Formula for lift: Question

[i4iq]

So, why is it 1/2 x rho (air density) in the formula?

I understand that it is dynamic pressure but why the one-half?

[baffler15]

So, why is it 1/2 x rho (air density) in the formula?

Correct me if I'm wrong, but I thought the 1/2 applied to the V squared part of the formula?

:8 or :confused:

The Baffler

[i4iq]

Correct me if I'm wrong, but I thought the 1/2 applied to the V squared part of the formula?

:8 or :confused:

The Baffler

Whatever! But why the 1/2?!

[Disguise Delimit]

It all goes back to the initial experiments with lift. They were able to measure the lift, and were trying to devise a formula that gave them the answer they already had.

All related to Kinetic Energy, which is 1/2 x mass x V squared (obtained by integration from momentum, mV)
To find mass, you need air density (rho) x surface area
Thus for airflow, you got 1/2 x (rho x s) x V squared

Plus the variable with angle of attack, the coefficient of lift.

Or near enuf .....

[i4iq]

Great. Thanks DD, it's been bugging me!

[Matthew Parsons]

Not sure if this is really a serious question, but here goes a serious answer.

The 1/2 rho v squared is essentially the kinetic energy density or kinetic energy per unit volume. Think of rho as mass over volume and the formula can be made to look like 1/2 mass v squared over volume. Of course 1/2 m v squared is the kinetic energy formula you would have learned during basic physics.

So where does the 1/2 come from in 1/2 m v^2? Try a simple derivation for an arbitrary mass that is initially at rest. If you move the mass over a distance, x, using a force, F. Then the work you perform is W=Fx. Substitute F=ma and recognize that without friction all the work you do increases the kinetic energy of the mass and you get KE=max. Now you assume constant acceleration over the whole distance and apply some basic calculus (or just borrow the answers from a textbook) and you kind that v^2=2ax, where v is the final velocity after moving distance x. Substitute back into the equation and you get KE = 1/2 m v^2.

It comes into the lift equation because that is developed using basic principles of physics. When the kinetic energy term (or more accurately KE density) is required a 1/2 shows up. It isn't associated specifically with the rho nor the v^2 but with the entire KE term.

A word of caution: with all physics you'll find that there are multiple ways of describing the same thing. It may be that you find a derivation where the 1/2 comes from somewhere else. That derivation may not be wrong, just different, but as long as the final answer is the same and the concepts are consistent then the alternate derivation is valid.

[paco]

And I always thought that the ½ was there to represent the average of a body’s velocity between the start and end of its travels. Oh well.

Phil

[Unhinged]

Basic calculus (if there is such a thing !!!)
Let me try for a simpler version of Matt's answer, and a more correct version of DD's answer.
The lift depends on the kinetic energy of the free stream
From physics we have:
momentum = mass x velocity, and
kinetic energy = the derivative of momentum
From any calculus 101 textbook:
If momentum = mv, then
kinetic energy = 1/2 mv^2
Now substitute rho for m, and you get the answer as it applies to free stream aerodynamics.
Does that help ? Dunno !! It's still simplified (a lot) but it's more accurate.

[NickLappos]

Paco, you are correct, 1/2 is the average velocity. Don't let the Calc fool you, since the relationship of momentum to velocity is linear, the 1/2 is just the average!

[Deemar]

Another way of looking at it is that the term 1/2 * rho * V^2 is the dynamic pressure. The 1/2 is there to ensure that the term is comparable with the static pressure.

Along any streamline the static pressure and the dynamic pressure sum to a constant. So where the velocity is higher, the dynamic pressure is higher and hence the static pressure is lower - Bernoulli's principle as we all know it.

If we didn't have the 1/2 term, then this relationship would not hold.

Of course, this relates to what Mathew Parsons was saying:

The 1/2 rho v squared is essentially the kinetic energy density or kinetic energy per unit volume.

Static pressure is the the kinetic energy density associated with the random thermal motion of the air molecules. Dynamic pressure is the kinetic energy density associated with the non-random motion of the air molecules.

Daniel

[Matthew Parsons]

Actually the 1/2 doesn't make an average velocity because the average is v/2 and when you square that you get v^2/4.

