Hoerner's Drag Calculation Question

[DarrenW]

I have been looking at Hoerner's drag analyisis of the Bf-109
(www.wwiiaircraftperformance.org/me109/Hoerner-Me_109.pdf) and I was hoping someone can explain how he equates CD = 0.036 as being the same as CDwet = 0.0105? ( bottom right portion of page 14-3). I can see how he calculated total wetted area (drag area/CDwet) but for some reason I'm unclear regarding how to determine CDwet. Any thoughts?

 

[wells]

I have been looking at Hoerner's drag analyisis of the Bf-109
(www.wwiiaircraftperformance.org/me109/Hoerner-Me_109.pdf) and I was hoping someone can explain how he equates CD = 0.036 as being the same as CDwet = 0.0105? ( bottom right portion of page 14-3). I can see how he calculated total wetted area (drag area/CDwet) but for some reason I'm unclear regarding how to determine CDwet. Any thoughts?

The CD is based on the area used in the calculation
0.036 x 174 is the same as 0.0105 x 590, the drag force is the same. Likewise, if you use area = 6.2, CD = 1

 

[DarrenW]

Thank you for the clarification, it was very helpful!

 

[drgondog]

I have been looking at Hoerner's drag analyisis of the Bf-109
(www.wwiiaircraftperformance.org/me109/Hoerner-Me_109.pdf) and I was hoping someone can explain how he equates CD = 0.036 as being the same as CDwet = 0.0105? ( bottom right portion of page 14-3). I can see how he calculated total wetted area (drag area/CDwet) but for some reason I'm unclear regarding how to determine CDwet. Any thoughts?

His Total Drag Co-efficient in his presentation CD=0.036 is based on the Drag build up for Parasite Drag plus Induced Drag divided by (1/2*rho*V^^2* Wing Area) at top speed in level flight. It is Not the same as Wetted Area Drag, which uses the entire surface area as another cut on comparisons but not the primary value for CD.

CD = (CDp + DeltaCDp1 + delta CDp2) CDm/CD + CDi:

Hoerner's illustrated method for calculating Total Drag in the first part of Chapter 14 is a nice approach for 'Kentucky Windage' solution for Parasite drag but not an approach that will yield insight to a.) reasonable accuracy for the component contributions (i.e. Cd of the wing, empennage, protuberances, gaps in control surfaces, cockpit enclosures, exhaust stacks, bomb/fuel tank racks, fuselage, friction on surfaces, etc = CDp above) of Parasite Drag, nor the contributions for Cooling drag, nor the pressure drag of the fuselage/wing enclosed in the prop vortex, nor the Pressure drag associated with Angle of attack/CL = delta CDp1 above, or b.) the compressibility factor expressed as CD=f(Mach No.), which derives CDm/CD above, as velocity enters drag rise envelope, or c.) as AoA must increase as altitude increases and density decreases, to maintain level flight (Delta CDP2 above). All the above are contained in the Parasite Drag build up. His CDi also assumes an Oswald factor that varies based on wing geometry - not the same for every aircraft.

He approaches the problem with some pretty 'loose assumptions', namely the validity of the THp equation which assumes a prop efficiency factor of .85, the contribution of exhaust Thrust to THp to yield a Total Thrust. (the prop efficiency value is based on several key factors including number of props, RPM, activity factor, et, etc -

He is not very clear that the value he derives for total CDo (zero lift CDo) is only close to being correct at the altitude and implied Reynolds Number of 22000 feet.

Hoerner does present the methodology to build up the Preliminary Drag build up, including wing profile drag, the drag components of the exhaust stacks, cockpit, fuselage, control gaps, surface friction including paint contribution -----------> which will then be tested in a rigorous wing tunnel evaluation driving corrections.

The CDo Drag Coefficient of the Wind Tunnel testing is always in turbulent flow regime but also a low speed velocities ranging from ~ 60mph to 100mph depending on each country's 'standards. At that 'low speed' the value of CDo often is expressed as 'The CDo' and folks carry it to the bank as a constant. On a Log plot CD as a f(RN) is a steep curve approaching a straight line until the RN approaches 300 mph (+/-) then levels out - The plot data is extracted based on Wind Tunnel data and extended as a function of calculated CDp that is unique to each tested airframe.

