It is not linear but some sort of hyberpolic function as the OP is describing: double the speed and you halve the travel time, you move closer to zero travel time but never reach it. With a linear relation you would reach zero travel time at a specific speed point.
Comment on The train that never came; how maglev technology was derailed
CanadaPlus@lemmy.sdf.org 5 days ago100km/h train = 4 hour journey 200km/h train = 2 hours 300km/h train = 1 hour 20 mins 400km/h train = 1 hour 500km/h train = 48 mins 600km/h train = 40 mins
It feels like you’re scoring returns logarithmically as you move the scale additively here. The faster you go, the sooner you arrive, it’s linear. I’m not actually sure if acceleration and deceleration has been a big issue at the scales involved.
pheet@sopuli.xyz 5 days ago
CanadaPlus@lemmy.sdf.org 4 days ago
Travel time is distance/speed. I suppose that’s only linear in distance in the technical sense, being inversely proportional to speed, but the point that there’s no dark magic or non-elementary school math involved stands.
pheet@sopuli.xyz 3 days ago
Travel time is just distance/speed And that makes the function like ’y = 1/x’ which is not a linear function. No dark magic, just math. The gist is the proportial part, not just inversely.
CanadaPlus@lemmy.sdf.org 2 days ago
Yes, you’re technically right, that’s at least what I was trying to say. “Linear” and “everything is in a multiplicative relation” are really close in my head, though, so I made a mistake.
InevitableList@beehaw.org 5 days ago
Doubling the speed turns a 4 hour journey into a 2 hour journey saving you 2 hours. Double speed again and it drops to 1 hour so you only save 1 hour, double again and you save 30 minutes. So the time saving is cut in half each time.
CanadaPlus@lemmy.sdf.org 4 days ago
Sure. And now the question is if halving the travel time is worth whatever it costs to double the speed.
In some cases, it is. There’s a grand total of one ocean liner left in the Western world, for example, despite the energy efficiency. The concord had problems with energy use getting ridiculously higher right after the sound barrier, which made it not worthwhile, and which is why 21st century passenger jets fly just below it, so that’s a straight example. I guess I just take issue with it being represented as mathematically inevitable.
InevitableList@beehaw.org 4 days ago
I read an article about China’s HSR that stated that a line with a top speed of 350km/h was 90% more expensive to build than a line built for 250km/h. The trains don’t spend much time at top speed during short journeys either. economist.com/…/china-has-built-the-worlds-larges…
A cubic meter of air weighs 1kg according to a Big, Bigger, Biggest episode about France’s TGV. Japan’s new Maglev is significantly smaller than the Shinkansen and the tunnels it runs through are 20% bigger since standard HSR already has problems with tunnel boom that can be mitigated at the tunnel entrance and exit. I also wonder how trains traveling in opposite directions will handle passing each other at 1000km/h given China is already working on next gen trains with that speed as a goal.
CanadaPlus@lemmy.sdf.org 3 days ago
Yeah, journey length is a huge factor. Over, like, a block or two walking is as dominant as a million years ago. Over continental distances airplanes are the thing to beat. Ordinary rail is promising, and vactrain concepts seem like the best very-long-term option. I did some napkin math that shows for an antipodal trip, even orbital travel can be energy-competitive, given one of a couple improvements beyond existing rocketry.
I also wonder how trains traveling in opposite directions will handle passing each other at 1000km/h given China is already working on next gen trains with that speed as a goal.
You have to adjust for Chinese truth in advertising a bit, so we might not find out, although apparently their rail infrastructure is a notable bright spot. You have to think the shockwaves would be loud, and potentially damaging to the trains, and the solution would be preventing them from ever passing close by, either with barriers and a wider allowance or careful scheduling.
ook@discuss.tchncs.de 5 days ago
Yeah, how is it so unbelievable that when you go twice the speed you are twice as fast but when you go a third faster in speed you only go a third fast in time. Diminishing returns is something else, like you would go a third faster in speed but arrive only a quarter faster.
Wrufieotnak@feddit.org 4 days ago
No, the other commentator is right.
What they said is that you add 100 km/h, and you gain 2h when you add it to a slow train with 100 km/h, but if you add 100 km/h to a fast train with 400 km/h, you only gain a few minutes.
That is called diminishing returns.
t3rmit3@beehaw.org 4 days ago
That’s not diminishing returns in terms of time and speed, which is CanadaPlus’ point. 100km/h faster is 100km/h faster, not 100% each time. It would be diminishing returns if doubling the speed each time didn’t halve the travel time, but “diminishing input = diminishing output”, or 100% -> 50% -> 25%, etc, is not diminishing returns, that’s linear.
An actual example of diminishing returns would be the cost to speed ratio, where doubling the budget each time will not result in a doubled speed.