View Full Version : Dimensional Analysis on Lift Equation not working out?

aviationluver

22nd Oct 2018, 19:26

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.

infrequentflyer789

22nd Oct 2018, 20:13

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 :)

aviationluver

23rd Oct 2018, 20:52

Just realized that. No need for the insult.

Derfred

24th Oct 2018, 12:11

No need for the insult.

Is this the new generation of pilots?

I need to start sorting out my affairs.

FakePilot

24th Oct 2018, 13:01

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".

VintageEngineer

1st Nov 2018, 14:53

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

Vessbot

1st Nov 2018, 15:02

I had this one landing last trip that I think was because of New Physics...

Chris Scott

1st Nov 2018, 15:55

...Imagine force’s being measured in Aviationluvers or Infrequentflyer789s

Didn't realise Newton was a grocer... ;)

Crabman

6th Nov 2018, 12:33

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.

India Four Two

6th Nov 2018, 13:33

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