Improved Methods of Estimating Tornado Intensity Version 4 (Please Don't Delete)

[Wade12345]

Improved Methods for Estimating Tornado Intensity
Version 4 Revised and Edited
By Wade D. Smith

Abstract
In spite of past improvements with the Fujita Scale and Enhanced Fujita Scale, some Tornado Wind Estimates remain inconsistent with other observations. This paper is designed to present at least four metrics for estimating Tornado Wind Speeds, and each metric has its own strengths and weaknesses. It is the theory of this author that no one metric is sufficient to fully understand tornado wind damage events. This paper will examine Sustained Winds, 3-second gusts, 1-second winds, and "Instantaneous Wind Maxima" of Tornadoes to best rate each type of tornado damage. A few of the higher instantaneous maxima will be shown to be "real, but unobservable". However, I find an instantaneous wind of 196mph in association with destroying a cinder block wall, 254mph in association with breaking a plywood and 7 studs on the corner of a house, and instaneous maxima of 185mph in association with flipping a one-ton pick-up truck. All of these calculations will agree with the Hurricane Michael and Camille Proxy data approach also presented in this paper. I further calculate a 215mph to 223mph instantaneous wind speed necessary to blow a home clear of its foundation, and suggest using a stronger bottom plate and heavy timbers on homes and businesses walls instead of 2x4s.

Extreme Hurricane eye-wall Vortices as Proxy Data for Strong and Violent Tornadoes.
Recently, the Arabi Tornado near New Orleans was rated by the National Weather Service as having "Instantaneous Winds" of 160mph. I believe I can easily show that the Arabi Tornado was much, much more powerful than this using all four metrics I will hereby describe. Using Hurricane Michael's Eye Wall Mesovortices as a proxy of a multi-vortex tornado is possible, since we know from Tyndale Air Force Base observations that Hurricane Michael was 160mph Sustained with gusts to around 200mph to 210mph. This barely hit the threshhold of blowing some Andrew Code and Pre-Andrew Code homes clear of their foundations in Mexico Beach. These homes were far enough inland to not be destroyed by the water from the Storm Surge, they were instead destroyed by the mesovortices of 160mph sustained with 200mph to 210mph gusts. But this was gradual across thirty minutes or so. In the Arabi tornado, most eye witnesses reported the entire event lasted as little as 2.5 seconds to totally destroy a house, and no more than 30 seconds. Calculations based on the width of 320yards and forward speed of 40mph or so, show the main vortex only persisted over any one house for about 16 to 17 seconds, so not even half of a one-minute sustained wind got applied to any one obstacle. This means the Arabi Tornado must have been at least 160mph Sustained with 3-second gusts in the 200mph to 210mph range, because it happened so much faster than the Hurricane Michael damage. The real instantaneous maximum wind was much higher than this: Leonard Traylor, a Concrete Contractor who has at times made Tornado Shelters, also estimates the Arabi Tornado as 160mph to 220mph Sustained, again based on hurricane proxy data, with an instantaneous Maximum wind "In excess of 400mph" (Traylor et al). See Instantaneous Destructive Potential topics below for my own calculations.

In contrast, Hurricane Charley is well known to be a 150mph sustained event with gusts from 185mph to perhaps 200mph. Charley did not blow houses clear of their foundations, but did peel rooftops and flip automobiles, agreeing with calculation later in this paper. We can know that 150mph sustained with 185mph gusts flips automobiles, but does not blow houses clear of foundations. We can then use this wind speed as a proxy for a tornado that is not strong enough to wipe the foundation clean for an Andrew-code or pre-Andrew code residence. So a 150mph Sustained Tornado with 185mph 3-second gusts should be blowing down the outer walls of a house and blowing the rooftops off the house, but not blowing the entire house clear of foundations.

Hurricane Camille did similar damage with 175mph sustained winds at landfall, and 3-second gusts of at least 225mph before the anemometer broke.

We may use Hurricane Dorian as a proxy for when Schools and Cinder Block business and churches are destroyed. Hurricane Dorian was believed to be a 185mph Sustained Hurricane with gusts to about 240mph. This hurricane hit the Bahamas and eventually destroyed a school made from cinder block and concrete fill. With this metric, we can then know that Cinder Block with concrete fill fails after "several minutes" of 185mph sustained wind with a gust to 240mph.

