An Explanation of Wind Speed and Power

[Raven]

Based on recent conversations regarding wind speed and its relationship to force, energy, power, etc, I did a few calculations that I thought would help explain this relationship for those who may want to know why the strength of the wind seems to increase so dramatically with speed. I also thought it best to begin a new thread with this. If you read to the end you may be surprised.

Background Info:

-Many people seem to know that when the speed of the wind doubles, something increases by 4 (the strength, the force, the energy, the power, etc) but this is where the details get murky. Here are the differences:

-For FORCE, look to the following few posts and their included links for a very thorough explanation that is much better than I can give.

What follows shows an explanation and then series of numbers meant to show the relationship of wind speed to wind power and to show the added effect of the increasing mass of the air hitting a person as the wind speed picks up.

-ENERGY is the ability to do work. Kinetic energy is the energy that moving things have. Things like moving trucks on highways, water moving downstream, moving air masses (wind) all have kinetic energy. This is where the 4x thing comes in. The KE depends on two things, the mass and the speed of the object (KE = 1/2mvv). But the speed gets multiplied twice, so as the speed doubles, the energy increases by 4 times! Here's an example from the football field. If you have the option of getting hit by the small guy (150 lbs) moving fast at 12 mph or the big guy (300 lbs) moving slow at 6 mph, take the big guy, because the small one has much more energy and will hurt more.

-Don't skip this part. In the above example, people always remember the 4 times thing but there's a more subtle, VERY important consideration. Mass of the air is in that formula. As the wind speed doubles, there is twice the mass of air molecules hitting your body per second. So, when the wind speed doubles, the energy actually increases by a factor of 8 times!

-POWER is energy used per second. If you walk up a flight of stairs you use energy. If you run up the same flight of stairs you use exactly the same energy but more power since it is used in less time. Some battery operated tools use up the battery faster because they take more power. A tool using less power will use the same battery up over a longer time period.

I did some calculations for wind speeds that I thought would make sense for people to see this. I've attached a PDF which includes the wind speeds 45, 90, 180, and 231 mph. For each speed I calculated power of the wind at that speed that might be felt buy a typical person and the results show how dramatic it is.

Results:

1. A Gale Force Wind of 45 mph will have entire trees swaying wildly and twigs breaking off. This is what we all tend to call "like 70-80 mph out there!" This is a STRONG wind. (Power = 5700 J/s)

2. Double this to 90 mph, a strong category 1 hurricane (nearly 2), and the power goes up by a factor of 8 to 45,000 J/s. In this wind, buildings can receive severe damage. People buckle down for these storms. To put the wind of 2/16/2015 in perspective, the date of Kate Matrosova's death, the average wind speed on Mount Washington that day was 91.2 mph, nearly a category 2 hurricane with 8 times the full power of a gale force wind.

3. Double this to 180 mph, a strong Category 5 hurricane and the most intense storms seen on earth. Hurricane Andrew at sea, when it was a 5, did not sustain these speeds. Wilma and Rita are the only Atlantic storms so far this century to have sustained these speeds for more than 60 s. Compared to a Category 1 storm, this is 8 times more powerful and 64 times more powerful than a gale force wind. Buildings have blown off Mount Washington in these winds. (P = 366,000 J/s)

4. 231 mph. 133 times the power of a gale force wind. Armageddon. (P = 760,000 J/s)

I hope this is somehow helpful in understanding the power of the wind.

 

[Tom Rankin]

Thanks, the 2x wind mass is something I've overlooked.

My only quibble is that a 20 mph gust vs 20 mph steady wind is still exerting the same force, but you are just not prepared for it.

 

[jfb]

My only quibble is that a 20 mph gust vs 20 mph steady wind is still exerting the same force, but you are just not prepared for it.

I had learned that the "summation" of forces equals mass times acceleration. If you're standing still in a 20mph wind, there's a wind force and a resisting force (provided by your legs) that keeps you stable. When the wind is still, there is no resisting force. If a 20 mph gust comes along, you will accelerate in the direction the wind pushes you.

Also, the I think force of the wind should be 1/2 rho times v-squared (dynamic pressure) times the frontal area of object.

http://www.engineeringtoolbox.com/dynamic-pressure-d_1037.html

 

[BillyRay]

Good write up. I sorta knew the "something increases by 4 " rule... but wasn't aware of the details you've provided.

Hearing this, I find it hard to believe anything would have been left atop Mt Washington back in 1934 when 231 mph was recorded!

Rick

 

[DougPaul]

I had learned that the "summation" of forces equals mass times acceleration. If you're standing still in a 20mph wind, there's a wind force and a resisting force (provided by your legs) that keeps you stable. When the wind is still, there is no resisting force. If a 20 mph gust comes along, you will accelerate in the direction the wind pushes you.

In a steady wind, you lean (ie provide forces through your legs) to counteract the aerodyamic forces. Any change in the wind (including a reduction or a change in direction) will throw you out of balance because the forces no longer sum to zero.

