109G-2 vs 109G-6 and parasite drag

[Anaxogoras]

The 109G-2 and 109G-6 are an interesting test of the AH fluid model because they have the same horsepower, 1475, but a different drag coefficient.  With the addition of larger guns in the cowl, and larger wheels to support the DB605A engine, the 109G-6 acquired its characteristic bumps and is consequently a little bit slower than the 109G-2.  At sea level there is a 5mph difference, 342mph for the G-2 and 337mph for the G-6.  Now, because parasite drag decreases with altitude, you would expect this difference to narrow with altitude, but in fact the opposite happens.  At 22,000ft, which seems to be the critical altitude for these two aircraft (I have tried 24, 23, 22, 21, 20 etc.), the G-2 and G-6 attain true airspeeds of 394 and 405 mph, respectively.  A 5mph difference has widened to 11.  What about indicated airspeed?  ~273.5 vs 281.5; that is still an 8mph difference.

Can anyone here explain why?

[2bighorn]

Induced drag ie weight difference -> diff AoA. Since induced drag is inversely proportional to velocity squared it would be larger at lower indicated speed.

my $0.02, but I'm not aeronautical engineer so I could be wrong

[Anaxogoras]

Yes, that's a correct explanation, but I get the same speeds if I burn off fuel to make them have the same weight.  Moreover, the influence of small weight differences on induced drag is greatest at low speeds, not high speeds.

Really, I should expect the speed differences to be in reverse.  5mph at 22k ft, and 8-11mph at sea level.

[2bighorn]

Moreover, the influence of small weight differences on induced drag is greatest at low speeds, not high speeds. 

Yes, and high altitudes, ie low indicated speeds...

[Anaxogoras]

280mph ias is more like a medium speed to me.   Regardless, the speed gap widens even when the G-2 and G-6 weigh the same.  Thanx for your help!

FYI, I just got the G-6 up to 395mph at 22k by only loading 25% fuel, and going WEP until she ran dry!   Final weight was 6306lbs.  With 75% fuel loaded the G-2 weighs 6675lbs, which is about the amount of fuel you have left once you get up to 22k and reach maximum speed with a full fuel loadout.  So even when 300lbs lighter, the G-6's speed deficit increases from 5mph at sea level, to 10mph at critical altitude.  Consequently, induced drag from extra weight accounts for <1mph of speed loss at 22k ft, as only 1 mph could be gained by making the G-6 300lbs lighter than the G-2.

The external drop-tank rack is also controversial because of the drag it causes even after the drop tank is released.  With the rack, I was able to get the G-6 up to 390mph at 22k ft, 5 mph slower than without, before running out of fuel (25% loadout).  At sea level, the G-6 also loses 5mph with the drop-tank rack.  That's not consistent with the parasite drag of the bulges and its effects (above).

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Edit, what if we look at these speed reductions in terms of %'s, does that make sense of it?  At sea level the G-2 is still 1.5% faster than the G-6, at 22k ft it is 2.5% faster; I guess not!

[Virage]

I don't think there is a fluid model Gavagai.

[Anaxogoras]

Hmmmm, I know that the effects of prop-wash are included in the flight model, so at least they are trying for an ad-hoc approximation of a fluid model.  

[dtango]

Now, because parasite drag decreases with altitude, you would expect this difference to narrow with altitude, but in fact the opposite happens.

Let me answer your question with a question (don't you hate that! ):  Why would you expect the difference in max level airspeeds between the G2 and G6 to narrow with altitude?  That's a hint for starters .

Tango, XO
412th FS Braunco Mustangs

[dtango]

I don't think there is a fluid model Gavagai.

Nonsense .  Why would you say this?

Tango, XO
412th FS Braunco Mustangs

[Anaxogoras]

Let me answer your question with a question (don't you hate that! ):  Why would you expect the difference in max level airspeeds between the G2 and G6 to narrow with altitude?  That's a hint for starters .

Tango, XO
412th FS Braunco Mustangs

Ok, I'll bite (I really do want some enlightenment here )

I would expect it because horsepower/engine is the same, but drag coefficients are not due to extra parasite drag on the G-6.  Assuming equal weight (or let's even have the G-6 weigh less by taking less fuel) and therefore equal induced drag, the only thing preventing the two aircraft from having the same top speed is the G-6's parasite drag.  Parasite drag lessens the higher you go, therefore the speeds should converge more the higher you go, or at the very least the gap should remain consistent.

How's that?

[dtango]

Parasite drag lessens the higher you go, therefore the speeds should converge more the higher you go, or at the very least the gap should remain consistent.

So if drag lessens the higher you go, why would the G6's drag lessen in proportion more than the G2's?  You're getting closer regarding the consistent part .

The equation for drag is:

Drag = .5 * air_density * CD * wing_area * V^2

Let's simplify this and assume everything in the right-hand-side of the equation stays constant except for air_density.  We know that air_density decreases as we go up in altitude.  So yes drag decreases with increasing altitude in this situation for the same airplane per unit velocity.

