How can I curve a line in CSS "roller coaster" animation?

You can consider border-radius. Here is a basic example that you can improve

.box {
  height:100px;
  margin-top:50px;
  border:10px solid transparent;
  border-bottom:10px solid red;
  width:100px;
  animation:
    loop   5s infinite alternate linear,
    radius 5s infinite alternate linear;
}
@keyframes loop{
  0% {
    transform:translateX(0);
  }
  40% {
    transform:translateX(100px) rotate(0deg);
  }
  60% {
    transform:translateX(100px) rotate(-360deg); 
  }
  100% {
    transform:translateX(200px) rotate(-360deg);
  }
}
@keyframes radius{
   0%,28% {
     border-radius:0%
   }
   35%,38% {
     border-bottom-right-radius:50%;
     border-bottom-left-radius:0%;
   }
   45%,55% {
     border-radius:50%
   }
   62%,65% {
     border-bottom-right-radius:0%;
     border-bottom-left-radius:50%;
   }
   70%,100% {
     border-radius:0%
   }
}
<div class="box"></div>

Another crazy idea where you can animate a rectangular shape behind a transparent curved path:

.box {
  height: 165px;
  width: 315px;
  position: relative;
  border-radius: 0 100px 100px 0;
  animation: hide 3s infinite linear alternate;
  overflow:hidden;
}

.box:after {
  content: "";
  display:block;
  height: 100%;
  background: white padding-box;
  border-radius: inherit;
  border: 15px solid transparent;
  border-left:0;
  box-sizing: border-box;
}

.alt {
  margin-top: -165px;
  transform: scaleX(-1);
  transform-origin: 170px 0;
  animation-direction: alternate-reverse;
}

.box:before {
  content: "";
  position: absolute;
  z-index: -1;
  width: 90px;
  height: 90px;
  background: blue;
  bottom: -40px;
  animation: loop 3s infinite linear alternate;
  transform-origin: 50% -20px;
}

.alt:before {
  animation-direction: alternate-reverse;
}

@keyframes loop {
  15% {
    transform: translateX(180px) rotate(0deg);
  }
  40% {
    transform: translateX(180px) rotate(-180deg);
  }
  50%,100% {
    transform: translateX(125px) rotate(-180deg);
  }
}

@keyframes hide {
  0%,50% {
    visibility: visible;
  }
  50.2%,100% {
    visibility: hidden;
  }
}
<div class="box"></div>

<div class="box alt"></div>

An optimized version with less of code and with transparency (will consider mask for this)

.box {
  height: 165px;
  width: 315px;
  position: relative;
  border-radius: 0 100px 100px 0;
  animation: hide 3s infinite linear alternate;
  overflow:hidden;
  -webkit-mask:
    linear-gradient(#fff,#fff) top left   /235px 15px,
    linear-gradient(#fff,#fff) bottom left/235px 15px,
    radial-gradient(farthest-side at left,transparent calc(100% - 15px),#fff 0) right/100px 100%;
   -webkit-mask-repeat:no-repeat;
   mask:
    linear-gradient(#fff,#fff) top    left/235px 15px,
    linear-gradient(#fff,#fff) bottom left/235px 15px,
    radial-gradient(farthest-side at left,transparent calc(100% - 15px),#fff 0) right/100px 100%;
   mask-repeat:no-repeat;  
}
.alt {
  margin-top: -165px;
  transform: scaleX(-1);
  transform-origin: 170px 0;
  animation-direction: alternate-reverse;
}

.box:before {
  content: "";
  position: absolute;
  width: 90px;
  height: 90px;
  background: blue;
  bottom: -40px;
  animation: loop 3s infinite linear alternate;
  transform-origin: 50% -20px;
}

.alt:before {
  animation-direction: alternate-reverse;
}

@keyframes loop {
  15% {
    transform: translateX(180px) rotate(0deg);
  }
  40% {
    transform: translateX(180px) rotate(-180deg);
  }
  50%,100% {
    transform: translateX(125px) rotate(-180deg);
  }
}

@keyframes hide {
  0%,50% {
    visibility: visible;
  }
  50.2%,100% {
    visibility: hidden;
  }
}

body {
  background:linear-gradient(to right,yellow,gray);
}
<div class="box"></div>

<div class="box alt"></div>

Another version with less pixel values and CSS variables where you can easily adjust everything.

Run the snippet on full page and have fun with all the coasters!

