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On Sunday, 6 March 2022 at 01:15:29 UTC, Phil Hobbs wrote:
John Walliker wrote:
On Friday, 4 March 2022 at 11:46:56 UTC, Don Y wrote:
On 3/3/2022 5:12 AM, Don Y wrote:
On the other hand, if you present a *real* problem needing solution,
students can \"see\" how a problem that they are facing can benefit
from such analysis.
Imagine setting out to design a cart/conveyance.
Start out with 4 wheels (you can, later, challenge that assumption).
How do you allow the cart to travel in anything other than a straight line?
You can implement a crude mechanism to change the angular orientation
of two of the wheels (e.g., put them on an axle that has a central?
pivot point and add a means of adjusting that pivot).
Gee, it has a large turning radius! How large? *Why*? How can we decrease
that? Hack together a mathematical expression that relates the physical
parameters of the design to the effective turning radius and \"graph\" the
result. Where is the minimum? What *limits* the minimum attainable?
What if we allowed the wheels to pivot \"locally\" (e.g., like rack and pinion)?
What does this buy us? What does it cost (mechanism complexity)
What if we allowed front and rear wheels to pivot? Why did we initially
assume the *front* wheels had to pivot?
Why does the wheel on one side get \"scuffed\" in turns?
E.g., with this sort of approach, you can move from a \"straight-line\" vehicle
to one with a \"swerve\" drive -- and SHOW the advantages and costs of each.
(What *technology* do you need to implement each?)
No need for computers or advanced math so you can involve kids of various
different capabilities without intimidating some.
I once read that one could throw a raw egg over the roof of a house and if it
landed on a grass lawn it would not break.
I tried it. It really was true (but only some of the time because there were some
stones in the lawn).
Less good were the trials where it didn\'t quite make it over the top.
I also found a way of shooting a hole through a glass light bulb with
an air pistol without completely shattering it - just leaving an entry and
exit hole. All it needed was sufficient precision in aiming so that
the pellet was perpendicular to the glass at the point of impact. And ways of
making the pellet emerge from the barrel at supersonic speed. And explode
on impact with a target.
Good luck making a pellet supersonic with a gas charge that starts at
ambient temperature. You need the propellant to stay in contact with
the pellet as it goes down the barrel.
That is where the fuel air mixture in the compression chamber comes in. I used the diesel fuel intended for model aircraft engines, atomised in the compression chamber by firing once without a pellet after introducing the fuel. The atomised fuel would ignite on the next firing if soon afterwards.