Draining E in turns

[dtango]

Crumpp:

You're getting closer .  However the following statement needs to be evaluated relative to total drag calculations between the aircraft.

Since pulling a tight bank will cause and increase in speed or force the pilot use excess speed to pay for the altitude you maintain the plane with the highest parasitic drag will bleed the most energy due to drag.

Vary the Cdi with relation to Cl per plane per turn g-loading per velocity and calculate total aircraft drag on these params.

Tango, XO
412th FS Braunco Mustangs

[Crumpp]

As speed increases Cdi goes down, right?

As speed increases parasitic drag goes UP, right?

When you conduct a sharp bank, your speed HAS to increase.

Imagine that you are initially trimmed for straight and level flight at, say, 100 knots. Then you inadvertently enter a steeply banked turn. Figure 6.12 shows the forces acting on the plane in level flight and in the turn. Let’s imagine that the plane weighs exactly one ton. In level flight the downward force of gravity is exactly canceled by the lift produced by the wings, so the wings must be producing one ton of lift.

The lift is produced both by angle of attack and a speed increase.  If you just banked and immediately slowed down I would wholeheartily agree.  At the instant you bank though, I understand the plane drops altitude to trade for speed to increase the lift, lots of speed.


BTW,

I missed your comments on the P51.  I am researching a book on the FW-190.  All the evidence I have points to the P51 as being the worst allied fighter for a FW-190A to encounter until the Tempest and Spitfire Mk XIV.

The Merlin Powered spits at best equaled the 190.  The only advantage the 190A had over the Mustang was roll rate, dive accelleration, and a similar turn radius (51B had a slight advantage).  Only if the Mustang let his "E" get lower than the 190 was the fight even IMO.

I hate punchin that calculator.  To me its dumb at our level. It's time wasted that I will never get back. Just like David Lednicer says, "Aerodynamics is all about the details."  At our level this is like an alchemist saying "I can transmute gold!  look at these calculations".  We don't have enough of the details.
Just look at the P51, even some of the top Aeronautical engineers of the day did not have the "details".



 Crumpp

[gripen]

Originally posted by Crumpp

All A/C where calculated under the following conditions:

Temperature - 65 *F
Atmospheric Pressure - 14.696 PSI

Why not standard conditions, ie 15 degrees celsius at sea level?

Overall it would help a lot if all values are in same system metric or US.

Originally posted by Crumpp

FW190A8 - Weight = 4272kgs
Wing Area = 735 sq. feet
Cl = .174662988

Spitfire Mk IX Merlin 66 (+25)- Weight = 7400kgs
Wing Area = 831.2 sq feet
Cl = .121352522

P51D- Weight = 9800lbs
Wing Area = 882.2
Cl = .151419443

The wing area's are all wrong, these are wet areas which Lednicer used as reference area for Cd. My calculations as well as the NACA and RAE graphs linked above use wing area as reference area for Cd. Generally calculations are much easier when the wing area is used as the reference area and then there is also a direct connection to the induced drag.

Originally posted by Crumpp

For the drag calculations I used "Cd wet" out of David Lednicer's article, as they are all real world tested with his sources listed at the bottom.

Lednicer writes:

"There are many conflicting claims as to the equivalent flat plate drag area (f) of these fighter aircraft, based upon my research, what I believe are the most accurate values are shown in Table 1."

Basicly he says that he choosed the ones he thought to be most accurate. The problem with the Lednicer's numbers is that if the wet area and flat plate area values he is using are true, then the planes mentioned could not have reached the real world measured performance.

gripen

[Crumpp]

Basicly he says that he choosed the ones he thought to be most accurate. The problem with the Lednicer's numbers is that if the wet area and flat plate area values he is using are true, then the planes mentioned could not have reached the real world measured performance.

I think the man would have spotted that Gripen.

He seems not only a whole lot more qualified than anyone on this BBS, AND much better equipped to do the analysis.

Crumpp

[Crumpp]

Wetted Area, Swet
The air can only create stress on surfaces that it touches, so the relevant area over which the friction or the pressure will act is the wetted area–the actual area exposed to the air. This value
is completely determined by the geometry of the aircraft and, in actuality, is quite difficult to calculate. CAD packages can make the process easier.

Seems a much more accurate approximation of the drag than just the wing area.

Crumpp

[dtango]

Crumpp:

>>>>As speed increases Cdi goes down, right?
Wrong.  Cdi varies with AOA.  If AOA increases Cdi increases.  If AOA decreases Cdi decreases.  In level flight AOA decreases with increasing speed therefore Cdi appears to go down as speed increases.  In a turn this is thrown out the window because Cdi varies with AOA and not speed.

>>>>As speed increases parasitic drag goes UP, right?
Right.

>>>>When you conduct a sharp bank, your speed HAS to increase.
No your speed does not HAVE to increase at all.

