Theoretical cycling scenario: silly answers welcome

[newfhouse]

your unit and its associated satellite talk to each other about your position

That’s not how public GNSS services such as GPS work.

 

[Drago]

Are there any large mountains, plamets, etc nearby? The effect of the apparent surface of spaecetime may affect the actual distance travelled.

 

[Drago]

That’s not how public GNSS services such as GPS work.

Absolutely correct.

GPS satellites are essentially becons which are regulated by hyper accurate clocks. Their function is to send out their precisely timed signal, and they do not "communicate" with ground based receivers - they simply broadcast their signal regardless of whether of not it is being recieved anywhere. They are, in essence, 'dumb'.

 

[slowmotion]

It's down to the sampling interval that the GPS calculates on. If they both sample only twice (once at the start and once at the end), they will both give the same reading on distance. If they sample the position and time more frequently, the straight line guy's gizmo will read a lower distance.

 

[mistyoptic]

Love me the coastline paradox.

I blame Slartibartfast

 

[ebikeerwidnes]

We have to consider whether or not the centre line of the road follows the same contours as the one following the kerb
but if the centre of the road rises and fall dramatically up and down while the kerb remains level
of course this would require than the downhill is SOOOOO steep that it has to be taken slowly for safety - otherwise they could cancel out

if this is the case then the kerb follower could be quicker

of course it would be a strange road that looked like this
maybe the road is only the width of a country road but it could be wider on the inside than the outside
probably require a major distortion in the Space Time Continuum requiring a Sonic Screwdriver to analyse

but we need to consider it

probably

you did say silly answers were allowed??????

 

[srw]

The scale only works in terms of the length of the road. In terms of width, it is a bit like a normal country road 😄

In which case the bike that takes the direct route gets bogged down the first time it goes off the tarmac.

 

[Archie_tect]

I don't understand the profile thing
The GPS is on a mobile phone in the cyclists' rear jersey pocket

Is now a good time to confess that 'your friend' forgot to turn the cycling app on to record the ride...

 

[Beebo]

In situations like this the only question is ‘What would miss Goodbody do?’

 

[Mr Celine]

The kerb hugger gets closer to the punks so is more likely to suffer a puncture from a discarded safety pin.

Every time I stop to fix a puncture, even though I barely move, strava shows me zig zagging around like a demented spider.

So GPS is more likely to show the kerb hugger going further.

 

[classic33]

GPS would give you the distance between both points, so these would be the same, or very similar.
Distance travelled, as in odometer, would be less for the straight line, as a straight line is the shortest distance between 2 points, meaning the kerb hugger cyclist would record a longer odometer.
The silly bit of the answer is why would you be including punks in your deliberations? They would probably not want to be included.

"The shortest distance between two points is never a straight line. It could be a spiral, a slow spiral around one point and then a loop into the other. Or a zig zagging path."

 

[Edwardoka]

"The shortest distance between two points is never a straight line. It could be a spiral, a slow spiral around one point and then a loop into the other. Or a zig zagging path."

We're talking trigonometry, not philosophy, "How long is this particular piece of string if you straighten it out" as opposed to "How long is a piece of string?" "Yes"

The question asked doesn't even take the curvature of the earth into question, much less the curvature of life's ebb and flow.

 

[lazybloke]

I'm not sure how serious the questions were, but having spent must of the last year with half an eye on home-schooling duties, I'm going to try a serious answer.

Here's a representation of one set of bends:
ACD (straight) or ABD (wavy).

Answer 1: It's pretty obvious that ABD is longer than ACD, and if you plug in some numbers you can work out how much longer.
It won't be much, because the width of the road is a limiting factor at how far the paths of the cyclists can diverge.
Also, for one cyclist to be able to cycle a straight line constrains how much the road can bend.
I doubt the difference would be more than 1%; but I'm not sure exactly what kind of road you're imagining.

Answer 2: No, GPS measurements will not be identical.
They are sensitive enough to show which side of the road you're on; perhaps not reliably, but it should be clear which rider is hugging the kerb.
However, GPS only takes periodic measurement of position, to the wave line will in theory resolve to jagged triangle like my diagram.

 

[Andy in Germany]

It will show as the same because GPS receivers malfunction in the presence of dragons.

 

[biggs682]

Word of warning @Fnaar is asking the question