You raised a heap of questions that need answering to get an idea what the problem is.
The gsxr250 developed a whole bunch of "interesting' habits
First of all if you're having to bump start the bike i suspect you have a dud battery.Usually due to the cold.
What happens is that when the battery is low on charge it still turns the motor over but there aint enufff oomph to charge the coils and get the spark plugs sparking.
The result is that gas is getting sucked into the motor-no spark so the plugs get fouled with unburnt fuel.
Then ya try to bump start it and it just dont wanna know -pluggs too fouled up.
Another issue may be overtight valves which make for hard starting.
In the older gsxr250's the carb diaphrams are starting to crap out.
The coils are also a weak point in the gixxer.
Sorry if Im not answering ya question but i need feedback to get an idea
To see a life newly created.To watch it grow and prosper. Isn't that the greatest gift a human being can be given?
Bookmarks