.box {
  --w:400px; /* Total width of the coaster */
  --h:180px; /* Height of the coaster */
  --b:90px;  /* width of the small bar */
  --t:15px;  /* height of the small bar */
  --c:blue;  /* Color of the small bar */
  
  width:var(--w);
  height:var(--h);
}

.box > div {
  height: 100%;
  position:relative;
  width: calc(50% + var(--h)/2 + var(--b)/2);
  border-radius: 0 1000px 1000px 0;
  animation: hide 3s infinite linear alternate;
  -webkit-mask:
    linear-gradient(#fff,#fff) top left   /calc(100% - var(--h)/2) var(--t),
    linear-gradient(#fff,#fff) bottom left/calc(100% - var(--h)/2) var(--t),
    radial-gradient(farthest-side at left,transparent calc(100% - var(--t)),#fff 0) right/calc(var(--h)/2) 100%;
   -webkit-mask-repeat:no-repeat; 
   mask:
    linear-gradient(#fff,#fff) top left   /calc(100% - var(--h)/2) var(--t),
    linear-gradient(#fff,#fff) bottom left/calc(100% - var(--h)/2) var(--t),
    radial-gradient(farthest-side at left,transparent calc(100% - var(--t)),#fff 0) right/calc(var(--h)/2) 100%;
   mask-repeat:no-repeat;
}
.box > div:last-child {
  margin-top:calc(-1*var(--h));
  margin-left:auto;
  transform: scaleX(-1);
  animation-direction: alternate-reverse;
}

.box > div:before {
  content: "";
  position: absolute;
  width: var(--b);
  height: 50%;
  background: var(--c);
  bottom: -25%;
  animation: loop 3s infinite linear alternate;
  transform-origin: 50% -50%;
}

.box > div:last-child:before {
  animation-direction: alternate-reverse;
}

@keyframes loop {
  15% {
    transform: translateX(calc(var(--w)/2)) rotate(0deg);
  }
  40% {
    transform: translateX(calc(var(--w)/2)) rotate(-180deg);
  }
  50%,100% {
    transform: translateX(calc(var(--w)/2 - var(--b)/2)) rotate(-180deg);
  }
}

@keyframes hide {
  50% {
    visibility: visible;
  }
  50.1%,100% {
    visibility: hidden;
  }
}

body {
  background:linear-gradient(to right,yellow,gray);
}
<div class="box">
<div></div><div></div>
</div>

<div class="box" style="--w:500px;--h:80px;--b:50px;--c:red;--t:5px">
<div></div><div></div>
</div>

<div class="box" style="--w:90vw;--h:200px;--b:100px;--c:purple;--t:20px">
<div></div><div></div>
</div>

To understand the trick, let's remove the mask and replace it with a simple gradient and remove the hide animation:

.box {
  --w:400px; /* Total width of the coaster */
  --h:180px; /* Height of the coaster */
  --b:90px;  /* width of the small bar */
  --t:15px;  /* height of the small bar */
  --c:blue;  /* Color of the small bar */
  
  width:var(--w);
  height:var(--h);
}

.box > div {
  height: 100%;
  position:relative;
  width: calc(50% + var(--h)/2 + var(--b)/2);
  border-radius: 0 1000px 1000px 0;
  /*animation: hide 3s infinite linear alternate;*/
  background:
    linear-gradient(red,red) top left   /calc(100% - var(--h)/2) var(--t),
    linear-gradient(green,green) bottom left/calc(100% - var(--h)/2) var(--t),
    radial-gradient(farthest-side at left,transparent calc(100% - var(--t)),black 0) right/calc(var(--h)/2) 100%;
  background-repeat:no-repeat; 
}
.box > div:last-child {
  margin-top:calc(-1*var(--h));
  margin-left:auto;
  transform: scaleX(-1);
  animation-direction: alternate-reverse;
}

.box > div:before {
  content: "";
  position: absolute;
  width: var(--b);
  height: 50%;
  background: var(--c);
  bottom: -25%;
  animation: loop 3s infinite linear alternate;
  transform-origin: 50% -50%;
}

.box > div:last-child:before {
  animation-direction: alternate-reverse;
  background:purple;
}

@keyframes loop {
  15% {
    transform: translateX(calc(var(--w)/2)) rotate(0deg);
  }
  40% {
    transform: translateX(calc(var(--w)/2)) rotate(-180deg);
  }
  50%,100% {
    transform: translateX(calc(var(--w)/2 - var(--b)/2)) rotate(-180deg);
  }
}

@keyframes hide {
  0%,50% {
    visibility: visible;
  }
  50.2%,100% {
    visibility: hidden;
  }
}

body {
  background:linear-gradient(to right,yellow,gray);
}
<div class="box">
<div></div><div></div>
</div>

The path created by the gradient is our mask and we will only see that part. Then we make our rectangle to follow the path and the trick is to have two symmetrical element to create the loop effect. The hide animation will allow us to see only one of them and the perfect overlap will create a continuous animation.


