thanks for your answers.
I got me a speedometer and actually I get 34 km, not 20. Which still is way too little for a 20Ah batt.
I've measured the amps with a multimeter (at full speed with wheel in air), it's 1,45 ampere. Then I measured the time how long the motor runs with wheel in air with a fully charged batt. It went for exactly 9,1833 hours.
That's 1,48 A * 9,1833 h = 13,59 Ah.
So that's definitely not a 20Ah battery.
I bought the battery from cammy_cc from ebay. I hope I can solve this problem with him.
I'll let you know how it turns out...
Greetings
Nicolai