So, Net-Net nobody in WWII started a Performance analysis with Thrust = Drag with conventional reciprocating engines.. The preferred approach was to build up the solution with Horsepower Available compared to HP required - in which Ram Air contributed to positive HP above FTH of bench tested engines at sea level, Cooling Drag and Pressure drag are expressed as a contribution to HP required, the complex prop derivatives enter the THp equation and Exhaust Thrust enter Horsepoer Available calcs - all as function of altitude and velocity.

Dr Clark Milliken's Aerodynamics of the Airplane is much better if you want insight to Lockheed/North American/AAF approach to Performance Analysis during WWII.

 

[DarrenW]

Thanks for the in-depth reply drgondog, I always value your insight, especially when were are discussing the science of aerodynamics. What I understand about the discipline wouldn't amount to a hill of beans, so I'm in a perpetual state of learning. I can see where the terms "drag coefficient" and "zero-lift drag coefficient" can be confused as one in the same if they are not expressed correctly and quantified specifically as such.

Speaking of this, I was looking at Dean's America's One Hundred Thousand recently and I noticed that he references NACA wind tunnel test results when discussing zero-lift drag coefficient of the major American players. Thing is, his figures do not match what I have personally seen in these publications. I was wondering if he is subtracting calculated induced drag from the actual NACA wind tunnel results, which I believe are total drag measurements, in order to arrive at the figures he presents in his book? I also remember reading on this forum somewhere that he did his calculations at 250 MPH @ 10,000 feet and was concerned about matching the Reynolds number based on their specific MAC in order to get the best possible results. Can you elaborate on this at all?

 

[drgondog]

Thanks for the in-depth reply drgondog, I always value your insight, especially when were are discussing the science of aerodynamics. What I understand about the discipline wouldn't amount to a hill of beans, so I'm in a perpetual state of learning. I can see where the terms "drag coefficient" and "zero-lift drag coefficient" can be confused as one in the same if they are not expressed correctly and quantified specifically as such.

Speaking of this, I was looking at Dean's America's One Hundred Thousand recently and I noticed that he references NACA wind tunnel test results when discussing zero-lift drag coefficient of the major American players. Thing is, his figures do not match what I have personally seen in these publications. I was wondering if he is subtracting calculated induced drag from the actual NACA wind tunnel results, which I believe are total drag measurements, in order to arrive at the figures he presents in his book? I also remember reading on this forum somewhere that he did his calculations at 250 MPH @ 10,000 feet and was concerned about matching the Reynolds number based on their specific MAC in order to get the best possible results. Can you elaborate on this at all?

I suspect that Dean used the 1946 NACA Drag publication for about 20 aircraft which breaks out the parasite drag for each key component . The RN would vary significantly for a constant velocity - and conversely for same RN across the board, the wind tunnel speed would have to be correspondingly adjusted. I'll find the NACA publication and let you know. It is on the web so you can down load it. Otherwise you could be correct if he starts with Total Drag in Level Flight and then subtracts Induced drag

That said, in the leading paragraphs he discusses the sources for CDo extracted from wind tunnel data and compares all the fighters for CDo at 250 mph and 10,000 feet. Those speeds will not require compressibility corrections but I have seen no evidence that CDo values he presents account for the 'delta CDp1 and CDp2 I explained above - and they are significant, particularly the pressure drag components of the prop vortex over inner wing and fuselage/empennage.

 

[DarrenW]

Those speeds will not require compressibility corrections....

At what speeds will compressibility become a factor when determining CDo?

 

[drgondog]

At what speeds will compressibility become a factor when determining CDo?

Depends. Compressibility begins when fluid properties of air no longer behave as incompressible. The phenomena occurs as low as 0.3M

That said, the Mustang and Spitfire drag rise over the wing occurred much later than the P-38/P-39 as an example. The 'point' usually associated with Compressibility factor being significant, is that region in which CDm/CDp (low speed Parasite) ~ 1.1. For a Mustang that is approximately 0.65M and quickly hits 1.2 at 0.68M. Actual local M=1 over the airfoil is at ~ 0.74 to 0.75M. By contrast the P-38/P-39 hits the respective CDm/CD of 1.1 at 0.62M and local M=1 at 0.68. This is all from memory. Look to Dean's comparisons of the P-39 and P-51 during his aero discussion in first Chapters.

 

[DarrenW]

Look to Dean's comparisons of the P-39 and P-51 during his aero discussion in first Chapters.

I most certainly will. I also need to get a copy of Dr. Clark Milliken's book as well.