Trolley Poles

Another fascinating seminar brought to you, by yours truly.

So there I was, thinking about them doings on the roofs of the trams in Llandudno.

Tramcars, trolley cars, cable cars?

Aha, thought I, I shall have me an google and see if the technical term is mentioned somewhere to describe the gubbins on trolley buses.

So, into google went 'trolley bus', lo and behold, trolley poles are mentioned.

So, me being me, looked into trolley poles.

Guess what?

Trolling gets a mention.

The term trolley predates the invention of the trolley pole. The earliest electric cars did not use a pole, but rather a system in which each car dragged behind it an overhead cable connected to a small cart – or "troller" – that rode on a "track" of overhead wires. From the side, the dragging lines made the car seem to be "trolling", as in fishing. Later, when a pole was added, it came to be known as a trolley pole.

Here

That's wor I like about WW dustaf. you can have a chat, a bit od a laff an' also learn loads of heducashunal stuff. Keep it up.

Better than feytin and falling out, Ray.

This lot started after commenting on Meccy's Llandudno thread on general.

You mentioned the Poles though

Roller Skate Lithuanians!

See why I put it on handbags?

Polish trolley dolly

Ooohh, very nice.


Coming soon:

'Pantographs, an essential guide.'

Explain that to a poster on p.o.d

Do you mean p.a.d?

Photo-A-Day

HAHAHAHAHA

Catenary coming to a website near you soon.

What did I tell you?

Do plants know this




T \cos \varphi = T_0\,
and
T \sin \varphi = \lambda gs,\,
and dividing these gives
\frac{dy}{dx}=\tan \varphi = \frac{\lambda gs}{T_0}.\,
It is convenient to write
a = \frac{T_0}{\lambda g}\,
which is the length of chain whose weight is equal in magnitude to the tension at c.[43] Then
\frac{dy}{dx}=\frac{s}{a}\,
is an equation defining the curve.

The horizontal component of the tension, Tcos φ = T0 is constant and the vertical component of the tension, Tsin φ = λgs is proportional to the length of chain between the r and the vertex.[44]

Derivation of equations for the curve[edit]

The differential equation given above can be solved to produce equations for the curve.[45]

From
\frac{dy}{dx} = \frac{s}{a},\,
the formula for arc length gives
\frac{ds}{dx} = \sqrt{1+\left(\dfrac{dy}{dx}\right)^2} = \frac{\sqrt{a^2+s^2}}{a}.\,
Then
\frac{dx}{ds} = \frac{1}{\frac{ds}{dx}} = \frac{a}{\sqrt{a^2+s^2}}\,
and
\frac{dy}{ds} = \frac{\frac{dy}{dx}}{\frac{ds}{dx}} = \frac{s}{\sqrt{a^2+s^2}}.\,
The second of these equations can be integrated to give
y = \sqrt{a^2+s^2} + \beta\,
and by shifting the position of the x-axis, β can be taken to be 0. Then
y = \sqrt{a^2+s^2},\ y^2=a^2+s^2.\,
The x-axis thus chosen is called the directrix of the catenary.

It follows that the magnitude of the tension at a point T = λgy which is proportional to the distance between the point and the directrix.[44]

The integral of expression for dx/ds can be found using standard techniques giving[46]
x = a\ \operatorname{arcsinh}(s/a) + \alpha.\,
and, again, by shifting the position of the y-axis, α can be taken to be 0. Then
x = a\ \operatorname{arcsinh}(s/a),\ s=a \sinh{x \over a}.\,
The y-axis thus chosen passes though the vertex and is called the axis of the catenary.

These results can be used to eliminate s giving
y = a \cosh \frac{x}{a}.\,
Alternative derivation[edit]

The differential equation can be solved using a different approach.[47]

From
s = a \tan \varphi\,
it follows that
\frac{dx}{d\varphi} = \frac{dx}{ds}\frac{ds}{d\varphi}=\cos \varphi \cdot a \sec^2 \varphi= a \sec \varphi\,
and
\frac{dy}{d\varphi} = \frac{dy}{ds}\frac{ds}{d\varphi}=\sin \varphi \cdot a \sec^2 \varphi= a \tan \varphi \sec \varphi.\,
Integrating gives,
x = a \ln(\sec \varphi + \tan \varphi) + \alpha,\,
and
y = a \sec \varphi + \beta.\,
As before, the x and y-axes can be shifted so α and β can be taken to be 0. Then
\sec \varphi + \tan \varphi = e^{x/a},\,
and taking the reciprocal of both sides
\sec \varphi - \tan \varphi = e^{-x/a}.\,
Adding and subtracting the last two equations then gives the solution
y = a \sec \varphi = a \cosh \tfrac{x}{a},\,
and
s = a \tan \varphi = a \sinh \tfrac{x}{a}.\,

