Why still no dive acceleration difference?

[BlackBerry]

Fw190A8

m----mass,4272 kg,max load for a standard A8,100% fuel
A----dive angle
p----engine output,1953 HP@sea level
r----propeller efficeincy=0.8=80%
Vmax ----max level speed at SL, 578km/h=160.6m/s
d----drag coefficient
g----gravity, 9.8 m/s^2
t---- engine thrust, N


when level flys at Vmax, fw190a8 in equilirium, zero acceleratiom, all forces are balanced.

t=P*r/V=1953*735*0.8/160.5=7155N

m*g* sin(0)+t=d*Vmax^2

d=t/Vmax^2=7155/160.5^2=0.2778

P47D

m----mass,5675kg, 12500lb, normal combat load(55% fuel)
A----dive angle
p----engine output,2300 HP
r----propeller efficeincy=0.8=80%
Vmax ----max level speed at SL 345mph=555km/h=154.3m/s
d----drag coefficient
g----gravity, 9.8 m/s^2
t---- engine thrust, N

when level flys at Vmax, P47D in equilirium, zero acceleratiom, all forces are balanced.

t=P*r/V=2300*735*0.8/154.3=8765N

m*g* sin(0)+t=d*Vmax^2

d=t/Vmax^2=8765/154.3^2=0.3681



55% fuel P47D vs 100% fuel Fw190A8 in 45 dive degree

for fw190A8, let the new equilirium speed as V:

new engine thrust should be 7155*(160.5/V)

m*g* sin(45)+t=d*V^2

4272*9.8*0.707+7155*(160.5/V)=0.2778*V^2

thus

v^3-106548V-4133828=0

we get fw190A8 V=344.5m/s=1240km/h.
And BMW801 still produce thrust as 7155*(160.5/344.5V)=3333N

for P47D let the new equilirium speed as V:

new engine thrust should be 8765*(154.3/V)

m*g* sin(45)+t=d*V^2

5675*9.8*0.707+8765*(154.3/V)=0.3681*V^2

v^3-106818V-3674109=0

we get P47D V=342.8m/s=1234km/h=1240km/h of Fw190A8

And R2800-59 still produce thrust as 8765*(154.3/342.8 )=3945N



55% fuel P47D vs 100% fuel Fw190A8 in 65 dive degree

for fw190A8, let the new equilirium speed as V:

new engine thrust should be 7155*(160.5/V)

m*g* sin(65)+t=d*V^2

4272*9.8*0.906+7155*(160.5/V)=0.2778*V^2

thus

v^3-136538V-4133828=0

we get fw190A8 V=384m/s=1382km/h.


for P47D let the new equilirium speed as V:

new engine thrust should be 8765*(154.3/V)

m*g* sin(45)+t=d*V^2

5675*9.8*0.906+8765*(154.3/V)=0.3681*V^2

v^3-136884V-3674109=0

we get P47D V=383m/s=1379km/h=1382km/h of Fw190A8


Conclusion:

1) 55% P47D and 100% fuel Fw190A8 share same equilirium speed at 45-65 degree dive.
2) 5675kg P47D=normal combat load, 4272kg Fw190A8=max load A8. There is only 0.454(12500-10700)=817kg difference between empty and normal load P47, but there is (4272-3050)=1222kg difference for fw190A8. In fact, 5675kg P47D is only 200 US galon fuel, not 100% fuel. if internal fuel is full(375 US gal), 6152kg for P47D which has better dive acceleration.

The P-47D-15 was produced in response to requests by combat units for increased range. The internal fuel capacity was increased to 375 U.S. gal (1,421 l) and the bomb racks under the wings were made "wet" (equipped with fuel plumbing) to allow a jettisonable drop tank pressurized by vented exhaust air to be carried under each wing, in addition to the belly tank. Five different auxiliary tanks were fitted to the Thunderbolt during its career: