# Roughness length, calculate z0

#### paulthomasrowland

##### New member
I have wind speeds at two heights, h1 and h2, and wind speed measurements at each height. I want to calculate z0, the roughness length. The formula is given as:

v2 = v1 (ln(h2/z0)/ln(h1/z0))

I cannot figure out for to solve for z0 correctly.

Can you help?

#### Subhotosh Khan

##### Super Moderator
Staff member
I have wind speeds at two heights, h1 and h2, and wind speed measurements at each height. I want to calculate z0, the roughness length. The formula is given as:

v2 = v1 (ln(h2/z0)/ln(h1/z0))

I cannot figure out for to solve for z0 correctly.

Can you help?
$$\displaystyle \displaystyle{\frac{v_2}{v_1} \ = \dfrac{ln(h_2)-ln(z_0)}{ln(h_1)-ln(z_0)}}$$

$$\displaystyle \displaystyle{\frac{v_2}{v_1} \ - \ 1\ = \dfrac{ln(h_2)-ln(z_0)}{ln(h_1)-ln(z_0)} \ - \ 1}$$

Now continue....

#### Ishuda

##### Elite Member
I have wind speeds at two heights, h1 and h2, and wind speed measurements at each height. I want to calculate z0, the roughness length. The formula is given as:

v2 = v1 (ln(h2/z0)/ln(h1/z0))

I cannot figure out for to solve for z0 correctly.

Can you help?
I would do it a slightly different way: Multiply though by ln(h1/z0)=ln(h1)-ln(z0) to get
v2 [ln(h1) - ln(z0)] = v1 [ln(h2) - ln(z0)]
or
v1 ln(z0) - v2 ln(z0) = v1 ln(h2) - v2 ln(h1)
and continue

#### paulthomasrowland

##### New member
Solved

Very many thanks to you both