Bein' an ex enjuneer I just had to check the term pantograph. It sounded right for the gubbins connecting the trolley to the cable but it is also a parallelogram type jointed linkage system which copies plans, drawings etc to scale or to a different scale. So theer.

And an copying/enlarging drawings, or engraving.

Mache, you norteet. You copied and pasted all that.

I think there's a close bracket missing from line 20 mache

He made a wotsit of it well before line 20.

Couldn't find me notebook in time

Last cosine I used was on a marriage certificate

This is bl**dy hard for an Incer. I'm tryin' to watch 'The White Queen', so gerrin' mi head round English court life in't 1480's, discuss pantographs, cateneries and chuffin' trolley poles. phew.

Fair enough, Ray.

An interlude.

Did you do that aide memoire thing for sines & cosines?

SOH CAH TOA

sine = opp over hypotenuse
cosine = adjacent over hypotenuse
tangent = opposite over adjacent

It's soooo easy

Brill dustaf
Remember trolleys when we were kids?

Ray, there's a marvelous recollection, worthy of publishing, by one poster on here about a trolley in Ince.

I think you'll really like it and have resurrected a trolley thread on general in the hope of finding it.

Is that manitou 'Did anybody have one of these as a kid'

Here's the link, Dostaf and Raymyjamie.

That's the thread I've asked on.

The story I mean was put on WW a couple of years ago, not on a post on the communicate section.

Still looking, it is a belter.

^Look up^

I missed your post, Jo Anne and was just about to announce that I'd found the item on Places.

Thanks.

I smell diesel

See the preserved trolley buses at Sandtoft Trolleybus Museum, especially on "Running" days when rides are provided .

Relativly local

Dustaf/Jo anne
I've replied on 'General' re that posting on 'trollies in Ince'. Absolutely brilliant piece of writing

Trig Off with them sums!

What was the Pole's name?

You're welcome, Raymyjamie - it is a great read. We never had trollies as children.

Was his name Vaulter, Tonker?! (WW has sent me off my trolley anway.)

You're welcome, Ray.


Incidentally, Mache's 'diesel comment was a suggestion that the removal lorries could be on their way to remove some comments/posts on General.

Also known as getting a Pickford

That's what happens when falling out occurs.

It happened just after the doctor arrived

I noticed.

I'm slowly gettin' mi yed round some of the banter now. There have benn many references to Pickfords & now I understand

At one time, the post would have something like 'Edited by Brian 24th Jun 2013 at 18:57' on them.

Then there was a change to 'Comment removed because it broke the rules'.

Removed - removal men- Pickfords.

Pickfords lorries - diesel.

Feel free to ask, if you aren't too sure of anything.

'Tandem' = Mispronunciation of tangent.

'Thread went thattaway' etc

Notreet = Mache.

So is Mache the 'only' notreet?

Also, some naughty types put their own Pickfords on.

(SCOUNDRELS!)

This then causes others to jump for joy, thinking they've been edited, when this is not the case.


See here


6th Jan 2013 at 23:55, genuine Pickford.

9th Jan 2013 at 01:43 & 9th Jan 2013 at 15:24, the work of charlatans and wrong uns.

Notreets abound.

Notreet is my term of endearment for Mache.

He's not really a dafty. (At least I don't think so, I don't know him personally)

Pickfords - understood
Pickfords lorries = diesel - understood
Tandem = tangent - understood
notreet = Mache - understood........but only Mache right?

No, not just Mache.

I just frequently call him that out of divilment.

So notreets - anybody worthy of the title got it dustaf

Ha ha - If t'cap fits

'Notreet' usually used in jest.

Similarly 'daft apeth'.

I'm sure there's a 'daft apeth/ha'peth' thread somewhere, just asking for a resurrection.

I'll check me change

got it

P.A.D. has had a smooth ride today