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I'm aware of some aircraft that have systems to calculate weight and balance. For those aircraft that don't have such systems, how does the pilot know they are within weight and balance limits?

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While I'm not a pilot, I think it goes along these lines:

  • Airlines typically assume a value for passengers depending on gender and age. This distribution in the cabin will typically be quite random and a little variation does not do any harm.

  • Baggage however is weighted on the scales at check in. Each bag is normally scanned as it is passed onto the plane, so that they know where is bag is located. The values are then passed onto the pilots who are able to work out that the numbers are ok. Sometimes there are preferences to load up bags in a certain way for fuel issues, so this is very important to make sure this is still resonable.

These values are then plugged into computers or worked out manually on a paper loadsheet to make sure they are good.

In fact the weight systems you are referring to are quite unusual I think, see this question.

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For commercial airliners this is generally how it's done - standard/assumed passenger weights, and an actual weight for baggage. It's worth noting however that some airlines operating smaller aircraft ("at least one" - Samoa Air) do actually weigh passengers and baggage (and in Samoa Air's case, adjust your ticket price accordingly). –  voretaq7 Feb 27 at 21:23
    
hmm, bags scanned as they're loaded? Hardly. Observed a lot of aircraft loading at major airports, and most often they're just tossed into the next available hold space (of course containerised and palletised luggage may well be weighed for even distribution before loading in the containers, but there too a typical density is likely assumed and just the entire container weighed).] –  jwenting Mar 12 at 10:09
    
@jwenting i've seen multiple documentaries where they scan the bags at some collection point or right before the plane, and i'm very much convinced it's to measure weight, as well as to know that the bag got onboard for security. examiner.com/images/blog/EXID18134/images/… –  TheFlyingEngineer Mar 12 at 12:09
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