delayed illumination of light

2012 ford mustang. i do not drive this car daily. one tire has a very slow leak, need to air it up about every month or two so i forget about it. i start the car
and drive away, but the low tire indication does not show until i am about 15 miles from my air compressor. what is with that?
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Are you asking if it can be set so it comes on when you are only 10 miles away?
Let's assume for the sake of discussion that the low pressure indicator works by detecting that one tire is consistantly turning at a different rate than the others -- a soft tire is smaller, therefore it turns more in a mile than the other tires, this sets the low tire indication on.
If the car goes around turns, then the inside tire turns less than the outside and if it is the soft one then the computer gets confused and has to start over. Then you go around another corner. Pretty soon you are too far to go home for air, so you stop at the gas station or tire store, and get some air.
It confuses me how one can have a leaky tire and forget about it so many times.
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