What is the purpose of runway grooving?
How does the airport drainage system work?
- Why do airports remove rubber from the runway?
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3$\begingroup$ Rubber removal is addressed here: Do runways need some special kind of tar or protective layer? and How often do runways need to have typical maintenance? $\endgroup$ – fooot♦ Feb 18 '16 at 16:48
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5$\begingroup$ This is three almost entirely separate questions. Stack Exchange tends to work best when there's only one question per question $\endgroup$ – David Richerby Feb 20 '16 at 5:20
What is the purpose of runway grooving?
The channels help to remove water from the runway. They also provide an area for the water to build up. With out these channels the water runs the risk of forming a thin surface covering the runway which can be very dangerous. As mentioned by john here in the comments this is usually known as hydroplaning and is the same as what happens to a car.
How does the airport drainage system work?
This is a bit of a guess but I assume they work like any other road drainage system and it will depend on where the airport is located. Here is a very dated report prepared for the DOT on runway drainage that you may find of some interest. Here is the FAA's full paper on designing surface drainage for airports, it's a bit long but should cover what you are looking for.
Why do airports remove rubber from the runway?
Tires obtain the best friction when they come in direct contact with the runway surface. Excess tire rubber that wears off and sticks to the runway can affect the tire/runway interactions. This wiki article covers the main points pretty well.
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3$\begingroup$ Wet rubber on the runway is especially slippery. Race cars have the same issue, and you will see drivers using the "wet line" or "carting line" when the track gets wet so they can avoid the build up of rubber on the track that is very beneficial when dry. $\endgroup$ – FreeMan Feb 18 '16 at 18:32