Hurricane Wind Strength Increases as the Square of the Velocity
We show the relative force strengths associated with the velocities starting the various category storms, and with the very high velocity of Hurricane Irma.
Force is generated by the change in momentum of the striking air in a unit time. The Force on a unit area is the momentum hitting it for density r and mass m, with velocity V, which is m X V in a unit time. But in a unit time, a horizontal column of length V, hits, with mass m = r X V. Substituting that for m gives F = r V^2. That is that the force per unit area or pressure is the density times the velocity squared. The relative situation is when a car is speeding through the air, the car hits the air, and the force of air friction goes as velocity squared.
We will give a table of the minimum velocity of each hurricane category of the Sappir-Simpson scale, the minimum velocity of each category, and then the velocity scaled by 100 mph and then squared for a relative measure. The last column scales the minimum velocities by that for Category 1, V1.
Category. Minimum Velocity. V^2/100^2 (V/V1)^2
- 74 mph. 0.55. 1.00
2. 96 mph. 0.92 1.68
3. 111 mph 1.23 2.25
4. 130 mph. 1.69 3.09
5. 157 mph. 2.46 4.50
Irma. 185 mph. 3.42 6.25
Note that a category 5 at minimum is twice the force of a category 3 at minimum. A category 3 at minimum is 2.2 times a category 1 at minimum. Since Irma’s velocity squared at its 185 mph maximum of 3.42 is twice the category 4 value of 1.69, it would have achieved Category 6, if their was one. The largest hurricanes have topped off at 185 or 186 mph.
One problem with using the scale on a map, is that right after the storm changes from 5 to 4, it is still close to a 5, yet could mislead viewers to think that it has sunk to the base of a 4. CNN is now showing a sliding scale to prevent this problem. It could also be solved by using a 4.5 or 4-5 label.
Below the hurricane scale is a tropical storm which starts at 39 mph to 73 mph. 39 mph scaled by 100 mph give a comparative entry for V^2/100^2 of 0.15.
The wind speed is the average over a minute at ground level at the eyewall of the hurricane.
The Catagory is determined by the maximum wind which occurs at tha edge of the eyewall. The width of the storm is an incredible 370 miles. The radii where Irma starts with Category 1 or hurricane force winds in the four different directions is 57, 57, 52, and 40 miles from the center.
With Irma, while the wind speed average was expected at 160 mph, the wind gusts could go up to 196 mph. Clearly the gusts could cause the worst damage. However, one commentator pointed out that the continued rattling of the steady wind causes the damage. Scaling 196 mph by 100 mph and squaring gives the relative V^2/100^2 of 3.84. Scaling it by V1 of 74 mph squared gives 7.02. Even though 160 mph is at the start of category 5, the gusts would increase the force by 56%.
CNN also gave an example of how the wind speed increases as you go up higher in a building. We give a short table of different floor heights, wind speed in the example, and velocity scales by 100 mph squared. The 145 mph is the expected wind speed from Irma in Miami.
Level. Velocity. V^2/100^2 (V/V1)^2
Ground. 145 mph 2.10 3.84
30 story. 174 mph. 3.03 5.53
80-100 story. 189 mph. 3.57 6.52
This says that if the wind velocity at the ground is midway between category 4 and 5, at a very tall building it would be at a Category 6 value. The rule that they use is that the wind speed increases 20% above the ground speed at 30 stories, and 30% above the ground speed at 80-100 stories.