Now let's consider two airplanes.  Our 109G-2 has CD = A and our 109G-6 has CD = B.  Again if we assume everything constant except for air density why would the difference in drag between the G-2 and G-6 be any different in proportion at sea level than it is at 22k?  Yes each plane's individual drag decreases with increasing altitude, but the proportion in drag difference between the two wouldn't change whether you were at sea level or at 22k because the only thing changing in this case is air density which would be the same for the G2 and the G6 at the same altitude.  Therefore the speeds would not converge.

Of course it gets trickier than all this because max velocity itself is constrained by where drag=thrust.  Also thrust varies with velocity as well.  We now open up even more questions - questions that I don't have time to address at the moment so I'll just cut to the chase!

The variation you're seeing in the G2 and G6's difference in max level speeds for different alts is due to the fact that we have a greater difference in total drag between the G2 and G6 at 22k than near sea level.  Back of the envelope, 19 lbs difference at sea level, 31 lbs difference at 22k.  The difference has to do primarily with the variation in lift dependent drag.  To maintain level flight at max speeds lift coefficients at 22k is greater than at sea level for both aircraft which means greater lift dependent drag due to higher aoa.

Tango, XO
412th FS Braunco Mustangs

[Anaxogoras]

The variation you're seeing in the G2 and G6's difference in max level speeds for different alts is due to the fact that we have a greater difference in total drag between the G2 and G6 at 22k than near sea level.  Back of the envelope, 19 lbs difference at sea level, 31 lbs difference at 22k.  The difference has to do primarily with the variation in lift dependent drag.  To maintain level flight at max speeds lift coefficients at 22k is greater than at sea level for both aircraft which means greater lift dependent drag due to higher aoa.

Tango, XO
412th FS Braunco Mustangs

Ok, I see that I've found the person who can help me learn something.   By lift dependent drag you mean the same thing as induced drag, right?

This is where you lose me:

the proportion in drag difference between the two wouldn't change whether you were at sea level or at 22k because the only thing changing in this case is air density which would be the same for the G2 and the G6 at the same altitude.

Back of the envelope, 19 lbs difference at sea level, 31 lbs difference at 22k.  The difference has to do primarily with the variation in lift dependent drag.

Assuming equal weights, the only thing I can pin down that would require a higher aoa for the G-6 than the G-2 is the parasite drag.  But then why does the G-6's total drag increase more quickly with altitude than the G-2's (since the proportional difference in parasite drag between these two aircraft does not change)?

Thank you for your patience, I think I'm almost there, but not quite.

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P.S. What about this?

The external drop-tank rack is also controversial because of the drag it causes even after the drop tank is released.  With the rack, I was able to get the G-6 up to 390mph at 22k ft, 5 mph slower than without, before running out of fuel (25% loadout).  At sea level, the G-6 also loses 5mph with the drop-tank rack.  That's not consistent with the parasite drag of the bulges and its effects (above).

It's as if in one case adding more parasite drag causes more speed loss at altitude and in the other case it does not.

[dtango]

By lift dependent drag I mean both the inviscid and viscous portions of induced drag.  When induced drag is discussed people usually are referring to the inviscid drag due to vortex formation.  There's also a viscous portion that exists that folks don't realize because it isn't accounted for in basic theoretical study on the topic.  That's why I chose my wording carefully.  Here's a good reference on the topic:

http://adg.stanford.edu/aa241/drag/induceddrag.html

Because aoa varies at different altitudes to maintain level flight at max speeds, the viscous portion of induced drag needs to be acccounted for (unless HTC has changed it they also address the viscous portion of induced drag).  The effect may be small but when drag varies with the square of airspeed, the faster you go the more noticeable it becomes.  Again, maybe not huge in the grand scheme of things at low aoa's but they still have a slight impact. 

For an example here's some results of quickie calcs to demonstrate basis some of the initial specs you gave for the G2 and G6.

CD (total drag coeff) at sea level:
G2 .026
G6 .027

CD (total drag coeff) at 22k:
G2 .030
G6 .032

Note that total CD increases for both aircraft between 0ft to 22k.  The reason for this is that aoa increases for both aircraft as we go up in altitude.  The difference is made up of both the "usual" induced drag as well as the typically unaccounted for viscous portions.  Since Cl is a proxy for aoa, I estimated them to be:

CL at sea level:
G2 Cl = .136
G6 Cl = .143

CL at 20k:
G2 Cl = .186
G6 Cl = .200

Greater Cl means greater aoa.  Greater aoa, more viscous lift dependent drag.  Remember the slower you go the more aoa you need to achieve the same amount of lift.  So even if your G6 and G2 are at the same weight, the sheer fact that the G6 has greater parasite drag than the G2 means at max level speeds at the same altitude the G6 will always have a slightly higher aoa because it's going just a tad slower.

Note the small change in difference in CD between the aircraft at sea level (.027-.027=.001 diff) vs at 22k (.032-.030=.002 diff).  That difference though accounts for why we're seeing the slight difference in max airspeed differential between the two aircraft from sea level vs. that of 22k.

Of course that's just my explanation with some cursory analysis.  To be 100% sure HTC would have to answer the question of why the difference exists .  Hope that helps!

Tango, XO
412th FS Braunco Mustangs

[dtango]

Accidently reposted.  deleted.

[Anaxogoras]

Very helpful!