Calculate lift from pressure distribution

[Jurgen M]

v=50m/s
∆Pg= -981Pa
∆𝑝𝑑 =490Pa
c=1m
𝜌 = 1,225 kg m3

𝐹3 = ∫ ∆𝑝3 ∙ 1 ∙ 𝑑𝑥 𝑐 2 0 = ∆𝑝𝑔 ∫ 2∆𝑝𝑑 𝑐 𝑥𝑑𝑥 𝑐 2 0 = 2∆𝑝𝑑 𝑐 ∙ ( 𝑥 2 2 ) c⁄2 | 0 = 2∆𝑝𝑑 𝑐 ∙ 𝑐 2 4 ∙ 2 = ∆𝑝𝑑 ∙ 𝑐 4 = 490,5 ∙ 1 4 = 122,625 N

Lift per unit of span = (F1) + (F2) +F3 + F4= 490.5+245.25+122,25+122,625=981N
Pressure push at all surfaces on airfoil,just push with less force on upper surface then lower surface, so F1 and F2 must has opposite direction than F3 ,F4.. so why they sum all forces with absolute values like pressure at upper surface pulling...?? pressure can not pull,only push

Dont understand final lift math and force orientation..

 

[FactChecker]

It's not a pressure, but a $\Delta p$, which is the pressure minus some baseline pressure. That can be negative.

 

[Jurgen M]

It's not a pressure, but a $\Delta p$, which is the pressure minus some baseline pressure. That can be negative.

If I know pressure distribution around airfoil, then geometry/shape/inclination of airfoil isn't necessary/relevant for calculate lift/drag?

 

[FactChecker]

If I know pressure distribution around airfoil, then geometry/shape/inclination of airfoil isn't necessary/relevant for calculate lift/drag?

The shape is relevant since it created the pressure distribution, but it is no longer necessary because the pressure distribution gives us all we need to know about the shape.
CORRECTION EDIT: The pressure distribution, surface area, and surface orientation are all needed to calculate the forces.

 

[Jurgen M]

The shape is relevant since it created the pressure distribution, but it is no longer necessary because the pressure distribution gives us all we need to know about the shape.

Same pressure distribution can have different airfoil shapes or inclination,so we don't know what is airfoil shape/angle from only pressure distribution.
Can you post some courses or videos or articles with examples of this lift calculation where I can learn better this topic?

 

[FactChecker]

Same pressure distribution can have different airfoil shapes or inclination,so we don't know what is airfoil shape/angle from only pressure distribution.
Can you post some courses or videos or articles with examples of this lift calculation where I can learn better this topic?

I stand corrected. The pressure distribution, surface area, and surface orientation are all needed to calculate the forces.

 

[Jurgen M]

I stand corrected. The pressure distribution, surface area, and surface orientation are all needed to calculate the forces.

What is surface orientation?

 

[FactChecker]

What is surface orientation?

It is the direction the surface is tilted toward at that (infinitesimal) position. It is usually specified by the direction of the vector normal to the surface at that point. That normal vector is handy in cases like this because it is the direction of the force due to the pressure, ignoring the surface drag.

 

[Jurgen M]

calculate F3 from average pressure..

or with integral

Why they calculate F3 like pressure distribution "triangle" act at bottom airfoil surface from 0 to C/2?
If I see there is no pressure distribution at bottom surface from 0 to X, pressure distribution is drawn from X to C/2

 

[russ_watters]

Why they calculate F3 like pressure distribution "triangle" act at bottom airfoil surface from 0 to C/2?
If I see there is no pressure distribution at bottom surface from 0 to X, pressure distribution is drawn from X to C/2

Since there are no surface angles provided, it looks to me like all of the pressures are vertical components only (simplified problem). So while there are certainly positive pressures on the airfoil from 0-X, the orientation of the airfoil surface makes the vertical component negligible.

 

[Jurgen M]

Since there are no surface angles provided, it looks to me like all of the pressures are vertical components only (simplified problem). So while there are certainly positive pressures on the airfoil from 0-X, the orientation of the airfoil surface makes the vertical component negligible.

The pressure plot is based at the zero line not the lower wing surface, I made mistake because I look at surface..

What surface angle you mean?

 

[cjl]

You don't need the surface angle. You can just assume it's all acting perpendicular but acting on the projected area rather than the true area. Sure, the actual pressure force acts along the surface normal, but the vertical component is the same proportion of the total force as the projected horizontal area is of the total area, so all the angle dependence cancels out. For the calculation, you can just treat all of those as if they're acting vertically on a flat horizontal plate and you'll get the correct answer.

 

[Lnewqban]

...
Can you post some courses or videos or articles with examples of this lift calculation where I can learn better this topic?

Consider that for same airfoil, the patterns of pressure distribution will change as AOA changes.
Also, high pressure differentials can’t be sustained close to the wing tips because some mass of air will naturally flow span-wise from areas of higher pressure to areas of lower pressure.

Please, see:
https://www.mh-aerotools.de/airfoils/velocitydistributions.htm

https://www.rcuniverse.com/forum/attachment.php?attachmentid=1385606&d=1375503690