Rails have a kinda slow default max sliding behavior; so, big hangers with sliding doors can only open so quickly. There are 4 good workarounds that I know of:
1 - The easiest solution is to use door or forcefield blocks instead of rails, they are not as pretty, but they reduce lag and open instantly.
2- Use rotators instead of sliding rails. These are also very fast, but the logic is more complex. They scale up better than sliding doors because rotation speed is based on angle instead of blocks moved, so a 100-block hanger can swing open just as fast as a 10 block hanger. Getting these to seal perfectly can be difficult, but you can add a seam of plex/blast door that opens to break the seal so that it can rotate, then closes again after its done rotating to reseal.
3- Use segmented doors. Basically, instead of one big 50m door, you might make (5) 10m door segments that are one rail entity on top of the next. Then you trigger them all at once with wireless blocks so while they all move slowly on their own, the door as a whole opens and closes 5x as fast because their speed is additive (also looks awesome.) Be aware though that these are a bit laggy; so, you'll want to zero your rail speeds while it is not in use.
4- Then there is the most likely to malfunction option, (but it does exactly what you are asking) for is to use a series of shoot-out and catch rails. Just be aware that if you try to use one while the game is lagging out, there is a good chance your door will fly off into space.