Customer Qualifications Section
Lecture and Notes 1
The Story of Air in Motion by "Dutchy" the Windmill
Air and Its Motion a "Weighty" Subject
Does everyone know that the same air we know so well passing through my 20 foot long blades at 15 mph (6.7 meters per second) has a mass flow of just about one ton (tonne) per second? Yikes! Here is the story about this.
Confusion maybe starts with the different measuring systems, the British (no longer used in the UK) and the metric. In the U.S. a well-known fast food restaurant offers a "quarter pounder" hamburger. Does anyone know how this is described in the metric system around the world? The beef patty would weigh about one newton in metrics and so this could be called a "newtoner" hamburger. But metrics uses kilograms for most weights and so it might be called instead a "100 grammer" hamburger. It turns out that one newton is slightly more than the weight of 100 grams and so the beef patty would be slightly larger in this case, not to make fun of such a serious subject as food.
It is fascinating to know that the two major world almanacs in English published annually in the U.S., the "World Almanac" and the "New York Times Almanac of Record", do not make completely clear the difference between "mass" and "weight" in their sections on weights and measures, the "New York Times Almanac" being a little better at this (e.g., comparing weights to those found on the moon). Neither one of them, however, cover wind energy except each as one or two brief line items, hard to find, aggregated into totals of the energy contributions by all renewable energies on their pages covering the industry sources of electrical energy generation nor does either one take any time to describe the atmosphere and the air in it as being anything of substance except that it is just so much Oxygen and Nitrogen with a few more gasses thrown in. Air seems to lack anything of interest to say about it.
More on this in additional website updates later. Much kindness and good will to everyone out there in wind energy. Any comments or corrections are welcome as are answers to questions posed. "Dutchy"
Lecture and Notes 2
Wind Velocity As Rate Of Mass Flow
Meteorologists "own" standard meteorology and aviation "owns" aviation aerodynamics. It may come as a surprise that wind energy has a meteorology and an aerodynamics that it "owns" as well.
Wind velocity is of little use to a wind turbine without the density factor, the mass of the air per unit volume, included. Debate on measuring windspeed as a massflow rate is inconclusive until it is discovered that the windspeed in miles per hour is almost exactly the same value in numbers, using the density of air at standard conditions, as the pounds per second per yard squared of mass flow(!). So one mph = one #/sec yd^2 to a close approximation.
Not only this but in metrics this conveniently becomes close to *one half* of the same mph figure. This means that one mph of wind velocity is also equal to about one half kg/sec meter^2. Wind turbines have been typically rated for full power at a wind velocity of about 30 mph, which converts to about 13.4 meters per second in metrics, a number not often seen or remembered. But in mass flow units this is about 15 to 16 kgs/sec meter^2, much easier to keep in mind.
Even a further step may be taken. "One kilogram per second per meter squared" is still hard to say. So a new unit of measurement may be defined for it, something which is often done in science. For example, the electrical unit of alternating current frequency was given the unit name of "hertz" not many years ago (from the name of Heinrich Rudolph Hertz, the German electrodynamics physicist of the 1800s) and so 60 cycles per second is now 60 hertz.
Among the candidates whose names may be chosen for this unit, though wind energy is still a relatively new technology, the one that stands out is the one of Poul la Cour of Denmark, the early pioneer of modern wind energy from the late 1800s, whose name has largely gone unrecognized. I, "Dutchy" the Windmill, hereby nominate Poul la Cour for this honor and, in support of this nomination, the IntegEner-W website has been updated to provide information and photos about him from the past.
If accepted by the wind industry, wind velocity would be measured and reported in units of "laCours" instead of miles per hour or meters per second. Then also wind speed averages for geographical localities and even their *energy weighted* wind speed averages would be calculated and reported in "laCours".
A question to answer, then, is this. About how many pounds per second per square yard of wind mass flow rate are expressed by a value of 15 laCours? Then, how many miles per hour wind velocity?
