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# Dimensional Analysis on Lift Equation not working out?

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# Dimensional Analysis on Lift Equation not working out?

22nd Oct 2018, 18:26

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Dimensional Analysis on Lift Equation not working out?

Hello,

I am showing that the equation for lift on a wing is
L=1/2 Cl (air density) (Area of Wing) Velocity^2

However, the dimensions aren't working out.

L is kg ; Cl is dimensionless; Air density is kg/m^3; Area is m^2; Velocity is m/s

If you work the dimensions it does not work out. You get L in kg and kg m on the other side.

What am I missing?

Thanks.
22nd Oct 2018, 19:13

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Originally Posted by aviationluver
Hello,

I am showing that the equation for lift on a wing is
L=1/2 Cl (air density) (Area of Wing) Velocity^2

However, the dimensions aren't working out.

L is kg ; Cl is dimensionless; Air density is kg/m^3; Area is m^2; Velocity is m/s

If you work the dimensions it does not work out. You get L in kg and kg m on the other side.

What am I missing?

Thanks.
First you are missing (1/s)^2 from the velocity term, this gives kg*m /s^2

Second, you are missing that lift is a force so it is in Newtons which is also (e.g. from F=ma) = kg*m/s^2

Sorry you didn't discover new physics, maybe next time
23rd Oct 2018, 19:52

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Just realized that. No need for the insult.
24th Oct 2018, 11:11

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Originally Posted by aviationluver
No need for the insult.
Is this the new generation of pilots?

I need to start sorting out my affairs.
24th Oct 2018, 12:01

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Originally Posted by infrequentflyer789
First you are missing (1/s)^2 from the velocity term, this gives kg*m /s^2

Second, you are missing that lift is a force so it is in Newtons which is also (e.g. from F=ma) = kg*m/s^2

Sorry you didn't discover new physics, maybe next time
I get the joke, like "new math".
1st Nov 2018, 13:53

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To add to the tongue-in-cheek ‘new physics’, I’m glad Newton got there first. Imagine force’s being measured in Aviationluvers or Infrequentflyer789s
1st Nov 2018, 14:02

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I had this one landing last trip that I think was because of New Physics...
1st Nov 2018, 14:55

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Originally Posted by VintageEngineer
...Imagine force’s being measured in Aviationluvers or Infrequentflyer789s
Didn't realise Newton was a grocer...
6th Nov 2018, 11:33

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Not sure if he was a grocer but I always think of apple's when I think of Newton.

Back to topic, the OP isn't the first person to have a "brain fart" and mix up mass and force in an equation.
6th Nov 2018, 12:33

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I was confused when I was first saw that the dimensions of a force are M.L.T^-2

However, it’s obvious when you look at F = m.a

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