However, you may be able to come up with a derivation that uses both the average velocity, v/2, and the final velocity, v.

Matthew.

[i4iq]

Not sure if this is really a serious question, but here goes a serious answer.

Yes, it was a serious question and thanks for the serious answers!:ok:

[Disguise Delimit]

The half has nothing to do with averages.

It has everything to do with integral calculus.

Start with momentum, MV. Integrate it once (with respect to V), you get 1/2 MV squared. If you integrated it again, you get 1/6 MV cubed, but this item means nothing to us, so we don't do it. (There are a few constants thrown in as well, but we won't worry about them either.) Purely mathematics, no averages.:8

[deeper]

It does not matter any way as it is incorrect theory, (and it was only a theory after all), before you start typing have a look at NASA's website and type "incorrect theory" in the search engine.

Only 2% of lift is generated by the bernouli theory and the rest is Coanda effect.

Don't argue with me argue with NASA, (you'll lose):confused:

[[email protected]]

Punto - I think you'll find Deemar mentioned Bernoulli first and since the argument is about a formula used in his theorem (or a derivation of it) then it seems fair to mention him. However, since his theorem concerns ideal, incompressible fluids and ignores friction it is not surprising that it had to be fudged to explain what happens in the real world (isn't that what scientists and mathematicians do?)

[puntosaurus]

HaHaHa. Deemar, Deeper it's all the same to me. Apologies to Deeper for the slur ! Post deleted.

[Gordy]

I know I posted it on another thread---but I believe this thread deserves it too..........Sometimes my brain hurts ! ! !

http://i76.photobucket.com/albums/j35/helokat/8uzn8y1164932566.jpg

[HillerBee]

Why would any pilot bother with where the lift formula comes from? You'll never need it. Unless you want to be a designer later don't bother.

[Heliringer]

Agreed Helibee, It makes no difference to a working pilots daily life. Lack power, dont lift to a higher DA/temp etc. so have a day off, easy as that, but they dont teach that stuff.:)

[Deemar]

It does not matter any way as it is incorrect theory, (and it was only a theory after all), before you start typing have a look at NASA's website and type "incorrect theory" in the search engine.

Only 2% of lift is generated by the bernouli theory and the rest is Coanda effect.

Don't argue with me argue with NASA, (you'll lose):confused:

Well, a quick search of the nasa site under incorrect theory doesn't show anything on the ongoing coanda/bernoulli/deflected airstream debate (well at least on the first page of results).

Nevertheless, it amazes me that people continue with the misconception that the three explanations are different. They are all different ways of looking at the same effect. It goes as follows if you decide to start with the momentum change associated with deflecting the airstream. You can, of course, start from coanda or bernoulli and get the same conclusions. It is the same physical effect.

1) In order to produce lift we need to produce a change in momentum (F = dp/dt, where p is momentum). This is achieved by deflecting the airstream passing over the airfoil.

2) In order to deflect an airstream, you need to have a pressure gradient across the airstream. To deflect the airstream downwards the pressure above the airstream needs to be higher than the pressure below.

3) For the air going over the top of the airfoil, the pressure above it is just the free stream pressure, therefore in order for there to be lower pressure below this stream, the pressure at the top of the airfoil needs to be lower than the free stream pressure.

4) Conversely, for the air going underneath the airfoil, the pressure below it is just the free stream pressure, so the pressure just below the airfoil needs to be higher than the free stream pressure.

5) The high pressure below the airfoil and the low pressure above it results in the airfoil being pushed up. This is the mechanism by which the force due to the change in momentum of the airstream is conveyed to the airfoil.

6) Because the pressure above the airfoil is lower, the air velocity needs to be higher to comply with bernoulli's law (P + 1/2*rho*V^2 = constant). Conversely, because the pressure below the airfoil is higher, the velocity needs to be lower.