Also, the I think force of the wind should be 1/2 rho times v-squared (dynamic pressure) times the frontal area of object.

http://www.engineeringtoolbox.com/dynamic-pressure-d_1037.html

This is the correct approach. Only it should be the "effective flat plate area" which is Cd * S (the coefficient of drag times the geometric frontal area). Cd will depend on the shape and orientation (in relation to the wind direction) of the object.

See http://www.vftt.org/forums/showthre...-Mt-Washington&p=391268&viewfull=1#post391268 for more detail.

Doug

 

[Raven]

I thought you might show up DP. Good to see the rest of you as well.

Appreciate the additional details on wind force from each of you. I have edited the force description from the OP to avoid any confusion. I did not need it in the calculation of power either way.

Bear in mind as well, I am not trying for accuracy as to the actual magnitude of the numbers presented for the power, it is the ratio of those numbers that I mean to point out, and the fact that the doubling of the mass of the wind is often missed as people look more to the squared velocity term as this is the larger factor.

The point of course is to help people understand this: if you are hiking above treeline and the wind is strong and you are considering going for the summit, just realize as the wind speed increases as you ascend (and it will), the power you will feel increases exponentially so.

 

[iAmKrzys]

I saw this discussion on wind speed and decided to share some of my thoughts. I am not an expert in the subject matter, so I would love to here from those more qualified if I get something wrong.

1) Force of the wind, or drag is fairly well described in a Wikipedia article at http://en.wikipedia.org/wiki/Drag_(physics) This force is proportional to velocity squared i.e. F = C * v^2 and so when velocity doubles the force gets scaled up by a factor of 4. I think, however, it may be a little bit more appropriate to look at wind gusts that say go from 60 to 80 mph or from 60 to 100 mph. In such cases the drag would increase by a factor 80^2/60^2 = 64/36 which is approximately 2, and similarly 100^2/60^2 = 100/36 which is approximately 3. Based on this, I imagine that hiking in 60 mph wind with gusts up to 80 or 100 mph probably feels like playing dodgeball where you are being hit with a 50-pound bag instead of a ball, and you are blindfolded, so you don't know it's coming until you actually get hit. Now, I have never hiked in such a strong wind (I have always chosen nice days for Mt. Washington hikes) but looking at the video of rescuers being thrown around by wind like little toys I suspect I am not far off with this interpretation of the wind force.

2) Energy or work ( http://en.wikipedia.org/wiki/Work_(physics) ). The amount of work W performed against the wind force F is W = F * d where d is the distance travelled (or displacement.) Hence, a car parked on a street in a hurricane-force wind does not do any work because it is not moving (it makes sense as it clearly burns no fuel.) When the wind hits such car it will make it swing a bit and the energy lost by the wind will get converted into heat by car shock absorbers. This is different for humans since our muscles have to do work to maintain balance. As our center of gravity is fairly high above ground our battle with wind gust requires us to expand quite a lot of energy even though we are not moving.

3) Power. Power measures the amount of work done within a certain time: P = W / t. Interestingly, not much power is needed to overcome large force as long as it is done slowly, for example, we are capable of overcoming crashing weight of our cars as long as we use a car jack and do it slowly. Similarly a car moving with ground velocity u against strong wind with ground velocity v will need P = W / t = F * d / t = F*u = C*(v+u)^2*u so the power requirement could actually be small as long as the car travels slowly (note that the velocity of car with respect to air is u+v.) Here is where the power piece gets interesting: if the car is moving through air that is stationary with respect to the ground (v=0) then there is no way to decouple the drag from the speed of the car and the power will be actually proportional to u^3: P = C*(0+u)^2*u = C*u^3. This is where the formula for power in the Wikipedia article on drag comes from ( http://en.wikipedia.org/wiki/Drag_(physics)#Power ), and indeed driving the car at twice the speed requires 8 times the power.

4) Heat loss. I remember from one of my classes that heat dissipation is much more efficient in presence of forced convection and the faster the air flow the quicker the heat loss. I don't really have any specific formulas that I could provide for this but I think enhanced convective heat transfer is behind convection ovens, snow-making equipment ( http://en.wikipedia.org/wiki/Forced_convection ), wind-chill factor, and that's why we blow air on our burned hands if we touched something hot. Hence taking a glove off probably results in a hand getting frozen really fast.

5) Finally, from my personal experience it seems to me that it is harder to breath in strong wind. I am not quite certain what the cause is. I wonder if it may be our body responding to the rush of air into the longs just like we cough when we get water in our windpipes. Alternative explanation that I can think of is by using Bernoulli's principle ( http://en.wikipedia.org/wiki/Bernoulli's_principle ) which basically says that as air flows around an object and speeds up the air pressure drops and so, I reason, it would be harder to breath it in.

Again, I don't know how it really feels in 100 mph wind but I imagine it is no fun.