## How does a diffuser/ride-height create drag?

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autogyro wrote:I am realy enjoying this.
Miles and miles of technical discourse and not a single conclusion with any bearing on the thread heading.

I guess you missed the 8th post where all the questions of the thread starter were answered...
kilcoo316
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Joined: 9 Mar 2005
Location: Kilcoo, Ireland

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Actually in defense of most that have replied to my thread (whom I thank greatly ) arguably the bickering going on isn't so much as petty bickering, but more as bickering of how they actually create drag, and how much . But yes there have been quite a few informative posts

raymondu999
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Joined: 4 Feb 2010

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raymondu999 wrote:Actually in defense of most that have replied to my thread (whom I thank greatly ) arguably the bickering going on isn't so much as petty bickering, but more as bickering of how they actually create drag, and how much . But yes there have been quite a few informative posts

Which does to show that the questions remain unanswered, even though some are so self important they think otherwise.
autogyro
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Joined: 4 Oct 2009

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A reduction in drag will result if the longitudinal component of pressure drag on the diffuser face is less than the diffuser exit area times the pressure that would have existed without a diffuser. This is how a diffuser may be used to reduce overall drag.

Assuming the exit pressure of the diffusers are the same and exit velocity ~= freestream. Both diffusers have the same length. For two diffusers, one at a lower height than the other:

Neglecting viscous effects (assuming no bl separation or viscous drag) & 3d effects

cp = pressure coefficient

Higher DF (larger exit area or lower throat area) diffusers may result in increased overall drag because they must recover more pressure. For arguments sake, let's use ideal diffusers (no spanwise flow) with throat velocities 2 (high ride height) and 3 (low ride height) times freestream. Our cp_mins are -3 and -8, respectively. If the pressure is to be recovered linearly (a bold assumption) with the same diffuser angle, the drag is proportional to the area contained in the pressure recovery region of the cp vs chord graph which, in this case, is just a triangle. The proportion of drag is then (.5*(8-0)*diffuser length)/(.5*(3-0)*dl) = 8/3. Now to calculate the Cl and Cd, the diffuser angle is 10 deg, and the throat length is equal to the diffuser length.

Low DF diffuser:
Cd = 0.5*3*0.5*sin(10deg) = .13
Cl = 0.5*3+0.5*3*0.5*cos(10deg) = 2.24
L/D = 17

High DF diffuser:
Cd = 0.5*8*0.5*sin(10deg) = .35
Cl = 0.5*8+0.5*8*0.5*cos(10deg) = 6.0
L/D = 17

The assumptions are the reason the efficiencies match. Obviously a myriad of viscous and 3d effects prevents these numbers from being realistic. These unaccounted for effects largely serve to reduce the efficiency of higher df diffusers. (real max cl for any single element (single deck) wing/diffuser is ~3). Although the magnitude of these coefficients are off, their ratio (~20:1) is not unrealistic (nor does it take into account any reduction the diffuser may have on the body's drag) because diffusers don't really suffer from induced drag. The L/D for even an 'inefficient' diffuser is still much higher than a wing's efficiency, so it is almost always worthwhile to increase diffuser df.

I believe someone mentioned induced drag being a problem with diffusers: The reason diffusers are so efficient is they have very little induced drag because tip vortices cannot form due to the diffusers proximity to the ground. Run a calculation for induced drag with an underwing's AR (<0.5) and it will seem worthless. Example: CL = 1, AR = 0.5, e = 0.85 (rectangular wing e). CDi = 0.75, L/D = low. Clearly not worth running if induced drag is a problem.

DF can be created without a drag penalty but, as someone said before, you're unlikely to generate df without drag on a well designed aero package.
cwatson
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Joined: 15 Jan 2010

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Interesting calculation. What is it derived from?
I am trying to see what it really is, i see the trig ratio sin and cos, which seems to be components of force, but is the diffuse being treated a plate at an angle?
Can you draw a diagram please.
For Sure!!
ringo
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Joined: 29 Mar 2009

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Not really derived from anywhere, just applying pressures to the faces with an idealized diffuser. Hopefully the following will clear it up:

Sorry about the weird line, did it on a notebook.

cwatson
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Joined: 15 Jan 2010

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