7) Circulation is defined as the integral of air velocity around a closed path encircling the airfoil. Basically, you can think of the faster upper surface velocity and the slower lower surface velocity as being comprised of an equal velocity above and below superimposed with a weaker circulating flow that goes from the back of airfoil to the front along the lower surface, and then comes back along the top surface. The flow circulating flow along the top adds to the base velocity leading to a higher velocity over the top of the airfoil. The circulating flow is subtracted from the flow underneath the airfoil, resulting in a lower velocity under the airfoil. Note very carefully that the circulation is really just a mathematical tool to describe the difference in speeds above and below the airfoil.

8) The coanda effect basically states that the lift of the airfoil is proportional to the circulation times the free stream velocity. But remember, we only have a circulation because there is a difference in speeds above and below the airfoil, and we only have the difference of speeds because bernoulli requires it to generate the difference in pressures, and we only have the difference in pressures because we are deflecting the airstream.

So, you can't claim that only 2% of the lift is due to the "coanda effect", it is all due to the coanda effect, but then it is also all due to the deflection of the airstream, etc... They are all part of one and the same physical phenomenon.

The theory of circulation (coanda effect) is important mainly from a theoretical point of view, it provides a mechanism for calculating the strengths of downwashes and trailing vorticies. All very useful when Nick Lappos and co want to work out how to make a more efficient, quieter rotor.

Questions?

Daniel

[NickLappos]

Daniel is precise, and correct.

The problem with explaining lift as a Bernuilli effect is that it is completely un-intuitive. Regardless of how you slice it, lift is produced when the wing makes a bunch of air go down, which makes the force to fly up.

I tell folks to imagine that they were at the bottom of a 15 foot swimming pool, and a 10 lb weight is tied to their feet. If they scoop water with their hands and work hard enough, they can scoop enough water and throw it downward to make them rise. Scoop fast enough and hard enough, and they get to the surface, stop and they sink back down. That is exactly how a helicopter does it. Push enough air down and your aircraft rises.

They call it an air "plane" because it planes on the air, for pete's sake, and delta pressures really don't say a thing.

deeper, you can say that because something is labeled a "theory", it is not really known, but that really quite incorrect. It is also the argument made by lunkheads in the US who think that evolution is "only a theory" and that the earth was created 4000 years ago by magic!

[Matthew Parsons]

I won't disagree with what you said, Deemar, but having the precise definitions about what the author in the NASA article (I don't have it) says could clarify things for us.

I have heard the theories broken down to Bernoulli being the portion of lift due to the difference in pressure and the remainder being due to the deflection of the free stream. You can describe the latter with coanda effect if you wish.

The point is, most of the descriptions of Bernoulli's theory don't discuss what happens to the air aft of the trailing edge, which as Nick points out is the lift that we can comprehend easily, and it is the majority of the contribution of the total lift according to the spectral NASA report on "incorrect theories".

If we only look at the deflection of the airflow, or more precisely the change in momentum of that airflow, then we miss the small contribution to lift due to the pressure differences.

So without seeing the NASA report, I can understand why someone may look at the theories in such a way as one being a small contribution and another being the most significant.

In the end, it doesn't matter too much to the average pilot. I disagree that line pilots don't need to know the lift equation. Understanding what your aircraft is going to do when conditions change is important, and I believe the lift equation is a good teaching tool to help us develop some anticipation. How you derive it doesn't matter too much because the formula that we use works well enough for the majority.

Matthew.

[i4iq]

It is also the argument made by lunkheads in the US who think that evolution is "only a theory"!

That would be over 50% of Americans then...:D

... and that the earth was created 4000 years ago by magic!

That would be 6,000 years, as opposed to 4.5 billions of years ago by magic! :ugh:

But back to the topic at hand...

I've found the dicscussion very useful and knowing a little more about it can only help, in my view.

[NickLappos]

i4iq,

It never fails to amaze me that those of us (and you, perhaps) who make a living in a very scientific endevor, where the physics of flight - the very topic we are discussing - is part and parcel of our occupation can just divorce a selected scientific fact when demanded by their religion. Precisely where is the line drawn between 1/2rho V squared and creationist theory? I cannot see how a fundamental religious belief can so vastly replace one section of the scientific firmament without leaving gaping holes!

Suppose you suddenly found a section in the bible that told you to shut down all engines at 10,000 feet, would you do it because of your belief? You are clearly a reasonable person, therefore I know the answer, and I am glad! Perhaps it is easier to argue against evolution because it doesn't seem to matter, we blindly follow this portion of religious fundamental belief because nobody dies if we are wrong.

