induced drag

[shdw]

Is velocity the same as speed with speed being time*distance?

Velocity is displacement with respect to time where as speed is distance with respect to time. For everyday use you can assume them the same with little error.

If thats the case, then is it accurate to say that while at slow speeds and higher AoA, the wing has more time to impart a spin, spillage, on the air going from under to above the wing, increasing the strength of the vortex,

This was my thought process here. However the formula for induced drag doesn't agree with it. A pure increase in velocity, leaving all else constant, results in an increase in induced drag. Unless I'm misapplying the formula.

 

[shdw]

Matt, sorry I forgot to correct you on this. You said "speed = distance * time"

It is actually speed in miles/hr = distance in miles / time in hours.

Expressing this in words, one would say: Speed is relative to distance traveled in a given period of time.

 

[Matt13C]

Velocity is displacement with respect to time where as speed is distance with respect to time. For everyday use you can assume them the same with little error.


This was my thought process here. However the formula for induced drag doesn't agree with it. A pure increase in velocity, leaving all else constant, results in an increase in induced drag. Unless I'm misapplying the formula.

Matt, sorry I forgot to correct you on this. You said "speed = distance * time"

It is actually speed in miles/hr = distance in miles / time in hours.

Expressing this in words, one would say: Speed is relative to distance traveled in a given period of time.

Woops, that I did know, just came out wrong, thanks though.

Thanks for trying to answer the question, Tgray also.

 

[shdw]

I think I found it and if I'm right we will both be kicking ourselves. The question was asked:

"So what is the cause for the reduction in wing tip vortex strength?"

We both quickly jumped to induced drag formulas as they are related to the vortex strength, but we didn't look at how vortex strength is calculated. Which, in my fumbling through a book far more advanced than I'm comfortable interpreting, I stumbled upon the bound vortex. The important discovery was in the derivation of lift coefficient shown below.

The text discusses Helmholts theorem for vortex arrangement and the term horseshoe vertex. A term it seems implies the configuration of the vortex arrangement Helmholts theorized.

Anyways, in the next section (p51) vortex width is determined. During this process they derive lift coefficient from 3 different equations into a final equation. It is assumed is unswept, constant chord wing in incompressible flow, and experiencing additional lift due to constant AOA. To avoid clutter, only two are shown:

Cl = L / (QS) = (2T / V) (n/c) where:

Cl = Coefficient of lift
L = Lift
Q = Dynamic pressure
S = Reference wing area
T = Vortex strength
V = Velocity
n = Wing lateral coordinate y (dimensionless)
c = Reference wing chord


Anyways, what you told me here was that the induced drag curve comes from induced drag coefficient and induced drag coefficient is calculated with lift coefficient. Now I found that lift coefficient has a factor of velocity. It is an inverse relationship, i.e. lift coefficient will go up when velocity goes down. Since induced drag coefficient and lift coefficient are directly proportional, if lift coefficient goes up as a result of decreased velocity, then induced drag coefficient will also go up.

Reference: Introduction to Aircraft Flight Dynamics - Louis V. Schmidt
Pages 49 - 52

 

[tgrayson]

Now I found that lift coefficient has a factor of velocity.

Not exactly. A specific AoA generates a specific lift coefficient and that is independent of airspeed (within a reasonable range of Reynolds' numbers). This is what enables us to have charts that have AoA on the x-axis and CL on the y-axis. The relationship Cl = L/(qS) is merely how the coefficient of lift is identified. Note that L and q are not independent variables; if you reduce q (by reducing V), you're going to get less L, too.

 

[shdw]

Not exactly.

This phraseology leads me to conclude that the answer is situational. As in, sometimes velocity is a factor, would this be true? When/why? Thanks again.

 

[tgrayson]

This phraseology leads me to conclude that the answer is situational.

No, I meant your inference was a bit off. When you look at the equation Cl=L/(qS), do you really think that increasing q is going to decrease the Cl? If it did, Cl would be a useless number. What happens is that if you increase q, then L increases the exact amount to keep Cl the same. That's the whole point of Cl. It's a factor that tells you how airspeed is converted into lift.

Now, if you want to construe a real cause/effect relationship, replace "L" by "W" and then you have an inverse relationship; note, however, that you still can't change q independently....Cl is the independent variable here and it controls q.

 

[shdw]

I must say, I'm still trying to figure out how you know what variables are dependent and which are independent. Did I miss some memo because this is really stumping me right now. On a serious note, can you point me to a book or an article that might lay this out for me?

Mechanics of Flight on google: http://books.google.com/books?id=6-...DEQ6AEwBQ#v=onepage&q=vortex strength&f=false

Here is what I found, again interpreting text I'm not comfortable with: (Page 462) From the vortex lifting law, the wingtip vortex strength is proportional to the product of the wing lift coefficient and airspeed. The vortex strength, (some funny letter), and spacing, b', can be evaluated from Prandtl's lifting-line theory.

 

[tgrayson]

I must say, I'm still trying to figure out how you know what variables are dependent and which are independent. Did I miss some memo because this is really stumping me right now. On a serious note, can you point me to a book or an article that might lay this out for me?

I'm not sure there is a mechanical way; you need to understand the physical processes underlying the formulae. You could solve the lift equation for air density, rho; do you think you can control air density by altering the other variables in the equation? Of course not. However, you could figure out what the air density was if you knew the values of the other variables.

<<Mechanics of Flight >>

I have the book, but the material is pretty much the same in all books that discuss the topic. The funny letter is gamma, also known as the circulation of the airfoil. It's not referring directly to the wingtip vortices, although the wingtip vortices are a result of the bound vortex.