Re: Aircraft Scaling Problem / Question


There's more to it than mass and volume, there's structural strength.
And that makes it an engineering problem, not just a math problem.


Yes, but your fixating on the enginering. Without the foundation in math
there would be no engineering. You do realize that no matter how you
manipulate the equations to increase efficiency some factors more important.
If we are to worry about all those details then we loose sight of the whole
point the original poster asked. He did not ask about engineering isssues.
He could care less(probably) about actually implementing this thing. What he
did was carry out at thought experiment just for fun. Actually the insight
gained by this is much more important than worrying about wether to use
titanium or alluminum and how much it will cost or how thick it needs to be
or which paint you should paint it with.




Hopefully this make sense. I'm not trying to be formal in my analysis and
there are many things I'm not taking into account. Think about ants and
how
strong they are per unit mass. They can lift very heavy things without
breaking there thin arms. If we tried to lift the same proportionate
amount we would be crushed.

So you now agree that it is an engineering problem?


Nope. He did not ask about the real thing. In any case if you don't
understand the mathematics you do not understand why the engineering does
what it does? Why do they use lighter materials? Why do they put holes in
the beams? Because mass/volume is the most important factor. Its more
important then any other factor. If you can reduce 1 kg of mass then you can
increase the lift by a factor that depends on the square.

e.g., L = LE/M = LE/V

LE is the lift equation which is somewhat independent of mass. It tells you
the lift of an object. I use L to represent the lift as it is really the
ratio of lift to weight. Obivously then if L < 1 there is no lift and the
object will not fly.


but LE = c*v^2*A

where c are some constants.


so L = v^2*A/V

so decreasing the volume is much more appropriate than increasing the
surface area A. Note that increasing the velocity works very well too but
when you do this you increase the mass and there is drag that exists too.

Now I assumed the density was constant throughout the plane. When they make
a plane hollow, use lighter materials, etc... they are decreasing the
mass(or changing the density function if you want).

Obviously the other factors are important such as structural strength and
stuff but I hope you do realize that no matter how stronge it is, if it is
to heavy it will not fly.

Do you think the wright brothers more more about strength than lift?

The problem is that your confusing theoretical analysis with practical
application. If you don't understand the theory then chances are you don't
understand how it works in practice.

All aeorodynamics are constrained to this physical law and there is no way
around it. Its sorta like how everything is constrained by the speed of
light. In computers you cannot make the electrical signals go any faster.
This is a physical law and is grounded purely in mathematics(the law comes
from geniuses and the mathematics tells us why it does what it does). What
do they do? they make the electrical paths smaller. Thats the only way to
counter the effect and increase the speed. There is absolutely no way
around it if you believe the special theory of relativity is true.

For example, the electricty that flows from your internet connection travels
at the speed of light. Its impossible to make it go faster. No amount of
engineering can change that. What is engineering is sitting around thinking
about how to make it look like its going faster. Like puting in parallel
lines so you and effectively increase the transmission rate by a certain
factor(ofcourse as you change one thing you change the other and so there is
a limit to this too).

These things are facts of life and once you know the limition then you can
figure out what doesn't work which sorta tells you what might work. They
didn't just randomly try stuff like trying to get a tank to fly if they put
wings on it. A tank is very structurally sound but it will not fly. Its
actually probably impossible to make one with controlled flight even if it
had wings. Ofcourse I suppose you could use wings that were 1000 feet long
and that are ultra light and made out of ultra strong alloy's but is that
really practical?


In actuality all engineering difficulties in flight come from this. If Lift
did not depend in such a way as engineers wouldn't have to look at how to do
all that stuff. If it did not depend on mass then they wouldn't worry about
how heavy planes were. They would just use steal 10 inches thick for
strength. In reality though they have to find the strongest materials that
are the lightest. It has to be strong enough for its purposes but the
lighter it is the more lift one will have and therefor the less velocity one
needs and so the smallar and cheaper the engines(or equivilently the faster
the plane can go on the same sized engine). Also then the plane can have a
larger payload which is important.

Anyways, all this stuff is moot as the original post had nothing to about
the actual engineering parameters of the situation. If he said he wanted to
make the model plane fly then thats an engeering problem. All he asked was
how large would the equivilent plane be if scaled up. That is mathematics is
independent of engineering. If you scale up something by a factor of 2(in
length) then the volume will change by a factor of 8. Simple as that. The
ramifications of this is far reaching. Much more than anyone knows.





.

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