[Cycloid]

t’s the Festive Season, a time for jollity and conundrums.
These may not be too demanding sitting down at home, but may be worth trying on your mates in the cafe after 40 hard miles

1)  It’s the Christmas Time Trial. Rider #9 sets off and rides down the road at 20mph. One minute later Rider #10 starts and rides at 30mph. 
How far along the road is it before number 10 catches his minute man?
Assume no time is lost accelerating up to speed.

2)  A man who weighs 14st 4lbs  pumps up both tyres on his bike to 100psi. He then gets on the bike
  What is the pressure in each of his tyres?
Assume his weight is equally distributed between both wheels. The Gatorskin tyre casing is rigid.

3) When you are riding along the road, do your wheels go round and round?
Discuss.

4) You have just finished your training ride and are pottering home for the last couple of miles. 
It starts to rain with big drops falling vertically from the sky. The tumble dryer is broken and you want to stay as dry as possible.
Do you a) Carry on riding slowly? Or b) Ride as fast as you can to get home sooner?
Assume you have perfect mudguards, so no road spray.
 

Topic

[AlsoSomniloquism]

Well being as Cycloid

Well being as Cycloid mentioned doing this with cycling mates at the cafe stop……you can see why Boo doesn’t know how to behave around them.

[Rendel Harris]

Just shows how weight is

Just shows how weight is completely relative – at the “height” of my playing career as a 6ft back row/utility back I weighed 13 stone 12 lb with a 30 inch waist, certainly had a much more impressive body (this was 20 years+ ago) than I have now I am 12 stone 11lbs!

[Gimpl]

Funnily enough I’m still

Funnily enough I’m still about the same height – maybe fractionally shorter thanks to age and the weight of responsibility. 

6’4″ – former second row.

My 18 year old, very skinny, 6’5″ son weighs around 13 stone – it’s amazing the difference a few inches makes 

[Argos74]

3) The wheels on the bike go

3) The wheels on the bike go round and round, round and round, round and round. The wheels on the bike go round and round, all day long.

I hope this is clear.

4) See 3.

[brooksby]

Were you, like, eight feet

Were you, like, eight feet tall?  I’m thirteen stone something, and have a 34-35″ waist…  (and no six pack).

[Gimpl]

Crikey – a 14st 4lbs person

Crikey – a 14st 4lbs person being referred to as a fatty!

That was my ‘skinny’ weight when I had a 31″ waist and a six pack!!

[mdavidford]

Garage at Large wrote:

Garage at Large wrote:

In any case who mentioned the man was on planet Earth?

It’s a fair point, given that the person answering the questions doesn’t spend any time there.

[Anonymous]

2) standard tyre inflators
2) standard tyre inflators measure the differential between an object and the ambient air pressure, which would give a reading of zero. In any case who mentioned the man was on planet Earth? You need to think outside the box a bit.

3) I was assuming the bike wheels were turning in a perfect circle, because in order for the earth to orbit the cyclist his tyres have to be blown up to an infinite pressure, resulting in an infinite force being exerted on the ground.

This means that the tyres become frictionless and are simultaneously bound to but not actually in contact with the ground. As a result, the planet cannot possibly do anything other orbit around the cyclist.

Try harder next time.

[Rendel Harris]

Garage at Large wrote:

Garage at Large wrote:

2) the pressure in the tyres would be 0 psi because the fat guy would insta pop the tyres as he sat down.  

In fact even if the tyres burst because of the weight of the “fat guy” (Maro Itoje weighs 18 stone 2 lbs, I would pay good money to see you calling him a fat guy to his face) the air pressure in the tyres would remain at the ambient pressure of one atmosphere (approximately 14 psi). A pressure of 0 psi would exist only in a perfect vacuum.

Garage at Large wrote:

3) Yes. Either that or the wheels stay still and the entire planet is orbiting the bike, take your pick.

What you actually mean is if the wheels stay still whilst the planet rotates underneath them, not orbits the bike, which would require the bike to be suspended in space.

You certainly are not the smartest person on road.cc, though I will accept your claim to be on about the same intellectual level as the former President. 

[Anonymous]

As the smartest person on
As the smartest person on Roadcc and an IQ even higher than Donald Trump – the world’s greatest ever President – I will give you the definitive answers:

1) Theoretically, 30mph takes 2 minutes to ride 1 mile, 20mph takes 3 minutes to ride one mile. Therefore the riders meet after 1 mile. However, in reality the distance covered will be slightly lower because the second rider will be riding against the highway code, head down over the handlebars, meaning the length of the rider’s head and neck, adjusted for the speed differential (1.5), would have to be deducted from the theoretical answer.

2) the pressure in the tyres would be 0 psi because the fat guy would insta pop the tyres as he sat down.

3) Yes. Either that or the wheels stay still and the entire planet is orbiting the bike, take your pick.

4) Not enough information – by definition if it’s only just started raining and assuming a cloud hasn’t spontaneously formed over your head, it may well be the case you’d get the least wet from staying stationary and letting the cloud move away from you, or possibly even turning around and cycling away from home temporarily.

[Cycloid]

F*ck off you thick b*st*rd

F*ck off you thick b*st*rd

[Cycloid]

Good reply

Good reply

Check out the Cycloid curve for question #3

Thanks for the link for question #4, I’ll follow it through
I was expecting the answer to involve some ‘orrible differential equations.

[Cycloid]

Two observations

Two observations
Wrong answers are always better than the right ones – keep ’em coming.
You can’t have a sensible conversation with your cycling mates in the cafe – they are too busy taking the p*ss (which is a good thing)
 

[TheBillder]

hawkinspeter]

hawkinspeter wrote:

TheBillder wrote:

*Supplementary question: what’s the smallest pet in the world?

I keep a small proton as a pet – it helps me stay positive.

It’s my newt.

[hawkinspeter]

1) Let’s see – after 1 minute

1) Let’s see – after 1 minute, #9 has cycled 1/3 mile and #10 has cycled 0 miles. But by the time #10 has cycled 1/3 mile, #9 has also cycled a bit further. So no matter how many times #10 cycles the same distance, #9 is always a bit further ahead. Therefore it is impossible for #10 to ever catch #9.

2) With a bit of finite element analysis, we can determine that the rider and bike are being supported merely by the pressure in the tyres and the rigidity of the Gatorskins. As the casing is assumed to be perfectly rigid, this means that the air pressure is not supporting any weight at all. Thus, we can prove that the tyres are merely subject to social pressure to perform well as tyres.

3) By examining the contact point between the road and the tyre, it’s clear that the tyre is static at that point (unless you’re performing some wicked skids) and so obviously, the entire wheel must be static too as it is a rigid structure.

4) I’ll take option b) please. Imagine if you will, the trajectory of a raindrop falling vertically onto my head. If I then move forwards, the raindrop will surely fall behind me as long as I am moving quickly enough for the time taken for the raindrop to fall is longer than the depth of my head. This means that I can remain completely dry unless the clouds are low – this also explains why misty rain is a lot wetter than ordinary rain as the clouds are lower.

 

TheBillder wrote:

*Supplementary question: what’s the smallest pet in the world?

I keep a small proton as a pet – it helps me stay positive.

For bonus points – see if you can connect the dots in this picture:

[Author]

Replies