Hurricane Mathew: Force of Wind & Its Impact on People

[bc1235]

I was surprised at the number of people thinking they should "ride out the storm" when Hurricane Mathew moved up the coast. They are assuming that because they've been in a cat 1 or 2 that a 3 or 4 is nothing to worry about. I was trying to explain to someone that force is not linier with delta velocity. I had to do some hunting to find a formula. f = A * e * v² where f = force, A = Area, e = mean density of air. v = velocity.
I used 1.225 kg/m3 for e and assume an area of 1 for simplicity. So Assuming a solid static wall at all velocities I simplified the formula to f = e * v² which, when I plot it appears to follow the curve I'd expect however I've seen other posts here now that make me question the equation I'm using.

Another post here was looking at force of wind at 100 MPH and was calculating a force of .17 psi and assumed a force of 1.7 psi at 1000 mph. That doean't make sense to me. Pressure shouldn't be directly proportional to velocity. However someone responding said that those were the correct numbers.

So now I question my equation. I know the numbers I used were metric but I found I found aproximately 2.35 for imperial at between 60º and 70º F.

So, is the equation I'm using correct? Are the numbers they are getting accurate? Am I missing something in my equation? Actually I would like to plot it in both metric and imperial units.

Thank you in advance for use of your brain power.

Bruce

 

[Simon Bridge]

f = A * e * v² where f = force, A = Area, e = mean density of air. v = velocity.

Where did you get this from?

I used 1.225 kg/m3 for e and assume an area of 1 for simplicity.

Force divided by area is pressure.

Another post here ...

Where? Link? Otherwise how can anyone here evaluate how applicable that post was?

...was looking at force of wind at 100 MPH and was calculating a force of .17 psi and assumed a force of 1.7 psi at 1000 mph.

I'm getting 0.36psi for 100mph - all other things remaining equal. If the air density were halved though...

That doean't make sense to me. Pressure shouldn't be directly proportional to velocity. However someone responding said that those were the correct numbers.

... and how do you know that "someone responding" was correct?

Note: 1000mph (1610kmph) would be al lot worse than 17 on the Beaufort scale (>222kmph) ... a strength that flattens towns.
On the saffir-Simpson scale for storms, category 5 (the worst) only needs about 160mph winds, and the record is something like 250mph.
So it is unclear how anyone can say anything so glibly about 1000mph winds - which I'd hazard would strip the flesh off bone.
See: https://what-if.xkcd.com/66/

So now I question my equation. I know the numbers I used were metric but I found I found aproximately 2.35 for imperial at between 60º and 70º F.
So, is the equation I'm using correct? Are the numbers they are getting accurate? Am I missing something in my equation?

We have no way to assess the equation ... it looks like it is based on change in momentum: so you imagine that a blob of air mass $m$ hits a wall at speed $v$ and all of it is stopped by the wall in time $t$, then the force the wall experiences is $F=mv/t$ (rate of change of momentum.)
If the wall stops over area $A$, then the mass stopped is $m = \rho Av T$ ($\rho$ is the density of the air) which gives you $F = \rho A v^2$ ... so the equation is correct for the model. But how good is the model for storm conditions? Does wind generally just stop dead at a wall? It is almost cerain that something is missing from such a simplistic model.

Actually I would like to plot it in both metric and imperial units.

The units you use don't matter to the graph - the curve is the same, only the numbers and labels on the axes are different.

You may want to have a look at:
https://en.wikipedia.org/wiki/Wind#Wind_force_scale

 

[bc1235]

Hi, thanks for your quick response. The link is here http://faculty.uml.edu/slaycock/95....s/GPHYS_Lecture_17_Fluids_in_Motion_2013F.pdf

 

[Simon Bridge]

That link is to a pdf of a lecture that seems to be taking an inordinate amount of time to download so I didn't bother.
Does the reasoning in the lecture match up with what I was speculating?
"proportional to the square of the speed" is pretty reasonable for a force/pressure law for wind btw ... it's also how terminal velocity gets calculated.

What I was modelling for you above is the way to assess statements you read online ... you ask a whole bunch of questions and check the statement against other sources.

 

[bc1235]

Thankyou, that really helps a lot. It really helps to have a resource online where one can get help. Thankyou again.

 

[Bystander]

- which I'd hazard would strip the flesh off bone.

"Degloving" velocities are around 200 mph; that's a rough figure given the broad range of skin texture/tone.

 

[bc1235]

Yeah, Simon, think I can figure better ways to die. The only reason I tested to 1000 is to compare the numbers. I really only cared to go to low end of tornado