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After fast driving
This is quite common.
Basically, what happens is, the MoT guy adjusts your carb lean for the emissions, then after a mad burn the carb gets hot from conduction/radiation.
Some carbs (HIF I think) have a waxstat thing built into the jet. What this does it reduce fuel flow when the carb heats up. It assumes the air is hot too! This attempts to keep a set mixture ratio in different climates.
After your mad sprint, the carb is hot, and the fuel is reduced, but the air may still be cold (the problem occurs more in winter).
What you end up with is an already lean mixture being made even more leaner! Stall time!
Revs dropping too low
"Every time when I stop, the engine drops the revs really
low down to 200rpm or so and then slowly comes back to 800rpm (in 3-4 secs).
Sometimes it dies completely hot or cold. Why?"
Dashpot oil is too thick.
What happens is, when you lift off the throttle the piston is taking a while to fall due to the thick oil (thicker when cold). This means the needle too far out of the jet and the air speed over the jet is very slow, this gives a lean mixture, and the revs drop low.
As the piston falls to it's correct level, the mixture picks up and the revs rise again.
Use light oil in the carb, not engine oil. '3in1' oil is popular.
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