# Help with calculate forces from pressure distribution

V=50m/s

deltaPg= -981 Pa

deltaPd=490,5 Pa

c=1m

r.com/PCshZ.png

Above is calculate Fz with integrals and with average pressure.

Why F3 is calculate from 0 to C/2 if pressure distribution is drawn at bottom surface from X to C/2?

What is pressure distribution at bottom surface from 0 to X?

If I know pressure distribution around airfoil, then shape of airfoil and airfiol AoA(inclination on diagram) is not relevant when calculate forces?

Why pressure is not drawn perpendicular to airfoil surface?

Can you explain how calculate lift,drag,total force and read this pressure distribution diagrams?

• I chink you’re reading it wrong. The pressure plot is based at the zero line not the lower wing surface.
– Jim
Commented Dec 10, 2021 at 22:14
• @Jim Yes I read wrong, I look at arrows at surface of airfoil, no arrows at lower surface from 0 to X, so I ask my self what is with pressure here! So airfoil picture in this diagram is completly irrelevant, I must look only at pressure distribution like is based on zero line?What if diagram look like this lh3.googleusercontent.com/proxy/… Commented Dec 11, 2021 at 8:13
• Your question neglects span. Given are pressures (force per area) but you only have an airfoil chord, no spanwise dimension. Only the area produced by chord times span will enable you to calculate a force. Commented Dec 11, 2021 at 15:26
• @PeterKämpf Yes Fz is force per unit of span. Commented Dec 11, 2021 at 15:33

Can you explain how to calculate lift, drag, total force and how to read this pressure distribution diagram?

Not with the given information. All what can be calculated is the lift per unit of span. Pressure is force per area, so in order to arrive at a force, it must be multiplied by an area. We only have chord, no span, so there is no area given. All I can do, therefore, is to calculate the lift force per unit of span. Drag cannot be calculated at all.

Let's take 1 m as this unit: This will give us 1 m² as the wing area. Since the pressure over chord is either constant or linear, no fancy integrals are needed. The plot already distinguishes four sections, each with their own gradient of pressure:

1. Upper forward: Constant pressure of -981 Pa which equals a suction force of 981 N per m². Per meter of span this is 490.5 N of upward force of the half square meter here.
2. Upper rear: The pressure grows from -981 Pa to 0 at the trailing edge. Therefore, lift per meter of span is half of what it is in the first section, namely 245.25 N of upward force.
3. Lower forward: Again a linear increase over chord, now from 0 to 490.5 Pa pressure at mid chord. Per meter of span this is 122.625 N of upward force.
4. Lower rear: Same thing, only in reverse: Pressure drops from 490.5 Pa pressure at mid chord to 0 at the trailing edge. Again, we have 122.625 N of upward force per meter of span.

If we sum up all four sections, the result is 981 N of lift per meter of span. Suction on the upper side contributes ¾ of this force and pressure on the lower side adds the fourth quarter. Funny how this coincides with the usual approximation of gravitational acceleration! Each meter of span lifts 100 kg of mass in Earth's gravity field.

Why F3 is calculated from 0 to C/2 if the pressure distribution is drawn at the lower surface from X to C/2?

X is a variable which starts at 0 at the root of the X axis. So F3 runs from X=0 to X=c/2. F3 is the force produced by the forward pressure ramp, nothing more.

What is the pressure distribution at bottom surface from 0 to X?

X is variable. At X=0 the bottom pressure is 0. It grows to 490.4 N/m² at X=c/2 and drops again to zero at the trailing edge when X=c.

If I know the pressure distribution around the airfoil, are the shape of the airfoil and the airfoil AoA (inclination on diagram) not relevant when I calculate the forces?

Yes, the shape and AoA are not relevant (or is this: No, the shape and AoA are not relevant?) German and English answer negated questions in opposite ways when meaning the same. Try to avoid negated questions when you want a clear answer.

Why is the pressure not drawn perpendicularly to the airfoil surface?

This is to simplify the calculation. You can either integrate the cosine of the inclined pressure over the actual length of the airfoil contour, or you can integrate the absolute pressure over the projection of the contour on the X axis. Both will give the same result when you want to find the lift force.

• "Not with the given information" I have question where this can be explanied: aviation.stackexchange.com/questions/90710/… Commented Dec 11, 2021 at 17:13
• +1 for "Funny how this coincides with the usual approximation of gravitational acceleration! Each meter of span lifts 100 kg of mass in Earth's gravity field." alone Commented Dec 12, 2021 at 21:45

Why F3 is calculate from 0 to C/2 if pressure distribution is drawn at bottom surface from X to C/2?

The pressure distribution is uniform from 0 to c/2, then uniformly different from c/2 to c. It does not start from point $$x$$, it starts from point $$x$$=0. $$x$$ is the horizontal co-ordinate.

What is pressure distribution at bottom surface from 0 to X?

Increasing linearly from zero to $$\Delta P_D$$

If I know pressure distribution around airfoil, then shape of airfoil and airfiol AoA(inclination on diagram) is not relevant when calculate forces?

The shape of the airfoil at this AoA is what results in the pressure distribution.

Why pressure is not drawn perpendicular to airfoil surface?

The picture seems to be relevant for upwards pressure only.

Can you explain how calculate lift,drag,total force and read this pressure distribution diagrams?

This pressure diagram is relevant to lift only.