I truly hope that professional pilots know where to draw the line between religion and the aviation procedures they follow, just as I know Doctors do when they use fundamental evolution as a means to develop new drugs and medical procedures, in spite of those who label things they don't understand as "theory" and therefore not valid.

[i4iq]

i4iq,

It never fails to amaze me that those of us (and you, perhaps) who make a living in a very scientific endevor, where the physics of flight - the very topic we are discussing - is part and parcel of our occupation can just divorce a selected scientific fact when demanded by their religion. .

Interestingly enough, Newton himself was a creationist (as you would label him). Which facts are you suggesting he divorced?


Precisely where is the line drawn between 1/2rho V squared and creationist theory?

You make the assumption that there are lines...


I cannot see how a fundamental religious belief can so vastly replace one section of the scientific firmament without leaving gaping holes!

Gaping holes such as those left by missing links, for example?!:eek:


Suppose you suddenly found a section in the bible that told you to shut down all engines at 10,000 feet, would you do it because of your belief?

This is a straw-man argument, Nick. :rolleyes:


You are clearly a reasonable person, therefore I know the answer, and I am glad! Perhaps it is easier to argue against evolution because it doesn't seem to matter, we blindly follow this portion of religious fundamental belief because nobody dies if we are wrong..

Nobody needs to blindly follow anything.


I truly hope that professional pilots know where to draw the line between religion and the aviation procedures they follow,.

Back to the straw-man argument...


just as I know Doctors do when they use fundamental evolution as a means to develop new drugs and medical procedures

That is known as elephant hurling but anyway, evolution requires additional information to arise, not changes/"adaptations" where loss of information is often the cause for drug resistance. (btw, Pasteur was a "creationist" too!)


in spite of those who label things they don't understand as "theory" and therefore not valid.

So, in your own words, you mention the "creationist theory" as something you dont understand and therefore invalid ;)

I dont think this is the right "forum" to be discussing this but I'd be happy to continue the discussion via PM...:)

[Matthew Parsons]

I dont think this is the right "forum" to be discussing this...

At least we can all agree on this.

[DeltaFree]

I suggest most scientists pre-Darwin were creationists as there was no Evolution theory to believe in. So saying Newton was a creationist is like saying Adam and Eve didn't believe a 747 could fly.

[deeper]

Hello Nick,

I wrote that to throw a spanner in the works.

I am a Newtons person myself, the old hand out the window of a speeding car does it for me, or any other ideas that get the point of helicopter aerodynamics across in an educational way.

So many of the younger pilots of today have little to no idea how these confangled machines work. This is in plain evidence by the posts that are put up.

Very frustrating at times when a basic aerodynamic question is put and so many off the planet reasons are put forward.

They fly, they fly the same way every time, fly one you can fly them all, (if you can start them),

I have enjoyed your posts for a long time because it gets told as it is. Yes I am an old person approaching the happy end of my career.

Performance you can add up and calculate but helicopter flight is still some thing that you understand in the back of you mind.

i4iq,

you know the old saying......... if God had really wanted us to fly he would have given us wings............

We got the helicopter instead.

Now bugger off with this religious crap.

[i4iq]

I suggest most scientists pre-Darwin were creationists as there was no Evolution theory to believe in.

Not so. Darwin popularised evolution but his grandfather Erasmus wrote much of what Darwin published and influenced his thinking before going on the Beagle. Prior to that, Empedocles (d. 435), Democritus (d. 370), Epicurus (d. 270) and Lucretius (d. 55) had ideas about life arising spontaneously and one life form arising from another!

It is illogical to asume that pre-Darwin, scientists would think something couldn't fly. Otherwise, why do experiments to understand new things? DaVinci was convinced!

But we digress! :ugh:

[i4iq]

Now piss off with this religious crap.

That's intelligent! And very brave of you!:rolleyes:

I think its reasonable to extend a different viewpoint on a forum, particularly in response to the comment posted. It was intended to be tongue in cheek and as you will see, I had suggested a better place to continue the discussion.

