Jump to content

Recommended Posts

Ralph is a helicopter student pilot at Big Rotor Helicopter School working on his private pilot certificate. The other day he was at Big Rotor waiting to take his lesson when he overheard two guys having a discussion about aerodynamic force –one guy said Bernoulli and the other guy said something about a spinning cylinder. Ralph was perplexed by the discussion because he knows aerodynamic force on an intuitive basis depends on the following physical properties: these include velocity of air, air density, viscosity of the air, the size of the body that the air flows over, and compressibility of the air. However, Ralph did not speak up because he did not know how to organize all the physical properties which also includes the angle of attack into a simple mathematical model that describes aerodynamic force. Help Ralph!

Edited by Tom22
Link to post
Share on other sites

All ya gotta do is deflect air downwards, and you get an equal and opposite force up (and back) called Lift (and Drag).

 

Whether you want to attribute it to Bernouilli, or Newton, or Vortex Theory, doesn't really matter.

 

Your simplest mathematical model, which most people start with, is Bernouilli.

Link to post
Share on other sites

All ya gotta do is deflect air downwards, and you get an equal and opposite force up (and back) called Lift (and Drag).

 

Whether you want to attribute it to Bernouilli, or Newton, or Vortex Theory, doesn't really matter.

 

Your simplest mathematical model, which most people start with, is Bernouilli.

 

If so, why is the top of the airfoil curved upwards?

 

Nasa has a lot to say about the generally accepted theories that get taught:

 

http://www.grc.nasa.gov/WWW/k-12/airplane/wrong1.html

 

http://www.grc.nasa.gov/WWW/k-12/airplane/wrong2.html

 

http://www.grc.nasa.gov/WWW/k-12/airplane/wrong3.html

 

http://www.grc.nasa.gov/WWW/k-12/airplane/right2.html

wrong2.gif

Link to post
Share on other sites

You said downwards with an opposing lift result so I just thought you meant #2, thats exactly how it reads. I can see what you mean though, as in downwards over the top.

 

The remainder was directed at the original post and towards people new to the subject matter that didn't actually know what the hell Ralph, or you, were talking about. I like these sources and they say NASA on them so that makes them right.

Link to post
Share on other sites

Ralph is a helicopter student pilot at Big Rotor Helicopter School working on his private pilot certificate. The other day he was at Big Rotor waiting to take his lesson when he overheard two guys having a discussion about aerodynamic force –one guy said Bernoulli and the other guy said something about a spinning cylinder. Ralph was perplexed by the discussion because he knows aerodynamic force on an intuitive basis depends on the following physical properties: these include velocity of air, air density, viscosity of the air, the size of the body that the air flows over, and compressibility of the air.

 

However, Ralph did not speak up because he did not know how to organize all the physical properties which also includes the angle of attack into a simple mathematical model that describes aerodynamic force. Help Ralph!

 

Like already noted in the post above, "All that is necessary to create lift is to turn a flow of air. An aerodynamic, curved airfoil will turn a flow. But so will a simple flat plate, if it is inclined to the flow." REF: NASA

 

We covered a similar subject last year. Check out the following post.

Helicopter Lift Theory - Equal Transit, Skipping Stone & 1/2 a Venturi - all wrong...

 

As to organizing all the physical properties into a simple mathematical model that describes aerodynamic force, that maybe a task beyond Ralph as a private pilot.

 

Helicopter aerodynamicists explain it by two basic theories, the "Momentum Theory" and the "Blade Element Theory." Again, both are two parts of the same explanation and analyses of the rotor aerodynamics.

 

The Momentum Theory follows Newton's third law, in the case of the helicopter in hovering flight; the action is the development of a rotor thrust equal to gross weight. The reaction is represented by the acceleration of a mass of air from a stagnant condition far above the rotor to a condition with finite velocity in the wake below the rotor.

 

The Blade Element Theory follows along with those airfoil vector diagrams you know so well in your textbooks. This theory looks at what is actually happening at the blade that results in producing the Total Aerodynamic Force (TAF).

 

Lookup these two theories (Momentum & Blade Element) and that should give you what you need.

 

Here’s a video about that spinning cylinder thing. Again, note, all that is necessary to create lift is to turn a flow of air.

