aye, aye, capn!

Here's an approach. Every wire gauge has a listed resistance, which may, as Amir shows, be totally unrealistic. But it's all we've got as a starting point.

Here's some arithmetic for you to do. I've listed below the supposed resistance per thousand feet of wire. You can use the values to figure out what you need.

Gauge followed by resistance per thousand feet in ohms.

26 40.81
24 25.67
22 16.14
20 10.15
18 6.385
16 4.016
14 2.525
12 1.588
10 0.9989

For instance, you've got a run of 16 ga that works. It's 89 feet long. You want to know, if you have to use 24 gauge, how long of a run will work just as well.

First, think. The skinnier wire will go a shorter distance, so the math will give an answer smaller than 89. Second, this is a matter or proportions, so something is going to be divided by something else.

We have two numbers, the resistance of 16 and the resistance of 24. The equation that will give the smaller number is 16ga/24ga = 4.016/25.67 = 0.156; multiply that times your working 16 ga length, 89 feet. A 13.92 foot length of 24 gauge will perform the same as an 89 foot length of 16 gauge.

This does NOT figure the maximum length that another gauge wire will work. It figures the length of the other wire with the equivalent resistance.