Posted on 09/14/2014 8:19:53 PM PDT by rey
I home school a young girl. In years past, we have gone to the local air show and done such things as measure the tops and bottom of wings and rotos and figure the ratio or difference between the area of the top of the wing versus the bottom and estimated which wings had more lift than others. We measure how much area the wheels occupied on the ground and consulted with the crew chief what the tire pressure was and calculated the weight of the plane.
In years past we were able to see F18s form a vapor cone around the plane and discussed how pressure can squeeze the moisture out of the air to give us this effect. There won't be any military jets this year, but there will be an Osprey, P38, Corsair from WWII, T38, the helicopter pilot from Red Bull who flips and rolls a helicopter.
Before going we review some physics books and discuss what properties of physics and laws of motion apply. We do a similar thing at the fair; she cannot go on any ride if she cannot name at least two laws of motion that apply. When we watch the planes or fair rides we point out what laws of motion we are witnessing.
My question is this; What other math problems could we review on the static displays or any other happening at the air show? She is 10 and is well into algebra. We have done a little trig when trying to figure target info for various firearms or catapults. WE have done very little calculus, but if someone can outline something well enough we can definitely figure it out.
We are open to any aspect of aeronautics, whether is is mathematics, chemistry, physics, scientific.
There are some very sharp people on this site and wish to thank everyone in advance for their help.
Consider looking into Newton's second and third laws, especially as to how they relate to thrust from jet and rocket motors.
Second law is, generally, f = m.a , and the f is thrust.
Third law (again, generally) is for every action there is an opposite reaction; and, for straight line thrust in one direction, there is force in the opposite direction.
Any physicist reading this is welcome to make corrections and amplifications, btw.
Again w physics, there is lots to a turbojet engine... compressor stages, spools, ignition cans, turbines...Some aviation museums have very nice cutaways.
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Dr. Lew, not to quibble, but an “airfoil” is presumed to have one of a number of quintessentially teardrop, although not necessarily symmetrical, shape. A catalog (obviously incomplete) of such shapes was once published as “Theory of Wing Sections - Including a Summary of Airfoil Data”. (Dover, 1949)
Nowhere in this volume is a rectangular or “plank” section described or presented as an airfoil, nor was data thought to be important enough to publish.
You may be alone as describing a “plank” section as an airfoil and I may be alone (although I suspect that I am not) in proving that it can function as one.
F is the net force on the object, or aircraft from all sources. This includes thrust, gravity, and the "force of the air on the wings".
Typically, for a plane in level flight, the horizontal component of the force is taken to comprise the thrust and the drag, which must be equal and opposite at constant speed. The vertical component component comprises lift and the force of gravity, which must likewise be equal and opposite in level flight.
for later consideration
Its the trim tab on jimmy lewards plane that broke causing the elevator to move in the full up position.You can see that its missing in the picture.I believe that picture is when the aircraft unloaded at the top headed back down to its impact with the ground.
A debate was raging about the shape of the wing, and one of the lead engineers reportedly fitted a piece of flat plywood, cut to a triangle the size of the proposed wing, to the clamp in the wind tunnel and it produced every bit as much lift as any “engineered” design. All displacement lift.
An example of displacement lift can be found in aerobatic wings, sometimes with curved upper and lower portions that are equal.
You’re correct. Click on that link and you’ll read, in that whole thread, my detailed post on it.
You are a cool dad!
Study density altitude and why it is an important matter of safety to consider. The less air density, the less lift, of course, and this can be calculated.
Related to this is calculating an aircraft’s ceiling. Discuss why one type of airplane has a ceiling of, say, 25,000 ft while another airplane might have a ceiling of, say, 14,000 ft. Why will the airplane rated for 14,000 ft never be able to fly at 25,000 ft, even if it were legal and the pilot had extra oxygen?
Find out the maximum altitude beyond which extra oxygen is required.
List some VFR conditions and some IFR conditions.
The sound barrier at sea level vs the sound barrier at 20,000 ft. 30,000 ft.
bkmk
pretty much
Combine trigonometry with elementary calculus, you know just derivatives which are quite easy and formulaic, but very useful to understand — just velocity, acceleration, impulse, position.
When I encountered the issue of home schooling here on FR, I had to think it over before I came to support it. And the thought that first tipped me into the positive camp on the issue was exactly what you say above - even if somehow you had found that home schooling your particular child proved not to work out, a lot of learning would have still occurred. What is wrong, in principle, with adults getting educated??The books available now are great. Danica Mckellor’s books though having too much boyfriend stuff in them are a help. There are some great you tubes and the Kahn academy is fantastic.If some adult, black let us say, has a poor education behind her or him, it would be tempting to say that the “experts” known as credentialed teachers need to take over. But that is precisely where the adult’s poor education came from in the first place. Thus, the Einstein definition of insanity seems to apply. Let the parent undertake the teaching role if s/he will. In the worst case, at least s/he will learn something!
. . . and again, when thinking about home schooling I hoped and expected that burgeoning Personal Computer availability and capability would lead (tho I had no concept then of the wonderful Khan Academy YouTube instructional video that would come available later) to significant help for home schoolers. Congratulations!Now as to your actual question:I speculate that you and your child would be able to do impulse-momentum calculations with no great difficulty. I never studied aerodynamics much, tho I worked as an engineer for an aircraft manufacturer. But the big picture of what happens when an aircraft flies is that the aircraft extracts the lift and thrust it needs from the air in which it is immersed, and that it does so by changing the velocity of the air locally.The thrust of a jet engine derives from the fact that it pumps the incoming air, hurling it backward at a higher speed than it came into the engine with. The actual thrust (which is impulse) can be calculated as the mass of air per second passing through the engine, times the change in velocity (which is the momentum) of that air. The impulse is equal to that change of momentum.
Likewise, the lift produced by the wing can only occur by knocking the oncoming air through which it passes downward. The lift of the wing is the impulse, and the mass times the velocity of the air it deflects downward is the change of momentum which causes the impulse.
In both cases, there is an efficiency advantage to be had if you can obtain your impulse by changing the velocity of a lot of air by a little bit. That is because it takes work to change the velocity of a mass - and the work required to do it goes up as the square of the change in velocity required, which is inversely proportional to the mass whose velocity is changed. (I know that could be a little technical for a ten year old).
Interesting topic, but I gotta run.
Measure the pitch angle of a fixed pitch prop and have her calculate the design speed. That would give her trig and geometry a workout.
Any moving object lends itself to discussion of acceleration and vectors. You might also bring up the difference between the aircraft heading and its actual ground course where a substantial side wind is present. Then there’s the phenomenon of the “p-factor” which applies to center-thrust propellor aircraft at high attack angles.
Heck, you could have a field day just exploring the aircraft sitting on the ground!
She’s a lucky girl.
What a great job you are doing! Too bad she has to miss out on the socialization benefits of public school - lowest common denominator education, crime, bullying, and such.
(The home schooled granddaughter in my tag had verbal skills well-beyond most adults when she was 12 and excels at Latin.)
If you join Civil Air Patrol as an educator, they will send you a huge box of educational materials for whatever age/grade you request. The cost to join is 35.00 and it is well worth it. Their educational materials are really good.
Mrs. AV
If plane B is AF 1 then never. Too many golf courses between NYC and LA.
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