Stoney, et al.
I need to clarify my original statement. It's misleading because it's a generalization. Things are a bit more complicated than that.
Here's the induced drag equation for level flight:
Di = 2*Weight^2
-----------------------------------------------------
pi*air-density*span-eff*V^2*wingspan^2
For a given airframe there are 3 variables that can increase or decrease induced drag:
(1) Weight
(2) Altitude (air density)
(3) Airspeed
For the 1st graph I posted (I didn't create it BTW) it plots drag vs. airspeed where weight and altitude are fixed.
Weight does impact overall drag by increasing induced drag. The question though is by how much does it effect the max level speed of an airplane. The following is a graph of induced drag and total drag for a P-51D at different fuel load outs at sea level:
(http://brauncomustangs.org/upload/drag1.gif)
At sea level the max speed of the P-51D is ~366mph. Notice that around that velocity the total drag curves are pretty much on top of each other which means the total drag is very similar to each other despite the differences in weight in fuel load.
Here's a closer look at what the differences in drag would mean in terms of max level speed:
Alt %F Weight rho Di CD0 Dp Dtotal Thrust V mph Mach
0 100 12100 0.0023 124 0.019 1427 1551 1552 361 0.474
0 75 10606 0.0023 93 0.019 1458 1551 1552 365 0.479
0 50 9486 0.0023 74 0.019 1477 1551 1552 367 0.482
0 25 8739 0.0023 62 0.019 1490 1552 1552 369 0.484
Note the lbs of induced drag (Di) for the given fuel weight and the max level airspeed associated for a given load out. There's not very much variation because at these speeds and alt parsite drag is much larger than induced drag.
The reason the change in loaded fuel weight doesn't impact a fighter as much is because the % distribution of the total weight is lower compared to that of a bomber.
Plane F % F_lbs Wt_lbs %Wt
P-51D 100% 1494 12100 12%
P-51D 25% 374 8739 4%
B-17G 100% 16680 65500 25%
B-17G 25% 4170 52990 8%
Altitude plays a part on induced drag as well. Here is a plot of the P-51D induced and total drag for different fuel loads at 24,500 ft:
(http://brauncomustangs.org/upload/drag4.gif)
The max level speed of the P-51D is ~437mph at 24,500. At an higher altitude the induced drag difference due to different fuel loads is little more noticeable. Around the 437mph mark the total drag curves are more spread out than how they look for the sea level graph.
Here's a closer look at the impact on max level airspeed for the P-51D at 24.5k alt for the different fuel load outs:
Alt %F Weight rho Di CD0 Dp Dtotal T V mph Mach
24500 100 12100 0.0010 199 0.022 1046 1245 1245 433 0.61777285
24500 75 10606 0.0010 148 0.0226 1096 1244 1245 440 0.629293089
24500 50 9486 0.0010 117 0.0229 1128 1245 1245 443 0.636493239
24500 25 8739 0.0010 99 0.0233 1145 1244 1245 443 0.640813329
The above estimate also factors in compressibility drag as well. The spread in max level speed between 100% fuel vs. 25% at 24.5k is a little more than what is was for at Sea Level.
Without compressibility drag factored in the max level speeds would look something like this:
Alt %F Weight V mph
24500 100 12100 433
24500 75 10606 444
24500 50 9486 451
24500 25 8739 455
If I get a chance, I'll try and work up similar estimates for the B-17G as well.
Tango, XO
412th FS Braunco Mustangs
Here are the estimates for the B-17G:
B17G Sea Level: assuming 1200hp ea. eng.
Alt %F Weight rho Di CD0 Dp Dtotal Thrust V mph Mach
0 100 65500 0.0023 1333 0.032 5305 6639 6642 216.0 0.275
0 75 61330 0.0023 1143 0.032 5423 6567 6569 219.0 0.278
0 50 57160 0.0023 974 0.032 5528 6503 6507 221.0 0.281
0 25 52990 0.0023 823 0.032 5623 6447 6451 223.0 0.283
B17G 25k: assuming 1200hp ea. eng.
Alt %F Weight rho Di CD0 Dp Dtotal T V mph Mach
25000 100 65500 0.0010 2084 0.032 3394 5479 5475 263.0 0.33
25000 75 61330 0.0010 1725 0.032 3596 5321 5319 270.0 0.339
25000 50 57160 0.0010 1430 0.032 3768 5198 5196 277.0 0.347
25000 25 52990 0.0010 1182 0.032 3916 5099 5097 282.0 0.353
Impact of increased drag due to weight, the effects are definitely seen more at altitude than at sea level.
I've updated the P-51D estimates as well. I had thrust set constant but modified it to vary with airspeed as it does in reality. Here they are:
P-51D SL: 1650hp + 200lbs exh. Thrust
Alt %F Weight rho Di CD0 Dp Dtotal Thrust V mph Mach
0 100 12100 0.0023 122 0.019 1441 1564 1564 362 0.476
0 75 10606 0.0023 93 0.019 1462 1555 1554 365 0.479
0 50 9486 0.0023 73 0.019 1475 1548 1548 367 0.481
0 25 8739 0.0023 62 0.019 1483 1545 1545 368 0.483
P-51D 24K: 1250hp + 200lbs exh. Thrust
compressibility drag factored
Alt %F Weight rho Di CD0 Dp Dtotal T V mph Mach
24500 100 12100 0.0010 220 0.021 891 1111 1112 411 0.616
24500 75 10606 0.0010 163 0.0213 933 1097 1097 418 0.627
24500 50 9486 0.0010 129 0.0216 959 1088 1090 421 0.631
24500 25 8739 0.0010 108 0.0218 981 1089 1086 423 0.634
P-51D 24K: 1250hp + 200lbs exh. Thrust
no compressibility drag
Alt %F Weight rho Di CD0 Dp Dtotal T V mph Mach
24500 100 12100 0.0010 203 0.019 872 1075 1076 428 0.642
24500 75 10606 0.0010 149 0.019 909 1059 1058 437 0.655
24500 50 9486 0.0010 117 0.019 930 1047 1048 442 0.663
24500 25 8739 0.0010 98 0.019 942 1040 1042 445 0.667
On the issue of compressibility drag, I used the following curves to estimate the amount to add based the NACA XP-51 compressibility drag curves.
(http://brauncomustangs.org/upload/cdrag1.gif)
There are other sources that have more generic compressibility drag polar estimations that have drag rise starting at a higher mach number than the polar I was using as seen here:
(http://brauncomustangs.org/upload/cdrag2.gif)
My gaming PC is dead at the moment (ugh!!!) so I haven't been able to flight test anything. For the P-47N tests that Stoney performed, if AH has compressibility drag modelled they may be using a model like the generic one above which means drag rise doesn't factor in until beyond Mach .7.
Tango, XO
412th FS Braunco Mustangs