More on this in additional website updates later. Much kindness and good will to everyone out there in wind energy. Any comments or corrections are welcome as are answers to questions posed. "Dutchy"
First, find the mass of a large volume of air such as that enclosed within a box that is visualized to cover one square mile of land and that is 1000 feet high. A height of one thousand feet is well within construction capabilities that have raised many tall buildings in large cities. At .0765 #s/foot^3 air density, the mass of atmospheric air enclosed within such a volume box comes to:
Lecture and Notes 5
The Ghost of Bernoulli Lingers On
Quite sensible individuals even with a reasonable grasp of science are still known to "lose it" when they partake in discourse on some of the more controversial aspects of aerodynamics. It has not helped that material published in earlier years soon after the close of WW II, complete with speculations from returning military flight pilots and other early aviators, was instilled into the minds of high school students for decades thereafter and became its guiding mantra, material such as that in these two pages following copied from a late 40s textbook and rightly to be dismissed as having little value:
(Basic Units in Physics by F.E. Stewart 1949, Republic Book Co., Inc., New York)
Since that time it has gradually dawned on most everyone with any curiosity about aerodynamics that this must be not quite true - even further that it must be just "baby talk" - and that airflow deflection must play an important, even a dominant, role in creating these forces, something that is given some newer treatment in presentations directed to popular understanding of flight by such Government agencies as NASA. Nevertheless, the logic is still not followed up with a solid basis for calculating aerodynamic forces in this newer way of thinking, something that was at least suggested in the older days as being just a matter of solving the Bernoulli Equation for the wing lift force. Nowadays animations on websites show the flow lines above and below airfoils along with some depictions of their angle of attack and the flow deflection at the trailing edge with much left unsaid beyond this.
What is needed to be done in supporting the weight of each aircraft is for the wings to force quite a large amount of air over their spans and above and below their passage downwards as they speed through it and do so with (a) the least amount of wing surface and wing structural weight and (b) drag on the engines propelling the airplane forward. It must be readily calculable somehow to arrive at just the right amount of air mass ( in "slugs" if in
the ordinary "pounds, feet, seconds" measurement system ) necessary to be so disturbed by this process and the wing configuration that needs to be made available in doing so. The same goes for wind turbine blades, which have even a greater imperative placed upon them to create some difference in the wind flow streamlines that approach them, moving them aside with great impact and into sharply different flow directions vectored into lower speeds over large volumes of space both near and far away from their surfaces as they rotate.
The impression that prevails in everything being said and done up to the present time is that the ghost of Bernoulli lingers on and wind turbine blades as a part of their active rotor areas are being fashioned in a way that satisfies only the slight bending of the few flow lines from computer animations that track near their surfaces as if this is all that matters. It should be added with haste that satisfying structural integrity requirements has become a well known study from past practice, something in which great comfort may be taken while not advancing the state of the art more rapidly than might be done without its continued assurance.
When the chapters of this series presented earlier are taken into consideration, it becomes more clearly understood that the great and weighty mass of air that is moving through the rotor areas should be given a high priority as the source of the energy that must be converted and that wind turbine design is a continuing process as the future unfolds that needs to further address the issue of extracting energy from this flow mass more efficiently.
A problem illustrative of what is being said here might entail the rate of air mass being impacted by the flight of a theoretical but quite realistic jet aircraft moving at 550 mph with a wing span of 200 feet and a weight of 400 tons at an elevation of 30,000 feet - air density .0286 #s/ft^3. For a wing angle of attack of just 2.0 degrees, the straight downward deflection impulse component of airflow by the wings is 550 mph x sin 2.0° = 19.2 mph = 28.2 feet per second ( termed "downwash" in aviation-speak ). The drawing below of the forces arising from this airflow deflection was taken from the
"Lift" Booklet of IntegEner-W:
The variation of Newton's Equation applicable to wing flow can be stated as - lift force in pounds = rate of air mass flow deflected downwards in slugs per second x velocity of the straight downward deflection impulse component in feet per second.
Solving this equation for the air mass flow results in 2.84 x 10^4 slugs per second which is about 3.19 x 10^7 ft^3/sec of air at this density. The cross sectional area of air thus impacted at the forward speed of 550 mph or 807 ft/sec is then close to 40,000 ft^2, which, if divided by the wing span of 200 feet, yields, of course, 200 feet, or an effective distance of 100 feet both above and below the wing surfaces. Due to conservation of mass in an approximately incompressible flow field over the pressure ranges involved, this is seen to be readily achievable and it is surprising but true that wings have such an impact so far removed from them in the vertical directions up and down.
Problem: if the aircraft drops to an altitude of 15,000 feet - air density of .0474 #s/ft^3 - and decreases air speed to 350 mph, what is the effective wing attack angle that is necessary to maintain the lift force at 400 tons, (a) about the same = 2.1 degrees, (b) about double = 4.2 degrees, or (c) nearly another degree = 2.9 degrees?
More on this in additional website updates later. Much kindness and good will to everyone out there in wind energy. Any comments or corrections are welcome as are answers to questions posed. "Dutchy"