[Graham Boak]

No-one is attempting to claim that weight has no effect on overall performance. There are very good reasons why the discussion is very specifically about maximum speed at sea-level.

The thread began with the statement that Fw 190s could always outrun any Allied fighter. There is no doubt that this does not apply at high altitudes: above the full throttle height, any contemporary turbocharged or two-geared two-stage supercharged fighter will outclass the Fw 190. Whichever fighter is faster at sea-level will also be faster up to the full throttle height (with different relative full throttle height, things do get tangled) so it is reasonable to restrict the study to sea-level.

In which case it is certainly convenient to study the one campaign where a significant amount of low-level "racing" took place, namely the cross-Channel Jabo campaign. As part of the resulting discussion, it was suggested that weight might play a part. Not in stall, climb, cruise or ceiling conditions, but specifically at maximum speed at low-level. As I have shown, and anyone educated in subsonic aircraft drag and performance will recognise, the effect of weight is insignificant AT THIS EDGE of the envelope.

I don't have a collection of "scholarly published references" to check, having left most of such behind on retirement, but am totally unconcerned. I suspect few will make such a blatant statement, for it follows automatically from an understanding of the relationship between speed, weight and drag. But for reasons of military classifications, I could have produced a large number of flight manuals that present the maximum speeds at different weights: although in all fairness many would have a Mach Number limit rather than being limited by conventional subsonic aerodynamics. Presumably you would wish to exclude the ones I calculated myself, despite having passed the scrutiny of my peers, my seniors and critical authorities such as those at Boscombe Down: not to mention the ultimate test of service use. There are also the ones I have updated, where my numbers agree with those of my more illustrious predecessors.

As for parametric studies, these are dangerous. They can only hold within limits that are rarely stated. They have their uses in early design studies, or for simplifying matters for those who do not need to know more: sorry, that may often include general aviation pilots. How often do GA pilots need to fly at the maximum speeds of their aircraft? Often, such aircraft are limited to speeds below their true maximum.

Your basic equation. V2/V1 = SQRT(W2/W1) is actually inverted. the greater the weight, the greater the drag, the lower the speed. I assume this is a simple typo. The equation is a concatenation of three relationships.

V2/V1 = SQRT(Dt1/Dt2), where Dt stands for total drag.
Di1/Di2 = L1/L2 where L is the lift. For WW2 aircraft, and for more modern types at low Lift coefficient, this linear relationship holds. The greater the lift, the greater the induced drag.
L1/L2 = W1/W2, I think that is fairly clear. The greater the weight, the greater the lift required. A one for one relationship.

so we have
V2/V1 = SQRT(Dt1/Dt2); SQRT(Di1/Di2) = SQRT(L1/L2) = SQRT(W1/W2)

Expressed this way, the error stands out. Dt1/Dt2 does not equal Di1/Di2.
Dt = Di + Do - where Do is the zero lift drag. Any increase in Di only leads to a lesser increase in Di+Do. In parts of the envelope where Di is greater than Do, the increase due to weight is a large proportion of the total drag, and the overall increase hence close to that in Di (but never equal). At the cruise, Di = Do, so a 10% increase in Weight gives a 5% increase in drag. In parts of the envelope where Do is greater then Di, then any increase due to weight is only a lesser proportion of the total. Near the maximum speed, Di is much less than Do, and so any effect of weight is only a small proportion.

If you want to check this, and your flight manual permits it, take your light aircraft, weigh it (and you) then fly it at its maximum speed. Any convenient low altitude will do. Hold this until stable - for ten minutes, I suggest. Note the pressure altitude, temperature and fuel consumption (to calculate the weight at the test point). I assume here that you can measure these things to a high quality, but suspect that normal aircraft instruments may be too coarse.
Repeat the exercise with three (weighted) passengers. Corrections for different heights, temperatures, and fuel states can be obtained. You might need to carry out the exercise several times to rule out random factors.

Alternatively, contact your professor and ask him what difference fuel weight would make to the top speed of a WW2 fighter.

My apologies to those who switch off whenever equations appear.