In the ATC Design Guide 2 "Basic Wind Engineering for Low-Rise Buildings" pg 9-10 there is a mention that

**"There are two approaches to modeling the effects of terrain roughness on mean wind-speed profiles. They are the power-law and log-law models of atmospheric wind profiles. The first model used for engineering purposes is the power law. It is represented by the equation:****U(z**_{1})/U(z_{g}) = (z_{1}/z_{g})^{ā}(Note: I am substituting an "a" for the "α" given my inability to find the "α" with the line over it)

where U(z_{1}) is the wind velocity profile, z_{g} is the gradient height, z_{1} is any other height in the same terrain exposure with a height lower than z_{g} and ā is the power law exponent dependent on terrain roughness. The basic assumption used to calculate mean velocities at various heights in different terrain exposures is that the mean wind speed at gradient height is the same for all terrain exposures. However, the gradient height and the power law exponent ā, vary from one terrain exposure to another. This equation is the basis for the variation in mean wind speed with height shown in figure 2-5. Table 2-2 lists values of z_{g} and ā that have historically been used in ASCE 7 to represent the variation in mean wind speed with height."I am uncertain as to whether you can extrapolate ... Working with the inverse ... . I will stop here. What often seems to follow a logical path in my mind may not make any sense. The pg 10 has the following.

"

*Meteorologists and atmospheric scientists prefer the log law as a mathematical model for the variation of mean wind speed with height. The derivation of the log-law equation has a more constant theoretical basis than the empirically-based power law. Consequently, the log law is frequently used as the basis for developing gust response relationships (gust factors). The expression for the log law is: U(z) = (1/k)u*^{*} ln(z/z_{o}) where U(z) is the mean wind speed, k is Karman's constant generally taken as ∼ 0.4, z is the height above the surface, z_{o} is the roughness length, u^{*} is the shear velocity of flow, which is a relationship between shear stress and air density, and ln is the natural log."

"Engineers should be aware that wind speeds measured by NOAA during hurricanes as they advance toward a landfalling location, are frequently obtained at flight levels between .. ." [A extremely loose and reaching connection to NOAA.]

One reference from the section

SEAW/ATC, 2004a,

*SEAW Commentary on Wind Code Provisions*, Volumes 1 and 2, SEAW/ATC 60 Report, prepared by the Structural Engineers Association of Washington, published by the Applied Technology Council, Redwood City, California.

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James Williams P.E., M.ASCE

Principal/Owner

POA&M Structural Engineering, PLC

Yorktown, VA

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Original Message:

Sent: 03-08-2022 07:50 AM

From: George Miles

Subject: wind analysis that I need help identifying

I have been asked to review a calculation by an engineer that they could not identify its origin. The Engineer is stating that the wind speed impacting a house will speed up over the ridge and the speed will increase in the example by a factor of 1.64. After spending a long time researching by old dynamics books and on-line; no source of any formula such as this could be found. Need opinions on this and any help identifying it if possible.

Thanks for any help

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George Miles P.E., M.ASCE

President

Alligator Engineering Inc

Edgewater FL

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