Furthermore, the discussion was one of science...

[deeper]

i4iq,

Back to your original question,

Lucretius (d.55) probably knew the answer but didn't have any thing to write on. He was a very free thinker for his time. He caused quite an uproar in his village constantly running around flapping his arms and making wokka wokka noises. Irritated everyone.:E

[i4iq]

Deeper

Its funny how quasi-philosophical statements can so often reveal the man in the mirror!

[deeper]

I have absolutely no idea of which you are speaking,

but systematically speaking from a diabolical point of view i find that your fundumental faculties are insufficiently sophisticated for me to associate an iota of credence to your head up XXXX, holier than thou, down the nose peering, obviously intelligent, (and want us to know it), but unfortunately misguided low level attack on us mere mortals.

Ask mummy to help you off the rocking horse and have a rum, and a merry christmas and a very very happy new year. All is forgiven.

P.S. Who said i was of the male gender.

[i4iq]

Deeper

You read a lot into posts about science - and attack the individual rather than the reasoning!

Anyway, "man in the mirror" is a turn of phrase. My apologies to you for offending your sensibilities.

[slowrotor]

Deemar said in post number 20 of this thread--
2) In order to deflect an airstream, you need to have a pressure gradient across the airstream. To deflect the airstream downwards the pressure above the airstream needs to be higher than the pressure below.

That seems to contradict the follow on statements that the wing creates a low pressure above and high pressure below.

How could a low pressure above a wing promote a mass flow down toward a high pressure area?

[Grainger]

Read points 3) and 4) again.

One of the clearest explanations I've read for a long time.

[DeltaFree]

We can all choose to believe what we like, wings do lift, helicopters do fly and we exist. Why and how? I have my beliefs, you choose yours, I am not losing any sleep over worries about someone out there believing different theories to me.
You all just have a Great Christmas...if you believe in that!

[deeper]

I'm with Nick and DeltaFree.

:ok: :E :ok:

I hope everybody on Rotorheads has a very good next year.

Also many thanks to HELIPORT for his moderation.

[i4iq]

I hope everybody on Rotorheads has a very good next year.


Me too! And thanks to everyone for the input on the lift formula... which is where it all began! ;)

[Deemar]

I won't disagree with what you said, Deemar, but having the precise definitions about what the author in the NASA article (I don't have it) says could clarify things for us.


Well if anyone does have this article, then I'd be interested to see how it explains things. This is certainly one of the most debated topics amongst amateur aerodynamicists.


I have heard the theories broken down to Bernoulli being the portion of lift due to the difference in pressure and the remainder being due to the deflection of the free stream. You can describe the latter with coanda effect if you wish.


Which misses the point soemwhat, they aren't two different effects, they are one and the same effect. If there is a deflection of the free stream, the there MUST be a difference in pressure across the lifting surface to cause this. If there is a difference in pressure across a lifting surface then there MUST be a deflection of the free stream. Two ways of looking at it, but one physical effect underlying it.


The point is, most of the descriptions of Bernoulli's theory don't discuss what happens to the air aft of the trailing edge, which as Nick points out is the lift that we can comprehend easily, and it is the majority of the contribution of the total lift according to the spectral NASA report on "incorrect theories".


You are correct in that proponents of the different theories will only talk about their favourite aspect of the physical process that is lift generation. I guess my previous post was an attempt to correct that gap.

It is also worth noting that there are incorrect explanations of some of these effects. One in particular is the theory that the air on top of an airfoil goes faster because it has a longer distance to travel and it needs to "keep pace" with its "brother" air particle that travels along the bottom of the airfoil.


If we only look at the deflection of the airflow, or more precisely the change in momentum of that airflow, then we miss the small contribution to lift due to the pressure differences.

So without seeing the NASA report, I can understand why someone may look at the theories in such a way as one being a small contribution and another being the most significant.


Actually, if you look at the lift created by the change in momentum, it will exactly equal the lift created by the pressure difference. This is because they are one and the same lift force.