>>>>He seems not only a whole lot more qualified than anyone on this BBS, AND much better equipped to do the analysis.
Whatever.

Tango, XO
412th FS Braunco Mustangs

[gripen]

Originally posted by Crumpp

I think the man would have spotted that Gripen.

He seems not only a whole lot more qualified than anyone on this BBS, AND much better equipped to do the analysis.

The whole idea of the equivalent flat plate area is to make calculations as well as comparisons easy. Therefore it can be very easily verified that the Lednicer's flat plate areas appear to be at least partially wrong.

Originally posted by Crumpp

Seems a much more accurate approximation of the drag than just the wing area.

Actually I was talking about using wing area as the reference area which you pretty much completely mixed up in your calculations. With the calculations I used, the drag is approximated from the measured speed and available thrust, not from wing area.

gripen

[Crumpp]

Wrong. Cdi varies with AOA. If AOA increases Cdi increases. If AOA decreases Cdi decreases. In level flight AOA decreases with increasing speed therefore Cdi appears to go down as speed increases. In a turn this is thrown out the window because Cdi varies with AOA and not speed.

Got it.

No your speed does not HAVE to increase at all.

Then your burning energy to keep you altitude. Otherwise the flight instructor and PhD. is putting out wrong information.


Gripen:

I picked 65 degrees just because it's a nice tempature and got the pressure at sea level form a weather website.  From there I calculated "r".

You were correct on the wing area's for the CL calc's so I redid them real quick.

All the other parameters are the same.

CL at 300 mph:

FW-190 Cl = .651727567

Spitfire Mk IX Cl = .416810811

P51D  Cl = .568493091

Crumpp

[dtango]

Then your burning energy to keep you altitude. Otherwise the flight instructor and PhD. is putting out wrong information.

Yes, this is true.  However your original statement is misleading because the physics doesn't require a plane to increase it's speed in a turn.

By the way, you don't have to increase your speed to maintain zero energy bleed in a hard turn.  A "hard turn" is also a little ambiguous but I think I understand what you're trying to say.  You would need to increase acceleration by putting nose down to offset deceleration due to energy bleed in a turn but your velocity could remain constant if you flew it that way.  This is what you would to do maintain a constant-g sustained turn (vs. a sustained level turn).

Tango, XO
412th FS Braunco Mustangs

[gripen]

Originally posted by Crumpp

I picked 65 degrees just because it's a nice tempature and got the pressure at sea level form a weather website.  From there I calculated "r".

It's not very good idea to use other conditions than standard atmosphere. Most performance data is corrected to the some sort of standard conditions which all are quite close to the current standard atmosphere. And if more calculations is needed, the standard atmosphere can be easily embedded to spreadsheet model.

Originally posted by Crumpp

You were correct on the wing area's for the CL calc's so I redid them real quick.

All the other parameters are the same.

CL at 300 mph:

FW-190 Cl = .651727567

Spitfire Mk IX Cl = .416810811

P51D  Cl = .568493091

Let's calculate Cl for the Fw 190 at 300 mph near sea level and at 1 g load right from the ground up.

The formula is (from NASA site):

Cl = L / (A * .5 * r * V^2)

where:

L = Lift
A = Wing Area
r = Density
V = Speed

Next we can convert all the needed values to the SI units for simple calculations:

L = 4272 kg * 9,81 m/s2 = 41908,32 N
A = 18,3 m2
r = 1,225 kg/m3
V = 300 mph = 483 km/h = 134 m/s

Then we just calculate Cl:

Cl = 41908,32 / (18,3 * 0,5 * 1,225 * 134^2)= 0,208

It should be also noted that to do total drag comparisons, we should know the thrust and for that we need exact amount of engine output. Therefore the easiest altitude for calculation is FTH.

gripen

[bozon]

Then your burning energy to keep you altitude. Otherwise the flight instructor and PhD. is putting out wrong information.

you misunderstood him.
read again:

Imagine that you are initially trimmed for straight and level flight at, say, 100 knots. Then you inadvertently enter a steeply banked turn. Figure 6.12 shows the forces acting on the plane in level flight and in the turn. Let’s imagine that the plane weighs exactly one ton. In level flight the downward force of gravity is exactly canceled by the lift produced by the wings, so the wings must be producing one ton of lift.

he keeps his AoA (and probably throttle setting to hold the speed) constant and roll.
he started with 1G and now he's pulling a 1G turn which means he's falling. In a level turn G-meter will always show G>1.

He doesn't HAVE TO loose energy if he pulls more than 1G. That's what he's got the noisy engine installed for. Given the power, he can pull hard , climb, turn and accelerate simultaniously.

Bozon

[Crumpp]

he keeps his AoA (and probably throttle setting to hold the speed) constant and roll.

   
I don't think so.  He is talking about the forces in steep turn not a roll.  He does combine an accidental spiral dive with it because the forces are the same.

