To inflate the kite, you need a “double action” pump, which pumps air both ways by pressing and by pulling its handle.
For what they are, they are sold pretty expensive by Kite brands (with price ranging from 35 bucks up to 50+) but the truth is that, even a double action pump for rubber dinghies sold online or at supermarkets will do, and you can find one for around 10 bucks.
I found a cheap one here for you.
The important thing is that you check that the provided nozzles/adapters are compatible with the inflation valves of your Kite before buying, as shapes and systems vary from brand to brand. Normally, when you purchase a new Kite, a pump should also be included, otherwise, get a cheap one, but don’t dare be seen with a foot pump ion the beach if you don’t want to get mocked by the whole beach.
Can I get a Pump?
The kite pump is undoubtedly the most forgotten object by Kiters, as witnessed by this hilarious (but realistic) video from Liquid Force.
Shit Kiteboarders Say… “Hey, Do you have a pump?”
Don’t be a shit kiter.