In the end, it doesn't matter too much to the average pilot. I disagree that line pilots don't need to know the lift equation. Understanding what your aircraft is going to do when conditions change is important, and I believe the lift equation is a good teaching tool to help us develop some anticipation. How you derive it doesn't matter too much because the formula that we use works well enough for the majority.

Fair point,
I guess if I was able to convince everyone then that would be one less conversation to have when you're not flying.

In terms of understanding what the aircraft is going to do as conditions change, then you are right. An understanding of the lift formulas, along with the Cl and Cd curves is probably a good thing for a pilot to have.

Daniel (I hope you all had a good Christmas)

[Graviman]

Deemar, very well thought out posts. The way i think of it is that the airflow follows the foil section by the coanda effect, which induces a rotation about the foil. The rotation component then causes the bernoulli lift, while the resulting downwash over the foil causes the induced drag. In simpler language, to paraphrase Nick: the airfoil experiences lift because it is throwing air at the ground, and drag because it is slowing it up.

NASA site on Bernoulli vs Newton (http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html)

i4iq, this is said tongue in cheek - i sincerely wish you a Merry Xmas:
Why can't you allow those of us who believe that the Earth is 4.5 bn years old to practice our beliefs? Having studied relativity, and being about to embark on quantum physics, then to paraphrase Shakespeare: there are more things in heaven and earth, i4iq, than are dreamt of in your philosophy.

Mart :ok:

[i4iq]

Hey Mart

(just as Deemar was getting this back on track...)


i4iq, this is said tongue in cheek - i sincerely wish you a Merry Xmas:
Mart :ok:

Thanks Mart, you too. I enjoy reading your posts!


Why can't you allow those of us who believe that the Earth is 4.5 bn years old to practice our beliefs? Mart :ok:

Yes, you must feel under an enormous amount of pressure to believe!;)


Having studied relativity, and being about to embark on quantum physics


I look forward to discussions and theories on gravitational time dilation, event horizons, dark matter (or not!) and other interesting stuff - but maybe not on this forum!


there are more things in heaven and earth, i4iq, than are dreamt of in your philosophy.


Mart, if you mean more than I can dream, yes of course - more than the philosophy itself, then logically, thats... illogical!

More than happy to hear your thoughts via PM.

Happy New Year!:ok:

i4iq

[Heli-Ice]

The simple formula for lift:

No money = no lift

Lots of money = Lots of lift



I must be close on this one :cool:

[i4iq]

Nice one Heli-Ice :D

[BGRing]

Can Some one here help me with this one..

I dont mean to fan any fire. but ..... Hang on. Fan..... what is the by product of lift ??? .... Hmmmmm.

whats that Law.. action reaction..

So would the 1/2 roh be because to put it to lift. we can only ever yeild half of the Potential.

IE. half for lift. and half for reaction. IE You go up. air goes down..

this is bugging me.

I do think either I dont understand Bernoulli theorem or it is wrong (Not completly) and looking at condra is helping.. (I think friction is the cause for the Pressure difference (IE any pressure sencor in the streem will have the Airmolicules removed from their pocket via friction and Attraction to the moveing streem..

Ne way. Ignore that last paragraph. it is just a little :yuk: during my Slow journy to become :8 towards Aeordynamics..

Oh. and is there a relation to Electricty. IE Electric fields can be influenced/generated by Magnetic/electric fields.. (these things all seem similar to me, again at this early stage of my journy to becoming a :8)

[NickLappos]

BGRing,

You have it wrong, the 1/2 x Rho x Vsquared is derived by integrating the rate of change of the momentum. Since the momentum is Rho x V, if you integreate it (using integral calculus) you get the 1/2 x Rho x Vsquared.

It is not that half of anything is lost, it is that the area under the momentum vs V curve is calculated by the formula.

[BGRing]

1/2? x Rhox (V squared) is derived by integrating the rate of change of the momentum.

Since the momentum is Rho x V, if you integreate it (using integral calculus) you get the 1/2 x Rho x (V squared).

it is that the area? under the momentum vs V curve is calculated by the formula.

The Purple and Greay parts confuse me. (Gentle reminder, Why 1/2)

Please remember I want to be :8 but curently I am :confused::ugh: so could you dumb it down a little(Lot) for me.


