Lift Equation, Why?

[brettjeepski]

In the lift equations- CL*V2*1/2P*S=lift

 

Why is Velocity squared?

 

Why is pressure 1/2?

 

Thanks in advance for your input

[HeliUtah]

First of all, pressure is not part of the equation, the P should actually be a lower case greek symbol, rho, which is used to represent the density.

 

1/2 is just a coefficient and has nothing to do with the density of the air ... it could technically be absorbed into the lift coefficient, as it is just a constant, but Bernoulli decided to pull out the constant from the coefficient, probably since it comes directly from the differential equation used to derive the kinetic energy (mv^2/2) which leads to the velocity term, which comes directly from the kinetic energy which is proportional to the square of velocity which is derived from the thermodynamic laws for force. If you want more on that, I could go on, but I think you get the idea.

 

Hope it helps

[Tom22]

Introduction to Flight by John Anderson is an excellent book if you want to know more about how aerodynamic equations are derived. Don’t be fooled by the title.

 

Bernoulli’s equation is derived from Euler’s equation, which relates a change in pressure to a change in velocity, or a change in momentum force. Euler’s equation is a momentum equation. The ½ rho velocity squared comes from integrating (from the calculus) between two points.

 

Euler’s equation holds for both compressible and incompressible flows. For a compressible flow rho is a variable; however, for an incompressible flow rho is a constant.

[brettjeepski]

First of all, pressure is not part of the equation, the P should actually be a lower case greek symbol, rho, which is used to represent the density.

 

1/2 is just a coefficient and has nothing to do with the density of the air ... it could technically be absorbed into the lift coefficient, as it is just a constant, but Bernoulli decided to pull out the constant from the coefficient, probably since it comes directly from the differential equation used to derive the kinetic energy (mv^2/2) which leads to the velocity term, which comes directly from the kinetic energy which is proportional to the square of velocity which is derived from the thermodynamic laws for force. If you want more on that, I could go on, but I think you get the idea.

 

Hope it helps

 

Wow Mike thanks man! Where did you get your training and why wasn't I taught that!

 

Thanks for the information. I was looking in Principles of helicopter flight by Wagtendonk it said the p equals air density. so that makes more sense.

 

I guess that is why I am not big into calculus. because both of your explanations was way over my head! If anyone has a more simple explanation I would love that explanation as well.

[Tom22]

Keep in mind that equation you presented is pretty much useless. It is only used as a training aid in pilot manuals.

 

Sorry, I didn’t mean to be condescending.

Edited February 5, 2010 by Tom22

[HeliUtah]

Wow Mike thanks man! Where did you get your training and why wasn't I taught that!

 

I think most of that came from my previous life as a physicist.

[Goldy]

Keep in mind that equation you presented is pretty much useless. It is only used as a training aid in pilot manuals.

 

Sorry, I didn’t mean to be condescending.

 

Almost useless....but if you remember the part about velocity squared, maybe you'll remember the importance of airspeed in everything we do !

 

Sorry, off on a tangent there....

[will]

actually, goldy, i think you're angle is the best way to look at the equation...as a teaching aid, that is. it presents a beautiful visual for how each component affects the total lift.

 

i.e.: with the reduced velocity in the retreating blade, lift is reduced, etc., etc., etc. it allows students to see how the actual numbers influence helicopter performance.