Given the power, he can pull hard , climb, turn and accelerate simultaniously.

As for the throttle setting, How many times in AH have you seen someone increase throttle to make a turn or climb?  In fact, everyone hits max WEP and yanks the stick.
I don't think there are any WWII fighters with enough power to instantly compensate for 4 times their weight.


 

You would need to increase acceleration by putting nose down to offset deceleration due to energy bleed in a turn but your velocity could remain constant if you flew it that way. This is what you would to do maintain a constant-g sustained turn (vs. a sustained level turn).

Exactly, by yanking the wings into an extreme bank, you now require more energy just to maintain altitude.  You have made a weight change to the A/C in effect and it requires much more lift to balance the forces.

Read about what he calls the "albatross" effect about sudden weight changes.  I see this all the time when I am skydiving.  A group of jumpers will leave the ramp and the plane will suddenly pitches up in the sky and gains altitude to compensate for their weight.  If a C130 has to compensate for a few guys leaving the plane then I am sure our tiny fighter must compensate too.

http://www.av8n.com/how/htm/aoastab.html#fig-bank-noload

http://www.av8n.com/how/htm/vdamp.html#sec-vertical-damping

The weight increases if an albatross flies in the window and sits on the seat beside you.

It's not very good idea to use other conditions than standard atmosphere. Most performance data is corrected to the some sort of standard conditions which all are quite close to the current standard atmosphere. And if more calculations is needed, the standard atmosphere can be easily embedded to spreadsheet model.

Not necessarily Gripen.  Unless you can relate your calculations to a particular condition of flight under the exact conditions, they are meaningless. Temperature and humidity play a very large roll in aerodynamics and much of the data we see is collected under real world conditions and not necessarily adjusted to standard atm.  Making the assumption it is can certainly lead to wrong conclusions.

Calculating at standard atmospheric conditions is just fine, too.  Simply change "r" and recalculate the drag if you want using the area, velocity, and CDwet provided.  The resulting numbers will change but their basic line up will not since they were all calculated under the same conditions in the first place.

Crumpp

[dtango]

Crumpp:

Exactly, by yanking the wings into an extreme bank, you now require more energy just to maintain altitude. You have made a weight change to the A/C in effect and it requires much more lift to balance the forces.

Yes this is all correct.  So the question still is which aircraft would have the greatest e-bleed in a turn - the higher wingloaded or the lower wingloaded?  The only way you'll know is to calculate and compare relative total drag.  

But if you don't want to do the calculations think about this.  Greater bank/greater AOA = greater lift = more induced drag as you have stated which is exactly right.  So which aircraft will have the greater AOA per given g-loading the higher wingloaded or the lower wingloaded aircraft?

Just using your calcs take a look at 1g:

CL at 300 mph:

FW-190 Cl = .651727567

Spitfire Mk IX Cl = .416810811

P51D Cl = .568493091

The highest wing-loaded a/c (FW-190) has the highest relative Cl = higest relative AOA = highest relative induced drag.  What does that mean?  The higher wing-loaded plane is producing more lift than the lower wing-loaded plane.

Now what happens to the Cl for all 3 planes if that becomes a 2g turn, 3g turn, 4g turn or 5g turn?  Is the lower wingloaded plane going to produce more lift than the higher wing-loaded plane? The answer is no given equal airspeeds and g-loading.  The factors that contribute to higher wing-loaded a/c having greater induced drag remain the same at 1g as they do at 5g's, but now the contribution of Cl/Cdi is more pronounced at higher g's.

But to check just double, triple, quadruple, etc. your weight and recalculate Cl and look at what your Cdi contribution to your to total Cd is.

It gets even more complicated than this actually and gripen alluded to that already because just looking at the total drag side of the equation actually isn't the total picture.  You also should factor in thrust contribution to get a more accurate net-drag picture.  That being said for a simple analysis you can start with examining relative total-drag between aircraft.

Tango, XO
412th FS Braunco Mustangs

[bozon]

As for the throttle setting, How many times in AH have you seen someone increase throttle to make a turn or climb? In fact, everyone hits max WEP and yanks the stick.

That's why they get shot down so easily...

I don't think there are any WWII fighters with enough power to instantly compensate for 4 times their weight.

not 4 times, but done gently enough it's possible.

Bozon

[gripen]

Originally posted by Crumpp

Not necessarily Gripen.  Unless you can relate your calculations to a particular condition of flight under the exact conditions, they are meaningless. Temperature and humidity play a very large roll in aerodynamics and much of the data we see is collected under real world conditions and not necessarily adjusted to standard atm.  Making the assumption it is can certainly lead to wrong conclusions.
/B]

Well, in the all tests I have quoted above, the results are corrected to the standard conditions as well as my calculations are in standard atmosphere. There is no need for any assumption.

gripen