Edit 1/2 hour later

Or is it

1/2 x Rho x Vsquared is derived by integrating the rate of change of the momentum.

Since the momentum is Rho x V, if you integreate it (using integral calculus) you get the 1/2 x Rho x Vsquared.

it is that the area? under the momentum vs V curve? is calculated by the formula.
Changes being the Green bits
end Edit


I may well be a Lost cause :(

[Whirlygig]

I don't whether this will make things better or worse but ....

Differential calculus is what Nick is talking about.

Differentiation is how one property changes with another and integration (i.e. integral calculus) is the reverse. I'll use a familiar example.

If we take the rate of change of distance with time (i.e. we differentiate distance over time) we get speed (i.e. Speed = distance/time). If we differentiate speed with time, we get acceleration (i.e. acceleration = speed/time and we know speed = distance over time) which equals distance/(time squared).

Therefore, if we integrate acceleration, we get speed and if we integrate speed, we get distance.

If you draw a graph with time along the x axis (horizontal) and speed along the y-axis, the area under the graph will be the distance covered. If the speed is constant, the the graph will be a horizontal line. However, the speed could vary but the area under the graph will be the distance. If the speed is uniformally increasing, then there will be a slope to the graph and this slope is the acceleration.

As a rough schoolgirl guide, I can remember that you integrate, you add one to the power and divide by the power (and add a constant!!). To differentiate, multiply by the power and take one off the power.

i.e. momentum = mass x velocity. This means velocity has a power of one. Therefore, to integrate it by adding one to the power means velocity is to the power of two i.e. squared. Divide by the power i.e. divide by 2.

This sort of maths (which I have dragged up from over 25 years ago) is best shown rather than read so if you can find a friendly maths teacher, it would help you no end. It is easy honest but not to learn by yourself.

Cheers

Whirls

[BGRing]

seeing as you are online. I will type a quick reply.

Thanks for the Reply and effort.
I ahavent read it yet. and I dont Imagin I will understand it first time round.

Will get back with my findings. (if that made things click for me)

Thanks again.

OK. reading it now (May take 10 min :) . may take 10 days :( )

[Whirlygig]

http://www.1728.com/calcprim.htm

This might also help!

Cheers

Whirls

[Dan Reno]

"When scientists say a "theory," they mean a statement based on observation or experimentation that explains facets of the observable so well that it becomes accepted as fact. They do not mean an idea created out of thin air, nor do they mean an unsubstantiated belief."

[Whirlygig]

What's that got to do with the price of eggs?

How would you reconcile Einstein's Theory of General Relativity and the Theory of Quantum Mechanics as postulated by Heisenberg and Schrodinger? Neither or both are fact as they essentially contradict each other!!

Schrodinger's Cat may (or may not) disappear into thin air (depending on whether you look in the box) and Heisenberg's Uncertainty Principle means you can never be sure where the cat is. Pauli's Exclusion Principle means that no two cats are ever in the same position or state of excitement.

Let's face it, some of these ideas pretty much came out of thin air (or maybe mescalin induced) and are very, very hard to substantiate.

Cheers

Whirls

[Davey Emcee]

the 1/2 rho should be in [1/2 rho] square brackets the rest in (--) round brackets and differentiate the rest providing rho < absolute § unity

[BGRing]

Davey. I think I know what You mean

My keyboard has no numpad so I can not do Alt codes.

as I had put it above 1/2 x roh x VSquared would work on it own. But that is not the formula so if the whole formula was to be writen this way it would come out incorect. thus the (brackets)

Lift = Cl x (roh x 0.5) x (VxV) x S

would that work or would you still need to add the [] for the roh portion. As I think i understand it. the brackets are to instruce you to use the answer to the math inside them.

where if it were not in brackets then CL would be halved and then Times roh (being the incorect method)

WirlyGig. You are way smarter than I could ever be (Due mainly to my Interests and needs) and I have decided that it is not all bad to be a bit of a :confused::}:ugh:. My brain cringes when I see the formula you had in the last link. I understood you Example about Distance over time is Speed and Speed variations over time give Aceleration differences and that the Area under them are Speed and Aceleration respectivly. I think I understood how you used time twice thus Squared it. but still dont know where you halved a Constant..

not to worry. I have a friend who i a math teacher. He understood the examples given, though due to is relativly lesser experience with Aerodynamics and Physics. was not (Just yet) able to describe the lift formula. though , he did say that the 1/2 goes with the (VxV).. So I will enlist his abilitys to bring my Relativly Slow Brain, and its comprehension, up to date.

