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In this answer to another question, it was stated that:

Take-off mass: If you take no payload, the aircraft will produce less induced drag and reach a slightly higher range

How does a change of weight inside the same shaped container increase induced drag, since the air doesn't come in contact with the cargo?

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For the same aircraft speed and an horizontal trajectory:

  • When the aircraft is lighter, less lift is required.
  • To decrease the lift, the angle of attack needs to be reduced (said otherwise: the aircraft flies more horizontal).
  • A smaller AoA creates less induced drag.

Lift and drag coefficients as a function of the angle of attack are represented in the following diagram.

enter image description here
(Source)

The ratio L/D is also represented, with its maximum L/D max. L/D max is an economical angle of attack. After L/D max, a gain in lift is at the expense of a larger increase in induced drag.

Side-effect of reduced drag:

  • The thrust can be reduced to achieve the previous speed.
  • The range is increased thanks to the thrust reduction.

For a more accurate representation of lift and drag coefficients against the angle of attack, and additional information: Lift and drag curves for the wing.

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Induced drag is caused by lift. (historically, Induced Drag was named "lift induced drag").

If weight(mass) of the aircraft decreases, the lift required to fly the aircraft decreases. And the drag associated to that lift also decreases.

The quoted statement is true, but "slightly" can be discussed. Because the increase in range depends a lot on how much payload the aircraft could carry. (If it's %50 of the max takeoff weight, the range could increase a lot).

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  • $\begingroup$ OK, "slightly" is only true for aircraft with good aerodynamics. Only if creating more lift does not impact drag significantly, "slightly" is justified. But I assumed that today we should be able to meet that goal without much effort. $\endgroup$
    – Peter Kämpf
    Commented Jun 6, 2015 at 23:55
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Two ways of generating more lift, which is needed to carry more weight: 1. increase angle of attack. 2. Increase speed with same angle of attack. Both create more drag, there for both require more gallons per hour to fly.

Because of higher AOA requirement for a given amount of lift at a given speed, a more heavily loaded aircraft will stall at a higher airspeed. This is why, when taking off and landing, it is a good idea to know the stall speed for your weight, and add in your safety margin accordingly.

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