Performance of the Fw 190A on the Deck?

[Crumpp]

That looks like Vmax for Kampfleistung, Notleistung, and Dauerleistung speeds for the FW-190F9 in the 1st and 2nd Gear supercharger for the aircraft with and without a load both indicated and true.

The time to climb, climb rate, and service ceiling at 4100kg is included as well.

That is from the Kennblatt and is used for flight planning purposes.

All the best,

Crumpp

[drgondog]

Originally Posted by Harri Pihl

However, you posted a formula:

V2/V1 = SQRT(W2/W1)

Which is valid only for the constant Cl/AoA and therefore wrong for this particular case. And this is exactly what Graham responded to you in the first page of this thread.

Actually if you look at the equations and substitute Weight for Lift and uses say a 5% increase in Fuel, your CL must increase by 5%. CL varies directly with Weight for Constant Velocity.

Also when the weight increases at the max Power setting for a given altitude, then the Velocity cannot increase, so the CL has to change, thereby increasing induced drag.

CD= CDi + CDp = Cl**2/(pi*AR*e) + CDp

CL=296*W/(S*density ratio*V**2)

For the case in which the velocity was maxed out at the lower weight and max power setting, the velocity must be reduced to achieve the required CL (increased by 5% in e.g.)



Note that the polar approach used by Graham and me works for any given flying condition while your approach works at one exact Cl/AoA.

I believe Crumpp is 100% correct

That is true and no one denies that. However, Graham was correct when he noted that at these particular conditions the effect of the fuel state is not that important, just few km/h.

Use the 51D versus the 51B-15 with the same 1650-7 engine. The weight increase was about 6%, the aerodynamics for Parasite Drag and Induced drag are the same for both airframes.

The 51B with same fuel load was about 600+ pounds lighter - mostly due to the extra pair of 50 cal plus 880 rounds extra ammo.

under these TO conditions the P-51B-15 was about SQRT (Wp51d/Wp51b) difference ~ 1.03 faster than the D... on the deck and at 25,000 feet and everywhere in between.

10+ mph is not insignificant - important enough for NAA to redesign the P-51B/D to the P-51H

[drgondog]

[quote=Graham Boak;70211]

Originally Posted by Crumpp

Weight very much affects our aircrafts envelope. It has a direct relationship with velocity.

V2/V1 = SQRT(W2/W1)

[End quote]

No. Weight affects the envelope, indeed, but the direct relationship is wrong. For aircraft of this vintage, it is probably true that induced drag has a linear relationship with weight, but induced drag is only part of the story. The effect of weight on speed varies with altitude, because it varies with induced drag only, and induced drag increases with altitude (at any given speed). At low altitude and high speed, the drag term is dominated by the zero-lift drag. This is made up of skin friction drag, profile drag and excrescence drag, none of which vary with weight.

Induced Drag varies as the square of CL, and for a 5% weight increase - CL varies 5% if speed constant. CL varies directly with Weight for level flight.

At max speed and power settings the same ship at 1.06 W (a P-51D versus B-15) using same engine and TO fuel weight, same aerodynamics but heavier frame by 500-600 pounds can not achieve the lower weight max V.. so AoA increases slightly to get new CL which must increase by 6% to maintain equilibrium.


For high altitudes and low speeds, the effect is reversed, as the drag is dominated by the lift-induced drag, and the top left corner of the envelope is notably smaller at higher weight. The bottom right is hardly affected.

I made my living doing these sums. There's a lot about aircraft performance I never knew, but I think this is fairly basic.

The rest of the posting is sound, and a very useful addition.

Graham, what you say about low speed/low altitude versus high speed/low altitude is true relative to discussions about relative induced drag and parasite drag

But whether the extra weigh is due to increased fuel, or internal load, or more structural weight for same basic airframe, the Velocity change for same power settings and the increased AoA resulting in a higher CL results in the SQRT (Wheavy/Wlight) change in V

[Franek Grabowski]

Bill, it is obvious that P-51B/C was aerodynamically slightly different than D/K. I cannot say for sure, but I suppose there might have been some other slight differrencies, eg. in props. That said, drop of maximum speed was the result of several minor changes, and not only one factor. Still, 10 mph is within marigin for error and may purely depend on quality of factory fresh aircraft, not to mention worn out airframes.
Overall, the point that Graham tries to make is not that the weight is unimportant. He just merely points out, that differencies of weight caused by fuel consumption are mariginal for aircraft performance in horizontal flight. It does matter in vertical manouvers, though. This is obvious for anyone, who ever attempted to calculate such things, just as it is obvious, that adding a few pounds of putty and lacquer will increase the horizontal speed!

[Harri Pihl]

For 600lbs increase from 9680lbs to 10280lbs in the case of the P-51B causes 1,48km/h speed reduction for max speed at sea level. The parameters being 352mph at sealevel and, 1580hp (67") and 120kp exhaust thrust, prop efficiency 80% and value of the e being 0,8. Calculated Cd0 being 0,02054.