 

http://youtu.be/23f1jvGUWJs

Edited by iChris
Link to post
Share on other sites

Thanks everybody for taking time to comment – I appreciate it. I realize it’s a trite subject; however, I was curious to see if anybody would actually derive the lift equation (L = ½ρ*Cl*V^2*S) commonly found in pilot training manuals. Now, it could be argued, that a simple mathematical expression that models flight includes the price of fuel + price of the helicopter + price of maintenance + the price of insurance + ∙∙∙ = lift. :)

 

 

As to organizing all the physical properties into a simple mathematical model that describes aerodynamic force, that maybe a task beyond Ralph as a private pilot.

 

Yeah I know, deriving equations is beyond the scope of piloting and you certainly wouldn’t subjugate a student to a bunch of mathematical modeling but it’s an interesting exercise – to me anyway.

 

 

VR Post.pdf

Link to post
Share on other sites
  • 2 weeks later...

Ralph was perplexed by the discussion because he knows aerodynamic force on an intuitive basis depends on the following physical properties: these include velocity of air, air density, viscosity of the air, the size of the body that the air flows over, and compressibility of the air.

 

However, Ralph did not speak up because he did not know how to organize all the physical properties which also includes the angle of attack into a simple mathematical model that describes aerodynamic force. Help Ralph!

 

 

As to organizing all the physical properties into a simple mathematical model that describes aerodynamic force, that maybe a task beyond Ralph as a private pilot.

 

Yeah I know, deriving equations is beyond the scope of piloting and you certainly wouldn’t subjugate a student to a bunch of mathematical modeling but it’s an interesting exercise – to me anyway.

 

The attachment you offered is an analysis for lift produced from a specific wing or airfoil. That analysis is in part, the Blade Element Method looking at local velocities at the airfoil and calculating non-dimensional coefficients to define specific airfoil characteristics.

 

However, when you look at the basis lift equation (L = ½ρ V2 CL S) it is derived, with respect to lift as an aerodynamic force, from one of Newton’s laws. For every action, there is an equal and opposite reaction. In the case of the helicopter, the action is the acceleration of a mass of air from above the rotor to a given velocity below the rotor. The reaction is the development of a rotor thrust (lift) equal to the gross weight.

 

Like any physical system, the helicopter must obey the basis laws of physics, in this case, the simple familiar relationship:

 

Force = (Mass) (acceleration) Acceleration is a change in the magnitude and/or direction of the velocity vector with respect to time.

 

Therefore, the Force (Lift) = (Mass flow per second) (total change in Flow velocity per second)

 

Or

 

L = (m/sec) (Δν/sec) – Therefore, all that is need to produce an aerodynamic force (Lift) is to cause a change in the velocity of the airflow.

 

Going back to the basis lift equation, you may recognize the terms “½ρ V2“ That is also what your airspeed indicator measures indirectly to give you airspeed.

 

Dynamic pressure = q = ½ρ V2 - That is the dynamic pressure or the kinetic energy per unit volume of a fluid particle. The dynamic pressure is a defined property of a moving flow of gas (in this case the mass airflow/sec).

 

How the basis lift equation looks like this: L = q CL S

 

The CL is a nondimensional coefficient that defines how efficient a solid body is at producing an aerodynamic force, change in the velocity of the airflow (Δν). A flat steel plate or your hand placed out the window of a moving car, simulating an airfoil, will both produce an aerodynamic force; however, neither is a very efficient body with respect to lift-to-drag ratio. Any turning of a moving fluid (airflow) creates an aerodynamic force.

 

S = Surface area and an increase in surface area allow us to work with (change the velocity) of a larger mass of airflow per second.

 

Therefore we’re back to:

 

Force = (Mass) (acceleration) Acceleration is a change in the magnitude and/or direction of the velocity vector with respect to time.

 

Or

 

Force (Lift) = (Mass flow per second) (total change in Flow velocity per second).

 

Or

 

L = (m/sec) (Δν) – all that is need to produce an aerodynamic force is to cause a change in the velocity of the airflow.

 

REF:

Lift is created by turning a moving fluid, and all parts of the solid body can deflect the fluid.

Edited by iChris
Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
×
×
  • Create New...