Here is a version in case you want a circle for the coaster

.box {
  --w:400px; /* Total width of the coaster */
  --h:180px; /* Height of the coaster */
  --b:90px;  /* width of the small bar */
  --t:15px;  /* height of the small bar */
  --c:blue;  /* Color of the small bar */
  
  width:var(--w);
  height:var(--h);
}

.box > div {
  height: 100%;
  position:relative;
  width: calc(50% + var(--h)/2);
  border-radius: 0 1000px 1000px 0;
  animation: hide 3s infinite linear alternate;
  -webkit-mask:
    radial-gradient(farthest-side at bottom right,transparent calc(100% - var(--t)),#fff 0 100%,transparent 100%) top 0 right calc(var(--h)/2)/calc(var(--h)/2) 50%,
    linear-gradient(#fff,#fff) bottom left/calc(100% - var(--h)/2) var(--t),
    radial-gradient(farthest-side at left,transparent calc(100% - var(--t)),#fff 0) right/calc(var(--h)/2) 100%;
   -webkit-mask-repeat:no-repeat; 
   mask:
    radial-gradient(farthest-side at bottom right,transparent calc(100% - var(--t)),#fff 0 100%,transparent 100%) top 0 right calc(var(--h)/2)/calc(var(--h)/2) 50%,
    linear-gradient(#fff,#fff) bottom left/calc(100% - var(--h)/2) var(--t),
    radial-gradient(farthest-side at left,transparent calc(100% - var(--t)),#fff 0) right/calc(var(--h)/2) 100%;
   mask-repeat:no-repeat;
}
.box > div:last-child {
  margin-top:calc(-1*var(--h));
  margin-left:auto;
  transform: scaleX(-1);
  animation-direction: alternate-reverse;
}

.box > div:before {
  content: "";
  position: absolute;
  width: var(--b);
  height: 50%;
  background: var(--c);
  bottom: -25%;
  animation: loop 3s infinite linear alternate;
  transform-origin: 50% -50%;
}

.box > div:last-child:before {
  animation-direction: alternate-reverse;
}

@keyframes loop {
  15% {
    transform: translateX(calc(var(--w)/2 - var(--b)/2)) rotate(0deg);
  }
  50%,100% {
    transform: translateX(calc(var(--w)/2 - var(--b)/2)) rotate(-180deg);
  }
}

@keyframes hide {
  50% {
    visibility: visible;
  }
  50.1%,100% {
    visibility: hidden;
  }
}

body {
  background:linear-gradient(to right,yellow,gray);
}
<div class="box">
<div></div><div></div>
</div>

<div class="box" style="--w:500px;--h:80px;--b:50px;--c:red;--t:5px">
<div></div><div></div>
</div>

<div class="box" style="--w:90vw;--h:200px;--b:100px;--c:purple;--t:20px">
<div></div><div></div>
</div>

thank you all, and especially Temani Afif for your inspiration :]

I eventually combined a lot of your answers using border-radius, hiding elements and a little more HTML I think I created a great solution for the animation.

* {
  box-sizing: border-box;
}

#container {
  width: 100px;
  height: 100px;
  margin-top: 50px;
  position: relative;
  animation: 5s infinite loop linear;
}

#coasterLine {
  height: 10px;
  background: lightblue;
  position: absolute;
  z-index: 20;
  bottom: 0;
  animation: 5s infinite c-line linear;
}

#coasterRound {
  width: 100%;
  height: 100%;
  border-radius: 50%;
  border: solid transparent 10px;
  border-bottom: solid lightblue 10px;
  position: relative;
  animation: 5s infinite c-round linear;
}

#whiteScreen {
  width: 100%;
  background: white;
  position: absolute;
  z-index: 10;
  top: 0;
  animation: 5s infinite white-screen linear;
}

@keyframes loop {
  0% {
    margin-left: -200px;
  }
  38%,
  43% {
    margin-left: calc(50% - 50px);
  }
  58%,
  63% {
    margin-left: calc(50% - 50px);
  }
  100% {
    margin-left: 100%;
  }
}

@keyframes c-round {
  0%,
  43% {
    transform: rotate(-45deg);
  }
  58%,
  100% {
    transform: rotate(-315deg);
  }
}

@keyframes c-line {
  0%,
  38% {
    left: 0;
    width: 60px;
  }
  43% {
    left: 50px;
    width: 0;
  }
  58% {
    left: 40px;
    width: 0;
  }
  63%,
  100% {
    left: 40px;
    width: 60px;
  }
}

@keyframes white-screen {
  0%,
  38% {
    height: 100%;
    transform: rotate(0deg);
  }
  43% {
    height: 50%;
    transform: rotate(0deg);
  }
  44%,
  57% {
    height: 0;
    transform: rotate(0deg);
  }
  58% {
    height: 50%;
    transform: rotate(180deg);
  }
  63%,
  100% {
    height: 100%;
    transform: rotate(180deg);
  }
}
<div id="container">
  <div id="coasterLine"></div>
  <div id="coasterRound"></div>
  <div id="whiteScreen"></div>
</div>

its been great!