Lift Formula

[Nimer767]

Guys , As we all know the lift formula determines the lift capabilities , So..

L = (1/2) d v2 s CL

* L = Lift, which must equal the airplane's weight in pounds
* d = density of the air. This will change due to altitude.
* v = velocity of an aircraft expressed in feet per second
* s = the wing area of an aircraft in square feet
* CL = Coefficient of lift , which is determined by the type of airfoil and angle of attack.

But can someone explain what does it mean when it says 1/2 the air density , what do you mean by half the density ?? is it half the total value of the air density at an altitude ?

[tarmac]

that 1/2 was put there by conducting experiments on airfoils.

we know lift is proportional to all those factors you mentioned in the formula. still we needed a proportionality constant to make it into an equation. so after lot of experiments it now stands at 1/2.

[Tinstaafl]

It's not correct to describe the '1/2' as a factor derived through experimentation to make the numbers work. That's more accurately assigned to Cl - a non-dimensional number that accounts for Angle of Attack & aerofoil shape.


Rough guide:

Lift formula is related to classical mechanics. Force, momentum, acceleration, mass etc.

It starts with mass x velocity = momentum

Kinetic energy = momentum squared / twice the mass. Substitute mv in the formula and it becomes

Ek = m v^2 or 1/2mv^2
----------
2

Force = mass x acceleration. Accelerating a mass requiress a force. If a mass of air can be made to accelerate than a force must have been involved and a reaction opposite that force.

L (a result of making the air accelerate) = CL x 1/2 x rho x v^2 x s where

Rho is the air density (a way of accounting for mass) and has an equivalent part in the lift formula as Mass has for Kinetic Energy. Substitute 1/2mv^2 and you have

L=CL x Kinetic Energy x area

In other words the energy contained in a parcel of air acts over a body with an area that, due to it's shape and angle, accelerates the air to produce a force (or a reaction, if you like). Anything that increases the amount of energy available to be put to work, the size of the area over which it works, or the ability of the shape or angle to modify how that work is done will increase the amount of lift.

[BOAC]

Like all good 'stories', Nimer, it's the way they are told:)

Look at it as L = 1/2( [d* v2* s]* CL). The 1/2 just happens (traditionally) to be written next to the 'd'

[Nimer767]

Thank you .........

[dClbydalpha]

I'm with BOAC on this although for me it is more of the form

(½*d*v²)*S*Cl

Although it can be debated about downwash/circulation versus Bernoulli/pressure difference etc. this form of the lift equation points towards the use of dynamic pressure as defined by Bernoulli and that is what you see in the equation in brackets. You then have a pressure term, and an area term which when multiplied gives you a force. The non-dimensional coefficient gives a scaling factor to account for the aerofoil efficiency.

[galahad]

1/2 is the change of velocity from Momentum Equation
dp = -rho VdV

(d=delta)

[BOAC]

Are you planning on explaining integration to Nimer?:confused:

[Nimer767]

(: ........

[artax]

L = 1/2 d v^2 S CL, but who came up with the formula?

DaVinci? Bernoulli? Ventuuri? Bob Smith?