I have worked with (and researched the history of) funicular curves for over twenty years, and I have browsed the Internet for about as long as it has been going, but I did not look up the song “Funiculì, Funiculà” until 5 minutes ago.
It’s actually quite interesting:
“Jammo, jammo ‘ncoppa, jammo jà,
Jammo, jammo ‘ncoppa, jammo jà,
funiculì, funiculà, funiculì, funiculà,
‘ncoppa, jammo jà, funiculì, funiculà!”
Just seeing the words I can sing the chorus.
Is this the same as a catenary? I occasionally look up catenary on the web and elsewhere, comes in handy for both the shape of suspension bridges and for the fastest descent down a hill.
On that topic, is a catenary also the fastest ascent of a hill? Let’s phrase the question a bit better, a person on a bicycle at the bottom of a hill is travelling at speed V and force per unit mass F/M, what shape of hill ensures that the person gets to the top of the hill in minimum time? Would it be a catenary?
mollwollfumble said:
“Jammo, jammo ‘ncoppa, jammo jà,
Jammo, jammo ‘ncoppa, jammo jà,
funiculì, funiculà, funiculì, funiculà,
‘ncoppa, jammo jà, funiculì, funiculà!”Just seeing the words I can sing the chorus.
Is this the same as a catenary? I occasionally look up catenary on the web and elsewhere, comes in handy for both the shape of suspension bridges and for the fastest descent down a hill.
On that topic, is a catenary also the fastest ascent of a hill? Let’s phrase the question a bit better, a person on a bicycle at the bottom of a hill is travelling at speed V and force per unit mass F/M, what shape of hill ensures that the person gets to the top of the hill in minimum time? Would it be a catenary?
> comes in handy for both the shape of suspension bridges
eg. I used it in my parachute design. Similar is http://www.google.com/patents/US2465409
mollwollfumble said:
“Jammo, jammo ‘ncoppa, jammo jà,
Jammo, jammo ‘ncoppa, jammo jà,
funiculì, funiculà, funiculì, funiculà,
‘ncoppa, jammo jà, funiculì, funiculà!”Just seeing the words I can sing the chorus.
Is this the same as a catenary? I occasionally look up catenary on the web and elsewhere, comes in handy for both the shape of suspension bridges and for the fastest descent down a hill.
On that topic, is a catenary also the fastest ascent of a hill? Let’s phrase the question a bit better, a person on a bicycle at the bottom of a hill is travelling at speed V and force per unit mass F/M, what shape of hill ensures that the person gets to the top of the hill in minimum time? Would it be a catenary?
A catenary is the funicular curve for a uniform cable hanging under its own weight (so a suspension bridge is not actually a catenary, after you add the bridge).
I thought the fastest route for a descent was a cycloid rater than a catenary, but I may be misremembering.
Whatever it is, I don’t see why the same curve wouldn’t also work in reverse (but I haven’t done the maths).
Ignoring friction losses, and assuming the only acceleration is gravity, the ascent would be the time reversal of the descent, so I think it must be the same optimum shape.
I have probably mentioned before, Robert Hooke’s comment on a related topic (the optimum shape of an arch):
“The true mathematical and mechanical form of all manner of arches for building, with the true butment necessary to each of them. A problem which no architectonick writer hath ever yet attemted, much less performed:
abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuvx”The Rev Dodgson said:
I thought the fastest route for a descent was a cycloid rather than a catenary, but I may be misremembering.
This is the version we learnt in primary school:
http://www.allmusic.com/song/funicul%C3%AC-funicul%C3%A0-mt0011682473/lyrics
Alan Sherman did it as well.
Bubblecar said:
This is the version we learnt in primary school:http://www.allmusic.com/song/funicul%C3%AC-funicul%C3%A0-mt0011682473/lyrics
I was QA* that the English words are totally different in meaning to the Italian.
*quite amused.