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Air Show Math
Vanity | 14 Sept. 2014 | Rey

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.


TOPICS: Miscellaneous; Science
KEYWORDS: aeronautics; aerospace; aircraft; airplanes; airshow; aviation; chemistry; engineering; math; mathematics; physics; science; technology
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To: rey

How much of a jet engine’s thrust is needed to overcome drag.


21 posted on 09/14/2014 9:14:41 PM PDT by Swordmaker (This tag line is a Microsoft insult free zone... but if the insults to Mac users continue...)
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To: Jet Jaguar
Sir, do you know if there is a standard equation for a given speed/altitude/air density to figure the speed of heat where aircraft surface temperature changes from cold to hot?

iirc it was about 500knots at a nominal altitude of 40,000'

thx

22 posted on 09/14/2014 9:22:26 PM PDT by Chode (Stand UP and Be Counted, or line up and be numbered - *DTOM* -vvv- NO Pity for the LAZY - 86-44)
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To: rey
she cannot go on any ride if she cannot name at least two laws of motion that apply

I like that. For a little variety, have her sometimes do a Conservation of Energy trace (don't worry, it just sounds tough, it's easy).

First recall that energy is the ability to do work.

Conservation of Energy: Energy cannot be created or destroyed, just transferred.

So here's an energy trace example. A plane taxing down a runway has kinetic energy (energy of motion). That energy has to come from somewhere, and go somewhere.

Where did the plane's kinetic energy come from? It came from gasoline in the plane's fuel tanks. Where did the gasoline's energy come from? From the ancient plants that formed oil. Where did those plants get that energy? From the sun. Where the sun got its energy is a religious question!

Now suppose the plane stops. Where did the plane's kinetic energy go? It has to go somewhere! The plane's energy was converted into heat by friction. The plane's tires get hot, and eventually the whole universe will get just a tiny bit warmer.

You can do such energy traces with a person walking, the energy stored in a hamburger, the energy stored in a brick at the top of a building, etc. I think it's quite fascinating.

If you have any questions about this, feel free to FRmail me. The first hundred questions will be free!

23 posted on 09/14/2014 9:25:10 PM PDT by Leaning Right (Why am I holding this lantern? I am looking for the next Reagan.)
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To: Chode

There is no cold. Only heat variance.

After that, I could not help you.


24 posted on 09/14/2014 9:27:07 PM PDT by Jet Jaguar (Resist in place.)
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To: rey

Can’t come up with a specific equation, but the effect of engine torque on controlling the aircraft — the Corsair had a lot of torque to overcome.

With the P-38, the effect of dual props turning in the same or different directions.

If you look around, you should be able to find some things that are at least interesting from a historical education perspective, but could give some math or physics education.


25 posted on 09/14/2014 9:33:29 PM PDT by MediaMole
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To: rey
I'm impressed getting that far along with a 10 year old girl. Congrats. She'll have a bright future in front of her.

Check out Aerodynamics for Students. Looks like there's a fair amount of material that is suitable for algebraic understanding. I'm sure you'll have her in to DiffEq real soon!

26 posted on 09/14/2014 9:35:12 PM PDT by ProtectOurFreedom
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To: Jet Jaguar
true, cold by definition is simply the absence of heat, but if you touched the surface of a plane doing say 400K at 40000' it would feel cold, where the skin of a Blackbird reaches 1000+

i thought there might be a standard formula to determine the crossing point, thx

27 posted on 09/14/2014 9:40:08 PM PDT by Chode (Stand UP and Be Counted, or line up and be numbered - *DTOM* -vvv- NO Pity for the LAZY - 86-44)
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To: Chode

I wish I could help.


28 posted on 09/14/2014 9:41:21 PM PDT by Jet Jaguar (Resist in place.)
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To: rey
Research "Aircraft Performance College Courses" and Aircraft Aerodynamics College Courses on "YouTube.com".
There's a lot of really good videos there.
Also study weather effects on airfoils, such as rain, clear ice, rime ice, and how humidity and temperature change air density and can result in longer takeoff rolls to create enough lift over the wing.
Take a look at the very dangerous effects of a micro-burst.
Study how flying through another aircraft's wake turbulence can create stalls or throw an aircraft out of control.

Also study how a helicopter rotor is an airfoil and how a helicopter auto-rotation can save a pilot.
And don't forget, weather can kill people in balloons.
29 posted on 09/14/2014 9:42:15 PM PDT by Yosemitest (It's Simple ! Fight, ... or Die !)
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To: rey
What ever comes of this, I will continue with my math. It is amazing what you can do if you simply do 15-30 minutes of calculations a day even if you ever so slowly increase the complexity. Furthermore, working with math causes one to view the world differently,more rationally. Giving your mind a mathematical work out daily will change you. Don’t fear it; own it.

Very inspirational. Great post!

30 posted on 09/14/2014 9:42:42 PM PDT by thecodont
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To: rey
Navigation- how to calculate wind drift. Start with vector diagrams, then use a flight computer and finally some trig.

Lots of other math can be demonstrated with a flight computer, which is essentially a circular slide rule. The ASA A6B paper flight computers are CAD $13.95 and the metal version is $32.95 here.

31 posted on 09/14/2014 9:45:47 PM PDT by Squawk 8888 (Will steal your comments & post them on Twitter)
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To: IncPen; Bartman

interesting


32 posted on 09/14/2014 9:46:02 PM PDT by Nailbiter
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To: rey

From tire pressure and flattening try to estimate total weight and center of gravity. Estimate fuel tank capacities and cg locations. Work out trimming needs and fuel management.


33 posted on 09/14/2014 9:51:08 PM PDT by ThunderSleeps (Stop obarma now! Stop the hussein - insane agenda!)
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To: Jet Jaguar
much appreciated, thx again...
34 posted on 09/14/2014 9:51:24 PM PDT by Chode (Stand UP and Be Counted, or line up and be numbered - *DTOM* -vvv- NO Pity for the LAZY - 86-44)
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To: rey
Here's some more on wake turbulence caused crashes:
35 posted on 09/14/2014 9:57:07 PM PDT by Yosemitest (It's Simple ! Fight, ... or Die !)
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To: rey

Good thread bump.


36 posted on 09/14/2014 10:04:51 PM PDT by TChad (The Obamacare motto: Dulce et decorum est pro patria mori.)
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To: John Valentine
Indeed. I once got into a discussion with someone who challenged by assertion that I could build a plane with NO airfoil at all, just a plank with an angle of attack of about 55 and it would fly.

This is a contradiction in terms, since "a plank with an angle of attack of about 55" is no other thing than an airfoil, however inefficient.

37 posted on 09/14/2014 10:04:57 PM PDT by dr_lew
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To: rey

http://www.airfieldmodels.com/information_source/math_and_science_of_model_aircraft/formulas/index.htm


38 posted on 09/14/2014 10:11:36 PM PDT by Kirkwood (Zombie Hunter)
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To: rey

http://www.knowitall.org/nasa/pdf/connect/flight-equation.pdf


39 posted on 09/14/2014 10:15:06 PM PDT by Kirkwood (Zombie Hunter)
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To: rey
Show her this and let her figure out what it's for. Take her to this web site skyvector.com and look at the VFR airspace above and around her.
40 posted on 09/14/2014 10:30:32 PM PDT by Yosemitest (It's Simple ! Fight, ... or Die !)
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