We may use Super Typhoon Haiyan as a proxy for even more powerful tornados. This Typhoon hit the Philippines with Sustained winds of 195mph and 3-second gusts to 255mph (JTWC data). The wind blew out and destroyed concrete panels in a parking garage where the eye-wall made landfall. Based on the Tensile Strength and Compression Strength of Concrete as 5000psi per inch thickness for this type of concrete (Traylor et al,) I was able to calculate the sustained winds and the 3 second gust required to break the 6 inch thick steel reinforced concrete panels. I found the panel breaks at exactly 266mph instantaneous wind, which is consistent with the 195mph sustained winds and 255mph 3-second gusts, as estimated by the Joint Typhoon Warning Center for Super Typhoon Haiyan's winds at landfall. Therefore, destroying the concrete panels of a parking garage, but leaving the concrete pylons standing, in a tornado is a close proxy to the tornado having 195mph sustained winds with a "common 3-second gust" to 255mph and higher "instantaneous winds". One would expect the walls of Hospitals and Factories to fail in such conditions as well.

P = pressure = 30,000PSI, to break 6 inch thick panel @ 5000PSI per inch thickness strength.

V = wind in MPH

It's a 3 meters tall panel, so that gives 39.4 inches * 3 for the surface of wind per inch width of base of the panel.

P = 30,000psi = 0.00256 * 3 * 39.4 * 1.4 * V^2

Move constants to the left:

70,816.7mph^2 = V^2

V = 266mph instantaneous winds

This figure rounds UP to 270mph 3-seconds gust for forecastable meteorology. It should be noted here that the taller the concrete wall panel, the easier it is for the wind to break the panel at the base.

Break a Piece of Plywood in Half
This is for no studs backing for a 4ftx4ft section as an example.

Tensile strength of Plywood is between 4000psi and 5000psi. I'll use the lower bound.

4000psi = 48in^2 * 0.00256 * 1.4 * V^2

V = 152.5mph instantaneous wind.

Break the plywood and 4 studs backing the plywood.

Tensile strength of a 2x4 stud is 11,400psi.

1.5x3.5x 11,400 = 59,850pound-force per stud.

Ignoring corner post of a house, there are 4 studs backing each sheet of plywood on exterior, plus the tensile strength of the plywood too.

4* 59,850pound-force = 239400pound-force

Adding tensile strength of the entire 3/4 inch plywood by 48 inches gives 383,400 pound force.

~383,400pound-force = 48in x 48in * 0.00256 * 1.4 * V^2

V = 215.5mph instantaneous winds

This is the instantaneous wind needed to break the wall down given a complete wrap of 3/4 inch plywood and ignoring the bottom plate as the wall's weakness, but is not sufficient to "blow the house clear of foundation"; For that you'd need a 3-second gust to take the house airborne. This then gives the limit to the structural strength of a house made from 2x4s. If you instead use heavy timbers, the house can withstand more wind.

Breaking the plywood on the Corner Post

A corner post on a house is three 2x4's nailed together in one plane and another 2x4 nailed backing it on the adjoining wall. Altogether, that's 7 2x4's backing the plywood attached to the corner post, and ignoring the other sheet of plywood orthogonal to this.

7 * 59,850 pf = 418950pf

Add plywood tensile strength to get approximately 530,000pf

530,000pf = 48 * 48 * 0.00256 * 1.4 * V^2

V = 254mph instantaneous wind

This is instantaneous winds to break all 7 studs and the plywood in half on the corner of a house with 3/4 inch plywood complete wrap, and ignoring siding and brick exteriors.

Rip up 2x4 bottom plate (aka "Green Plate") on exterior walls.

This is the weakest point on a house, and needs to be replaced with 4x4 bottom plates and more anchor bolts and nails.

Surface area of washers on anchor bolts is .785in^2. There are only about 1 anchor bolt per 4 feet of wall, and only a few nails, which I estimate double the average number of anchor bolts.

This gives:

17898 pf for the strength of the anchor bolt-bottom plate junction, which is pathetic.

17,898pf = 48 * 96 * 0.00256 * 1.4 * V^2

V = 33mph

However, there are other structural factors which prevent this from breaking so easily, such as adjoining T's from interior walls and the Joists and Fire-Blocks of the walls preventing racking from happening so easily. A better way of calculating the exterior wall bottom plate failure is to find the wind load needed to disintegrate the bottom-plate along a wood-grain down the center of the 2x4 where the Anchor Bolt(s) are screwed on.

11400psi board strength * 1.5 inches board thickness * 48 inches length per plywood sheet = 820800 pf

820,800pf = 48 * 96 * 0.00256 * 1.4 * V^2

V = 223mph instantaneous winds

That closely agrees with the 215mph instantaneous winds to break the plywood and 4 studs. So a 2x4 bottom plate will disintegrate at 223mph instantaneos winds, which is about the same as the maximum 3-second gust recorded in Hurricane Camille just before the steel anemometer famously broke. So the limit of home construction when made of 2x4s is about 215mph to 225mph instaneous winds. Anything meeting or exceeding this margin of winds will blow the home clear of the foundation within a time frame ranging from a single instant to no more than 3 seconds.