Thanks to you all for your help.
PS. Nick. My heli book says it is an average of the start and End velocity. I couldn't see it due to the placement of it at the r instead of after (VxV) x 0.5 x S . and because the book told me to refer to Dynamic energy.
and in this book. it says

Dynamic Energy is (1/2xM) x (VxV)

thinking on it.
the total Energy spent is Momentum. IE MxV
but that is the end result. not the average of both.

My brain hurts.. I still see that it is because you are minusing the action from momentum to get reaction. THats it. I am lost..

Gona call the Math teacher now. :(

[Brian Abraham]

For anyone wondering where the 1/2 comes from find a copy of "Theory of Wing Sections" by Abbott and Von Doenhoff, page 35. All explained.

[Brian Abraham]

If you have a handle on maths http://en.wikipedia.org/wiki/Bernoulli's_principle
pretty much steps you through it.

[BGRing]

Thanks for the link. That thing has me buged also.

I dont dispute the Phenomenon. just the Explanation of what is happening.
untill recently I would have said something like the following;


has anyone ever tested the Airpressure measured as a particle traveling through said Venturi. (IE not from a Port on the wall of the tube. where the port could have particle removed from it by the stream)

IE
have a Pressure guage on a neutraly boyant ballon float through the tube (Increase the length of tube) same for Water.

Personaly. I am Not beleiving the pressure difference.

I belive there is Equality in the tube. (Its is relativly neutral inside, as a ballon floats through it is relative to the air, without dynamic energy)

Show me a Specific example of why you think there is a pressure difference. and I could explain (Without math) why it appears that way.

friction and attraction with a little bumping in general direction. think of these when you look at every example of the measuring methods of a Venturi. (Thing is it works. IE the Venturi tube dose draw air liquid etc into the stream. but I'm not sure it is pressure difference.


But recently. I am Leaning toward just accepting the Pressure difference Explanation. well almost :)

Seen wiki and nasa and plenty other sites. seen Bernoulli water device and it all seams to be explainable in another way to me. Look at the Scram jet. dose air pressure drop at the Point of Squish ? ... More investigating by be and some more reprograming of my current Physics modle inside my head may be needed :(

Oh. I was good at math. but only when I understand the Reason for performing the calculations. (Never did calculus or Dont remeber it, Never did Physics either... and kinda did bad in English. and My spelling never improved either. But ... Spelling and Math is not everything. though they can be applyed to everything : )

[Matthew Parsons]

Don't worry about the 1/2. Coefficients in an equation are there just to give you a number, not really to give you understanding. The 1/2 could just as easily be embedded into the Cl, although then some other equations would need a factor of 2 included.

The funny thing is that the 1/2 is typically kept in the equation to aid the understanding. As has been mentioned before, that number just falls out of the mathematics and not the physics. And here we are concerned with the physics, but wondering about the 1/2. Be much more concerned with the exponent on the airspeed term...it actually matters.

As far as having a different understanding than Bernoulli, don't be too concerned. These theories do not define how nature behaves, they are just an attempt at quantifying how nature behaves. You can describe many systems using different physical concepts without revealing an inconsistency. An example of this is in basic kinematics, describing the motion of an unaccelerated particle. You can give its mass and momentum, its velocity and momentum, its velocity and energy, its momentum and energy, etc. Just because you're using different terms and concepts, doesn't mean there is anything different about nature.

Bernoulli's theorem is consistent with everything known about classical mechanics (for fluid dynamics, perhaps not for airfoils). You can define static and dynamic pressure, and then demonstrate that static pressure in a moving fluid decreases with the velocity of the flow. You can then demonstrate it experimentally. If you want to describe it using concepts other than static and dynamic pressure, go ahead. Doesn't mean that Bernoulli was wrong.