It was incredibly windy yesterday. A tree even blew over on Lowmoor Road so we had to make a diversion going home. However, we made the most of the day before the rain came. Here is the author of this blog on top of Latrigg. It was one of those days when it was possible to lean into the wind and not fall over. So I've done some Physics to measure the wind speed.
Essentially we need to consider two forces. The red arrow shows my weight acting through my centre of gravity. It causes anticlockwise turning around the pivot so my weight would make me fall forwards. The green arrow is a representation of the force of the wind. This will act all over the front of me but I have assumed that it can be averaged in such a way as to act through my centre of gravity. It produces clockwise turning around the pivot. Provided the clockwise and anticlockwise moments (technical term for turning) are equal, then I won't fall over.
Anticlockwise moment = weight x distance from pivot = 65kg x 10 x 0.15m roughly = 100 Nm roughly.
To calculate the force of the wind I'm going to use Impulse = change in momentum.
I am assuming that the air stops dead when it hits me.
Momentum = mass x velocity.
If I take a time of one second, a volume of air hits me that I will assume is rectangular in area and cuboid in shape. It's area will be my area, roughly 1.8m x 0.30m. It's depth will be the distance the air travels in 1 second ie the velocity of the wind v. Volume of air stopped in 1 second = 1.8 x 0.30 x v. The density of air is about 1.2 kg per cubic metre so mass of air stopped in 1 second = 1.2 x 1.8 x 0.30 x v = 0.65v roughly.
So change in momentum = mv = 0.65 x v-squared.
Impulse = force x time but time was 1 second so finally
Force of wind = 0.65 x v-squared. This is the green arrow
Clockwise moment due to wind = force x distance from my feet to my middle = 0.65 x v-squared x 0.9 = 0.6 x v-squared to 1sf
Set the two moments equal to each other:
0.6 x v-squared = 100
v-squared = 170 ish
v = 13 metres per second
This is about 30 mph.
It's impressive that this rough method gives a not unreasonable answer. Consulting the Beaufort Scale suggest it might have been nearer 40 mph.