A 4x4 bottom plate would be more than twice as strong in pound-feet (3.5in vs 1.5in thickness).

1915200pf = 48 * 96 * 0.00256 * 1.4 * V^2

V = 341mph instantaneous winds

So we should build houses from heavy timbers with a 4x4 treated bottom plate instead of a 2x4 treated bottom plate.

Vertical Updraft of Cinder Blocks.
I have calculated the wind speed needed to lift a Cinder Block vertically in order to "Sweep Clean" the foundation of a cinder block structure. This is Cinder Block with Mortar, but no concrete filling. Cinder block is typically 8"x8"x16", which I converted to metric to get the surface area of one face of the block. In brief terms, I found the vertical sustained winds required to be exactly 142mph sustained on the holed sides and 149mph sustained length-wise.

Cinder Block Dimensions converted to Metric.
W = 8" / 39.4in/m = 0.203m
L = 16" = 0.406m

A = 0.0454147234m^2 (for the holed sides)

The mass is 16kg.

F = A* P *Cd

P = 0.613V^2

Cd = 1.4

16kg*9.8m/s^2 = A*P*Cd

156.8 = 0.0454 * 0.613 * V^2 * Cd

V^2 = 4023m^2/s^2

V= 63.43m/s

V = 142mph

That's vertical sustained wind with implied higher gust to around 170mph. A similar calculation shows accelerating the cinder block vertically and length-wise requires 149mph sustained vertical updraft. This is not enough to initially, instantaneously break the mortar of the cinder block wall. This is just the minimum requirement to make the blocks hover once they are broken down. This is approximately the weakest vertical sustained wind and associated gust to lift a cinder block vertically and make it hover above ground against the force of gravity.

Instantaneous Horizontal Displacement of Cinder Blocks
According to the American Society of Civil Engineers, it takes "several minutes" of 135mph Sustained wind to destroy a Cinder Block Wall with no concrete fill. We should realize this would have an associated 3-second gust to around 170mph. This puts the diagonal wind required to blow cinder blocks clear of a foundation at around 195mph sustained. I calculated an instantaneous wind of 196mph is required to instantaneously break down an 8 foot high cinder block wall at the base, assuming mortar has a tensile/compressive strength of 3000psi per inch thickness. As you can see, this instantaneous wind is higher than the common gust associated with a 135mph sustained wind. The Arabi tornado destroyed at least one cinder block structure "in 16 seconds or so", and this instantaneous wind is consistent with the Hurricane Michael 3-second gust proxy data of 200mph to 210mph.

Average thickness of mortar across cinder block: 4.4in.

3000psi/in * 4.4in = 13,219psi mortar strength

13,219psi = 0.00256 * 8 * 12 * V^2 * 1.4

Move constants to right:

V^2 = 38,420mph^2

V = 196mph instantaneous wind

Ironically, this is weaker than stick frame construction. Instantaneous wind only breaks the wall down, but does not blow it clear of foundation. For that you need a 142mph to 149mph vertical sustained wind in addition to wind blowing at least a few miles per hour horizontally for the next several seconds, depending on foundation size parameters.

One Second Ballistic 2x4 Calculations
These calculations should be used sparingly and only when necessary, but are to demonstrate a problem with any one rating system for tornadoes. The 75mph ballistic projectile is usually modelled by NWS and other meteorology officials to mimic a 2x4 thrown in hurricane and tornado winds. Using different techniques and circumstances, I found the 1-second winds needed to accelerate a 2x4 length-wise from rest to 75mph impact velocity ranges from ~330mph to as much as 700mph, depending on acceleration time and acceleration distance. I found cross-ways acceleration in one second requires 160mph one-second winds, and accelerating laterally requires 205mph one-second winds. These values cannot be ignored, but for the purpose of forecastable meteorology, I believe we should use Sustained winds and 3-second gusts, except in the case of the failure point of the cinder block wall at 196mph and concrete wall at 266mph instantaneous winds. Wind speeds above the reasonable failure point of the entire house probably do happen in the tornado, but we'd need a hand-held radar gun pointed at the tornado from an unsafe range in order to measure such winds, which should not be attempted even by a trained professional...unless we could do it with an unmanned probe or drone.

