# Glider Flying Handbook page 5-6 error on effects of weight to stall speed?

I've been reading the FAA's Glider Flying Handbook, 2013 (FAA-H-8083-13A). Page 5-6 in chapter 5 states the following, but it doesn't seem right to me.

The heavy glider has a higher stall speed and a higher minimum controllable airspeed than an otherwise identical, but lighter, glider. The stall speed of a glider increases with the square root of the increase in weight. If the weight of the glider is doubled (multiplied by 2.0), then the stall speed increases by more than 40 percent (1.41 is the approximate square root of 2; 1.41 times the old stall speed results in the new stall speed at the heavier weight). For example, a 540-pound glider has a stalling speed of 40 knots. The pilot adds 300 pounds of water ballast making the new weight 840 pounds. The new stalling speed is approximately 57 knots (square root of √ 300 + 40 = 57).

Increase of stall speed is not proportional to the square root of the raw increase in weight, it's proportional to the square root of the percentage change in weight. So in this case, the new stall speed would be

= StallSpeed * sqrt(NewWeight / OriginalWeight)
= 40 * sqrt(840/540)
= ~49.9


Another way to see this is incorrect is to do what the example says at first and double the weight (540 * 2 = 1080), which should increase the stall speed by 40% to 56.4 knots. So surely only increasing the weight by 300 pounds doesn't have the same effect. And by the math at the end of the paragraph, sqrt(540) + 40 = 63.2 knots which is clearly not equal to 56.4 knots.

Am I correct in my thinking here, and there is an error in the handbook?

The handbook is correct in the earlier example -- double the weight, stall speed increases by $$\sqrt{2}$$.