FPA Hyd. MATH

[Ganger]

Just had an apprentice ask me this the other day and still drawing a blank.....In regards to hydraulic 2:1 ration cylinder area. I understand obviously that the 2:1 has twice the force extension with twice the retract speed, because of the fact that the piston will have twice the rod area, however the question is:

Why is the sum of half the "area" of 2" not equal to the total area of 4"?

[SchweinAero]

I don't recall there being that level of precision in stock KSP hydraulics. Are you asking about a mod? If so, you should probably consult its particular thread.

[Ganger]

Nah it's just the area question I want the answer to. if you take the circular area of 4 and double it, why does it not equal the total area of 8? If 4 is half of 8.......why is the area not half

[Streetwind]

...Are you looking for help with your homework on a videogame forum, by any chance?

[Ganger]

haha it looks that way! thnx

[The_Rocketeer]

I think you're lost. Try this page for your answer.

EDIT: I think what you're asking is why does 2 squared (4) not equal half of 4 squared (16 divided by 2 = 8). It's because this is a 2-dimensional maths problem - it's exponential, not linear.

Edited August 29, 2015 by The_Rocketeer

[Vanamonde]

Since this is not about KSP itself, the thread has been moved to Science Labs.

[Shpaget]

Because area of a circle is a function of a square of radius.

area = radius² * Pi

[PB666]

Because area of a circle is a function of a square of radius.

area = radius² * Pi

I think we nedd K^2's help with this one. lol

Work = force * distance. If you apply 10 N of force over 0.1 m, then you have 1 joule of energy, IIRC. If the energy is delivered over a piston 2wice the radius then then

Cylinder 1 dimension = .1 x 1xr therefore volume moved = .1 x pi*1x² =pi*0.1x²

cylinder volume is height times square of radius * pi.

If cylinder 2 is 2x then its xsectional are is (2x)² *pi = pi * 4x². Therefore since volume pi*0.1x² = d₂ * pi * 4x². (pi * x² cancel)

d₂ = .1/4 = .025 ..... Therefore 1 j = F * .025. If so then force = 40 N.

The process is the reverse as well.

^{My bro had an old japanese built american eco car knockoff that his sig other used to commute one mile to work, the people at the shop told her to change the old every 1000 Miles, but this seemed extreme. So one day the engine locked up. I went to start it and the engine bounced back and forth, but didnt move. I knew exactly what the problem was. I removed the four spark plugs and i told everyone not to stand close to the engine. My bro didnot head. So thats a 1500 cc engine which means each cylinder has 375 cc. Now the starting RPM of ~300 RPM. This translates A cylinder up speed 100 U times d travel of about 0.05 so about 5 meter/sec. The spark plug hole is about 1/50th diameter of the piston. Therefore if the starter is infinitely resistent to back pressure, then what is in the cylinder will pass through the spark plug hole at 150 m/sec however it will spread and slow. The car did not start because gasoline trapped in the oil boiled over and was sucked up by the EGR valve. Oil is not compressible as gas so the engine locked, and turning engine without spark plug forces the oil out strait into bro's face. Very surprised he was at the physics.}

^{Solution take the car for a considerable drive every weekend to boil the gas out of the oil and change frequently.}

Edited August 30, 2015 by PB666
adding missing pi elements