Riddle: A hurricane strikes a city on the Gulf coast with a maximum sustained wind of 100 miles per hour. The city rebuilds from this hurricane. There is another hurricane heading toward the same area of the Gulf coast. A weathercaster mentions that this next hurricane will have the wind power to do twice as much damage as the previous hurricane. Under this condition what would be the expected maximum sustained wind from the next hurricane?
Answer to Riddle: There is not a linear relationship between wind speed and the damage that is produced. For example, a 150 mph wind would not do twice as much damage as a 75 mph but rather it would produce many times over the damage of the 75 mph wind. The relationship between wind power and damage is going to depends on factors such as building design, wind gusts, wind duration, wind direction change and the amount of buildings per unit area. When considering wind power alone there is a cubic relationship between wind speed and the power produced by the wind. For example, suppose the wind speed is 15 mph and produces 3,375 units of power (15^3). If the wind speed is doubled to 30 mph then the power produced by the wind would be 27,000 units (30^3). As the wind speed increases the power produced increases at a rapid rate.
Assuming the cubic relationship mirrors reality which is does not for all wind speeds and situations, if the wind is 100 mph the damage produced will be 1,000,000 units of damage (100^3). If the units of damage are double to 2,000,000 then the wind speed that produced this damaged can be found by taking the cube root of 2,000,000 which has a value of 126 mph. Thus, the damage produced increases significantly as the wind speed increases, especially as it increases above hurricane force. The 126 mph wind does twice the damage as the 100 mph although the increase in wind speed is about a fourth greater. Damage increases at an exponential rate as wind speed increases in a hurricane.