Understanding Lift Force and the Bernoulli Equation in Small Aircraft

Click For Summary
SUMMARY

This discussion focuses on calculating lift force in small aircraft using the lift equation and Bernoulli's principle. The lift force is defined by the equation Lift Force = Cl * ρ * A * V², where Cl is the lift coefficient (0.3), ρ is air density, A is wing area, and V is air speed. Participants clarify that the air speed V refers to the average speed over the wing surfaces. The relationship between pressure differences (P1 - P2) and lift is established, emphasizing that the lift force is generated by the pressure differential across the wing surfaces.

PREREQUISITES
  • Understanding of the lift equation: Lift Force = Cl * ρ * A * V²
  • Familiarity with Bernoulli's equation: P1 - P2 = 1/2 * ρ * (V2² - V1²)
  • Knowledge of basic aerodynamics, including lift and drag forces
  • Concept of pressure differentials in fluid dynamics
NEXT STEPS
  • Research the implications of varying the lift coefficient (Cl) in different aircraft designs
  • Study the effects of air density (ρ) on lift force at different altitudes
  • Learn about the relationship between wing area (A) and lift generation
  • Explore advanced applications of Bernoulli's equation in real-world aerodynamics
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in understanding the principles of lift and aerodynamics in small aircraft.

Donna14
Messages
27
Reaction score
0

Homework Statement


See attachment

Homework Equations



Maybe lift force = ClρAv2

A=area
Cl= lift coefficient= 0.3
ρ= air density
V=air speed but don't know which one it represents... Under or below wing or average?

And the bernoulli equation seems to be needed as well...

The Attempt at a Solution



To keep the plane just in the air the lift force must be equal to the gravitational force I guess. But I'm not sure how to continue from there...
 

Attachments

  • image.jpg
    image.jpg
    36.1 KB · Views: 466
Physics news on Phys.org
Donna14 said:
V=air speed but don't know which one it represents... Under or below wing or average?
...
I think the diagram shows that explicitly.

Donna14 said:
And the bernoulli equation seems to be needed as well...
...
Yes, can you try and apply it here?
 
But I am stuck on how to continue... Can you please help me a bit?
 
Why don't you start by stating Bernoulli's equation and maybe try and substitute some values into it?
 
Last edited:
P1-p2=1/2ρ(v22-v12)

But I don't know the pressure and I don't understand what to do with drag and lift force?
And do I have to use the given engine power?

Sorry this is completely new to me...
 
Last edited:
Donna14 said:
P1-P2=1/2ρ(v22-v12)

But I don't know the pressure and I don't understand what to do with drag and lift force?
And do I have to use the given engine power?

Sorry this is completely new to me...
Forget that equation for lift force. I assume there are more parts to this problem, which you didn't show us. Some of the given information may be needed for those -- or may just be extra information.


You have P1-P2=(1/2)ρ(v22-v12) .

Do the subscripts, 1 & 2 refer to the bottom surface of the wing and the top surface of the wing respectively?

How much lift force is needed?

What part of the plane generates the lift?

How are force, area, and pressure all related?
 
Going with the idealized assumptions about lift for this problem, you can assume the pressure below the wing is some ambient pressure P1 (for pressure below), and above the wing it's P2. The the difference in pressure (P1 - P2) times the wing area will equal the weight of the aircraft.
 
  • Like
Likes   Reactions: 1 person
But P x A= force isn't it? So you say (Pbelow-Pabove)xA=mass? Or mg? And I haven't got any other info about P...

I have substituted (Pbelow-Pabove) for mg/A and my result seems to be correct now. But I am not sure why I can say that the difference of P is this...
 
Last edited:
Maybe show your work explicitly but the difference in air pressure is what generates lift.
 

Similar threads

Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 9 ·
Replies
9
Views
5K
Replies
2
Views
4K
  • · Replies 30 ·
2
Replies
30
Views
4K
  • · Replies 1 ·
Replies
1
Views
5K