[Harri Pihl]

Originally Posted by drgondog

But whether the extra weigh is due to increased fuel, or internal load, or more structural weight for same basic airframe, the Velocity change for same power settings and the increased AoA resulting in a higher CL results in the SQRT (Wheavy/Wlight) change in V

The power is constant, however, the propeller thrust increases when the speed decreases and therefore the speed reduction can't be calculated directly but using the iteration to reach new balance between the drag and the thrust.

[Crumpp]

The power is constant, however, the propeller thrust increases when the speed decreases and therefore the speed reduction can't be calculated directly but using the iteration to reach new balance between the drag and the thrust.

You didn't understand what he said.

[Harri Pihl]

Originally Posted by Crumpp

You didn't understand what he said.

I did; because the drag must equal thrust:

D=T

Then at constant power the thrust increase when the speed decrease because:

T = (n*W) / V

Where n is efficiency and W is engine power. Therefore the iteration process is needed to find the new balance between the drag and the thrust.

[drgondog]

Originally Posted by Franek Grabowski

Bill, it is obvious that P-51B/C was aerodynamically slightly different than D/K. I cannot say for sure, but I suppose there might have been some other slight differrencies, eg. in props. That said, drop of maximum speed was the result of several minor changes, and not only one factor. Still, 10 mph is within marigin for error and may purely depend on quality of factory fresh aircraft, not to mention worn out airframes.

Gene lednicer did a very nice study and published reports based on VSAERO for both the B and D in comparison with Spit IX and Fw 190A and D-9. The reason I mention this is that in his modelling the 51D was actually slightly cleaner, and the difference was that the bubble canopy had complete lift distribution w/o separation from the top of the windscreen, aft. In addition the sloped windscreen of the D (more than B) suggested less stagnation at the windscreen. The B quickly separated above the cockpit. No Malcolm Hood version was modelled for the B.

The reason I bring this up is to suggest that when you add the same extra internal weight for the B as the airframe increases for the D, the report implies that the same P-51B, loaded an extra 600 pounds, or conversely take out the guns and ammo, and re-test..

would show an even greater Vmax difference than 10+ mph as the 51B was slightly 'draggier' in parasite drag than a D.

All you say is true generally speaking..but having said that, the delta Weight causes the airspeed to vary as V2/V1 = SQRT(W2/W1)
using the same exact airfame and power conditions.

Overall, the point that Graham tries to make is not that the weight is unimportant. He just merely points out, that differencies of weight caused by fuel consumption are mariginal for aircraft performance in horizontal flight. It does matter in vertical manouvers, though. This is obvious for anyone, who ever attempted to calculate such things, just as it is obvious, that adding a few pounds of putty and lacquer will increase the horizontal speed!

Franek - Respectfully, I made a living for several years "calculating such things" following a Masters Degree in Aero. Having said this, my real expertise was Structures, Aeroelasticity and finite element modelling.

It is not so obvious to me that Weight delta does not affect top speed - because it does. You may not agree my math or logic, but respectfully, bring your own if you have a different POV.

Marginal seems to be what you are debating and I'm ok with you and Graham dismissing the value to Max speed available to say a P-51B after getting rid of its Fuselage tank 85 gallons. The math says it's about 10-12 mph.

If that is insignificant to you we can agree your terminology, but the delta is not due to plugging gun ports, or polishing the airframe, or switching engines...

Hari - two things about your comments.

First- at Vmax the Thrust Hp is maximum for that altitude and weight.

When weight increases, for the same airframe, the Thrust Hp remains the same, but Vmax decreases alightly as the AoA must increase to maintain level flight for that Thp and weight condition.

In other words the Thrust available is the same for both weight conditions, but the velocity Attainable is Less for the heavier weight conditions.

In other words, Thrust HP may not increase beyond the max Thrust Hp available in level flight.

If you want to demonstrate the math that proves a slight increase in AoA from freestream impingement on the propeller plane increases the change in momentum of the mass flow through that plane (positively) - give it your best shot.

By your anology , as the ship climbs at a steeper angle relative to freestream, the thrust would increase?

By using the Propeller/Engine thrust equation as you used it (which is appropriate for level flight) then as the angle of Attack increases you would quicly reach a point where sustainable velocity is much lower than it was in level flight... and your thrust increases dramatically above it's max rated Hp Thrust in level flight. Do you believe this?

[drgondog]

Originally Posted by Harri Pihl

For 600lbs increase from 9680lbs to 10280lbs in the case of the P-51B causes 1,48km/h speed reduction for max speed at sea level. The parameters being 352mph at sealevel and, 1580hp (67") and 120kp exhaust thrust, prop efficiency 80% and value of the e being 0,8. Calculated Cd0 being 0,02054.

Your specific references for each claim you just made for the P-51B?

For example "e" is derived empirically, because the effect of spanwise lift distribution, increase in trim drag and the increases in all forms of drag on the airframe. .8 is a good rule of thumb for conservative preliminary design purposes - but only that unless you have test results?

Ditto prop efficiency. .8 to .85 are good Prelim Design numers. So where would point me to .8 as being correct for the P-51B?..

Cd0 = .02054? and your source is? That is higher than the Ames wind tunnel model with real airframe.

Having said that, how do you arrive at approximately 1mph delta for a 6% weight increase? What math are you using?