No.
Using a larger ring does not mean taller flame height. The height of the flame is dependent on the amount of gas being supplied to the burner itself. If the gas pressure being supplied does not measure up to the BTU requirements of the burner, a larger ring will broaden the flame, but take away from the flame height. Most customers think of a larger flame as equating to the overall flame height, not so much the width. If the delivery of gas cannot be increased, then “reducing” the fire ring size will increase the flame height.
