How does scaling of UAV size impact range?
If you compare geometrically similar aircraft, the larger one will have more range.

First, its volume grows by the third power while areas grow only with the square of its scale, so wing loading will be higher for the larger aircraft. This will translate into a higher cruise speed, because the range optimum dictates an optimum speed for each aircraft. In a first order approximation, an aircraft of twice the size will fly at 1.41 times the speed of a smaller aircraft. The much higher internal volume will allow it to carry much more fuel, but even when the fuel fraction for both designs is kept constant will the larger aircraft fly farther.

If we restrict fuel to the same fraction of total mass, the exponent for mass increase is slightly above 2. All surfaces grow by an exponent of 2, but the stresses would be higher in a linearly scaled structure, so the structure of the larger aircraft needs no be beefier. An exponent between 2.2 and 2.3 has been found to best represent reality. This means that doubling dimensions will result in a mass increase by a factor of 4.76. In order to fly at the same polar point, the large aircraft needs to fly at 109% of the speed of the small aircraft.

In a more detailed analysis, we need to first look at the installed power: If we focus on piston engines and scale the engine in the way we scale the aircraft, for a size increase by a factor of two will the displacement grow by a factor of eight while the engine speed will decline by a bit less than a factor of two. The smaller engine will have higher friction, thermal, sealing and combustion losses, so it will have a noticeably lower efficiency. If we just look at statistical data, power output grows slightly less than linearly with displacement:



Statistical data for power over displacement. Source: Menon, S., and Christopher P. Cadou. "Scaling of Miniature Piston-Engine Performance, Part 1: Overall Engine Performance." Journal of Propulsion and Power 29.4 (2013): 774-787

Next, we need to look at Reynolds number effects. The larger aircraft will fly at a higher Reynolds number for two reasons: Increased length and increased speed. Together, a doubling in length will translate into a first-order Reynolds number increase by a factor of 2.18. The coefficient of friction will scale with Re$^{-0.3}$, so doubling the length of an airplane will reduce the friction coefficient of the large airplane to 79% of that of the small airplane. This will not only affect total drag, but also the polar point for best range. Since the optimum lift coefficient is proportional to the square root of zero-lift drag, the optimum lift coefficient for the large airplane will only be 89% of that of the half-size airplane and cruise speed will be higher by a factor of 1.225. This means that dynamic pressure is higher by a factor of 1.5.

Ideally, this calculation needs to be iterated, but for now I keep it at one iteration step.

This higher dynamic pressure now needs to be multiplied by the increase in reference area to arrive at the zero-lift drag: 1.5 times 4 times 0.79 means that doubling the size will let zero-lift drag grow only by a factor of 4.74. Since zero-lift and induced drag are of the same size at the optimum cruise point, the same factor applies to the total drag. The required power, however, is proportional to speed, so doubling the size will increase the power demand by a factor of 5.78. This is well below the power increase from a scaled-up engine, so the larger aircraft actually needs a proportionally smaller and lighter engine, leaving more reserves for fuel. Or it can scale up the engine linearly and load proportionally more fuel.

Fuel consumption is proportional to engine power, but we get another advantage from the larger engine: Its specific fuel consumption will be slightly better:



Specific fuel consumption over displacement (same source as figure above).

In sum, the larger aircraft will


cruise at 122.5% of the speed of the small aircraft
will consume 5.5 times as much fuel per time for a mass increase by a factor of 4.76. Combined with the speed increase this leaves only a 5.5% advantage.
If we assume a scaled-up engine with an increased power by a factor of 7.27, the mass increase can be by a factor of 6 with maybe twice the fuel fraction of the smaller aircraft and 7 times higher fuel flow per time. This takes into account that the cruise speed will grow with aircraft mass.


This 70% longer flying time coupled with the then 24% higher cruise speed will leave the smaller aircraft in the dust.