Bmw engine

yesterday, on my way home form work, my 2001 bmw 325ci began to shake and a thumping noise came form the fornt of the car. i pulled over - thought i had a flat. no flat, so i proceeded again. the same noise and shake began around 40mph, and then seemed to improve at about 53mph. i was very low on gas - less than a gallon, for the 1st time ever in this car. i stoped, filled my tank (always premium 93), and proceeded home. same shake and thump. this mornign, it ook the car for a spin aorund the nieghborhood, no issues at speeds 40mph or less, but am obvisouly concenred. could this have been some negine knock generated form crappy gas at the bottom of the tank ? what other possibilites ?

I think you have a tire that has a broken belt or tread separation. You have not duplicated yesterday’s situation. Get it back over 40MPH and report back.

Does this car have run-flat tires?

If the problem is a broken belt or tread separation, is it wise to take the car up to 40 mph or beyond?

regular tires – not run flats, and i chekced the tires a few times – visually, they look fine…

Check your drive shaft guibo (flexible rubber coupling), the symptoms you describe indicate that the coupling is failing.