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How it's actually done:

Weight and balance need to be calculated before every flight. This includes the total weight.

Large aircraft use load sensors in each gear strut to calculate the suspended weight (the weight below the sensors doesn't change with loading: rims,tires, brakes, etc)

During maintenance and inspection, load sensors are calibrated to ensure they're correct.

Small aircraft are weighed on scales that are put under each wheel and the weights are combined. Once the empty weight is known for that particular aircraft, adjustments can be made when equipment is installed or removed, passengers and luggage loaded or unloaded, and fuel weight for each flight by using the as-measured empty weight.

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