Adverse Pressure Gradient and the Transition Ponit

[Tonkenna]

Can someone explain to me how the Adverse Pressure Gradient affects the position of the Transition Point. I am covering Zero Lift Drag and whilst I understand how Surface condition, speed of flow and size affect the TP I just don’t see how the adverse pressure gradient does. The explanation in AP3456 is very short and whilst it explains what it is that is as far as it goes.

Does this make sense to any one out there, if so, please help.

Tonks
<img src="confused.gif" border="0"> <img src="confused.gif" border="0">

[Dan Winterland]

Yes, I can mate. (A2 and bar!) I can't right now as I will have to draw a diagram (4 colours naturally!) and I don't have the technical ability to include it in this post. Besides, Im off to San Fran in a few minutes. I you e-mail me your snail mail address, I will pop it in the post when I get back on Sunday.

A good book on the subject, and seemingly written for befuudled A2 candidates is 'Aircraft Flight' by Barnard and Philpot ISBN-582-00338-5

Cheers, Dan.

PS Can the Tutor get to San Fran? (VMC of course) :)

[Tonkenna]

Cheers Dan, address on its way. I knew you our BEagle would be able to help.

I wish the Tutor could get to San Fran (or anywhere out of the UK for that matter). It would have to be VMC though as we have all lost our IRs now!!!!

Have a good trip.

Tonks <img src="smile.gif" border="0">

[ 14 January 2002: Message edited by: Tonkenna ]</p>

[Tonkenna]

Dan,

Just had another look at that book you suggest in the Boundry Layer section and I think I am getting there. Would still appreciate you help though when you get back.

Cheers,

Tonks <img src="confused.gif" border="0">

[BEagle]

Hey Tonks - the exciting things you do these days, eh mate?

Just about to dash off overseas again, but before I go, a quickie explanation of the effect upon transition point of the adverse pressure gradient:

Remember that Bernie Ooli tells us that, (blah blah inviscid, incompressible flow, low speed aerodynamics blah blah, etc...) for all intents and purposes the sum of static and dynamic pressure will be constant? Well, aft of the point of maximum thickness on a aerofoil, the airflow begins to decelerate in the direction of flow. Thus the dynamic pressure reduces and hence the local static pressure begins to increase (Thanks Bernie!) - if the static pressure is increasing in the direction of flow (and AP3456 unfortunately forgot to include the word 'static' in the text here), then it has been found to be a physical impossibility for flow to remain laminar - it just can't. Not even for the RAF!! Where you have increasing static pressure in the direction of flow, you have what is termed an adverse pressure gradient - the greater the rate of increase of static pressure in the direction of flow, the earlier the transition from laminar to turbulent flow with its corresponding increase in drag. Hence the transition occurs very close to the point of maximum thickness of the aerofoil.

Have you found out why minimum power speed and minimum drag speed are related by a factor of 1.32 yet? Not many people will be able to explain that one to you......

[Tonkenna]

Thanks BEagle,

I get it now. There is hope yet. Having one the top hat on CFS ground school, the only way is up.

Tonks :)

[Newguy]

O.K. BEagle, if no-one else is going to ask, I will. Why are min. power speed and min. drag speed related by a factor of 1.32?. And while were on the subject, why is the speed for best endurance not the same as min. drag speed.


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stop animal testing.
use taliban prisoners instead.

[BEagle]

OK Buster – since you asked!

1. First the 1.32 mystery. Remember that Total Drag is the sum of zero lift drag which increases with the square of speed and lift dependant drag which decreases with the square of speed – or algebraically D=AV²+B/V². To find the value of minimum drag speed, differentiate this expression and equate to zero and you get the result that at minimum drag speed dD/dV=0=2AV-2B/V³. In other words V at min drag = (fourth root) (B/A).

However, for minimum power speed, we are looking for the minimum value of work rate, i.e. the minimum rate of (Force x Distance)/Time - the force in this case being Total Drag. This is the obviously the same as Total Dragx(Distance/Time), i.e. Total Drag x Speed (or rather more correctly, the product of Total Drag and Velocity). Go back to our first equation and you get P=DV=AV³+B/V. Do the same differentiation as before and this time you get the result dP/dV=0=3AV²-B/V², or in other words V at min power = (fourth root)(B/3A). Divide the 2 results algebraically and you find that Vmin drag =V min power x (fourth root) 3. And the fourth root of 3 is 1.316074 – or 1.32!!

2. For endurance, you are interested in the minimum value of fuel burn with respect to time, for range you are interested in the minimum fuel burn with respect to distance. But since fuel burn/distance is the same as fuel burn/time x time/distance, for range you fly at the speed which is the best value of Endurance/Speed. By their very nature, jet and propeller engined aircraft produce thrust and power differently; max endurance in a piston engined aircraft occurs at the lowest practical BHP, IE at the minimum power speed – and hence max range is obtained at the speed equating to the minimum value of BHP/speed – but since BHP is proportional to Total Drag x Speed, then max range is fairly obviously obtained (in theory) at the speed equating to the minimum value of (Total Drag x Speed)/Speed – i.e. at minimum drag speed which is 1.32 x minimum power speed. For a jet engined aircraft which produces thrust pretty well irrespective of speed, similar number crunching and algebra will show that maximum endurance is obtained at minimum drag speed and maximum range at the speed which gives best TAS/Drag ratio – and this equals 1.32 x minimum drag speed.

[ 20 January 2002: Message edited by: BEagle ]</p>

[Newguy]

Thanks BEagle, I have printed out your answer and will now retire to a darkened room to let it all soak in.


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stop animal testing.
use taliban prisoners instead.

[Dan Winterland]

Sorry Tonks, been a bit busy applying for jobs recently. Explaination on the way soon - I hope.

[Tonkenna]

No probs Dan, thanks for taking the time, I know that your are busy. I have been away for a few days having fuin on the Flt Safety Cse (which was great).

BEagle, didn't want to ask myself as I knew it would be difficult. Cheers for that, I shall take a print out to bed with me for some lite reading :)

Tonks

[john_tullamarine]

Just a little confused reading this thread .. is the concern

(a) laminar to turbulent transition - basically an Re consideration ?

(b) boundary layer separation due to surface flow reversal associated with an adverse gradient - basically a velocity profile consideration ?

[ 25 January 2002: Message edited by: john_tullamarine ]</p>

[BEagle]

I suspect that CFS 'simplification' of aerodynamics is causing the confusion, john_t. The transition point from laminar to turbulent is primarily affcted by Reynolds No effects, the thickening of the boundary layer due to velocity profile effects is also considered; these changes in flow are seemingly being regarded as both down to the presence of an adverse pressure gradient - whereas as you infer, the 2 effects should really be considered seperately.