Performance of the Fw 190A on the Deck?

[PeterVerney]

There are so many variables in an actual combat situation that performance graphs, valuable as they may be, are only a factor.
Pilot skill comes first, initial attitude, i.e can acceleration be got by diving. mishandling controls can loose speed, firing guns, especially the cannon, soon knoks off a few knots, wrong setting of rad flaps. I could go on, but it comes back to the pilot in general unless the aircraft are seriously mismatched.

[Crumpp]

Hi Graham,

Let's not confuse our concepts. To avoid confusion and hurt feelings lets define our conditions. I am going to cover some basics again for everyone.

Let’s look at the entire curve and affect of weight. This avoids confusion when we get down in the weeds. When we get in the weeds it does seem like adding weight increases our speed and based on conditions the relationship is direct or inverse depending on what we hold constant. When we put it all together it requires more power to achieve the same performance. Increasing weight means we must travel faster to achieve the same performance and out limits of performance have been reduced.

Credit to Professor David F Rogers United State Naval Academy:




What we notice is that at any point on the L/D curve, the corresponding lighter weight requires less power and our aircraft can achieve a faster velocity. The effect is clear; add weight and our aircraft's performance is reduced. Vmax occurs at a slower speed.

If we get into the weeds on the specific effect:

Where some confusion on this issue seems to lie is in the fact in coefficient form, lift, drag, both have a fixed and finite relationship with Angle of attack. A Coefficient of lift has only one corresponding coefficient of drag and these occur at a specific angle of attack. For the reader, coefficients of lift and drag simply represent the ratio between lifting or drag pressures and the dynamic pressure.

If we keep velocity constant adding weight means the coefficient of lift must increase to meet the new lift required. This means the angle of attack must increase and with it the coefficient of drag.

If we cannot increase our coefficient of lift to meet the new lift required, then we must increase the amount of dynamic pressure to meet the new lift force required. The ratio of lift and drag pressure must remain constant if we are to keep our angle of attack the same. However to meet the higher lift forces required, we must raise the specific values of lift force to dynamic pressure.

The only way to increase the forces and maintain the same ratio at the same angle of attack is to increase the speed.

The confusion lies in the fact we no longer have the power available to overcome the higher drag forces required at the new velocity. Our sustained aircraft performance envelope shrinks and the angle of attack increases as our performance is now thrust limited.

Here is a "big picture" on these relationships:




Does this mean that "heavy" aircraft are "bad"? Aircraft are not a single characteristic but are a system. The effects of weight are easily mitigated through proper design. I certainly would not be so presumptuous as to assume any of the design firms in WWII were incompetent.

Facts are they were all the best and the brightest of their perspective countries. The design contemporary aircraft they produced were the F22 raptors of their day.


All the best,

Crumpp

[Graham Boak]

Your first graph makes the point very well indeed. At the point of maximum speed (top right) changing the weight has only a very small effect on the speed. Away from this point (bottom left) changing the weight has a more significant effect.

My apologies if my explanation was unclear, but that's what I thought I said.

[Crumpp]

My apologies if my explanation was unclear, but that's what I thought I said.

No problem at all. Aerodynamic discussion can get very sticky especially if conditions are not well defined.

While weight effects are smaller at high velocity, they are far from insignificant. Weight certainly makes a difference not matter what portion of the envelope we examine.

The relationship with velocity is direct at a constant Angle of Attack. The reality is that the aircraft does not always have the power available to maintain the necessary angle of attack so it must increase the angle of attack to account for weight.

I have enjoyed this discussion with you, Graham.

All the best,

Crumpp

[Graham Boak]

Thanks, but I think we can still differ on the term "significant".

Can we place some numbers into this discussion? Turning to "Putnam's Hawker Aircraft since 1920" - purely for convenience, I'm sure other sources will do - we find the Typhoon quoted at an empty weight of 8,840lb, and a loaded weight of 13,250lb with 2x1000lb bombs. So for the Typhoons chasing Fw 190 Jabos we have a maximum weight, full fuel, of around 11,000lb. The fuel capacity of the aircraft is 140 gallons (actually quoted for the Tornado, so if anyone knowns different?) which will give a fuel weight of some 1120lb, using the specific gravity of kerosene not gasolene, but near enough I think.