The Case of a Steel Truck Frame Wrapped Around a Tree Trunk
Much of this ballistic projectile damage is done instantaneously. I have done calculations in the past for an automobile taken airborne by Hurricane Sustained winds, and found the threshhold to be about the same as the beginning of Category 5 on the Saffir-Simpson Hurricane scale, which is to say 157mph sustained with about 210mph 3-second gusts. In the Arabi Tornado, a victim's truck was found wrapped around the stump of a tree shaped like a pretzel. The truck was not accelerated over a time period of multiple seconds, because it had been parked just across the street. This is an example of an "Instantaneous Max Wind" of "Several Hundred Miles Per Hour" ripping the truck up and slamming it into the tree hard enough to wrap the steel frame around the tree. So the bare minimum to accelerate the truck over "several seconds time" would be 157mph sustained with a 210mph gust, but this actually happened in less than 3 seconds. This means the Arabi tornado's 3 second winds were in excess of 210mph, and it's "Instantaneous Maximum" was believably in excess of 400mph for some phenomena, not the 160mph reported by the NWS forensic team. I am just stating the facts that they've under-estimated the Arabi tornado by quite a large margin.

Vertical Updraft of one-ton pick-up truck:

Weight = 1000kg * 9.8m/s^2 = F

F = A * 0.613 * V^2 * Cd

9800(kg*m/s^2) = 12.5m^2 * 0.613 * 1.4 * V^2

V = 68mph

That's sustained vertical, which is not very much in terms of tornadoes. In this case the horizontal winds needed to impale the truck's steel frame on a tree are much higher and "nearly incalculable". A grown man can swing a carpenter's hammer in excess of 140mph, but that does not bend nor break the handle of the hammer. So we can immediately see that bending the truck's frame around the tree requires an impact velocity greater than 140mph. Calculating how high it really needs to be depends on the exact dimensions and quality of the steel frame, but I suspect the true impact velocity is in excess of 200mph. This would require 3-second winds in excess of 210mph, and one-second and instantaneous maxima higher still. I think this already shows the Arabi Tornado was much more powerful than "instaneous winds of 160mph" as rated by the NWS office in New Orleans. The reader may object to these very high wind maxima not utterly disintegrating everything, and may assume I've made mistakes in these calculations. I would argue that we could use Nuclear Bomb test detonations as an example of why 500mph to even 1000mph winds do not necessarily disintegrate everything they hit. In those videos, trees are left standing and many other structures are sometimes barely damaged due to this paradox.

Horizontal Winds Taking Truck Airborne Without Vertical Updraft

The cab of the truck is about 2 meters tall, and the body of the truck is about 1.25 meters tall, so I'll use an average height of 1.44meters. The length is roughly 5 meters and the truck is about 0.33m above the ground. So this gives a broad-side area of about 5.55m^2.

weight = 9800N

friction =~ 0.3

Force = 9800N = 0.3 * 5.55m^2 * 0.613 * 1.4 * V^2

Isolate constants:

V^2 = 6858.4(m/s)^2

V = 82.8m/s = 185mph instantaneous winds

That's instantaneous horizontal wind required to flip the truck one time on its side, which is consistent with about 150mph one-minute sustained winds in a hurricane. Taking the truck fully airborne and wrapping it around a tree trunk requires even greater instantaneous winds than this, but should be limited by the 223mph instantaneous winds calculated for the failure of the bottom plate of residential homes outter walls.

Arabi Tornado Ratings
I believe based on these proxy data and calculations that the Arabi tornado should be considered as 160mph to 175mph sustained with a 3-second gust of around 210mph to 225mph, one-second winds of at least 223mph, and an instantaneous maximum wind greater than that in some cases. That overlaps Hurricane Michael Proxy Data and hurricane Camille data, and the failure point I calculated for a cinder block and mortar wall being 196mph instantaneous winds. According to NWS Storm Prediction Center data for this tornado, the surface CAPE that day was over 3000J/kg on land and over 4500J/kg over water for several hours leading up to the tornado. The Mixed Layer CAPE was less, at a bit more than 2000J/Kg over land. This leads me to believe the surface winds of the tornado were much higher than the winds a few hundred to a few thousand feet aloft, where radars would be observing. I've seen data suggesting similar phenomena in the most intense hurricanes (Wilma, Dorian, Irma,) so I suspect tornadoes behave the same way.

Mayfield Tornado Ratings
Because this tornado met the "Cinder Block Blown clear of foundation" parameter, I would rate it as 195mph Sustained with a 3-second gust of 255mph and instantaneous maxima higher still.

Joplin Tornado
Based on damage to Hospital Building, I'd rate this tornado as 195mph sustaned with a 270mph 3-second gust and again higher instantaneous maxima.

Conclusion
I believe the EF rating of tornadoes should be the Sustained Winds. We can no longer rate tornados using only one wind speed metric. We need to test materials in wind tunnels and ballistic missile scenarios, and engineer new housing codes and new small business construction codes to withstand these four major types of phenomena: One-Minute Sustained Winds, 3-second Gust winds, 1-second winds, and "Instantaneous Maximum Winds".