It's usually pretty hard to win against the government , it ends up costing you as much or more. I'd be cheesed off too but in the end I'd just pay the money and try and get on with life.
Maybe the cop was just lazy with his paperwork.
Maybe this guy radared you at 31 in the 25 zone and just wanted to get you to slow it down early in the morning for your own safety what with you bein' on a bike and some drunk in a cage maybe likely to bang into you. Getting side swiped by a car or van when you are in a car or van is a complete different situation.
Sometimes things happen for a reason , for every time you have been speeding and got away with it this is a token payment.
Hope I don't sound unsympathetic or like I'm trying to be a smart ar$e but sometimes you just can't win so turn it round and make the situation work for you.