So the total fuel weight is close to 10% of the total aircraft weight. Given that no aircraft will continue fighting without reserves and fuel to get home, nor without expending fuel to reach the combat area, we have a realistic weight range of about 5% of the total aircraft weight. (Obviously slightly more for a P-51 that has just dropped its tanks)

The induced drag, the only part affected by weight, is some 15% of the total drag at maximum speed, sea level - and that may be slightly generous. You'll have to trust me on that, but given a set of aircraft characteristics you can calculate it, and it won't be far off. So we have a range of 5% of 15%, or a total of 0.75% of drag due to the variation in combat fuel weights. The speed change is proportional to the square root of the difference in drag - so we are looking at perhaps half a percent of speed - less than 2 mph top.

This is less than the effect of a poor coat of paint, or that snazzy non-standard rear-view mirror, or a badly-fitting engine cowling. Certainly less than aircraft-to-aircraft (or engine-to-engine) variation.

I know that every little helps, especially for a low-fuel Fw 190 running for home with a fuller Typhoon behind it, but I don't think that's significant.

[Crumpp]

Hi Graham,

There is no need to guess. We can simply use normal BGS formulation to make a sound prediction.

V2/V1 = SQRT(W2/W1)

V1 = 300KEAS

V2 = ?

W1 = 10000lbs
W2 = 10500lbs

V2 = {SQRT(W2/W1)}*V1

V2 = {SQRT(W10500lbs/10000lbs)}*300KEAS
V2= 307.4 KEAS

If we hold angle of attack constant, we must increase our speed 7.4KEAS or 8.5 mph if we add 500lbs weight. Well one just might think that is insignificant. It certainly isn't gong to make much difference in what we can we catch or run from.

Now lets look at it from the Power required relationship in our fictional aircraft. Using standard BGS formulation for a power producer:

Pr1 = 2000thp

Pr2/Pr1 = (W2/W1)^3/2
Pr2 = {(W2/W1)^3/2}*Pr1
Pr2 = {(10500/10000)^3/2}*2000thp

Pr2 = 2680thp

Or a 34% increase in the amount of power required! That 4-5 KEAS in reality represents a very significant reduction in the designs power available.

The induced drag, the only part affected by weight,

Not really. The induced drag is the only a direct affect of weight increase. The reduction in power available certainly does effect our ability to overcome the power of drag other than that due to lift. Remember the power of drag other than due to lift increases at the cube of velocity.

All the best,

Crumpp

[Nick Beale]

For what it's worth, there's a data sheet on National Archives AIR40/152 that gives fuel loads, payloads, armament and performance for the Fw 190 F-3, F-8 and G-3.

Speeds, common to all three sub-types are given as:

a) 380/0

b) 430/0

v= a) 410/5,5

v= b) 470/5,5

I'm guessing that a = loaded (bombed-up?) and b = unloaded, while the figures are kilometres per hour/kilometres of altitude (remembering that in German a comma is used where English uses a decimal point).

[Harri Pihl]

The correct way to to calculate the effect of the weight to speed is to calculate the change of the induced drag due to changed Cl and find the new balance between thrust and the drag by iteration method.

As an example if we assume that the Typhoon does 580km/h at sea level with 2200hp and 80% propeller efficiency at 4800kg. With these parameters a 500kg weight increase will decrease speed by 1,92km/h.

[Crumpp]

I'm guessing that a = loaded (bombed-up?) and b = unloaded, while the figures are kilometres per hour/kilometres of altitude (remembering that in German a comma is used where English uses a decimal point).

You are correct Nick! The speeds wouldn't be labeled Va, Vack, Vw, Vwck would they?

[Crumpp]

The correct way to to calculate the effect of the weight to speed is to calculate the change of the induced drag due to changed Cl and find the new balance between thrust and the drag by iteration method.

I assure, we are using the correct BGS Algebraic formulation to predict performance in the event of a weight change.

Credit to John E Lewis and Charles E Dole:

A former Marine, the late CHARLES E. DOLE taught flight safety for 28 years to officers of the U.S. Air Force, Army, and Navy, as well as at the University of Southern California.

JAMES E. LEWIS is a former aeronautical engineer for the Columbus Aircraft Division of Rockwell International and a retired Ohio National Guard military pilot. He is currently an Associate Professor of Aeronautical Science at Embry Riddle Aeronautical University in Daytona Beach, Florida.

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All the best,

Crumpp