Posted by beardyw 10/24/2025
The same confusion I have when trying to imagine satellites going around Earth or slingshot maneuvers. Would an X-Wing turn in space differently than in the atmosphere of Hoth? Would it in space just rotate, but keep its forward (now backwards) momentum instead of turning like a fighter jet?
I can't recommend KSP enough. It's a "silly" game with "on rails physics" (so not exactly 100% accurate wrt general relativity stuff) but it's got a very nice interface and it will make you "get" orbital mechanics by dragging stuff around. You'll get an intuition for it after a few hours of gameplay / yt video tutorials. Really cool game.
Your train is decelerating, and then accelerating southwards. It really is.
If you were on a train that was travelling in a straight line northwards and the driver applied the brakes, it would decelerate, which really is acceleration with a negative value (and I can hear that in my old high school physics teacher's voice, hope you're doing well, Mr Siwek). You would feel yourself being thrown forwards if the acceleration was strong enough because your momentum wants to keep you moving north.
If you were on a train that was travelling around a U-shaped bit of track looping from northbound to southbound, then you'd be thrown towards the outside of the curve. Guess what? The train is not moving north so fast, and your momentum is trying to keep you moving north.
The difference here is that if you brake the train to a stop and throw it in reverse then you're dissipating energy as heat to stop it, and then applying more energy from the drivetrain to get it moving again, but if you go round a U-shaped track the energy going north is now energy going east. You have not added or removed energy, just pointed it a different direction.
The energy question is this: going from a 100kmh-due-north momentum to a 100kmh-due-south momentum via slowing, stopping, and accelerating again clearly takes energy. You can also switch the momentum vector by driving in a semicircle. Turning around a semicircle takes some energy, but how much - and where does it come from? Does it depend on how tight the circle is - or does that just spread it out over a wider time/distance? If you had an electric train with zero loss from battery to wheels, and you needed to get it from going north to going south, what would be the most efficient way to do it?
No it doesn't, but we're talking about identical spherical frictionless trains in a vacuum.
See, now you're talking real physics!
The force from the rails at all points is at right angles to the direction of motion. So your energy doesn't change. Your momentum is constantly changing. And you're doing it by shoving the Earth the other way. But the Earth is big enough that nobody notices.
Now to the orbital example. In the Newtonian approximation, an orbit works similarly. In a circular orbit, you're exchanging momentum with the planet, but your energy remains the same. The closer the orbit, the more speed you need to maintain this against a stronger gravity, and the faster you have to move.
In an elliptical orbit, you're constantly exchanging momentum with the planet, but now you're also exchanging between gravitational potential energy, and kinetic energy. You speed up as you fall in, and slow down as you move out. Which means that you are moving below orbital speed at the far end of your orbit, and above when you are close.
Now to this paradox. Slowing down causes you to shift which elliptical orbit you are in, to one which is overall faster. Therefore slowing down puts you ahead in half an orbit, and then you'll never stop being ahead.
Doing a U-turn generates less heat, but still quite a bit. The train will have to slow down depending on the radius of the curve, and even then the turn will slow it down some more.
But yeah, less heat generation means kinetic energy is conserved.
Cars have to slow down when they turn because it’s too much to ask of the tires to accelerate (throttle) and turn, since turning is in itself acceleration.
It’s just the average driver doesn’t realize how much margin is available.
A fighter jet (or X-Wing in orbit) kind of generates its own "track" with the guiding forces of the wings. You can still do a 180° turn and keep a significant part of your momentum. Though the guiding effects are a lot softer, so your losses are a lot worse
A satellite (or an X-Wing in orbit) has no rails that can go in arbitrary directions. Any momentum is in "orbit direction", but orbits work in weirder ways. If you make your orbit highly elliptical then at the highest point you will have traded nearly all your kinetic energy for potential energy and can make a 180° turn pretty cheaply (because it's only a small change in speed)
I understand it, intellectually. It's pushing sideways against the surface as it leans and spins, but it just doesn't feel right. I have no intuition for it.
Run towards a pole and then try to come back around it, once without touching it and once using it to swing around. That's the role the curved tracks play. You exchange momentum with the object, and in the end with the Earth.
It's only costly due to the waste heat from breaking. If you captured that energy with perfect regenerative breaking you could return to the same speed in the opposite direction. (In a spherical cow sense anyway.)
Your car, depending on how much grip it has + other variables, will have a theoretical minimum diameter circle it can drive around at various speeds. The higher the speed the bigger the circle. Finding your racing line is just a matter of fitting the biggest circular arc inside the space available in the corner.
Ideally you want to break in a straight line before the corner and reach the speed your car can drive the circle at at just the moment you enter it.
Theres more nuance when it comes to compound corners, FR vs FF cars, oversteer understeer, hills bumps etc. But the basic theory is simply fitting circles.
But that is a more subtle and advanced concept though (like dealing with elevation changes).. People should understand the big circle first.
Its so common it surprises me racing games have always been so popular.
What I have also noticed is that over time racing games have changed their physics to be totally wacky in order to meet the general public's wacky expectations.. (eg. mario kart or GTA5) I cant play those games cus the physics are so strange.
Racing games are very different. They tend to have adaptive AI - you are more likely to win with the naive approach you describe than the physically perfect route. The physically perfect result will get your through the race several minutes faster, but the AI opponents become impossible to beat. Thus the ideal path is the worst thing you can learn. (I haven't played games in years, but IIRC the games you mention don't pretend to be about racing, I wonder how ones that pretend to be a real race compare)
The circle thing is aimed at most people here. If your average person implemented that they would dramatically improve their times.. All the other stuff (of which of course there is a lot) would result in relatively marginal improvements.
> The effect of taking a too wide racing line though means a large multiple in the distance travelled.
On race strategy it's rare for drivers to be pushing their cars to the limits for entire races because tire wear and the stops required to replace them is a major time sink because you can only drive so fast in pit lane so even the 1-2 second stops F1 cars go through today lose drivers position that then has to be regained using the extra performance fresh tires provides.
Then driver skill can put the better driver in the correct position to take the correct line more often when you include other cars in the mix and they also know better how to deal with suboptimal routes (eg being force to take an inside route by traffic so you have to know how much harder you need to break to not wreck into another car).
On an unrelated side note because I'm just personally annoyed by the 12 pArSecS!? misunderstanding. The 12 parsec run is impressive because Kessel is in a part of space ridiculously dense with hazards so the usual route to it loops through a narrow region where it's relatively safe to travel through. Han's 12 parsec run cut through the dangerous parts through either luck, superior navigation, or he was just lying the commentary is mixed. [0]
[0] https://static.wikia.nocookie.net/starwars/images/1/17/Kesse...
You also tend to spend more time on the straight after the corner, than in the corner itself
So you mostly optimise for corner exit speed, especially if the car has particularly slow acceleration and a long straight comes after the corner.
very annoyoing, the subject looks good, open tab and rohhhhhhhh... paid or register.
Paste link, good to go. https://archive.is/qrP0p
In this case I expected it just links to https://www.youtube.com/watch?v=bcvnfQlz1x4 and didn't even notice in links to Wired.
> The answer is that paywalls are allowed when there are workarounds (such as archive links) which allow ordinary readers to read the article without paying or subscribing, while hardwalled domains (i.e., without such workarounds) are banned. - https://news.ycombinator.com/item?id=43876575
https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
