.  While this is true (i.e. the
faster something gets the slower it accelerates, such as a car in a changing
gears), actual pickup rates may be different, depending such things as
adhesion between rail and wheel.

Also, your results have a V-set taking 43 seconds, or thereabouts, to get to
60km/h, while the K-set takes 45.25 seconds.  From experience, I'd be
surprised if either of them accelerated that slowly (trucks can go faster than
that).  Any drivers want to time it next time?? Thanks...

Also, using power to calculate acceleration can be misleading.  One advantage
of electrical motors (and steam engines) is that they produce infinite torque
at rest (reciprocating internal combustion engines can't, which is why cars
and diesel locos need to idle).  Consequently, the torque that is produced by
the motor which will get transmitted into tractive effort needs to be
considered, as it is this torque (exerted by the wheels turning on the rail)
which will accelerate the train.  You've even supplied the equation for it,
Newton's 2nd Law, F=m.a.

Ahah, rememberance from 1st and 2nd year.  P=V.I, i.e. power equals voltage
times current, but P= T.w (should be omega), i.e. power equals torque times
rotational speed.

Therefore V.I = T.w, or T = V.I/w.  So when w = 0, T is infinite, decreasing
as w increases, thus leading to an acceleration curve which will asymptote
towards 0.  The electrical system will show voltage decreasing as current
increases (BTW current Australian standards are for household powerpoints to
be 240V +/- 10%).  Again, any drivers of electrics out there may correct me,
but I'll bet that the volt meter drops the most when starting off, then
settles back towards the supply voltage.

To work out anything more substantial, I would need more info, such as wheel
diameters, motor ratings (voltage, current, power etc), and the mass of the
train.

Ah, to be an engineer.


--
Al Pout

Men are from Earth.

Women are from Earth.

Deal with it.

PS to Adam Dunning, this is what you'll find engineering is all about, tying
in 2 or 3 fields together, such as mechanical and electrical (like I have
above).  Good luck.